kasm distribution network losses and strategies for ...€¦ · distribution system operators...

KASM

Distribution

Network Losses

and Strategies for

Reducing Losses

Bigwood Systems, Inc. in

Collaboration with UK Power

Networks

February 7, 2017

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Executive Summary Electricity distribution losses, on average, account for 8% of transported volumes and vary between

3.1% to 10% for the individual distribution network operators (DNO). This brings higher overall costs

to both the energy providers and the customers to make up for the lost power. As the energy

industry in the UK progresses to more renewable energy integration and DNOs transition to

distribution system operators (DSO), there is also a strong interest in understanding and reducing

network losses.

The Kent Active System Management (KASM) Network Losses project presents an in-depth

assessment of the distribution network losses for UK Power Networks and provides strategies for

reducing network losses, along with their implementation results. This project is an extension of the

previous UK Power Networks (UKPN) and Bigwood Systems, Inc. (BSI) collaboration, which

developed and implemented a real-time network monitoring, analysis, optimization, and control tool

called Advanced Data Analytics for Power Networks Tool (ADAPT) or previously, Contingency

Analysis Solution (CAS). This advanced control center tool helps elevate UKPN from a DNO to a

DSO by providing a holistic view of the network from 400 kV down to 0.4 kV while providing real-

time and look-ahead data and network computations for operators, control engineers, planning, and

other utility departments. BSI utilized cutting-edge technologies and provided UKPN data to tailor

the power flow engine to compute overall system and zone losses down to the individual

components and renewable energy sites. Studies on component, load, and loss correlations as well

as sensitivities were performed to investigate trends. Then, network reconfiguration schemes were

tested and implemented to reduce losses. Finally, an extension program for loss analytics was

developed and integrated into the ADAPT tool. This program allows loss analysis and reduction to

be conducted in a study mode. As the tool is continually running, this ongoing study can further

understand losses in the UKPN system.

This is an initial study of the KASM area and is based on data from a limited number of days. The

program will continue to run at UKPN and compile more data to continue validating the analysis and

trends.

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Table of Contents

1 Background .............................................................................................................................. 5

1.1 Challenges with Network Losses ....................................................................................... 5

1.2 The Current State in the UK ............................................................................................... 7

1.2.1 Network Reconfiguration ........................................................................................... 13

1.2.2 Power Factor and Voltage Regulation) ..................................................................... 14

1.2.3 The Taiwan Power Company (TPC) AVC Project ..................................................... 16

1.3 The KASM Project ........................................................................................................... 23

1.4 Modelling ......................................................................................................................... 24

2 Project Objectives and Goals ................................................................................................. 27

2.1 Task 1 – On-Line Loss Calculation for Every 30 Minutes ................................................. 27

2.2 Task 2 – On-Line Component-Level Loss Sensitivity Calculation for Every 15 Minutes ... 27

2.3 Task 3 – Relate Power Losses with Loading Conditions, Renewable Locations, and

Penetrations...................................................................................................... 28

2.4 Task 4 – Relate Power Losses with Network Topologies and Identify the Best Network

Topology ........................................................................................................... 28

3 Methodology .......................................................................................................................... 29

3.1 Methodology Overview .................................................................................................... 29

3.2 Power Network Losses .................................................................................................... 30

3.3 Power Loss Visualization ................................................................................................. 31

3.4 Loss Sensitivity Calculation ............................................................................................. 33

3.5 Validation of the Sensitivity Calculation ............................................................................ 35

3.6 Loss Minimization via Line Switching ............................................................................... 38

3.6.1 Particle Swarm Optimization (PSO) .......................................................................... 38

3.6.2 Deterministic Heuristic Search .................................................................................. 39

3.6.3 Results ..................................................................................................................... 40

4 Analyses of UKPN System Losses ......................................................................................... 49

4.1 System Behavior .............................................................................................................. 49

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4.2 The Most Lossy Branches (System) ................................................................................ 50

4.3 The Most Lossy Transformers (System) .......................................................................... 52

4.4 The Largest Load Components ........................................................................................ 53

4.5 The Largest Generation Components .............................................................................. 54

4.6 System Loss and State Estimation Quality ....................................................................... 57

5 Additional Technology ............................................................................................................ 59

5.1 Optimal Capacitor Placement .......................................................................................... 59

5.1.1 The Study ................................................................................................................. 60

5.2 Maximizing Available Delivery Capability ......................................................................... 63

5.3 Another Scheme for Reducing Transmission Losses Through Line Switching ................. 67

5.4 Multi-Objective Optimal Network Reconfiguration ............................................................ 69

5.4.1 Multi-Objective Operation Problems.......................................................................... 71

5.4.2 Formulation for Loss Reduction and Load Balancing ................................................ 72

5.4.3 Numerical Results ..................................................................................................... 73

6 Future Technology ................................................................................................................. 79

6.1 Optimal Multi-Period Network Reconfiguration ................................................................. 79

6.1.1 Introduction ............................................................................................................... 79

6.1.2 Problem Formulation ................................................................................................ 81

6.1.3 Toward Optimal Multi-Period Methodology ............................................................... 83

6.1.4 References ............................................................................................................... 84

7 Document References ............................................................................................................ 87

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1 Background

1.1 Challenges with Network Losses

Network loss is the energy lost during transportation from production to consumption. According to

a UKPN loss report, electricity distribution losses, on average, account for 8% of transported

volumes and vary between 3.1% to 10% for the individual DNOs. Losses are an integral part of

electricity distribution, and better understanding losses on the network will enable operators to

make informed decisions around how to best operate, maintain, renew, and enhance the network.

These decisions factor into providing a safe, secure, and reliable network at the lowest possible

cost, as well as regulatory and environmental obligations. Electrical losses are an inevitable

consequence of transferring electricity across the distribution network and have a significant

financial and environmental impact on both consumers and distribution network operators.

However, it is important to understand the location of these losses. As a result, additional actions

are required to improve our understanding and better manage electricity losses on the networks.

Loss reduction obligations and incentives for network companies feature a number of price control

codes, such as health, safety, and environmental impact. As part of the Energy Efficiency Directive

(EED), a set of binding measures to help the EU reach its 20% energy efficiency target by 2020, the

Office of Gas and Electricity Markets (Ofgem) has recognized that a key way to improve the energy

efficiency of the network infrastructure is to reduce its losses. Despite the use of more energy-

efficient appliances as we move to a low carbon economy, the electricity demand on our network is

expected to grow as a result of the ongoing electrification of heat and transport.

According to the Citizens Advice Bureau on the impact of electricity leakages through the

transmission network, about 1.7% of the electricity transferred over the transmission network is lost.

An additional 5-8% of the electricity transferred over the distribution networks is also lost. These

losses on the power networks account for approximately 1.5% of the UK’s greenhouse gas

emissions. They also influence consumer costs, since the greater the leakages, the more energy

will need to be generated and consumed for the shortfall, leading to increased costs. According to

the UKPN loss report, the average bill is around the £1,000 mark at the domestic level. About half is

the wholesale element, about £500. Considering losses of about 5% or 8% on distribution and 1%

or 2% on transmission, it is estimated that the total cost due to loss is around £50. This cost can be

reduced on consumer bills by determining effective ways to reduce losses. With a greater

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understanding of what causes loss, it is possible to better plan how to minimize this loss via the

replacement of assets and improved procedures.

Technical network losses, also known as commercial losses, are caused by losses in power

distribution. An example is the increased number of digital devices that have contributed to not only

domestic load growth, but also to potentially worsening the power factor. This is exacerbated by the

fact that some “high efficiency” (compact fluorescent) light bulbs also have a poor power factor. The

impact of new low-carbon technologies such as heat pumps might further degrade the power factor

and increase network loading in the future. The non-linear relationship between load growth on a

network and its losses means that an increasing load growth on our network will lead to even

greater losses. As such, it is increasingly important to manage losses, given that they have both an

environmental and economic impact on our energy system. As more energy is lost in transport,

more energy must be generated to replace the loss, meaning greater carbon intensity and financial

cost per MWh. A variety of sources for technical losses exists, with the two principal types being

fixed and variable. Around 30% of the technical losses will be due to fixed losses and around 70%

will be due to variable losses. The graph in Figure 1.1 below from the World Bank website shows

losses in percent over the last few years.

Figure 1.1. A World Bank graph for losses over the years.

https://data.worldbank.org/indicator/EG.ELC.LOSS.ZS?end=2014&locations=GB&start=1960&view=chart

https://data.worldbank.org/indicator/EG.ELC.LOSS.ZS?end=2014&locations=GB&start=1960&view=chart

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1.2 The Current State in the UK

The responsibility for ensuring efficient energy networks is shared between the government, Ofgem

(the independent regulator), and the companies that own and operate the networks. According to

the UK parliament website, based on evidence submitted by the Department of Energy and Climate

Change, the bulk of electricity transmission expenditures is associated with the cost of connecting

new generation in more remote parts of the country and reinforcing more constrained parts of the

existing network to improve the efficiency of electricity flow across Great Britain. However,

modelling undertaken for Ofgem by the National Grid to investigate different charging options

implies that growth in post-2020 electricity transmission costs flattens out towards 2030. For

electricity distribution, however, the majority of the expenditure is in replacing aging assets and

maintaining resilience and reliability, with only a small investment portion associated with extending

the network. The cost of connecting low carbon technologies at this level is not expected to make a

significant impact on network costs until the 2020s. Government policy also seeks to meet low

carbon objectives through energy efficiency. This could significantly reduce network costs relative to

what they would have been without such policies. It was estimated that total energy consumption

would be 10% lower in 2020 than it would have been without these policies. However, it is not

possible to estimate the impact of these energy savings on network costs at present. Network costs

are driven by a number of factors, including the need to:

replace and upgrade aging infrastructure;

extend the networks to connect new generation;

accommodate changing flows of energy;

ensure continued, reliable day-to-day network operation.

There is therefore a need for tools that facilitate an understanding of losses and how these losses

can be reduced through the management of existing devices on the distribution network.

In terms of strategy for UKPN, UKPN’s Losses Strategy, published in March 2014 as an annex to

the ED1 submission, provides a comprehensive overview of the technical and non-technical losses

to which an electricity network is subject and suggests possible approaches to minimize these

losses. UKPN’s plan consists of three stages.

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Stage 1: Understand the losses

This will primarily involve research, studies, monitoring, and other actions that increase our

understanding of losses on our network, where they are most prevalent, what causes them, and

how they can best be determined, quantified, managed, and finally, optimized.

Stage 2: Plan and design

Begin changing policies and implementation. Identify timescales over which benefits may be

delivered; and further quantify the extent of benefits that may be provided.

Stage 3: Build and operate

This stage will see the deployment of changes on the network to reduce losses, both for ED1 and

ED2. As part of this phase, UKPN will periodically complete a full economic assessment of any

implemented changes to validate the assumptions made and track the benefits achieved.

The strategy recognizes that there are areas that can be tackled with almost immediate effect,

whereas others require a short period of research and learning prior to implementation. Conversely,

some of the areas/approaches that rely on new technologies or processes can only be implemented

once a deeper knowledge and understanding have been gained or when new technologies have

become more widely available. This will give UKPN a complete understanding of the losses across

our entire network, allowing us to create an appropriate and balanced plan to manage them while

ensuring that we consider their impact in the widest possible sense. This opportunistic approach will

give rise to greater and more cost-effective opportunities for loss mitigation, since they will largely

incur incremental costs over those required to meet a given investment driver.

The economic justification of measures to mitigate losses will be determined through cost benefit

analysis based on Ofgem’s RIIO-ED1 guidance which, as well as valuing the energy cost of

supplying losses, also recognizes the real, but declining, carbon impact arising from electricity

production. The approach to cost benefit analysis will primarily be based on the incremental cost

benefit, comparing the NPV of intervention options, and factoring in the discounted value of losses

(and any other ongoing costs and benefits) in the overall investment appraisal.

For example, the incremental cost of installing a higher-rated cable to serve a new development

might be small compared with the value of the reduced losses benefit, whereas overlaying an

existing adequately rated cable for no other reason than to reduce losses is unlikely to be cost-

effective. The strategy recognizes that pressures to cost-effectively accommodate new low carbon

technologies will result in networks being driven harder. It follows that, in MWh terms, losses will

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inevitably increase as a direct consequence of the increased energy flow. Moreover, the

unmitigated use of low carbon technologies (i.e., in terms of usage time of day) is likely to give rise

to network peak demands, increasing disproportionately to the underlying increase in distributed

electrical energy. This, in turn, would have a further disproportionate impact on circuit losses, which

vary with the square of the electrical current passing through the conductors. Taking all of these

factors into account, a challenging target would be to maintain losses as a percentage of energy

distributed at current levels.

It is assumed by some that, across Great Britain, distribution network technical losses are at around

6%, but with variations of between 4.5% and 9% for urban and rural networks. However, there is

considerable uncertainty over the current level of technical losses. This is due to both inaccuracies

inherent in the existing electricity market reconciliation assumptions and the fact that “measured”

losses comprise both technical and non-technical losses.

The strategy is to:

Control losses at a level that is economically justified and continue to represent best values

to customers, making use of opportunities as they arise and taking additional proactive

measures where possible.

Take a holistic view of future investments where the benefits of loss mitigation, as well as

other societal benefits, must be considered and contribute to part of any wider investment

decision.

Ensure that our appraisal of options to manage losses considers the impact of spending

money now against the incremental savings and benefits over the future lifetime of the

asset.

Embrace modern technologies that allow us to identify, measure, and report our losses

more accurately, giving us a more comprehensive overview of losses on our network.

Aim to maintain losses at an average of 6% in spite of a changing load growth on our

network, as the result of new development activity and an increase in low carbon

technologies.

Exchange findings and knowledge with stakeholders and the wider industry to improve the

understanding of energy efficiency within the UK.

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Engage with our customers and industry peers, encouraging their influence in the ongoing

evolution of our strategy so that it matches our ambition to be a world-class DNO and better

serve our customers. The benefits of delivering this strategy are wider than the direct

financial benefit of the energy saved. When losses are reduced:

o less generation is required to sustain the losses.

o the availability of network assets to deliver useful energy instead of losses will be

maximized.

o maintaining and reinforcing the network will cost less.

Network utilization can increase as reduced losses enable better voltage management. This

strategy involves an initial assessment to better understand and manage our losses before

we implement the specific actions we have identified so that we can best understand their

impact, cost, and benefits.

In the UKPN Losses Report, the following chart in Figure 1.2 provides an indication of the expected

contribution that each of the measures described in this strategy will make towards the anticipated

savings in network losses (in GWh) over the RIIO ED1 period.

Figure 1.2. UKPN published report on strategies and their expected impact on losses.

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In a report made by SP Energy Networks on network losses, the present practice in quantifying

losses is to measure and record energy entering and leaving the distribution network. Energy

entering the distribution network at transmission GSPs is measured with high accuracy metering

and is readily quantified. However, the quantification of energy exiting the distribution network is

currently dependent on aggregating all customer-metered consumption. There are two issues to be

addressed.

The first issue is to develop:

methods of measurement within our networks.

evaluation techniques to assess potential savings in technical losses on our LV networks.

evaluation techniques to assess the loss impacts of developments in complex parts of our

HV network.

The second issue is to achieve consistency in the approach, or at least in accuracy, across all UK

DNOs so that Ofgem can report properly to the government on the contribution that the distribution

part of the industry is making towards climate change targets. This also supports the Ofgem

proposal for assessing and incentivizing the DNO’s relative performance on losses.

The Network Losses Minimization Strategy for both DNOs’ express requirement is to develop

approaches to assess losses in the network and develop effective methods to reduce these losses

with the available devices and components in the network. Losses in the US, the UK, and Australia

are shown in Table 1.1.

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Table 1.1

Company/Region Transmission or Distribution Losses (%)

Con Edison T&D 4.8%

Orange & Rockland T&D 5.0%

Eastern Interconnect T&D 5.82%

US T&D 7%

ERCOT T&D 7.99%

Western Interconnect T&D 8.21%

UK EDFE EPN Distribution 3.7%

UK CN East Distribution 3.9%

UK CN West Distribution 4.3%

AU CitiPower Distribution 4.5%

Au United Energy Distribution 4.7%

UK Electricity North West Distribution 4.8%

AU Alinta Distribution 4.9%

UK CE NEDL Distribution 5.0%

UK WPD S Wales Distribution 5.1%

UK CE YEDL Distribution 5.5%

UK EDFE LPN Distribution 5.5%

UK EDFE SPN Distribution 5.6%

NYSEG Distribution 5.67%

Hydro One Distribution 5.86%

UK SP Distribution Distribution 5.9%

UK SEE Southern Distribution 6.2%

UK WPD S West Distribution 6.3%

UK WP Manweb Distribution 6.6%

Au PowerCor Distribution 6.9%

Au Sp Ausnet Distribution 7.9%

UK See Hydro Distribution 8.1%

Source: CEER, ECRA, NYSEG, RG&E, EPA, Con Edison, Orange & Rockland

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1.2.1 Network Reconfiguration

There are two types of switches in primary distribution systems: normally closed switches, which

connect line sections and normally open switches, which connect two primary feeders or two

substations or loop-type laterals. The former are termed sectionalizing switches and the latter are

referred to as tie switches (see Figure 1.3). These switches are designed for both protection (to

isolate a fault) and configuration management (to reconfigure the network).

Figure 1.3. A sample distribution system.

Network reconfiguration (or feeder reconfiguration) is the process of altering the topological

structures of distribution feeders by changing the open/closed status of the sectionalizing and tie

switches. During normal operating conditions, an important operation problem in configuration

management is network reconfiguration. As operating conditions change, networks are re-

configured for two purposes:

(1) to reduce the system real power losses, and

(2) to relieve overloads in the network.

The former is referred to as network reconfiguration for loss reduction and the latter as load

balancing. Another configuration management operation involves the restoration of service to as

many customers as possible during a restorative state following a fault. This problem is called

service restoration.

In fact, the network reconfiguration can be performed for both loss reduction and load balancing.

Conceptually, this problem belongs to the so-called minimal spanning tree problem: Given a graph

(i.e., the nodes of the system), find a spanning tree (i.e., a radial configuration) such that a desired

objective function is minimized while certain system constraints are satisfied. This problem has

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been formulated as a nonlinear optimization problem with a differentiable objective function. All the

solution algorithms proposed in the literature for solving the problem employ various techniques

belonging to the class of greedy search techniques, which accepts only search movements that

produce immediate improvement. As a result, these solution algorithms usually achieve local

optimal solutions rather than global optimal solutions. In other words, these solution algorithms can

lead to different degrees of loss reductions.

BSI presented a scheme to minimize network losses through network reconfiguration on a practical

utility distribution network and showed the feasibility of reducing T&D losses at several major

utilities in North America and Asia. Minimization of power losses and maximization of the load

balance are the two most common criteria that are used to reconfigure networks. Engineers at BSI

performed a comprehensive study on losses in the New York State Electric & Gas (NYSEG) system

before and after network reconfiguration. The following numerical observations were made:

Network reconfiguration reduced real power and reactive power losses by 16.6% and

20.8%, respectively.

Overall, the loss reductions amounted to 1.88% of the system load, an amount that, if similar

for Abu Dhabi, could help the sector surpass the 8% suggested above.

The value of network reconfiguration and network applications, in general, is that the network

efficiency can be improved without additional costly capital expenditures.

1.2.2 Power Factor and Voltage Regulation

A low power factor is one of the primary causes of excess losses in a system. Internationally, it is a

best practice to keep the substation power factor as high as possible. As an example, Orange &

Rockland, a New York-based utility serving approximately 300,000 customers, maintains a

substation with at least a 0.95 power factor at peak demand. Similarly, ERCOT’s operating

guidelines require that all substations minimally have a 0.95 power factor during peak demand, with

special directives to some counties requiring at least a 0.98 power factor.

For this project, BSI recommended the application of optimal Volt/VAR management in distribution

networks, as explained in the following. Capacitors are widely installed in distribution systems for

reactive power compensation to achieve power and energy reduction, voltage regulation, power

factor improvements and system capacity release. The extent of these benefits depends greatly on

how capacitors are placed in the system. The problem of how to place capacitors in the system to

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achieve these benefits and/or maximize against the cost associated with capacitor placement is

termed the general capacitor placement problem.

The general capacitor placement problem consists of determining the locations for capacitor

installation, the types and sizes of capacitors to be installed, and the necessary control. Hence, the

problem of general Volt/VAR control via capacitor placement and control is in determining:

1. The locations at which to install, reposition, or replace capacitors.

2. The types and sizes of capacitors to be installed.

3. The control schemes for the capacitors of a distribution system such that an objective

function is minimized while the load constraints, operational constraints (e.g., the voltage

profile, power factor), and engineering constraints at different load levels are satisfied.

4. A capacitor placement scheme such that line losses are minimized and power factors are

improved.

Cost benefit analysis needs to be performed on loss minimization options, including network

reconfiguration, equipment sizing and cost, operating cost, the potential benefits. A variety of

options to improve the network’s power factor and reduce network losses includes the following.

1. Reactive Power Compensation

Reactive power compensation is the standard tool for correcting power factors. Shunt

capacitors and switched shunt capacitors must be carefully designed to maintain high power

factors daily and seasonally without under or over compensation. Moreover, the high capital

cost of capacitors requires that they be placed and timed optimally to improve voltage levels

and reduce losses.

2. Optimal Coordination of Voltage Regulators and Capacitors

Network applications are relatively low-cost software applications that optimally coordinate

voltage regulators and shunt capacitors to reduce losses, maintain voltage levels, and

minimize reactive power. Network applications (e.g., loss minimization through network

reconfiguration, and Volt/VAR management though optimal capacitor placement) can

optimally reconfigure switching configuration, place capacitors, recommend new capacitors,

and operate in real time to recommend capacitor switching and voltage regulator operations.

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3. Customer Load Management

It is common for utilities to penalize customers with very low power factors. Typically, the

lower limit at the point of connection for large users is 0.95 to 0.90. Abu Dhabi requires

corrective equipment when a customer power factor is below 0.90, but according to

stakeholder meetings, this standard is not normally enforced.

4. Distribution Line and Transformer Sizing

Distribution lines and transformers should be sized to minimize the cost of equipment and

losses. Increasing the capacity of distribution lines will increase the capital investment, but

minimize the losses over the equipment lifetime.

5. Data Management

There are discrepancies in the DISCO and ADWEC loss reports (different utility reports

completed by BSI). The first step to eliminating network losses is the identification of areas

with high network losses and low power factors.

1.2.3 The Taiwan Power Company (TPC) AVC Project

1.2.3.1 Project Overview

The objective of this project is to design a real-time, closed-loop automatic voltage control system

and to assess its feasibility for implementation. Our approach is to construct this system as a three

level, multi-tiered system. In the third tier, or Tertiary Voltage Control (TVC) level, the system will

utilize BSI’s on-line VSA engine to coordinate regional voltage control centers to ensure system-

wide efficiency and security. In the second tier, or Secondary Voltage Control (SVC) level, the

system will utilize BSI’s Super OPF tool to minimize the losses for each TPC regional control

center, while satisfying system-wide constraints. In the first tier, or Primary Voltage Control (PVC)

level, the simulation will model controllers in power plants and substations to meet the requirements

of the SVC level.

1.2.3.2 System Design

The three-tiered AVC System for TPC follows a three-level hierarchical voltage control architecture.

The third tier is performed every hour and focuses on increasing system available transfer capability

(ATC), subjected to stability constraints. It will decide the optimal pilot bus selection and their

voltage setting and pass them to the second tier. The second tier will perform every 15 minutes to

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optimize the regional optimization objective, such as enhancing operating efficiency, while

maintaining the voltage setting of the pilot buses and satisfying system operational constraints.

Available controls include generator terminal voltages, transformer taps, shunt capacitor settings,

etc. The optimal setting decided by the second tier will be sent to the first tier as control signals and

will be executed by the control devices.

Compared with other AVC systems, based on zone division and the selection of pilot buses, the

presented AVC system can select the most suitable and effective pilot busses on-line without off-

line zone division. This gives the presented AVC system high flexibility with network changes to

achieve more optimal AVC results.

In the following part of this section, the overall architecture of the three-tiered AVC system for TPC

will be presented first. More detailed designs and implementations of each tier will then be provided.

1.2.3.3 Architecture

The Smart Three-tiered AVC System for TPC is designed as a hierarchical AVC system. In the third

tier, or Tertiary Voltage Control (TVC) level, the system will utilize an on-line voltage stability

analysis (VSA) engine to coordinate regional voltage control centers to ensure system-wide

efficiency and security. In the second tier, or Secondary Voltage Control (SVC) level, the system will

utilize an optimal power flow (OPF) tool to minimize the losses for each TPC regional control center

while satisfying system-wide constraints. In the first tier, or Primary Voltage Control (PVC) level, the

simulation will model controllers in power plants and substations to meet the requirements of the

SVC level.

The Taiwan Power Company has a central control center located in Taipei, and three regional

control centers located in the North Region, Central Region, and South Region, respectively. The

Smart Three-tiered AVC System, described in the previous paragraph, can be implemented by TPC

in either of two system architectures. Architecture 1 is simpler in terms of implementation, where all

the system analysis and optimization are done in the central control center, and the regional control

centers only receive the control signals and monitor the control devices. In Architecture 2, part of

the optimization work is done by each regional control center, giving them opportunities to set their

optimization objectives based on regional factors. Both architectures are presented below.

Architecture 1 of the three-tiered AVC system for TPC is shown in Figure 1.4. In this design, on-line

VSA and OPF are performed in the central control center located in Taipei. The on-line VSA will be

performed once every hour for voltage stability and transfer capability optimization. Every 15

minutes, the OPF engine will optimize all available controllers for the optimization objective, such as

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minimum power losses. The controllers in the first tier will track and keep the control settings sent

from the control center in real time. The first-tier control devices will be monitored by the regional

control center of the region in which they are located.

Figure 1.4. The three-tiered AVC system – Architecture 1.

In Architecture 2, the transfer capability optimization of the whole network is still performed in the

central control center; however, the OPF is decentralized and performed by individual regional

control centers (Figure 1.5).

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Figure 1.5. The three-tiered AVC system – Architecture 2.

This scheme allows different optimization objectives for each regional control center, which is

preferable for satisfying regional interest. In detail, the third-tier function will be to run on-line VSA at

the central control center and perform voltage stability and transfer capability optimization every 1

hour, using the entire system data. Its calculation results then will be distributed to each individual

regional control center, where the OPF engine will perform regional optimization every 15 minutes,

resulting in regional optimal control settings. These control settings are sent to the controllers of

each region in real time and will be tracked by the corresponding regional control center.

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Figure 1.6. Components of the AVC system.

The diagram above in Figure 1.6 shows the objective, output, and frequency of three components in

a general AVC system. The following are more detailed explanations of individual components,

focusing on a brief introduction of the objectives, methods, input and output data, and performing

frequency of each component.

1.2.3.4 Evaluation

The proposed AVC system has been evaluated on TPC’s production system. The results showed

that the following benefits can be brought to TPC by applying the proposed AVC system:

Increased transfer capability: By applying the proposed AVC system, the increase

percentage for system transfer capability ranges from 8.58% through 13.66% for the

February 2014 offline planning cases, depending on the system loading condition. For the

July 2014 offline planning cases, the increase percentage for the system transfer capability

ranges from 6.19% through 32.89%, depending on the system loading condition. For the

July 2016 planning case, the increase percentage for the system transfer capability is

361.17%, and for the October 2014 online operating cases, the increase percentage for the

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system transfer capability ranges from 0.71% through 27.20%, depending on the system

loading condition.

Decreased system power losses: For the February 2014 cases, the decrease percentage

for system real power losses ranges from 2.18% through 2.37%, depending on the system

loading condition. For the July 2014 cases, the decrease percentage for the system real

power losses ranges from 1.63% through 2.58%. For the July 2016 cases, the decrease

percentage for the system real power losses is 5.88%.

Eliminated system operational violations: After applying the proposed AVC system, there

is no thermal violation over all the system transmission lines and no voltage violations at the

monitored buses.

These benefits are valid for both the base-case system and the post-contingency system, should

any contingency (up to N-2) occur in the system. All these benefits are achieved by just applying

the controls that are obtained by applying the proposed AVC system over existing system

infrastructure, without any requirement for additional investments of new system devices. In other

words, the system can be operated in a more economical way by taking full advantage of the

existing system infrastructure, bringing noticeable economic benefits to the power company.

Table 1.2. System transfer capability improvements.

Case

Base-case System Post-Contingency System

Before AVC After AVC Improvement Before AVC After AVC Improvement

Case 1 4324MW 4695MW 8.58% 2220MW 2423MW 9.14%

Case 2 3408MW 3829MW 12.35% 957MW 1078MW 12.64%

Case 3 3030MW 3444MW 13.66% 1077MW 1208MW 12.16%

22

Table 1.3. System power loss reduction.

Case Before AVC After AVC Reduction

Case 1 194.22MW 189.61MW 2.37%

Case 2 293.27MW 286.89MW 2.18%

Case 3 344.54MW 336.48MW 2.34%

(a) Before AVC (b) After AVC

Figure 1.7. System voltage contour profiles.

23

1.3 The KASM Project

United Kingdom Power Networks (UKPN) provides power to a quarter of the UK’s population via its

electricity distribution networks in London that span to the east and southeast of England. To

achieve the Ofgem and UKPN goals, the Kent Active System Management (KASM) project was

completed over three years to facilitate integration of renewable energy and help elevate UKPN

from a distribution network operator to a distribution system operator (DSO). The KASM

Contingency Analysis Solution (CAS) tool, aka the Advanced Distribution Analytics for Power

Networks Tool (ADAPT), is an advanced real-time monitoring, state estimation platform armed with

contingency analysis, corrective control, and a portfolio of analysis and operational tools. In

addition, the look-ahead platform (30 minutes to 2 hours ahead, up to 24 hours ahead, time horizon

set by the user) offers forward time horizon assessment of the network, considering the

uncertainties of renewable energy. ADAPT is comprised of energy forecasting tools that provide

input into forecasting future system cases (e.g., 1 hour ahead to 24 hours ahead). ADAPT is

composed of the following key functions for active distribution networks: State Estimation, Power

flow, Contingency Analysis, the Interactive Single Line Diagram (132 kV, 33 kV, and external

connections), an Energy forecaster (for load, solar, and wind), Corrective control for removing

violations in the system, and a proprietary Data Bridging engine, which merges DMS output files

and planning tool files to be input into the platform. Implementations of the BSI ADAPT are

configured for each of UKPN’s three required operation modes: (i) Real-time mode (reliability

management using on-line data), (ii) On-line Study mode (infrastructure planning using historical

data and archived on-line cases), and (iii) On-line Look Ahead mode (outage planning using

forecasted data).

The ADAPT platform provides operators and engineers with real-time situational awareness and

facilitates network reliability management as new distributed generation comes online. It also

enhances the capability of outage planners to minimize constraints placed on the output from

distributed generators during the summer maintenance season and during any major construction

and reconfiguration activities. The Look-Ahead mode allows engineers to include the uncertainty of

renewable output as well as energy forecasting to produce forward-looking cases with new

renewable contingencies and alternate dispatch cases. Some challenges faced during the

development of ADAPT will also be presented. A by-product of the tool’s analysis capabilities can

also identify root causes of system and component power losses as well as ways to minimize them.

24

1.4 Modelling

Modeling for the Power Losses study was completed with the production of the Kent Active System

Management (KASM) Contingency Analysis Solutions (CAS) tool, which takes a holistic approach

to modeling the system from 400 kV to 33 kV. The modeling incorporates SCADA information from

GE PowerOn Fusion, parameters from the DigSilent Power Factory, and multiple other data

sources integrated together. Figure 1.8 below is a high-level diagram of the various systems and

related data involved in performing the contingency analysis.

DigSILENT

PowerFactory

GE

PowerON Met OfficeOSI Soft

Pi Historian

Forecasting

Engine

Data Bridge,

State Estimator &

Power flow solver

Study Mode

Look-Ahead Mode

(Analysis &

Control Engine)

Real-Time Mode

(Analysis &

Control Engine)

UK Power Network Systems External Systems

Offline Data

Mapping Engine

ENTSOE

National Grid

Control Centre

National Grid

System Operation

Single Line

Diagram Builder

Contingency Analysis Suite

Viewer

Figure 1.8. External data integration into the tool.

An accurate model is built, utilizing a mixture of the static data, measurement data, and forecasted

data to ultimately achieve a converging (base-case) model. The configuration and inputs of the

model vary, depending on which mode is being activated for the contingency analysis.

Measurement data reflect the current operating state of the power system and are updated in near

real time.

The construction of an accurate model involves importing data from various sources to create the

base-case scenario, which is essential in building a real-time network monitoring system. The real-

25

time base-case scenario is a model of the power system in its normal steady-state operation. To

develop a real-time base-case scenario, the following information is required:

Network connectivity, including switching status

Voltage level for the system

Line parameters (resistance r, reactance x, susceptance b, rating)

Transformer parameters (r, x, rating)

Transformer tap changer parameters (side, ratio, angle, upper limit, lower limit or, using

another way, tap position, high step and low step, neutral voltage, and neutral position)

Shunt capacitor parameters (for those that will participate in control, their controlled bus

and voltage schedule are required)

Load data (direction of power flow)

Generator data (Pmax, Pmin, Qmax, Qmin, voltage schedule, and controlled bus)

Quad booster data (side, ratio, angle, upper limit, lower limit or, using another way, tap

position, high step and low step, neutral voltage, and neutral position)

Measurements (P, Q, Amps, V).

In addition to the data for the base power system model outlined above, the following data are

required to execute and report the contingency analysis:

Single line diagram of the power network

Forecast data for loads, wind generators, and solar generators

Other additional information is required, such as the:

a. contingency list

b. monitoring list

c. capability curve (optional)

d. wind farm list

26

e. solar generator list

f. separate renewable generator list.

Project look-up tables that allow matches between the GE PowerOn name, the DIgSILENT

PowerFactory name, and OSISoft Pi Historian tags.

27

2 Project Objectives and Goals

This section lays out the objectives of the Losses Minimization project and the goals we are trying

to achieve in reducing losses for UKPN.

2.1 Task 1 – On-Line Loss Calculation for Every 30 Minutes

Through the UKPN KASM Real-Time State Estimation result, BSI develops a tailored power flow

engine to produce the following loss information under each network configuration:

1. System losses (active and reactive losses);

2. Losses due to each transformer;

3. Losses due to all the transformers;

4. Losses due to each line;

5. Losses due to all the lines;

6. Area-based losses;

7. Zone-based losses.

Optional:

1. 15-minute interval for heavy loading conditions;

2. 30-minute interval for medium loading conditions;

3. 1-hour interval for light loading conditions.

2.2 Task 2 – On-Line Component-Level Loss Sensitivity Calculation for

Every 15 Minutes

With each network configuration and a power flow solution for each 15-minute period, the following

loss sensitivity was calculated for each high-sensitivity component and for each renewable location:

1. Loss sensitivity (real power losses with respect to each power injection) at each node

(site);

2. List of high-loss-sensitivity transformers;

3. List of high-loss-sensitivity lines.

Optional:

28

1. 15-minute interval for heavy loading conditions;

2. 30-minute interval for medium loading conditions;

3. 1-hour interval for light loading conditions.

2.3 Task 3 – Relate Power Losses with Loading Conditions, Renewable

Locations, and Penetrations

This task was performed at the system level/substation level/feeder level. Some data mining and

data analytics techniques were used in this task.

2.4 Task 4 – Relate Power Losses with Network Topologies and Identify

the Best Network Topology

This task was performed at the system level/substation level/feeder level. Some data mining and

data analytics techniques were used in this task to identify the best network topology which offers

the lowest losses. This task also studies the relationship between UKPN’s system losses and

interface flows from the National Grid into UKPN.

29

3 Methodology

3.1 Methodology Overview

This project enriches the functionality of the current KASM project by providing UKPN with the

capability of analyzing system losses and gaining more insights into both sources of the losses and

ways to reduce system losses for more economical operation of the network.

BSI Loss Analytics Program

Online Input Data

BSI CAS Online Engine

BSI Loss Compute Engine

LAN/WAN

Loss Database

BSI Smart State Estimator

BSI Online Power Flow Solver

Figure 3.1. A loss system overview.

An overview of the methodology and the system structure for the integrated power network

computing and analytics system is shown in Figure 3.1. Provided with the online input data (SCADA

measurement data), the CAS online engine first carries out the state estimation (SE) function to

estimate the system state and the network topology. Based on this SE solution, an online power

flow solver is then applied to compute an accurate network power flow solution. Taking advantage

of the obtained real-time power flow solution, the loss analytic engine can compute all loss-related

metrics, such as the system losses, area losses, all component losses, and all component loss

sensitivity. In the meantime, the loss analytic engine also computes the best recommended line

switching actions to reduce the current system losses. These computing engines are hosted on the

server and automatically perform calculations periodically (with 15-minute intervals for the current

KASM practice). All these computed data are stored in the loss database and are accessible via the

operation using the loss analytics program.

Loss analytics provides a front-end with user-friendly graphical interface to access the computed

loss data stored in the database. Besides this basic functionality, the loss analytics program also

30

provides the operator with handy analytics tools, enabling him/her to dive deeply into the data to

gain deep insights into the system operations.

3.2 Power Network Losses

Transmission of electric power through power grids from power plants or stations to consumers is

subject to losses. The amount of power losses varies, depending on many factors such as power

network configurations and loading conditions. Electric power losses in power grids have a direct

economic impact. Each percent of power loss (with respect to the electricity consumption) can be

translated to an annual economic loss of almost billions of pounds. Besides their economic impact,

electric power losses also result in an environmental impact. Consider that most electric power

generation is from fossil fuel and natural gas, whose energy efficiency in electricity production is

about 35-40%. An estimate indicates that each percent of power loss is responsible for the

emission of millions of tons of CO2 each year.

In considering the significant economic and environmental impacts associated with power losses, it

is very important to accurately evaluate losses occurring in the power system to provide a basis for

analyzing the effects associated with power losses and to design and implement effective means to

control and reduce these losses. In the meantime, the level of losses also reveals the running

status of the power system, and thus, visualizing system losses in an informative way will be very

helpful in the control center.

Power system losses can be divided into two categories: technical losses and non-technical losses.

Technical losses are inherently occurring losses and are caused by actions internal to the power

system. These losses consist mainly of power dissipation in electrical system components, such as

transmission lines, power transformers, measurement systems, etc. More specifically, technical

losses in power systems can originate from the following sources:

• I2R losses or heat loss;

• Unoptimized location of transformers;

• Lengthy single-phase lines;

• Phase imbalance;

• Loose joints;

• Low power factor loads;

31

• Overloading of transmission lines;

• Low quality of insulators and conductors;

• Low-quality earthing at consumer premises.

Non-technical losses, on the other hand, are caused by actions external to the power system, or are

caused by loads and conditions that the technical losses computation failed to consider. The most

probable causes of non-technical losses include:

• Electricity pilferage;

• Tampering of meters;

• Non-payment by customers;

• Erroneous meter reading and/or billing;

• Errors in technical losses computation.

Technical losses are possible to compute and control, provided the power system in question

consists of known load quantities; on the other hand, non-technical losses are more difficult to

measure. Therefore, non-technical losses will not be covered in this report.

3.3 Power Loss Visualization

Effective visualization of power system conditions, including system losses, can help power system

operators maintain improved situational awareness. This section presents two ways to visualize

transmission line losses of a power system: visualization at the one-line diagram level and

visualization at the area-wise level.

(a) Low power loss (b) Medium power loss (c) High power loss

Figure 3.2. Visualization of power loss on individual transmission lines, using different thicknesses of

arrow lines to indicate the direction of power flow as well as the level of power losses.

The first way is to visualize power losses over individual transmission lines in the system. Figure 3.2

illustrates this visualization scheme based on the one-line diagram of the system. In this scheme,

Bus 1 Bus 2 Bus 1 Bus 2 Bus 1 Bus 2

32

the power flow through a line or branch is represented as triangles located over the line, whose

direction indicates the direction of the power transferring through the line, and the size is

proportional to the magnitude (or its logarithmic value) of the power flow. The magnitude of the real

power loss occurring on the transmission line is proportional to the thickness of the line; therefore,

the thicker the transmission line presentation, the higher the real power loss occurring on the line. In

addition to the absolute magnitude value (or its logarithmic value) for the real power loss, the line

thickness can also be illustrated as being proportional to the ratio of the loss with respect to the total

power flow magnitude through the line. Other visual cues can be adopted to accent the loss

differences in the transmission lines.

Figure 3.3. Area-wise visualization of system losses.

Another way is to visualize power losses over different areas in the system. Figure 3.3 above

illustrates this visualization scheme. In this scheme, the real power losses occurring over the

transmission lines within each area are summed up and each area in the system is covered by a

colored overlay. The magnitude (or its logarithmic value) of the total real power loss occurring in an

area is proportional to the darkness of the overlay color; therefore, the darker the overly area

presentation, the higher the real power loss occurring in the area. In addition to the absolute

magnitude value (or its logarithmic value) for the real power loss, the darkness of the overlay color

can also be illustrated to be proportional to the ratio of the loss with respect to the total load

demand or power generation in the area.

Low

High

Area 1 Area 2

Area 3

33

3.4 Loss Sensitivity Calculation

Loss sensitivity analysis evaluates the influence of control changes over system losses (noted as

L). Mathematically, the system loss sensitivity (noted as 𝑆𝐿𝐶) with respect to the value change of a

specific component in the power network (noted as C) can be defined as

𝑆𝐿𝐶 =ΔL

ΔC , (3.1)

that is, the ratio between the change in the component value (load demands, generation outputs,

switched shunt capacitor, transformer tap positions, etc.) and the change in system losses

introduced by the component value change. For instance:

The loss sensitivity of a load can be described as the change in system loss (in MW) if the

specified load demand is increased by 1MW.

The loss sensitivity of a renewable generator (wind or solar) can be described as the change

in system loss (in MW) if the specified generator output is increased by 1MW.

The loss sensitivity of a tap-changer transformer can be described as the change in system

loss (in MW) if the specified transformer is adjusted to increase the tap position by one step.

Based on the definition, intuitively, we could compute the system loss sensitivity with respect to a

specified component state or control change through the following steps.

One Simple Method for Loss Sensitivity Calculation

Step 1: Compute the base-case power flow solution and compute the system power losses,

noted as L0.

Step 2: Adjust the specified component state or control by a small amount, noted as Δ𝐶, for

instance, by increasing the load demand or generator output by 0.1MW or by increasing the tap

position of the specified transformer by one step.

Step 3: Compute the power flow solution after the adjustments and compute the system power

losses, noted as L1.

Step 4: The system loss sensitivity with respect to the specified component can then be

approximated as

34

𝑆𝐿𝐶 =𝐿1−𝐿2

Δ𝐶 (3.2)

This intuitive method is practical for evaluating the loss sensitivity with respect to only a few

components. This method becomes impractical if we want to investigate system losses that are

most sensitive to the changes of each component(s). The loss sensitivity is not static; instead, it

varies with the change in system loading conditions, renewable generation output, system network

topology changes, and changes in other system optional conditions. Therefore, the most sensitive

components for one snapshot of the power system operations are very likely not the most sensitive

components for other snapshots of the power system operations. To this end, we need a systematic

way to evaluate loss sensitivity with respect to all the different types of components in the power

networks at the same time.

The systematic loss sensitivity calculation can be derived through the concept of optimal power flow

(OPF) for loss minimization. Consider the following OPF problem for system real loss minimization:

min 𝑃𝐿𝑜𝑠𝑠(𝑉, 𝜃)

𝑠. 𝑡. 𝑃(𝑉, 𝜃) + 𝑃𝐷 − 𝑃𝐺 = 0

𝑄(𝑉, 𝜃) + 𝑄𝐷 − 𝑄𝐺 = 0 (3.3)

where 𝑃𝐿𝑜𝑠𝑠 is the system real loss, 𝑃𝐷 and 𝑄𝐷 are the real and reactive load demands at each bus,

𝑃𝐺 and 𝑄𝐺 are the real and reactive generations at each bus, and 𝑃(𝑉, 𝜃) and 𝑄(𝑉, 𝜃) are the real

and reactive power injections into the power network at each bus.

Denoting 𝑃𝐼 = 𝑃𝐺 − 𝑃𝐷 and 𝑄𝐼 = 𝑄𝐺 − 𝑄𝐷, the Lagrangian function for the OPF problem (3.3) can

then be formulated as follows:

𝐿(𝑉, 𝜃) = 𝑃𝐿𝑜𝑠𝑠 + 𝜇𝑃𝑇(𝑃(𝑉, 𝜃) − 𝑃𝐼) + 𝜇𝑄

𝑇 (𝑄(𝑉, 𝜃) − 𝑄𝐼) (3.4)

Where 𝑃𝐼 and 𝑄𝐼 are the real and reactive power injections at the bus I and 𝜇𝑃 and 𝜇𝑄 are the

vectors of Lagrangian multipliers for the real and reactive power injections at each bus,

respectively. The optimality conditions for the OPF problem (3.3) can then be specified as

𝜕𝐿

𝜕𝜃=

𝜕𝑃𝐿𝑜𝑠𝑠

𝜕𝜃+ (

𝜕𝑃

𝜕𝜃)

𝑇𝜇𝑃 + (

𝜕𝑄

𝜕𝜃)

𝑇𝜇𝑄 = 0

𝜕𝐿

𝜕𝑉=


𝜕𝑉+ (

𝜕𝑃

𝜕𝑉)

𝑇𝜇𝑃 + (

𝜕𝑄

𝜕𝑉)

𝑇𝜇𝑄 = 0

𝜕𝐿

𝜕𝜇𝑃= 𝑃(𝑉, 𝜃) − 𝑃𝐼 = 0

𝜕𝐿

𝜕𝜇𝑄= 𝑄(𝑉, 𝜃) − 𝑄𝐼 = 0

(3.5)

35

From (3.4) and (3.5), we see that the sensitivity of the system loss with respect to the change of

power injections at each bus will be

[


𝜕𝑃𝜕𝑃𝐿𝑜𝑠𝑠

𝜕𝑄

] = − [𝜇𝑃

𝜇𝑄] = [

𝜕𝑃

𝜕𝜃

𝜕𝑃

𝜕𝑉𝜕𝑄

𝜕𝜃

𝜕𝑄

𝜕𝑉

] [


𝜕𝜃𝜕𝑃𝐿𝑜𝑠𝑠

𝜕𝑉

] = 𝐽𝑇 [


𝜕𝜃𝜕𝑃𝐿𝑜𝑠𝑠

𝜕𝑉

] (3.6)

where 𝐽 is the system Jacobian matrix. This enables us to calculate the system loss sensitivity with

respect to power injections at all buses at the same time.

In summary, one systematic method for calculating the system loss sensitivity can be described as

follows.

One Systematic Method for Loss Sensitivity Calculation

Step 1: Compute the power flow solution.

Step 2: Evaluate the system Jacobian matrix (which is a by-product of the power flow

computation) and the derivatives of 𝑃𝐿𝑜𝑠𝑠 with respect to 𝜃 and 𝑉.

Step 3: Compute the system loss sensitivity using (3.6).

3.5 Validation of the Sensitivity Calculation

In this section, the system loss sensitivity calculated using the systematic method is validated with

the naïve method. Several generator components with the largest loss sensitivity are chosen from

three snapshots, that is, 00:00, 09:00 and 19:00 on February 28, 2017, representing different

loading conditions.

For the snapshot at 00:00, the two generators, V000e0649COMPGEN and G00022fd9COMPGEN,

are identified as having the largest sensitivity (in terms of the magnitude of sensitivity). To compute

the sensitivity via the naïve method, the output of the generator is increased by 0.1MW. Then, the

power flow solution is re-calculated, and the power losses are updated. It should be noted that, to

balance the increased generation at the specified generator component, the system slack bus

generation will be adjusted, too. Therefore, the change in the system loss needs to take into

consideration both the generation changes at the generator under study and the slack generator.

The validation process is carried out separately for the two generators with the largest loss

sensitivity.

36

The comparison results are summarized in Table 3.1, where

Δ𝑃𝑔𝑒𝑛 is the change of real power generation at the generator of interest.

𝜆𝒈𝒆𝒏, 𝒕𝒉𝒆𝒐𝒓 is the real power loss sensitivity of the generator calculated via the systematic

method.

∆𝑃𝑠𝑙𝑎𝑐𝑘 is the change in real power generation at the slack bus to balance ∆𝑷𝒈𝒆𝒏 to get the

power flow solution.

𝜆𝑠𝑙𝑎𝑐𝑘, 𝑡ℎ𝑒𝑜𝑟 is real power loss sensitivity of the slack generator calculated via the systematic

method.

∆𝑃𝑙𝑜𝑠𝑠, 𝑡ℎ𝑒𝑜𝑟 is the theoretical change of the system loss that is calculated based on the

actual generation changes and the loss sensitivity.

∆𝑃𝑙𝑜𝑠𝑠, 𝑟𝑒𝑎𝑙 is the actual change of the system power loss.

𝑑𝑖𝑓𝑓 is the difference between theoretical and actual changes of the system real loss, which

is defined as

𝑑𝑖𝑓𝑓 = ∆𝑃𝑙𝑜𝑠𝑠, 𝑡ℎ𝑒𝑜𝑟 − ∆𝑃𝑙𝑜𝑠𝑠, 𝑟𝑒𝑎𝑙 = (∆𝑃𝑔𝑒𝑛 × 𝜆𝑔𝑒𝑛, 𝑡ℎ𝑒𝑜𝑟 + ∆𝑃𝑠𝑙𝑎𝑐𝑘 × 𝜆𝑠𝑙𝑎𝑐𝑘, 𝑡ℎ𝑒𝑜𝑟) − ∆𝑃𝑙𝑜𝑠𝑠, 𝑟𝑒𝑎𝑙.

From Table 3.1, we can observe that the difference between the theoretical and actual changes of

the system loss is very small, of magnitude 0.0001MW.

37

Table 3.1. Snapshot: 2017-2-28 00:00

Generator ID

Δ𝑃𝑔𝑒𝑛

(MW)

𝜆𝑔𝑒𝑛, 𝑡ℎ𝑒𝑜𝑟

∆𝑃𝑠𝑙𝑎𝑐𝑘

(MW)

𝜆𝑠𝑙𝑎𝑐𝑘, 𝑡ℎ𝑒𝑜𝑟

∆𝑃𝑙𝑜𝑠𝑠, 𝑡ℎ𝑒𝑜𝑟

(MW)

∆𝑃𝑙𝑜𝑠𝑠, 𝑟𝑒𝑎𝑙

(MW)

𝑑𝑖𝑓𝑓

(MW)

V000e0649COMPGEN 0.1 0.046 -0.097 0.0200 0.00266 0.00283 -1.7e-4

G00022fd9COMPGEN 0.1 -0.039 -0.106 0.0200 -0.00602 -0.00599 -3e-5

Table 3.2. Snapshot: 2017-2-28 09:00

Generator ID

∆𝑃𝑔𝑒𝑛

(MW)



(MW)



(MW)


(MW)

diff

(MW)

i00170b89COMPGEN 0.1 0.263 -0.0977 0.2423 0.00263 0.00229 3.4e-4

G00022fd9COMPGEN 0.1 0.1834 -0.1128 0.2423 -0.00899 -0.01281 3.8e-5

Table 3.3. Snapshot: 2017-2-28 19:00

Generator ID

∆𝑃𝑔𝑒𝑛

(MW)



(MW)



(MW)


(MW)

diff

(MW)

i00160da9COMPGEN 0.1 2.096 -0.105 2.044 -0.00502 -0.00554 5.2e-4

V0005bee8COMPGEN 0.1 1.973 -0.101 2.044 -0.00899 -0.00093 8.05e-3

i00170b89COMPGEN 0.1 1.988 -0.095 2.044 0.00472 0.00505 3.24e-4

Tables 3.2 and 3.3 show the validation results for the other two snapshots, from which we can

observe that the system loss sensitivity, calculated using the systematic method, works very well for

38

different loading conditions. It can also be observed that the most sensitive components keep

changing from snapshot to snapshot.

3.6 Loss Minimization via Line Switching

3.6.1 Particle Swarm Optimization (PSO)

The original particle swarm (PSO) algorithm was introduced and discussed in [7, 8]. It imitates birds

flocking and fish schooling as it searches in D-dimensional real number space for the best position.

In this algorithm, a certain number of particles is utilized, with each particle's position representing a

solution to the problem. Particles move across the search space partially randomly and partially

dependent on the personal and global best position discovered thus far.

Formally, let f: Rn → R be the objective function to optimize, and let the swarm contain P particles,

each of which consists of a pair of real valued vectors (xi, vi) with position (optimization variables)

xi ∈ Rn and velocity vi ∈ Rn, ∀ i ∈ {1, ⋯ , P}. Denote �̃�i and 𝑓i as the current best position and fitness

value of each particle and let 𝑥∗ and 𝑓∗ be the global best position and fitness. Then, a PSO

procedure generally consists of the following steps:

1) Initialization: initialize 𝑥𝑖 and 𝑣𝑖 as 𝑥𝑖𝑗 ∈ 𝑈(𝑎𝑗, 𝑏𝑗) and 𝑣𝑖𝑗 = 0, ∀𝑖 = 1, ⋯ , 𝑃 and ∀𝑗 = 1, ⋯ , 𝑛,

where 𝑎𝑗 and 𝑏𝑗 are the given limits of the search domain in the i-th dimension and 𝑈(⋅)

represents the uniform distribution. Initialize 𝑓𝑖 = ∞, ∀𝑖 = 1, ⋯ , 𝑃 and 𝑓∗ = ∞, and set the

iteration counter to k=1.

2) Fitness evaluation: evaluate the fitness 𝑓(𝑥𝑖), ∀𝑖 = 1, ⋯ , 𝑃. If 𝑓(𝑥𝑖) ≤ 𝑓𝑖, then 𝑓𝑖 ← 𝑓(𝑥𝑖) and

�̃�𝑖 ← 𝑥𝑖. Let 𝑓 = min{𝑓(𝑥1), ⋯ , 𝑓(𝑥𝑃)}, and �̃� = arg min{𝑓(𝑥1), ⋯ , 𝑓(𝑥𝑃)}. If 𝑓 ≤ 𝑓∗, then

𝑓∗ ← 𝑓 and 𝑥∗ ← �̃�.

3) Updating: For each particle, create random vectors 𝑟1 and 𝑟2 with 𝑟1𝑗, 𝑟2𝑗 ∈ 𝑈(0,1), ∀𝑗 =

1, ⋯ , 𝑛. Then, the velocity and position of the particle is updated via

𝑣𝑖(𝑡) = 𝑤 ⋅ 𝑣𝑖(𝑡 − 1) + 𝑐1 ⋅ 𝑟1 ∘ (�̃�𝑖 − 𝑥𝑖(𝑡 − 1)) + 𝑐2 ⋅ 𝑟2 ∘ (𝑥∗ − 𝑥𝑖(𝑡 − 1))

𝑥𝑖(𝑡) = 𝑥𝑖(𝑡 − 1) + 𝑣𝑖(𝑡)

where w is the inertial constant, 𝑐1 and 𝑐2 are constants that say how much the particle is

directed toward good positions, and the ∘ operator indicates the element-by-element

multiplication.

39

4) Checking the stopping criterion: stop the process if the stopping criterion is satisfied;

otherwise, increment the iteration counter k=k+1 and go to Step 2) to start a new round of

swarm movement.

The canonical PSO is generally for solving continuous optimization problems. However, for the line

switching problem, the target is to switch off some lines that result in the largest reduction in system

loss, or more specifically, to change the operating status of the lines from online (“1”) to offline (“0”).

Therefore, the line switching problem is a discrete problem, instead of a continuous problem. To

this end, a binary version PSO algorithm [9] is considered for line switching for system loss

reduction.

3.6.2 Deterministic Heuristic Search

Considering that the system size is not very large, a deterministic heuristic search method for loss

reduction is also implemented. This method consists of two stages: stage 1 for an exhaustive

search of the best schemes for removing only one line for loss reduction, and stage 2 for a search

of the best combination schemes for loss reduction. The method is described as follows.

The Deterministic Heuristic Line Switching Method

Stage 1: Single line switching

For each branch component (a normal branch or a transformer branch), switch it off and

compute the power flow solution and the system losses.

Rank the branch components in terms of the reduction in system losses.

Select, say, the 15 best components that introduce the most system loss reductions.

Stage 2: Multiple line switching

For each combination (2 or 2 branches) of the best components selected in stage 1, switch

it off and compute the power flow solution and the system losses.

Rank the branch combinations in terms of the reduction in system losses.

Select at most 10 line switching schemes that result in the largest reduction in system

losses.

The power flow and loss computation for each candidate line switching is inherently independent to

each other; therefore, the search method can take full advantage of parallelization utilizing multiple

40

CPU cores. On a desktop PC equipped with an INTEL Core i7 4790K CPU (4 cores, 8 hyper-

threads), the full line switching process on the UKPN system can be accomplished in about 20

seconds. The computational efficiency of the implemented method enables the online deployment

of the UKPN system.

3.6.3 Results

The results of system loss minimization via line switching are shown in Figures 3.4 and 3.5. More

specifically, the comparison between the system losses before and after line switching is shown in

Figure 3.4, while the system loss reduction rates introduced by the line switching process are

shown in Figure 3.5. The results cover 287 snapshots from July 5, 2017, 00:00 to July 7, 2017,

23:45, with 15-minute intervals (one snapshot is not available because the state estimation and

base-case power flow diverged).

Figure 3.4. The effectiveness of line switching for loss reduction.

0

20

40

60

80

100

120

140

160

7/5/2017 0:00 7/5/2017 12:00 7/6/2017 0:00 7/6/2017 12:00 7/7/2017 0:00 7/7/2017 12:00 7/8/2017 0:00

Syst

em L

oss

(M

W)

Date Time

Effectiveness of Line Switching for System Loss Reduction

Before Line Switching

After Line Switching

41

Figure 3.5. Loss reduction percentage by line switching.

From the result figures, we have the following observations:

Line switching can effectively reduce system losses at peak loading conditions.

At normal loading conditions, line switching introduces no reduction or a negligible reduction

in system losses.

Among the 287 snapshots, line switching can introduce a more than 2% reduction in system

losses for 50 snapshots.

The largest reduction in system losses introduced by line switching is almost 30% where the

highest system loss occurred (July 6, 2017, 11:45).

These observations suggest that line switching is an enabling tool for reducing system losses,

especially for system operating conditions where large losses occur. This is achieved by switching

off no more than three transmission lines in the power network.

Table 3.4. Lines to be switched off for loss reduction (reduction > 2%).

Time Loss Before

(MW) Loss After

(MW) Switched Lines

Reduction Rate

7/5/2017 7:00 51.45711 50.354323 V000df43fCOMP e0003f077COMP e00038061COMP

2.1%

-5%

0%

5%

10%

15%

20%

25%

30%

35%

7/5/2017 0:00 7/5/2017 12:00 7/6/2017 0:00 7/6/2017 12:00 7/7/2017 0:00 7/7/2017 12:00 7/8/2017 0:00

Syst

em R

eal L

oss

Red

uct

ion

Date Time

Loss Reduction by Line Switching

42

7/5/2017 7:30 60.39346 57.868532 V000df43fCOMP c000c54cfCOMP e00038061COMP

4.2%


6.0%


6.1%


2.9%


8.0%

7/5/2017 9:15 59.18527 57.922005 V000df43fCOMP c000c54cfCOMP i00119b83COMP

2.1%


2.8%


14.8%

7/5/2017 12:00 93.21703 79.778522 V000df43fCOMP c000c509bCOMP c000c54cfCOMP

14.4%


14.4%


14.5%


4.4%


6.1%


6.2%

43


4.7%


4.9%


4.1%


3.0%


3.0%

7/5/2017 19:15 63.09116 60.670815 V000df43fCOMP c000c54cfCOMP i00119b83COMP

3.8%

7/6/2017 6:00 88.09084 72.832268 V000df43fCOMP e00038053COMP G000376f8COMP

17.3%


3.5%


3.2%

7/6/2017 8:15 66.25641 63.370183 V000df43fCOMP V00028943COMP e00038053COMP

4.4%

7/6/2017 8:30 65.7177 62.843955 V000df43fCOMP c00236d98COMP e00038053COMP

4.4%


8.2%


8.1%


10.4%

44


29.9%

7/6/2017 16:15 80.09746 71.965674 V000df43fCOMP i0010db1cCOMP e00038058COMP

10.2%

7/6/2017 16:30 59.69885 58.401233 V000df43fCOMP e00038058COMP i00119b83COMP

2.2%


2.1%


8.3%

7/6/2017 17:15 62.62561 60.928707 V000df43fCOMP i0010db1cCOMP e00038058COMP

2.7%


4.3%

7/6/2017 17:45 71.97618 66.988216 V000df43fCOMP c000c509bCOMP e00038058COMP

6.9%


4.0%


8.1%


6.1%


2.8%

7/7/2017 5:00 83.57635 69.548771 V000df43fCOMP c000c3b15COMP e00038053COMP

16.8%


10.7%

45


8.1%


5.5%

7/7/2017 8:45 65.12453 63.739903 V000df43fCOMP c000c3b15COMP e00038061COMP

2.1%


3.9%


3.8%


4.3%


5.0%

Table 3.5. Statistics of the lines switched off for loss reduction.

ID Component Frequency

1 V000df43fCOMP 50

2 c000c54cfCOMP 25

3 e00038058COMP 17

4 e00038061COMP 16

5 e00038053COMP 12

6 i00119b83COMP 7

7 c00236d98COMP 6

8 c000c509bCOMP 6

9 V00028943COMP 4

10 i0010db1cCOMP 2

11 c000c3b15COMP 2

12 V00028948COMP 1

13 e0003f077COMP 1

46

14 G000376f8COMP 1

The lines (normal branches or transformers) to be switched off, resulting in the largest loss

reduction for the 50 snapshots with more than a 2% reduction, are summarized in Table 3.4. The

frequency of the lines to be switched off among the 50 snapshots is summarized in Table 3.5. From

these two result tables, we have the following observations:

The lines to be switched off for the 50 snapshots are concentrated in only 14 lines.

The line with component ID V000df43fCOMP, which is a 400kv line, is switched off in all the

50 snapshots. Figure 3.2 shows the branch loss and Figure 3.3 shows the correlation

between the branch loss and the system loss. From these figures, it can be observed that

switching off branch V000df43fCOMP contributes to most of the loss reduction. The

correlation between the branch loss and the system loss is also very high: 0.708.

Losses of the lines that have been switched off more than 10 times within the 50 snapshots

are shown in Figure 3.4. Their correlations with the system loss are shown in Figure 3.6. It

can be observed that these lines contribute to only a negligible fraction of the system losses,

and their correlations with the system are also very low (less than 0.25 in terms of

magnitude).

Figure 3.2. The loss of branch V000df43fCOMP (along with the system loss).

47

Figure 3.3. Correlation between branch V000df43fCOMP and the system loss.

Figure 3.4. Branches that have been switched off more than 10 times.

48

Figure 3.5. The correlation between branches and system loss.

49

4 Analyses of System Losses

4.1 System Behavior

The system behavior (within the period from July 05, 2017 00:00 to July 07, 2017, 23:45) of system

losses and loads, including that of the UKPN and the system loss after line switching, is shown in

Figure 4.1. The system switch status within the same period is shown in Figure 4.2. The

correlations between these system quantities with the system loss are shown in Figure 4.3.

Figure 4.1. The system value curves (losses and loads). This figure shows system losses before and

after switching is performed, along with the total load.

Red means the switch is open while blue means the switch has been closed.

Figure 4.2. The system switch status matrix for the same period with the switch status color coded.

From the figures, we have the following observations:

System and UKPN losses increase as the UKPN load increases; that is, the system

changes and the UKPN losses are highly correlated with the change in UKPN load. This

50

correlation is also clearly shown in Figure 4.3, which shows that the correlation is very high:

0.842.

The system and UKPN losses are not highly correlated with the system load. As shown in

Figure 4.3, the correlation between the system load and the system loss is only 0.342.

Line switching can effectively reduce system losses at peak loading conditions. At normal

loading conditions, line switching introduces no reduction or a negligible reduction in system

losses.

From the switch status in Figure 4.2, system loss changes more noticeably during time

periods when the switches are changed frequently, but not during time periods when the

switches are changed less frequently.

Figure 4.3. Correlations between the analyzed data and the system loss.

4.2 The Most Lossy Branches (System)

51

The most lossy normal non-transformer branches are shown in Figure 4.4, and their correlations

with the system loss are shown in Figure 4.5. Among these branches, the loss of branch

V000df440COMP is highly correlated with the system loss, with a correlation of 0.708. This branch

also contributes to the spikes that can be observed in the system loss.

Figure 4.4. The most lossy branches being studied.

Figure 4.5. Correlation between the most lossy branches and the system loss.

52

4.3 The Most Lossy Transformers (System)

The most lossy transformer branches are shown in Figure 4.6, and their correlations with the

system loss are shown in Figure 4.7. Among these transformers, the loss of transformers

G00037620COMP and G00037860COMP is large and highly correlated with the system loss, with a

correlation of 0.91.

Figure 4.6. The most lossy transformers being studied.

Figure 4.7. Correlation between the most lossy transformers and the system loss.

53

4.4 The Largest Load Components

The largest load components are shown in Figure 4.8, and their correlations with the system loss

are shown in Figure 4.9. The following loads are highly correlated to the system loss (with a

correlation larger than 0.6 in magnitude):

EquiLoad_00001

V0013d925COMPLOAD

V0013d92bCOMPLOAD.

In particular, load component EquiLoad_00001 is negatively correlated to the system loss; in other

words, change in this load component is usually in the reverse direction from change in the system

loss.

Figure 4.8. Two components with maximum load vs. the system loss.

54

Figure 4.9. Correlation between the max-load components and system losses.

4.5 The Largest Generation Components

The largest generation component (component ID: V000dcd99COMPGEN) does not necessarily

have a high correlation with the system loss, since the correlation is only 0.294. Instead, the

following generators are highly correlated to the system loss (with a correlation larger than 0.6):

EquiGen_00007

G00038847COMPGEN

G0003884aCOMPGEN

G00038850COMPGEN

55

Figure 4.10. The max-generation components (system).

The largest generation components within the UKPN are shown in Figure 4.11; their correlations

with system loss are shown in Figure 4.12. It can be observed that these generations possess a low

correlation with system loss, since they are less than 0.2.

Figure 4.11. Correlations between the max-generations and system loss.

56

Figure 4.12. The largest generation components (only UKPN).

Figure 4.13. Correlations between the largest generation components (UKPN) and system loss.

57

4.6 System Loss and State Estimation Quality

The accuracy of real-time loss analytics relies on accurate state estimation results. The transformer

(component ID: G00037620COMP) is contributing the most losses belong to the National Grid (NG)

part (400KV-132KV). The correlation between this component loss and the system loss is shown in

Figure 4.14. It can be observed that the correlation is very high: 0.91.

Figure 4.14. The most lossy component is a transformer (component ID: G00037620COMP).

58

Figure 4.15. The correlation between the most lossy transformer and the system loss.

However, after inspecting the data, as shown in Tables 4.1 and 4.2, the tap position is always 1.0

p.u.; however, the two terminal buses exhibit a large voltage difference of 0.156 p.u. Such a big

voltage difference is not reasonable, resulting in the unreasonably large loss over this transformer.

Therefore, the accuracy of loss analysis relies heavily on the accuracy of state estimation, which, in

turn, relies heavily on the accuracy of the system model and measurements, and also relies on the

comprehensiveness of the modeling capability of the state estimation tool.

Table 4.1. Transformer data records (power flow solution).

633, 485, 0,'1 ',1,1,1, 0.00000, 0.00000,1,' ',1, 1,1.0000 0.00131, 0.07952, 100.00 1.00000, 0.000, 0.000, 240.00, 240.00, 240.00, 1, 485, 1.01429, 0.96429, 1.10000, 1.04000, 14, 0, 0.00000, 0.00000 1.00000, 0.000, /* [G00037620COMP] */

Table 4.2. Terminal bus data records (power flow solution).

485,'GRAIN 40', 132.00, 1, 0.000, 0.000, 1, 1, 1.1617446, -23.4257, 1, /* [G00037867COMP] */ 633,'GRAIN 40', 400.00, 2, 0.000, 0.000, 1, 1, 1.0055799, 2.0437, 1, /* [V000df266COMP] */

59

5 Additional Technology

5.1 Optimal Capacitor Placement

The strategy of optimal capacitor placement and sizing is becoming popular in improving the

various aspects of distribution systems, such as power loss reduction, voltage profile enhancement,

total cost minimization, and capacity release.

Using the optimal capacitor placement technique, the unnecessary reactive power flow in the

distribution feeders will be reduced and therefore, the power transfer capability of distribution

networks would be increased. Technically, as the last link between production and consumers, the

distribution system can play a key role in improving the reliability and power quality of the supply. In

comparison to the generation and transmission networks, the distribution system has a low load

density, and outages/failures of this part have a local effect on consumers. Indeed, the strategy of

optimal capacitor placement and sizing is becoming a popular way to improve different aspects of

distribution systems, such as:

1. power loss reduction

2. voltage profile enhancement

3. (peak) load reduction

4. hosting capacity enhancement

5. capacity release.

According to the failure statistics, distribution systems have the most influence in the unavailability

of supply for consumers. In recent years, a wide range of research has been conducted to examine

the unique features of optimal capacitor placement and sizing. The solution methods of the optimal

capacitor placement problem can be divided into the following four main categories:

1. Analytical techniques

2. Meta-heuristic methods such as PSO, GA, Firefly, and Ant Colony

3. Nonlinear optimization programming-based methods

4. Artificial intelligence and machine learning.

60

In the past, the focus of these studies has been traditional single objective functions such as:

minimizing the system total losses;

minimizing the cost of active power losses, energy losses, and capacitor investment;

minimizing the total power losses, voltage deviation, and total harmonic distortion;

minimizing both active and reactive power losses, as well as the voltage deviation of buses.

A new hybrid method based on differential evolution and pattern search has been suggested to

solve the multi-objective capacitor placement problem considering voltage profile enhancement,

power loss reduction, and total cost minimization.

A literature survey reveals that some traditional objective functions such as active/reactive power

losses, voltage deviation, and total cost have been the key issues of capacitor placement and

control. While the strategy of optimal capacitor placement and control can be effective for reliability

reinforcement, there is yet very little work available to investigate this aspect of the problem.

For instance, the strategy of optimal capacitor placement and control can increase the maximum

delivery capability of distribution networks. In addition, the objective function, the Average Energy

Not Supplied (AENS) index, which deals with the energy-oriented reliability criterion, can be

improved via the strategy of optimal capacitor placement and control. In addition, the customer-

oriented reliability indices like System Average Interruption Frequency Index (SAIFI) and System

Average Interruption Duration Index (SAIDI) can be improved by the strategy of optimal capacitor

placement and control. SAIFI and SAIDI are reliability indicators used by electric power utilities in

the states. SAIDI is the average outage duration for each customer served while SAIFI is the

average number of outages that a customer would experience.

5.1.1 The Study

As part of a bonus study, to be completed outside the scope of the UKPN Losses study, BSI

considered the potential of optimal capacitor placements on the UKPN system. The study of optimal

capacitor placements involves strategically installing capacitors on various buses for voltage

support, power factor correction, or, in this case, loss minimization. The use of optimization and

power flow methods can determine the best location for capacitor placement as well as bank sizes.

BSI engineers determined various optimal capacitor placements on the network to drastically

reduce power losses. These network losses ranged from 11% all the way up to 40% loss reduction.

61

The initial study was run for February 17, 2017 and found a potential loss reduction of 40% with

optimal capacitor placements throughout the network. This result is shown in the following graph in

Figure 5.1.

Figure 5.1. Potential saving via capacitor placement and control.

To further validate, the study was performed on 4 snapshots of data:

- May 17, 2017 9:30-23:45

- July 5, 2017 00:15-23:45

- July 6, 2017 00:15-23:45

- July 7, 2017 00:15-23:45

Evaluations performed on the 4 additional data files found that the potential loss reduction rates ran

from 11% to 38% with optimal capacitor placements at target bus locations. The number of

capacitors recommended per case averaged out to be 3 capacitors (2.833) strategically placed on

identified buses to reduce losses. Capacitor placement and settings were found to reduce network

losses when placed on certain identified buses and with capacitor MVAR settings.

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

0

10

20

30

40

50

60

pss

e022820170000

pss

e022820170045

pss

e022820170130

pss

e022820170215

pss

e022820170300

pss

e022820170345

pss

e022820170445

pss

e022820170530

pss

e022820170615

pss

e022820170700

pss

e022820170745

pss

e022820170830

pss

e022820170915

pss

e022820171030

pss

e022820171115

pss

e022820171200

pss

e022820171245

pss

e022820171330

pss

e022820171415

pss

e022820171500

pss

e022820171545

pss

e022820171630

pss

e022820171715

pss

e022820171900

pss

e022820171945

pss

e022820172030

pss

e022820172130

Capacitor Placement

Original Loss (MW) Optimal Loss (MW) Reduction (%)

63

Table 5.1. Potential saving studies via capacitor placement and control.

5.2 Maximizing Available Delivery Capability

The integration of DG with distribution networks may have several additional merits, such as

minimizing the network losses, deferring investments in transmission and distribution upgrades,

improving the system voltage profile, and enhancing the system stability. Nevertheless, there are

some technical and safety problems arising from the integration of DG, such as increasing fault

currents and voltage oscillations and the more complicated setting of protection devices.

Furthermore, operational conditions of the system will become more severe when both the time-

varying characteristic of loading conditions and the uncontrollability of DG outputs are considered.

One of the countermeasures is to restrict DG outputs by using some control devices. However, it is

undesirable to reduce the power outputs of DGs from the viewpoint of effectively using renewable

energy.

Available delivery capability is defined as the capability of a distribution network to deliver power

from the source area (such as a collection of nodes to which renewable energies are connected) to

the sink area (such as a collection of loads) with no thermal overloads, voltage violations, or static

stability violations. For a specified distribution network topology, its available delivery capability

(ADC) for supporting renewable penetrations is fixed under specified network parameters, such as

loading conditions and load models, among others. To compute the ADC, the variation of loads and

generations must be specified. This specified vector of load variations and generation variations,

say, according to load forecasting and generation rescheduling, is also needed in the calculation of

ATC (available transfer capability). To support more DG power injections, the network

Time PFLOW

Losses (MW)

OPF Losses

(MW)

Loss

Reduction

Rate

bus 564 bus 485 bus 1080 bus 1537 bus 1546 bus 3385 bus 6859

Case 1 39.7273 35.5017 11% 300 1.64 16

Case 2 50.3064 43.1817 14% 650 3.6 8 28.7

Case 3 18.7662 16.035 15% 300 5

Time PFLOW

Losses (MW)

OPF Losses

(MW)

Loss

Reduction

Rate

bus 225 bus 485 bus 1567 bis 2416 bus 2615 bus 6891

Case 4 64.046 42.6362 33% 56 8 27

Case 5 27.6968 21.9684 21% 500 1.6

Case 6 62.4369 38.4244 38% 38 8 10

64

reconfiguration technique can be an effective and economical measure to resolve the operational

problems resulting from DG integration without any additional investment.

Distribution networks are usually constructed in a meshed network and operated in a radial

topology. The network topology can be altered through opening the sectionalizing switches and

closing the tie ones. Distribution network reconfiguration (NR) entails altering the topological

structure of the distribution network by changing the opening/closing status of the switches. NR has

been applied to reduce network losses, balance transformer loading, and restore supply service

after a power failure.

The PV-curve method is popular in studying the steady state stability limit in power systems. As

illustrated in Figure 5.2 below, the (load) node voltage magnitude tends to decrease with increasing

loading conditions, and when the loading condition reaches the so-called nose point, the

phenomenon of voltage collapse can happen. On the other hand, as shown in Figure 5.3, the node

voltage magnitude tends to rise with the increase of DG outputs and then begins to dip as it

approaches its peak value, at which DG power injections reach their maximum at the nose point,

which can be regarded as the maximum of the DG power injections. For a given distribution

network configuration, with a set of specified DG outputs and load variations, there is a unique

available delivery capability (ADC) from the source to the sink (load demands). For instance, by

increasing the power injections from a selected set of DG units and decreasing power outputs from

the substation and conventional generators, the difference in the total amount of power injections

from the DG units between the nose point and the current operating point is the ADC of the

network.

0 0.1 0.2 0.3 0.4 0.5

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Loading Factor/λ

Voltage M

agnitude/p

.u

Nose Point

65

Figure 5.2. The PV curve of a node of the 1001-node distribution network. The horizontal axis is the

loading factor above the current base load. For example, the loading factor of 0.3 means the total load

is 130% of the current base load.

We seek to maximize the available delivery capability of distribution networks via NR to

accommodate the high penetration of DGs. The goal is to find the optimal network configuration that

has the maximum capability of DG integration, considering relevant engineering and operational

constraints. We assume that the location, size, and number of DGs are given. These issues are

related to the planning stage while the proposed study is for operational purposes. Our concern is

to evaluate whether the network topology can deliver the power generated from DGs to loads and

how a network topology can deliver the maximum power generated from DGs to loads.

Figure 5.3. The 394-case bus-99 PV curve with increasing DG.

The problem formulation of maximizing ADC via network reconfiguration can be represented as

follows:

Objective:

Subject to:

Voltage constraint

0 1 2 3 4 5 6 7 80.85

0.9

0.95

1

1.05

1.1

DG Factor/λ

Voltage M

agnitude/p

.u

Nose Point

1

max

i

t

DG

i

P

66

Thermal-limits constraint

Radial configuration constraint

Static stability constraint

where

: Outputs of the distributed generation

: Voltage at bus i

: Minimum acceptable bus voltage at bus i

: Maximum acceptable bus voltage at bus i

: Current in branch I, : line current limit of branch i

: The element of incidence matrix of the network topology in the row and column. It is 1

when bus i and bus j are connected and 0 when not connected. The on-diagonal element is 0.

: Load margin, defined above for the static stability constraint definition, which needs to be

greater than the desired threshold (i.e., a desired load margin). The load margin is a direct measure

of ADC.

min maxi i iV V V

maxi iI I

2( 1)

ij

i Vertices j Vertices

k n

margin

iDGP thi

iV

iminV

imaxV

iIimaxI

ijk thithj

67

5.3 Another Scheme for Reducing Transmission Losses

Through Line Switching

Reducing transmission loss is effective in improving power transmission efficiency and saving

energy. Significant work has been applied to reducing transmission loss using various methods.

These methods can be classified into two categories: power injection-based methods, which include

active or reactive generation rescheduling, VAR sources optimization, and the network-topology-

based methods that include network topology optimization, which alters network topology without

adjusting any control variable or adding any auxiliary equipment.

Line switching is an economical and efficient action for network topology optimization, as it is

relatively easy to implement and can save both time and cost. Relevant work has demonstrated its

efficiency and effectiveness in corrective control and optimization, such as reducing transmission

loss or generation costs, alleviating line overload, and improving the voltage profile. Some

proposals in the literature combine the line switching method with Optimal Power Flow (OPF) as

constrained Mixed Integer Nonlinear Programming (MINLP). It is an effective scheme but may not

be suitable for online application due to its high cost in computation time and the need to adjust

many control variables.

We present a novel online method for reducing transmission loss in power systems while satisfying

the operational and engineering constraints of post-optimizing power systems. As the line switching

method has been an online practice, Stage I of the proposed method presents another application

of the online line switching method for reducing transmission loss. Stage II presents an online

modified OPF (M-OPF) method as a back-up or follow-up method if further transmission loss

reduction is needed.

It is well recognized that linear methods are usually fast but may not be sufficiently accurate,

whereas nonlinear method are usually accurate but may not be sufficiently fast. Thus, the proposed

method is a hybrid of linear and nonlinear methods instead of dealing with the combinatorial

character of the Optimal Transmission Switching (OTS) problem solved by mixed integer nonlinear

programming (MINLP). In addition, to balance the speed (short computational time) and accuracy

(high quality of solution) for online application, both stages of the proposed method are composed

of three stages: screening, ranking, and detailed analysis. The screening stage speedily screens

out effective candidate transmission lines and generators for transmission loss reduction. The

ranking stage quickly and accurately ranks the screened candidates according to their performance

68

on transmission loss reduction. The detailed analysis stage analyzes precisely the effectiveness of

top-ranked candidates on transmission loss reduction.

The distinguishing features of the proposed online two-stage method for reducing transmission loss

in power systems are summarized as follows:

Provides multiple high-quality and low-cost solutions (line switching with or without M-OPF) from

which operators may choose a desired one for transmission loss reduction.

Satisfies the operational and engineering constraints of post-optimizing (line switching with or

without M-OPF) power systems.

Generation

Schedule

State

Estimator

Load

Forecast

Input

Run base case AC

power flow

Analysis Indentification Output

High quality line

switching solutions

Post-optimizing

transmission loss

Sub-stage I-1

Screening

Stage I: Line Switching

Compute

base case

transmission loss

Further reduction

needed?

Network

Topology

Candidates

Sub-stage I-2

Ranking

Sub-stage I-3

Detailed Analysis

Sub-stage II-1

Screening

Sub-stage II-2

Ranking

Sub-stage II-3

Detailed Analysis

Stage II: Modified OPF

High quality generation

rescheduling solutions

YES

NO

Figure 5.4. Architecture of the online two-stage method.

Architecture of the Online Method

The proposed method is composed of two stages, with each stage containing three stages serving

different purposes: screening, ranking, and detailed analysis, as displayed in Figure 5.4. The major

input data required for the proposed method are:

(i) The current network topology and operation state of the power system.

(ii) Candidate switchable transmission lines and adjustable generators.

The major output results are:

(i) High-quality solutions (line switching with/without M-OPF).

69

(ii) Reduced transmission loss in MW by the corresponding action.

Architecture of Stage I (Line Switching)

Stage I-1 (Screening): Performs the task of screening out candidate lines whose switching out leads

to transmission loss reduction. In this stage, we employ a linear method to speedily estimate the

variation in transmission loss with each candidate line switched out from the base case.

Stage I-2 (Ranking): Performs the task of ranking each remaining line according to their

performance on reducing transmission loss. In this stage, we employ a semi-nonlinear method to

quickly and accurately estimate the post-switching transmission loss. Top-ranked lines will be sent

to Stage I-3 for detailed analysis.

Stage I-3 (Detailed Analysis): Performs the task of analyzing precisely the effectiveness on

transmission loss reduction of each top-ranked line. In this stage, we employ a nonlinear method to

precisely compute the post-switching transmission loss.

Architecture of Stage II (Modified OPF)

Stage II-1 (Screening): Performs the task of screening out generators whose active power

generation increase, or decrease leads to loss reduction. In this stage, we employ a linear method

to speedily divide generators into two lists, reducing transmission loss by increasing or decreasing

active power generation. Then the candidate generation rescheduling groups will be a Cartesian

production of these two lists.

Stage II-2 (Ranking): Performs the task of ranking the groups formed in Stage II-1 according to their

performance on loss reduction. In this stage, we employ a semi-nonlinear method to quickly and

accurately estimate the post-rescheduling transmission loss. Top-ranked groups will be sent to

Stage II-3 for detailed analysis.

Stage II-3 (Detailed Analysis): Performs the task of analyzing precisely the effectiveness on

transmission loss reduction of each top-ranked group. In this stage, we employ a nonlinear method

to precisely compute the post-rescheduling transmission loss.

5.4 Multi-Objective Optimal Network Reconfiguration

As discussed before, in distribution networks, there are two types of switches in primary distribution

systems: normally closed switches, which connect line sections, and normally open switches on the

tie-lines, which connect two primary feeders or two substations or loop-type laterals. The former are

70

termed sectionalizing switches and the latter are referred to as tie switches. These switches are

designed for both protection (to isolate a fault) and configuration management (to reconfigure the

network).

Network reconfiguration (or feeder reconfiguration) is the process of altering the topological

structures of distribution feeders by changing the open/closed status of the sectionalizing and tie

switches. During normal operating conditions, an important operational problem in configuration

management is network reconfiguration. As operating conditions change, networks are re-

configured for two purposes:

(1) to reduce the system real power losses, and

(2) to relieve overloads in the network.

The former is referred to as network reconfiguration for loss reduction and the latter as load

balancing. Another configuration management operation involves the restoration of service to as

many customers as possible during a restorative state following a fault. This problem is called

service restoration. We can consider the network reconfiguration problem for both loss reduction

and load balancing. Conceptually, this problem belongs to the so-called minimal spanning tree

problem. Given a graph (i.e., nodes of the system), find a spanning tree (i.e., a radial configuration)

such that a desired objective function is minimized while certain system constraints are satisfied. In

the past, most of the solution algorithms for solving the problem employed various techniques

belonging to the class of greedy search techniques, which accept only search movements that

produce immediate improvement. As a result, these solution algorithms usually achieve local

optimal solutions rather than global optimal solutions.

A further study is suggested as follows. First, to truly reflect the objective of load balancing, we

propose a system load balancing index that is a Chebyshev norm of each branch load balancing

index. The purpose of load balancing is then realized via solving a min-max optimization problem.

Second, because these two objective functions—loss reduction and load balancing—are

incommensurable, we should formulate the network reconfiguration problem as a constrained,

multi-objective and non-differentiable optimization problem with both equality and inequality

constraints. This is a step toward practical formulation of the network reconfiguration problem.

To this end, BSI suggests a two-stage solution methodology for general multi-objective optimization

problems. This new solution methodology allows designers to find a desirable, global non-inferior

71

solution for the problem. Given a desired number of switch-on/switch-off operations involved in

network reconfiguration, the proposed solution algorithm can identify the most effective operations.

5.4.1 Multi-Objective Operation Problems

We consider the following general multi-objective optimization (MO) problem, where

min𝑥

𝑓1(𝑥)

min𝑥

𝑓2(𝑥)

⋮

min𝑥

𝑓𝑚(𝑥)

such that

𝐹(𝑥) = 0

𝐺(𝑥) ≤ 0.

A major distinction between the MO problem and a traditional single objective problem is the lack of

a complete ordering of the 𝑓𝑖′s, i = 1,2,…,m. In the single objective problem, say c(x), a point 𝑥∗ is a

global minimum if 𝑐(𝑥∗) ≤ 𝑐(𝑥) for all x lying in the region of interest. In the MO problem, a point x

such that every component of f simultaneously reaches its global minimum is usually nonexistent.

This mainly occurs when some components of f compete so that one component of f decreases

while another increases. In other words, when objectives compete, there is no “optimal solution” to

the MO problem. In this case, the concept of non-inferior (also known as efficiency, Pareto

optimality) is used to characterize the solution to the MO problem.

Definition: The feasible region 𝛺 is the set of state vectors x that satisfies the constraints, i.e., 𝛺 =

{𝑥: 𝐹(𝑥) = 0, 𝐺(𝑥) ≤ 0}.

Definition: A point 𝑥 ∈ 𝛺 is a local non-inferior point if there exists an 𝜖 > 0 such that in the

neighborhood 𝑁(𝑥, 𝜖) of 𝑥, there exists no other point x such that (1) 𝑓𝑖(𝑥) ≤ 𝑓𝑖(𝑥), 𝑖 = 1,2, … , 𝑚 and

(2) 𝑓𝑗(𝑥) < 𝑓𝑗(𝑥) for some 𝑗 ∈ {1,2, … , 𝑚}.

72

In other words, 𝑥 is a local non-inferior point if there exists a neighborhood 𝑁(𝑥, 𝜖) such that, for any

other point 𝑥 ∈ 𝑁(𝑥, 𝜖), at least one component of f will increase its value relative to its value at 𝑥 or

𝑓𝑖(𝑥) = 𝑓𝑗(𝑥), i = 1,2,…,m.

Definition: A point 𝑥 ∈ 𝛺 is a global non-inferior point if there exists no other point x such that (1)

𝑓𝑖(𝑥) ≤ 𝑓𝑖(�̂�), 𝑖 = 1,2, … , 𝑚 and (2) 𝑓𝑗(𝑥) < 𝑓𝑗(𝑥), for some 𝑗 ∈ {1,2, … , 𝑚}.

In general, there is an infinite number of (global) non-inferior points for a given MO problem. The

collection of such points is called the non-inferior set. We call the image of the non-inferior set a

trade-off (or non-inferior) surface. From a design point of view, a non-inferior point corresponds to

an optimum trade-off design where attempts to improve any objective will lead to a degradation in at

least one of the other objectives. Thus, the availability of the non-inferior set will allow a designer to

reach a final design based on a pre-defined, desired priority.

The most widely used method of generating non-inferior points is to minimize a non-negative

convex combination of the functions 𝑓𝑖, i = 1,2, … , m, i.e., minimize {∑ 𝛼𝑖𝑓𝑖𝑚𝑖=1 } where 𝛼𝑖 ≥ 0 and

∑ 𝛼𝑖𝑚𝑖=1 = 1. This method suffers from the drawback that it cannot generate the entire non-inferior

set. In particular, the non-inferior points whose images are on the non-convex part of the trade-off

surface cannot be found, irrespective of what values of 𝛼𝑖 are used. On the other hand, three

methods that can generate the entire non-inferior set have been developed: the 𝜖-constraint

method, the weighted minimax method, and the shifted minimax function method.

5.4.2 Formulation for Loss Reduction and Load Balancing

The problem formulation for loss reduction and load balancing is summarized as follows. Given a

transmission/distribution network composed of n nodes with a network configuration 𝑔0, we seek

the optimal network configuration among all possible network configurations 𝑔𝑖 by changing the

open/closed status of the sectionalizing and tie switches such that both loss reduction and load

balancing are optimized while load constraints and operational constraints are satisfied. In

mathematical terms, this problem is expressed as

min𝑔𝑖

∑ 𝛾𝑖𝑃𝑖

2+𝑄𝑖2

|𝑉𝑖|2

𝑛𝑏−1𝑖=0 (5.1)

min𝑔𝑖

[𝑚𝑖𝑥𝑖𝑚𝑢𝑛 𝑜𝑓 (𝑆𝑖

𝑆𝑖𝑚𝑎𝑥 , 𝑖 = 1, … , 𝑛𝑏)] (5.2)

such that

73

𝐹(𝑧, 𝑔𝑖) = 0 (5.3)

𝐺(𝑥, 𝑔𝑖) ≤ 0 (5.4)

𝑁(𝑔0, 𝑔𝑖) ≤ 𝑛𝑑. (5.5)

The above formulation of a network reconfiguration problem is a constrained, multi-objective and

non-differentiable optimization problem.

We have developed a hybrid meta-heuristic and local search method to solving the above multiple-

objective optimization problem with nonlinear equality and inequality constraints. The details are

omitted in this report and are available upon request.

5.4.3 Numerical Results

The proposed solution algorithm has been implemented into a software package. We present

several numerical results for loss reduction in this section to illustrate the performance of the

proposed solution algorithm.

The test system is a hypothetical 12.66 KV system with 69 buses and 7 laterals. There are 5

looping branches (tie lines) in the system and sectionalizing switches on every branch of the

system. The algorithm parameters were set as follows: 𝑛𝑚𝑎𝑥 = 4, 𝑛𝑙𝑖𝑚𝑖𝑡 = 70, 𝛾𝑙𝑜𝑚𝑖𝑡 = 350. The total

system loads are 1107.9081 KW and 897.931 KVAR. The system real power loss is about 5.92%

(or 69.760 KW). Although the percentage of real power loss may seem low, loss reduction is always

desirable (if possible). By applying the proposed solution algorithm, the optimal network

configuration for loss reduction is attained after 15 iterations of the proposed algorithm

The percentage of real power loss for the optimal network configuration is around 2.64%. This

shows that a 3.37% further reduction in real power loss (or equivalently, around a 56.87%

improvement) is achieved. The total system loads are 1107.9081 KW and 897.931 KVAR. We also

consider the effect of load variations on the optimal network configuration. We assume a uniform

variation of system load demands for the test system by multiplying the real and reactive load

demands of each bus by a constant to construct a heavy-loaded system (multiplying each load

demand by 1.2) and a light-loaded system (multiplying each load by 0.5).

The optimal network configuration of each system for loss reduction is attained by applying the

proposed solution algorithm. From the results, we have the following observations:

74

The real power loss can be reduced significantly via proper network reconfiguration. For the

heavy-loaded system, the percentages of real power loss before/after network

reconfiguration are 7.27% and 3.26%, respectively. This represents nearly a 57% reduction

in real power loss. For the light-loaded system, a 1.39% further reduction in real power loss

(or equivalently, around 49.46%) is achieved during the process.

The voltage profiles of the system are considerably improved via proper network

reconfiguration. For instance, in the heavy-loaded case, the voltage magnitude at each bus

is between 0.893 p.u. and 1.0 p.u. before the network reconfiguration and is greatly

improved to between 0.9319 p.u. and 1.0 p.u. after reconfiguration.

The optimal network configuration for varied load conditions of a distribution system are

different.

The proposed solution algorithm has been implemented into a software package. We present

several numerical results for loss reduction in this section to illustrate the performance of the

proposed solution algorithm. The test system is a hypothetical 12.66 KV system with 69 buses and

7 laterals. The schematic diagram of the test system is shown in Figure 5.5. There are 5 looping

branches (tie lines) in the system and sectionalizing switches on every branch of the system. The

total system loads are 1107.9081 KW and 897.931 KVAR. The system real power loss is about

5.92% (or 69.760 KW). Although the percentage of real power loss may seem low, loss reduction is

always desirable (if possible). By applying the proposed solution algorithm, the optimal network

configuration for loss reduction is attained after 15 iterations of the proposed algorithm (see Figure

5.6). We note that stage 2 execution is faster than that of stage 1 (20% faster for this case). This is

because stage 1 optimization steers the system closer to the stage 2 optimum: loss reduction

normally promotes load balancing.

Table 5.2. Real power loss and voltage profiles before and after network reconfiguration.

Type

SYSTEM CONDITION

Real Power Loss

Voltage Profile

Real Power Loss Reduction

% of Total

P % of n2 power

Heavily Loaded

Case

Before reconfiguration

104.229 (7.27%)

Vmax : 1.0000 Vmin :

0.8930

75

After

reconfiguration 44.817 (3.26%)


0.9319

59.412

4.14% 57.00%

Normally Loaded

Case


69.760 (5.92%)


0.9126

After reconfiguration

30.085 (2.64%)


0.9439

39.675

3.37% 56.87%

Lightly Loaded

Case


16.052 (2.82%)


0.9583

After reconfiguration

8.11 (1.44%)


0.9720

7.939

1.39% 49.46%

PG & E distribution system : 69 buses/5 tie-linesORIGINAL SYSTEM

0 1 2 2e 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

40 41

27e 28e 65 66 67 68 69 70 88 89 90

27 28 29 30 31 32 33 34

57 58

55 56

42 43 44 45 46 47 48 49 50 51 52 53 54

35 36 37 38

Figure 5.5. The test system with 69 buses and 5 tie lines.

76

Case 1: Normally Loaded SystemOPTIMAL SYSTEM

0 1 2 2e 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

40 41

27e 28e 65 66 67 68 69 70 88 89 90

27 28 29 30 31 32 33 34

57 58

55 56

42 43 44 45 46 47 48 49 50 51 52 53 54

35 36 37 38

Load Demand P = 1107.9081 kW Q = 897.931 kVARInitial Injected P: 1177.668 kWFinal Injected P: 1137.993 kW

Figure 5.6. The optimal configuration under the normal load level for loss reduction.

Case 2: Heavily Loaded SystemOPTIMAL SYSTEM

0 1 2 2e 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

40 41

27e 28e 65 66 67 68 69 70 88 89 90

27 28 29 30 31 32 33 34

57 58

55 56

42 43 44 45 46 47 48 49 50 51 52 53 54

35 36 37 38


Figure 5.7. The optimal configuration under the heavy load level for loss reduction.

77

Case 3: Lightly Loaded SystemOPTIMAL SYSTEM

0 1 2 2e 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

40 41

27e 28e 65 66 67 68 69 70 88 89 90

27 28 29 30 31 32 33 34

57 58

55 56

42 43 44 45 46 47 48 49 50 51 52 53 54

35 36 37 38


Figure 5.8. The optimal configuration under the light load level for loss reduction.

The percentage of real power loss for the optimal network configuration is around 2.64%. This

shows that 3.37% further reduction in real power loss (or equivalently, around 56.87%

improvement) is achieved. The tie lines before/after the network reconfiguration are also listed. The

total system loads are 1107.9081 KW and 897.931 KVAR.

Next, we consider the effect of load variations on the optimal network configuration. We assume a

uniform variation of system load demands of the test system by multiplying the real and reactive

load demands of each bus by a constant to construct a heavy-loaded system (multiplying each load

demand by 1.2) and a light-loaded system (multiplying each load by 0.5).

The optimal network configuration of each system for loss reduction is attained by applying the

proposed solution algorithm (see Figures 5.7 and 5.8). The results regarding improvements in loss

reduction and in voltage profile after network reconfiguration are also summarized in Table 5.2.

From these results, we have the following observations:

The real power loss can be reduced significantly via proper network reconfiguration. For the

heavy-loaded system, the percentages of real power loss before/after network

78

reconfiguration are 7.27% and 3.26%, respectively. This represents a near 57% reduction in

real power loss. For the light-loaded system, a 1.39% further reduction in real power loss (or

equivalently, around 49.46%) is achieved during the process.

The voltage profiles of the system are considerably improved via proper network

reconfiguration. For instance, in the heavy-loaded case, the voltage magnitude at each bus

is between 0.893 p.u. and 1.0 p.u. before the network reconfiguration and is greatly improve

to between 0.9319 p.u. and 1.0 p.u. after reconfiguration.

The optimal network configuration for varied load conditions of a distribution system are

different.

79

6 Future Technology

6.1 Optimal Multi-Period Network Reconfiguration

6.1.1 Introduction

The past twenty years have seen a global significant growth in the use of distributed generation

(DG) due to technological progress and environmental concerns. The hosting capacity (HC), i.e.,

the available delivery capability (ADC), is defined as the capacity to deliver power from the source

area (containing renewable energy) to the sink area (containing loads) with no thermal overloads,

voltage violations, and static stability violations [1]. Significant effort has been directed toward

increasing the HC to support renewable energies using various types of controls (for example, see

[2]-[12]). These controls can be classified into three classes. The first class includes reactive power

control and active power curtailment (see, for example, [3]-[7]). The second class optimizes network

topology via network reconfiguration (NR), which uses the existing assets without auxiliary facilities

(for example, see [8]-[10]). The third class coordinates the aforementioned measures (for example,

see [11]-[12]). There are various methods and strategies to facilitate higher photovoltaic penetration

in low voltage systems [2]. A detailed study of widely used measures to increase HC is presented in

Table 6.1.

Table 6.1. Measures to increase the hosting capacity.

Reference Strategy

[3] Power curtailment

[4]-[6] Reactive power control

[7] Reactive power control and active power curtailment

[8]-[10] Network reconfiguration

[11] Network reconfiguration and voltage control

[12] Reconfiguration, voltage control, and power factor

control

Distribution networks are usually constructed in a meshed network and operated in a radial

topology. Distribution NR entails altering the topological structure of the distribution network by

changing the opening/closing status of the switches. Multi-period NR is a very complex nonlinear

optimization problem from both temporal and spatial viewpoints. This problem involves determining

when and how to operate the controllable switches so as to optimize certain objectives. Most

studies determine the operation time first to simplify the optimization problem [14,15] or the NR

80

problem was solved for each operating condition and then dynamic programming was used to

adjust the topologies [16,17]. A fuzzy c-means (FCM) clustering algorithm was used to obtain

representative centroids from the annual DG, and power demand profiles and optimal system

configuration for each representative centroid was obtained by a genetic algorithm [18].

In this chapter, a problem formulation of multi-period network reconfiguration to increase the host

capacity to a sufficient level with a minimal switching operation (SO) number for a 24-hour period is

presented. In addition, multi-scenario DG outputs are considered in the problem formulation to deal

with the variability of DG outputs.

BSI has developed a four-stage method that includes the assessment stage, time-partitioning

stage, network reconfiguration design stage, and evaluation stage to solve the constrained large-

scale nonlinear integer optimization problem. Regarding the modeling of renewable uncertainties, a

scenario set is generated to capture the uncertainty of DG outputs using the linear, distribution-free

method proposed in [18]. We then apply a fuzzy C-means method to perform the task of scenario

reduction. First, the linear distribution-free method is summarized as follows.

Step 1: Build the correlation matrix G according to temporal correlations and spatial correlations.

Apply Cholesky decomposition to G, i.e., G=PP’, where P is a lower triangular matrix.

Step 2: Use the Latin hypercube sampling method to sample and obtain the uncorrelated sample

matrix X.

Step 3: Obtain the correlated scenario matrix by the transformed vector XP’.

The structure of generated scenarios based on the forecasted DG outputs can be expressed as

follows:

1,0 1,23 1,0 1,23 1,0 1,23

,1 ,1 ,2 ,2 ,3 ,

,0 ,23 ,0 ,23 ,0 ,23

,1 ,1 ,2 ,2 ,3 ,

,0 ,23 ,0 ,23 ,0 ,23

,1 ,1 ,2 2 ,3 ,

, ,

, ,

, ,

DG

DG

DG

DG DG DG DG DG DG N

s s s s s s

DG DG DG DG DG DG N

MS MS MS MS MS MS

DG DG DG DG DG DG N

P P P P P P

P P P P P P

P P P P P P

L L L

L L L

L L L(24 )DGMS N

where MS is the number of generated scenarios and NDG is the number of DGs.

Although increasing the number of scenarios improves the capture accuracy of the uncertainty of

DG outputs, the task of dealing with a large number of scenarios is usually challenging for practical

applications. To decrease the computational complexity required in simulating a large number of

81

scenarios, a smaller set of representative scenarios can be generated by using a clustering scheme

to cluster similar scenarios (according to a distance metric) into representative scenarios.

In this chapter, a FCM-based clustering algorithm is applied to cluster similar scenarios to obtain

representative scenarios. The fuzzy c-means (FCM) clustering algorithm is based on minimizing the

following objective function [20]:

2

1 1

( , , )MS c

m

m ij i j

i j

J X U V x v

(6.1)

where X={x1,…,xi,…,xMS} is input vector (MS scenarios) to be clustered, and μij is the membership

degree of xi to the cluster vj and is given by a number between 0 and 1, where the sum of the

membership degrees for a data point to all clusters is equal to 1. U={u1, …,uk,…,uc} is the output

vector of membership degrees. V={v1, …,vj,…,vc} is the output vector of the cluster centers, m∈[1,∞)

is a parameter controlling the fuzziness of the clustering procedure. The calculation of the cluster

centroids iteratively repeats until a set of optimal solutions is obtained, and then the cluster

centroids serve as representative scenarios [18].

6.1.2 Problem Formulation

Given a distribution network with an operating point and given a set of (forecasting) look-ahead (say

60 minutes ahead) power injections of each bus (a load bus or a renewable bus), there is a unique

value of HC, defined as the maximum DG outputs that the network can accommodate without

violating security constraints [1]. This hourly HC can be computed using the Continuation

Distribution Power Flow (CDFLOW) method [21]. If this hourly HC is greater than the forecasted

renewable energy, then the current network topology can provide sufficient delivery capability

(alternatively, load margin) to deliver produced renewable energy to loads. Figure 6.1 shows a day-

ahead forecasted load curve for a system. The load is forecasted in 1-h intervals in this prediction

horizon. Each operating point of the day-ahead period A0, A1…A22, A23 depends on the topology at

hour k-1 and the SOs at hour k. The problem of multi-period network reconfiguration (NR) aims to

determine the optimal SO schedule with a minimal SO number in the look-ahead horizon for the

predicted operating points A0, A1… A23, such that a preset desired NHC is maintained.

82

Figure 6.1. Day-ahead forecasted load curve.

To minimize the SO number over the 24 hours while meeting the requirement of hourly HC to

support renewable integration for all scenarios, we propose the following problem formulation:

24

1 1

1 1 1 1 1

1min min

2 ij ij

Nc Ns Nb Nbst st t t

n n

st n t i j

s s

(6.2)

Subject to:

1. Radial network constraint

1

1

0, , 1 , 2,3,j ij ij ij

Nbt t t t t

ji

j

i Nb

L (6.3)

2. Parameterized power-flow constraint

, , , , , , ,, ,

1 1

( cos sin )i t s i t ij ij t ij t ij t ij t

Nb Mt k k k k k

t i t j t

j k

P P V V G B

(6.4)

, , , , , , ,,

1 1

( sin cos )i t i t ij j t ij t ij t ij t ij t

Nb Mt k k k k k

t i t

j k

Q Q V V G B

(6.5)

3. Voltage constraint

min , max , 1,2, 24i tV V V t L (6.6)

4. Current constraint

min , max , 1,2 24k

ij tI I I t L (6.7)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240

0.2

0.4

0.6

0.8

1

Time Point

Lo

ad L

evel

/[p

.u]

Prediction interval

(1-h)

0A

A1

23

Predicted operating point

A

83

5. Hourly NHC constraint

, 1,2 24t th t L (6.8)

6. Daily NR operation number constraint

maxNc NC (6.9)

7. For each scenario, the constraints (6.2)-(6.9) must be satisfied.

where Nc is the daily NR operation number over the 24-hours and Ns is the controllable switch

number. sst

n is the status value of switch n during period st., which takes the value of 1 when the

switch is on; otherwise, sst

n is 0. If bus i and bus j are connected, αt

ij is 1; otherwise, αt

ij is 0. α0

ij is the

ending connection status value of bus i and bus j on the previous day. βt

ij is 1 if bus j is the parent of

bus i at time t, whereas βt

ji is 1 if bus i is the parent of bus j. Pφ

i,t and Qφ

i,t are the real and reactive

power injections at phase φ for bus i whose voltage magnitude is Vφ

i,t , and Iφk

ij,t is the current of the

line connecting bus I, phase φ and bus j, phase k. λt is the NHC at time t and λth is a desired NHC.

NCmax is the maximum number of daily allowable NR operations.

6.1.3 Toward Optimal Multi-Period Methodology

To develop a solution methodology for minimizing the SO number over the 24 hours while meeting

the requirement of hourly HC to support renewable integration for all scenarios, we propose to

partition the 24-hour period into multiple periods based on the assessment results of the hourly

NHC of the original network from the starting hour for all scenarios. The resulting challenges are

how to obtain a high-quality period-partitioning of the 24 hours and, for each sub-period partitioned,

how to design a NR to increase the NHC to a sufficient level with a minimal SO number.

84

Figure 6.2. Architecture of the proposed multi-period NR method.

To solve the large-scale nonlinear, non-differentiable integer optimization problem with nonlinear

equality and inequality constraints, we propose a four-stage solution methodology whose

architecture is shown in Figure 6.2, as described below.

Stage 1 (Assessment): Compute the hourly NHC of the original network from the starting hour for

all scenarios and identify the first hour during which the NHC is insufficient.

Stage 2 (Time-Partitioning): Partition the (remaining) time period into multi-periods based on the

similarity of hourly forecasting information to facilitate the design of a minimal SO number.

Stage 3 (NR Design): For the considered time period determined in Stage 2, design a NR to

increase each hourly NHC of the time period to a sufficient level for supporting all scenarios with a

minimal number of switching operations.

Stage 4 (Evaluation): Evaluate the hourly NHC of the post-NR network for the (remaining) time

period for all scenarios. If each hourly NHC is sufficient, then stop and output the results; otherwise,

identify the next hour for performing a NR and go to Stage 2.

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