frequency and voltage regulation in electrical grids

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ReGrid: Frequency and Voltage

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I. Introduction 2

II. Table of contents

1. Assessing the solar thermal potential (potential analysis) 6

2. Awareness raising: broad campaigns targeting the general public 8

3. Awareness raising: targeted campaigns to develop specific market areas 10

4. Financial incentives: VAT reductions 12

5. Financial incentives: public loans at preferential conditions 14

6. Regulatory measures: energy efficiency requirements for buildings 16

7. Regulatory measures: solar obligations 18

8. Building permits – solar thermal in listed buildings 20

9. Quality Assurance: product standards and certification 22

10. Health & Safety requirements 23

11. Qualification of skilled personnel 24

12. Research & Development programmes 25

III. Further Reading 27

ReGrid: Frequency and voltage regulation in electrical grids

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Table of Content

LIST OF ABBREVIATIONS .......................................................................................................3

LIST OF SYMBOLS .................................................................................................................4

LEARNING TARGETS .............................................................................................................5

1 BASIC CONCEPTS.....................................................................................................5

2 WHY FREQUENCY AND VOLTAGE CONTROL?.......................................................... 12

2.1 CONTROL VARIABLES FOR FREQUENCY AND VOLTAGE STABILITY IN AN ELECTRICAL POWER SYSTEM ....... 15

3 POWER QUALITY IN ELECTRICAL GRIDS ................................................................. 22

4 CONTROL OF INTERCONNECTED POWER SYSTEMS ................................................ 25

4.1 REQUIREMENTS IN DIFFERENT INTERCONNECTED SYSTEMS ......................................................... 26 4.2 PROVISION OF ANCILLARY SERVICES IN ELECTRICAL GRIDS ........................................................... 27

5 ELECTRICAL SYSTEM FREQUENCY AND ACTIVE POWER REGULATION ..................... 27

5.1 FREQUENCY CONTROL IN POWER SYSTEMS .............................................................................. 28 5.2 EXCERPT: ELECTRICAL SYSTEM FREQUENCY AS A COMMUNICATION LINK FOR ACTIVE POWER SHARING .. 32

6 REACTIVE POWER AND VOLTAGE CONTROL ........................................................... 34

6.1 EFFECTS OF ACTIVE AND REACTIVE POWER FLOWS ON VOLTAGE ................................................... 34 6.2 LOAD FLOW CALCULATIONS .................................................................................................. 34 6.3 MITIGATION OF VOLTAGE STABILITY PROBLEMS/REACTIVE POWER MANAGEMENT ............................ 35

7 INTEGRATION OF RENEWABLE ENERGY GENERATION IN POWER SYSTEMS ............. 41

7.1 VOLTAGE EFFECTS .............................................................................................................. 41

7.2 ACTIVE AND REACTIVE POWER FROM RENEWABLE ENERGY GENERATORS ........................................ 42 7.3 CODES AND REGULATIONS ................................................................................................... 44

SUMMARY ......................................................................................................................... 46

REFERENCES AND RECOMMENDED FURTHER READING ...................................................... 47

GLOSSARY .......................................................................................................................... 48

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List of abbreviations

AC Alternating current

DC Direct current

ENTSO-E European Network of Transmission System Operators for Electricity

FACTS Flexible alternating current transmission system

IEEE Institute of Electrical and Electronics Engineers

kV Kilovolts

LV Low voltage

MV Medium voltage

PWM Pulse width modulation

PV Photovoltaic

RE Renewable energy

STATCOM Static synchronous compensator

TSO Transmission system operator

UCTE Union for the Coordination of Transmission of Electricity

VAR Volt-ampere reactive

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List of symbols

Symbol Description

AC generator providing a sinusoidal voltage source

Resistor

Inductor

Voltage node

Load

Earth

Capacitor

Thyristor

Transformer

DC-AC inverter

Solar photovoltaic generation

AC

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Learning targets

After studying this chapter you will:

Understand the basic technological principles governing the operation of electrical power systems.

Be aware of the parameters that affect frequency and voltage stability in power sys-tems.

Be familiar with the methods and tools available to guarantee frequency and voltage stability in the event of contingencies in power systems.

Learn about the principles governing power flow in electrical power systems in addi-tional mathematical modules.

Understand the differences in electrical grid interfacing between conventional genera-tion units and renewable energy generation units.

1 Basic concepts

The purpose of this section is to introduce the main electrical concepts necessary for an un-derstanding of the operation of electrical systems.

A very simple electrical circuit can be built by connecting a 100W (watt) incandescent light bulb to an electrical socket. 100 watts is the nameplate rated electrical power of the incandes-cent bulb. The electrical power supplied by the mains to the incandescent light bulb enables it to do work (in this case in the form of light). The simplest way to calculate the electrical power in watts (W) consumed by an appliance such as an incandescent bulb is to multiply the applied voltage, in volts (V), by the current which flows through it, in amps (A). Voltage is the differ-ence in electrical potential between two points. The higher the potential, the more energy that can be transferred between those points. In good conductor materials, electrons are not tightly bound to the nucleus of the atom. When a voltage is applied, these “free” electrons wander from atom to atom, constituting an electrical current. There are two types of current, as shown in figure 1.

When “free” electrons flow at a steady rate in one direction only, the current is said to be direct current (DC).

When the amount of “free” electrons and their direction change cyclically, usually si-nusoidally, the current is called alternating current (AC). The number of times the cur-rent waveform reaches its positive peak per second is called the current frequency. In Europe, the AC electricity delivered by utility companies has a frequency of 50 cycles per second, or 50Hz (hertz).

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Figure 1: a) Direct current (DC) waveform, b) Alternating current (AC) waveform. Source: RENAC

The amount of electrical energy used by an appliance is found by multiplying its consumed power by the length of time of operation. Thus, for example, a 100W incandescent light bulb that is operated for 10 hours will consume 100Wx10h, that is to say 1000Wh or 1kWh (kilo-watt hours) of energy.

Electrical circuits are composed of a limited amount of different components. The basic circuit elements which can be found in electrical models of power systems are generators, resistors and inductors. Generators are usually modelled as voltage sources. Voltage sources generate a given voltage independent of the current drawn from the generator. The general expression for the sinusoidal voltage waveform delivered by a conventional generator is:

𝒗(𝒕) = 𝑽𝒑𝒆𝒂𝒌 ∙ 𝒔𝒊𝒏(𝝎𝒕 + 𝜽) (0.1)

where v(t) is the voltage, a function of time; Vpeak is the amplitude of the voltage waveform; ω is the angular frequency (measured in radians/s); and θ is the phase angle (radians) shows the different parameters that define a voltage sinusoidal waveform.

Figure 2: AC voltage sinusoidal waveform. Source: RENAC

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The meaning of the peak voltage (Vpeak) is straightforward. The angular frequency ω of a si-nusoidal waveform is related to the linear frequency f mentioned above by the following ex-pression:

ω = 2π (radians/cycle) ・ f (cycles/s) = 2πf (0.2)

Regarding the phase angle 𝜽, it must be mentioned that any sine wave that does not pass through zero at t = 0 has a phase shift. θ is the phase angle in degrees or radians that the waveform has shifted either left or right from the reference point along the horizontal refer-ence axis. There will usually be a phase difference of the same frequency between two sinus-oidal waveforms.

Sinusoidal waveforms can be represented by vectors called "phasors", where the vector length is determined by the peak amplitude and the direction given by the phase angle θ (see figure 3).

Figure 3: Phasor representation of sinusoidal waveforms. Source: RENAC

Resistors are passive elements that model the effect of electrical resistance in electrical cir-cuits, defined as the opposition of a material to the flow of an electric current. As stated by Ohm’s law, the voltage drop through a resistance is directly proportional to the current across it. The constant of proportionality is the resistance value R measured in ohms (Ω).

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Figure 4: Symbol and voltage-current relationship in a resistor. Source: RENAC

When connecting an AC voltage generator to a resistor, the voltage across the resistor is the same as the voltage delivered by the generator. The current that flows though the resistor can be calculated using the expression as follows:

𝑰 =𝒗(𝐭)

𝑹=

𝑽𝒑𝒆𝒂𝒌

𝑹𝒔𝒊𝒏(𝝎𝒕) (0.3)

The phase angle of the resulting current is the same as the phase angle of the voltage (zero), as can be observed in Fig. 5 b) and c).

Figure 5: a) AC voltage generator connected to a resistor, b) Voltage and current through the resistor, c) Phasor

representations. Source: RENAC

Another passive element that is often used in electrical circuits that model power systems is an inductor. An inductor is a passive electrical component which stores energy in a magnetic field. The effect of an inductor in a circuit is to oppose changes in current through by develop-ing a voltage across it proportional to the rate of change of the current. The relationship be-tween the time-varying voltage v(t) across an inductor with inductance L and the time-varying current i(t) passing through it is described by the following expression:

𝒗(𝒕) = 𝑳𝒅𝒊(𝒕)

𝒅𝒕 (0.4)

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The inductor is again connected to an AC voltage generator, as in the case of the resistor. The voltage across the inductor is the same as the voltage delivered by the generator. The current can be calculated using relation (0.4):

𝒊(𝒕) =𝟏

𝑳∫𝒗(𝒕)𝒅𝒕 =

𝟏

𝑳∫𝑽𝒑𝒆𝒂𝒌𝒔𝒊𝒏(𝝎𝒕)𝒅𝒕 = −

𝑽𝒑𝒆𝒂𝒌

𝝎𝑳𝒄𝒐𝒔(𝝎𝒕) (0.5)

The current and voltage waveforms are illustrated in Fig. 6. As can be observed from relation (0.5) and

b):

The current through the inductor has the same frequency as the applied voltage.

The current lags behind the voltage by a quarter of a cycle. Referring to relation (0.2),

where the concept of angular frequency was introduced, a complete cycle is equivalent

to an angle of 2π. Therefore, a waveform lagging behind by a quarter cycle corresponds to a phase shift angle of θ = −90°. The corresponding phasors for voltage and current are illustrated in

c).

The proportionality factor between voltage and current is not just the inductance L, but the reactance Lω. The reactance will be denoted by the abbreviation X in the re-mainder of the module, and depends on the inductance value of the inductor and on the frequency of the voltage applied through the inductor.

The expressions derived for the relation between current and voltages for different electrical components form the foundation for the introduction of the very important concepts of ap-parent (S), real (P) and reactive power (Q).

Figure 6: a) AC voltage generator connected to an inductor, b) Voltage and current through the inductor, c) Phasor representations. Source: RENAC

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In order to calculate the instantaneous power supplied by the voltage source to the resistor and inductor, it is necessary to multiply the waveforms of the voltage and current. The results are illustrated in Fig. 7, with the green waveform being the instantaneous power transferred from the generator to the load (resistor or inductor). In the case of the resistive circuit, the product of voltage and current is positive at all times, indicating that the power flow direction does not change. Real power is transferred from the generator and is dissipated at the resistor. The situation changes in the second circuit, with an inductor as the load. During every cycle, for half of the cycle the product of voltage and current is positive, but for the other half of the cycle the product is negative. On average, exactly as much energy flows from the generator to the inductor as flows back. There is no net energy flow over one cycle; only a transfer of reac-tive energy takes place.

Certain appliances do not have a purely resistive or inductive character. A good example is a motor. There is a portion of the current absorbed by a motor which is in phase with the volt-age in the motor. This is the current that creates real power in the motor and which can be used to create mechanical work. There is another part of the current which is required by the stator of the motor to create the magnetic field necessary for the motor to operate. As men-tioned above, inductors are the components that store magnetic energy. The stator of a motor can therefore be modelled as an inductor and, as we have seen, the current in an inductor lags behind the voltage by 90 degrees. This magnetising current in the motor does not create real power, but reactive power.

Figure 7: Instantaneous power in resistive and inductive circuits. Source: RENAC

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A concept that is very useful in analysing the relation between load current and magnetising current – that is to say, real and reactive power – is what is known as the power triangle. For appliances like motors, voltage V and current I are not in phase, but instead present a certain phase shift θ. The pure product of the current drawn by the motor (amps) and the voltage (volts) across the motor equals the apparent power consumed by the motor (S, measured in volt-amperes). The real power consumed by the motor, which can be used to produce me-chanical torque, is the horizontal projection, which is given by the expression S*cos𝜽=V*I*cos𝜽 (measured in watts). The vertical projection is the reactive power, which cannot be converted into work, and in the case of motors is mainly used to magnetise the sta-tor. Reactive power can be calculated using the expression S*sin𝜽=V*I*sin𝜽, and is measured in VAR (volt-amperes reactive).

Figure 8: Power triangle. Source: RENAC

The power factor of an AC electric power system is defined as the ratio of the real power (P) flowing to the load to the apparent power in the circuit (S). In purely resistive circuits, voltage and current waveforms are in phase and therefore all the apparent power is real power and can be consumed. In this type of circuit the power factor is 1. Circuits containing purely resis-tive loads, for example a filament lamp, have a power factor of 1. When the load is not purely resistive – e.g. induction motors – the apparent power does not equal real power. The power factor will consequently be less than 1.

The apparent power is a vector quantity that can be represented as a complex number:

either in rectangular format with real and imaginary components, such as 𝑺 = 𝑷 + 𝒋𝑸

or in polar format

S 𝜽

with S being the amplitude (S=V*I). is simply a symbol to denote that the value beside it is an angle, in this case θ, the phase shift of the apparent power S.

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2 Why frequency and voltage control?

The main purpose of an electrical power system is to efficiently deliver reliable electricity to consumers. Voltage and system frequency are the main variables to guarantee the stability of an electrical system.

The simplest electrical power system consists of a single electric generator and a load. An elec-tric generator converts rotational kinetic energy to electric energy. The law of energy conser-vation requires that, at any instant, the power demanded by the load is supplied by the gener-ator and/or by energy stored within the system1. If the consumption in the load increases, the extra energy demand is initially supplied by the rotational inertia of the generator through a decrease of its speed. The frequency of the voltage in an electrical generator is directly pro-portional to the rotational speed of its rotor. All the alternators connected to an electrical sys-tem rotate with the same electrical angular speed, according to the relation

𝒇 =𝒑∙𝒏

𝟔𝟎 (1.0)

where f is the frequency, p the number of poles in the alternator and n the rotational speed of the rotor in rpm (revolutions per minute). Consequently, the decrease in rotational speed will be accompanied by a proportionate decrease in the frequency of the voltage generated by the generator.

An electrical power system consisting of thousands of interconnected generators and loads behaves much like a simple one-generator one-load system, with the frequency being the same for the whole interconnected power system. However, there is never a perfect equilibri-um between generation and demand in a power system; since the amount of storage is usually rather limited in a power system when compared with the load demanded, there will be fre-quency shifts as a result of the imbalances between generation and demand, as shown in Fig. 9. Frequency drifts downwards when demand exceeds supply and vice versa.

1 Leon Freris, David Infield (2008): “Renewable Energy in Power Systems”. John Wiley & Sons, New York, NY. p. 55

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Figure 9: Frequency behavior due to imbalances between generation and demand. Source: RENAC

Regarding the first variable necessary to guarantee the stability of an electrical system, there are several reasons why it is desirable to keep frequency in a power system within narrow bounds, as mentioned by Freris et al [2]:

It ensures that electric motors operate at a virtually constant speed. A fixed speed is required in many consumer applications where an AC electric motor is used to drive a device at an approximately constant rate, e.g. a pump in a washing machine.

In electronic applications, the mains frequency can be used as a basis for timing vari-ous processes.

Transformers are sensitive to frequency variations and may be overloaded if the fre-quency drifts substantially from the nominal value.

Finally, and most importantly, in traditional power stations the performance of the generators is dependent on the performance of all the auxiliary electric motor drives that deliver fuel and air to the boiler, oil to bearings and cooling services to several sys-tems. If these auxiliaries underperform due to low speed caused by low frequency, power station output can be reduced. This phenomenon could lead to a runaway situa-tion with cascaded shutdowns of power stations and blackouts.

Regarding the second variable – voltage – manufacturers of electrical appliances design their products to operate with a certain nominal voltage in order to achieve effective performance and comply with safety standards. The electrical grid operator is therefore obliged by law to provide electricity at consumer terminals at voltage levels that do not deviate from a nominal value by more than a certain percentage. So, for example, following voltage harmonisation, electricity supplies within the European Union are now nominally 230 V ± 6% at 50 Hz2. Oper-ating appliances outside the specified voltage level range can lead to overheating, malfunc-tions, reductions of the expected equipment lifetime, etc. Electric drives and motors are af-fected by voltages below and above the nameplate voltages:

2 CENELEC Harmonisation Document HD 472 S1:1988

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Since power is proportional to the product of current and voltage, when electric mo-tors are subjected to voltages below the nameplate rating, current must increase to provide the same amount of power, which increases the build-up of heat within the motor. Furthermore, the mechanical torque is inversely proportional to the square of the voltage. Thus a 10% reduction from nameplate voltage would reduce the torque by a factor of 0.9 x 0.9, that is to say, the resulting torque would be 81% of the original value.

Contrary to what would be expected, a higher than nominal voltage also leads to over-currents. High voltage to a motor tends to push the magnetic portion of the motor into saturation. This causes the motor to draw excessive current in an effort to magnetise the iron beyond the point to which it can easily be magnetised3.

In order to achieve voltage stability at consumer terminals, the voltage at all nodes in a power system must be maintained within limits. This is a task which is performed by TSOs and DSOs (transmission system operators and distribution system operators), which are the entities en-trusted with carrying electrical power over long distances, allowing for generation and con-sumption to be geographically separated. The lower voltage levels of an electrical power sys-tem are commonly named distribution systems, while higher voltage levels are commonly named transmission systems. Increasing the voltage reduces the current in the transmission lines, and hence the size of conductors and distribution losses, making it more economical to distribute electrical power over long distances. Fig. 10 shows a simplified diagram of an elec-trical power system with different voltage levels. Transformers are the interfaces between the different voltage levels.

3 Discussing the operation of electrical motors is beyond the scope of this webinar, but further details can be consulted in references [2] and [8].

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Figure 10: Voltage levels in electrical power systems. Source: RENAC

Furthermore, the following table lists typical voltage ranges for the different voltage levels present in electrical grids.

Voltage level Voltage range

Low voltage <400V, for industrial applications up to 690V

Medium voltage 6kV to 30kV

High voltage From 50kV to 750kV

Table 1: Voltage ranges for different voltage levels in electrical grids. Source: RENAC

2.1 Control variables for frequency and voltage stability in an electrical power system

2.1.1 Frequency

As explained in the previous section, for a near constant frequency to be maintained, the pro-duction and consumption of active power has to be in equilibrium at every point in time. The better the balance between generation and consumption, the smaller the frequency variation in the grid, and consequently the better the electricity quality.

The electricity demand for a single load is characterised by a high variability. Fig. 11 shows the load curve for a single household in Germany, with a time resolution of 1 min and partially averaged. With a finer time resolution the variability would be higher and the ratio between minimum and maximum demand would be greater (for example, due to power spikes from switching off appliances, etc.).

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Figure 11: Demand curve for a household in Germany. Source: RENAC

However, the electricity consumption of different consumers is not correlated. By combining the loads of different electricity accounts, the demand curve is smoothed and the ratio of peak demand to lowest demand decreases. This effect becomes stronger as more electrical power systems are interconnected. For large power systems, demand aggregation and interconnec-tion makes it fairly feasible to forecast the expected load for the day ahead, thus facilitating the task of scheduling the generation required to supply the demand, plus a reserve which will be needed to regulate frequency in the system.

Figure 12: Power generation scheduling in electrical power systems. Source: RENAC

The transmission system operator is the entity in charge of plant scheduling. In systems in lib-eralised electricity markets, the main criteria used to decide which generators meet which

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part of the demand is economic, and allocation is usually carried out through bidding systems. In national power systems without electricity markets, the dispatch centre is responsible for allocation.

Base load is usually defined as the minimum level of demand on an electrical power system over 24 hours. This continuous energy demand is covered by what are known as base load plants, which are production facilities delivering electricity at a constant rate, usually at a low cost relative to other production facilities available to the system4. Their efficiency decreases at less than full output. Base load power plants include coal, nuclear and biogas plants. Medi-um load power plants operate for between 20% and 60% of the day, typically during the day-time and early afternoon. They fill the gap between the base load and peaks in electricity de-mand. Intermediate load power can be increasingly supplied by renewable energy sources such as wind and solar power.

To meet peak demand, peak load power stations are designed to run for short periods of time each day. They can be started quickly from cold, and vary the quantity of electrical output by the minute. Gas-fired plants as well as hydro-electricity are typically used to provide peak load power. As mentioned in section 0, if power consumption is greater than production, the grid frequency is below the nominal value. Similarly, if production is greater than consumption the grid frequency is above the nominal value. A certain portion of the peak power generation capacity available in a power system – which is highly responsive to changes in electrical de-mand – is used to guarantee frequency stability in the system. These reserves will be used by the different frequency control levels (primary, secondary and tertiary) which will be explained in detail in section 5.1. The active power reserves that can be activated automatically by fre-quency changes are usually classified as below:

The frequency response reserve is provided by generators usually equipped with gov-ernors. Following a loss in supply, the additional energy demand is initially supplied by the rotational inertia of the generator, and its speed is decreased due to the increased mechanical load. The function of a governor is to sense any changes in speed and to adjust the fuel supplied to the prime mover so that the speed (and therefore the fre-quency) is controlled. The frequency response reserve is used for primary frequency control and, therefore, is usually named primary reserve.

The spinning reserve is extra generating capacity available by increasing the power output of generators already in operation (used as secondary/minute reserve).

The operating reserve includes generating capacity available within a short period of time to meet demand in case a generator goes down or there is a disruption in supply (used as secondary/minute reserve).

The replacement or long-term reserve is reserve power provided by generators that require a longer start-up time (30-60 min) and is used to relieve the generating capaci-ty available to meet demand in case a generator goes down, in case there is a disrup-tion in supply or to cover system capacity or congestion.

4 "Energy Dictionary - Baseload plant". Source: EnergyVortex.com: http://www.energyvortex.com/energydictionary/baseload_plant.html/ Accessed 2011-08-05.

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The Time responses for different kinds of reserve power are illustrated in Fig. 13.

Figure 13: Time response for different kinds of reserve power. Source: RENAC

2.1.2 Voltage

In order to guarantee voltage stability at the different nodes in an electrical power system, the line impedances in the transmission system must be considered. The Fig. shows a simplified equivalent circuit of a transmission line. Cables used in overhead lines or underground cables are made out either of copper, aluminium, steel and alloys. These materials present a small but not negligible resistance to the flow of electrical current when considering the long dis-tances covered by transmission lines . The most common method for alternating current pow-er transmission and distribution are three-phase systems, where three circuit conductors carry three alternating currents (of the same frequency) that reach their instantaneous peak values at different times5. Fig. 14 shows a high voltage overhead line. The steel towers carry double-circuit three-phase lines with two conductors per phase bundle. Furthermore, an earth wire conductor has been strung at the top of the steel towers in order to shield the phase conduc-tors from direct lightning strikes and to provide a low impedance path in case of faults.

The current that is carried by single-phase conductors creates a magnetic field around the conductor. When the current changes, the magnetic flux changes correspondingly. Conse-quently a voltage is generated within the conductor itself as well as in the conductors around it. Therefore, conductors in a transmission line behave like an inductor. The conductors exhibit self and mutual inductance. As explained in the introductory section 1, the reactance XL can be calculated easily once the line inductance has been obtained.

5 William D. Stevenson, Jr. (1975): “Elements of Power System Analysis”. Third Edition, McGraw-Hill, New York, NY. p. 2. ISBN: 0070612854.

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Figure 14: High voltage overhead lines. Source: RENAC

Assuming that the three-phase system is balanced, the transmission line can be simplified to the single-line circuit in Fig. 15 a). Both the line resistance RL and the line reactance XL have been included. Fig 15 b) shows the voltage drops across the different elements of the trans-mission line. As already mentioned in section 1, due to the presence of an inductive element the current I is not going to be in phase with the voltage UA. The voltage drop in the line re-sistance UR=RL*I will be in phase with the current I, while the voltage drop in the line reac-tance XL will lead the current by 90°.

Figure 15: Equivalent circuit of a transmission/distribution line and phasor diagram of voltages and currents.

Source: RENAC

I

U B

U A

R L X L

I U

B

U A

U R

U X

- U AB

U AB

U R U X

U AB

a) b)

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In order to calculate the voltage at the two ends of this transmission line, the voltage across the line impedance is calculated according to Ohm’s law6:

𝑼𝑨𝑩 = 𝑼𝑨 − 𝑼𝑩 = 𝑰 ∙ 𝒁𝑳 = 𝑰 ∙ (𝑹𝑳 + 𝒋𝑿𝑳) (1.1)

The complex impedance ZL includes the resistance RL as well as the reactance XL mentioned before. Due to the reactive and inductive character of the line impedance, there will be active power (P) flowing through the line as well as reactive power Q. The apparent power S flowing through the transmission line is related to the voltage and current by

𝑺 = 𝑷 + 𝒋𝑸 = 𝑼𝑨𝑰∗ (1.2)

where I* is the complex conjugate7 of I.

Combining equations (1.1) and (1.2), a general relationship for the voltage drop can be ob-tained:

𝑼𝑨𝑩 = ∆𝑼 = 𝑰 ∙ 𝒁𝑳 =𝑺∗

𝑼𝑨∙ 𝒁𝑳 =

(𝑷−𝒋𝑸)∙(𝑹𝑳+𝒋𝑿𝑳)

𝑼𝑨=

(𝑷𝑹𝑳+𝑸𝑿𝑳)

𝑼𝑨+ 𝒋

(𝑷𝑿𝑳−𝑸𝑹𝑳)

𝑼𝑨 (1.3)

Usually the main interest is in the real (or scalar) value of the voltage drop in the line imped-ance, which equals the voltage difference between the two nodes A and B. As can be observed in figure 15 b), this scalar difference is mainly influenced by the real part of 𝑼𝑨𝑩 (its horizontal component). Equation (1.4) can be simplified to the scalar relationship:

∆𝑼𝒓𝒆𝒂𝒍 ≈𝑷𝑹𝑳+𝑸𝑿𝑳

𝑼𝑨 (1.4)

This relation provides a convenient way to estimate the voltage drop in a transmission line given the active and reactive power carried by the line.

Expression (1.4) can be further simplified if the characteristics of the transmission line ana-lysed are taken into account. Due to the geometry and low resistance of the conductors used, medium and high voltage transmission lines present a higher value of reactance XL than re-sistance RL. This transmission line ratio, often denoted X/R, varies depending on the voltage level.

6 The detailed derivation can be found in: Leon Freris, David Infield (2008): “Renewable Energy in Pow-er Systems”. John Wiley & Sons, New York, NY. p. 158 7 The complex conjugate of a complex number is another complex number with the same real part but with imaginary parts of equal magnitude and opposite signs. For example, 2+5i and 2−5i are complex conjugates.

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Line voltage (kV) X/R

400 16

275 10

132 6

33 2

11 1.5

Table 2: Transmission line parameters. Source: Leon Freris, David Infield: “Renewable Energy in Power Systems”,

John Wiley & Sons

High X/R ratios mean that the first term in equation (1.4) will be small compared to the second term, and therefore the following approximation can be made:

∆𝑼𝒓𝒆𝒂𝒍 ≈𝑸𝑿𝑳

𝑼𝑨⇒∆𝑼 ∝ 𝑸 (1.5)

Equation 1.5 provides a very important insight into the voltage stability of electrical power systems: network voltages at the different nodes of the middle and high voltage distribution layers of an electrical power system are mainly determined by reactive power flows. There-fore, in order to guarantee voltage stability and maintain a flat network voltage profile, it is necessary to control components of the electrical power system capable of absorbing or in-jecting reactive power.

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3 Power quality in electrical grids

Different IEEE8 standards define power quality in a different manner, but an overall valid defi-nition would be a set of conditions for the provision of electrical power so that the user of an electric system can utilise electrical energy from the distribution system in their intended manner without interference, interruption or significant loss of performance.

Ideal power quality for an electrical system with a defined line-neutral voltage for each phase of 230V and 50Hz providing electrical power to single- and three-phase loads is represented by the corresponding single-phase and three-phase waveforms of voltage depicted in Fig. 16.

Figure 16: Ideal single- and three-phase voltage waveforms. Source: RENAC

There are several types of distortions of the voltage waveforms that might occur in an electri-cal power system. The following table summarises the main distortions that frequency and voltage instability might cause:

8 Institute of Electrical and Electronics Engineers

23


Disturbance types Description Causes

Deviations in the fre-quency of the trans-mission system from the nominal value (50, 60Hz) during several cycles.

Imbalances be-tween demand and supply.

Variation in the ampli-tude of one or more phases relative to the other three-phase voltages and their nominal value.

Imbalance in the electrical loads on the phases, light-ning, etc.

Variations or repeti-tive fluctuations in the voltage amplitude, either positive or neg-ative, for several cy-cles. In an extreme case an outage oc-curs, when there is a zero voltage condition for one or several phases.

Sudden varia-tions in electri-cal loads, ground faults, lightning, etc.

Table 3: Overview of power quality disturbances relating to voltage and frequency instability. Source: RENAC

24


Different frequency quality indices can be used in order to characterise the frequency quality in a power system:

The absolute frequency deviation

∆𝒇 = 𝒇 − 𝒇𝒏

where fn is the rated frequency (50Hz or 60Hz) and f is the actual frequency (Hz).

The relative frequency deviation (in %)

∆𝒇

𝒇𝒏=𝒇 − 𝒇𝒏𝒇𝒏

∙ 𝟏𝟎𝟎

The integral deviations during the day

𝑰𝒊𝒏𝒕𝒆𝒈𝒓𝒂𝒍 = ∫ ∆𝑓 ∙ 𝒅𝒕𝟐𝟒𝒉

𝟎

Various standards address the issues of power quality in electric systems. Standards are need-ed so that all end users (industrial, commercial and residential) and transmission and distribu-tion suppliers (the utilities) speak the same language when discussing power quality issues9. Standards also define recommended limits for events that degrade power quality. A good overview of applicable standards (e.g. IEEE Standards 519 and 1159) to power quality can be obtained from references [3] (chapter 3) and [4].

9 Alexander Kusko and Marc T. Thompson: “Power Quality in Electrical Systems”. McGraw-Hill Profes-sional. p. 15. ISBN: 0071470751. DOI: 10.1036/0071470751

25


4 Control of interconnected power systems

The positive effect of interconnecting electrical systems in terms of the smoothing of electrical demand curves associated with aggregating electrical loads has already been mentioned in section 2.1. Furthermore, the interconnection of electrical systems presents other advantages:

It increases the possibilities for electricity trading.

It improves the reliability of electricity supply.

The overall peak load is lower than the sum of the peak loads of the individual inter-connected power systems. This in turn reduces the installed capacity needed.

As a consequence the reserve capacity needed is also lower.

It produces more favourable operational conditions for individual generation units, in-creasing their efficiency which again reduces fuel consumption.

Interconnection also has some drawbacks. It increases complexity and also the impact of dis-turbances, since the number of electricity consumers affected is higher in large interconnected systems. Therefore, the stability of power systems is a major concern in the operation of large interconnected power systems. Power systems can be expanded by connecting the power sys-tems of several countries to work synchronously, i.e. with a common nominal frequency.

Dy Liacco [5] classified the possible states in an electrical power system into five different states according to their operational conditions. These are classified in relation to the grid or load/frequency risk levels and urgency of actions related to risks of propagation.

A prerequisite for power system reliability is a Normal operating state. Any other state de-creases system reliability. During this state there is no risk to interconnected system operation. Frequency and voltage are within their predefined allowed limits. After one or more contin-gencies the new state will be Alert, which implies some degree of risk to interconnected sys-tem operation, although the system is still within acceptable limits. If the situation deterio-rates, there may be a transition to an Emergency state. The system, however, would still be intact, and emergency control action could be initiated to restore the system to an alert state. If these measures are not taken in time or are ineffective, the system will break down and reach an In Extremis state. This state is equivalent to a partial or total blackout, which is char-acterised by a partial or total absence of voltage in the transmission power system. Restora-tion is carried out from this state, gradually re-energising and re-synchronising the power sys-tem. From this state, the system can transition to either the alert or the normal state, depend-ing on the circumstances.

26


Figure 17: Electrical power system operating states.

Overall, the stability of interconnected electrical power systems requires effective control of its operational conditions in normal and emergency states.

4.1 Requirements in different interconnected systems

The control performance requirements for an interconnected system are normally prescribed and regulated by a coordinating authority10. A good example of an interconnected system is the European Network of Transmission System Operators for Electricity (ENTSO-E), represent-ing 41 transmission system operators from 34 European countries. Through the ENTSO-E grid, 532 million customers are served, and 880GW net generation capacity is connected, supplying 3,200TWh of electricity consumption through 305,000km of transmission lines managed by the TSOs11.

10 Antonio Gómez-Expósito, Antonio Conejo, Claudio Cañizares (2009): “Electric Energy Systems Analy-sis and Operation”. CRC Press. ISBN: 978-0-8493-7365-7 11 http://www.entsoe.eu/

27


The operation of the ENTSO-E/UCTE system is regulated through the UCTE Operation Hand-book. The Handbook prescribes the following requirements regarding frequency regulation:

Activation of primary control: primary control is activated if the frequency deviation exceeds ±20mHz.

The quasi-steady-state deviation in the synchronous area must not exceed ±180mHz.

The instantaneous frequency must not drop below 49.2Hz.

Load shedding (automatic or manual, including the possibility to shed pumping units) starts at a system frequency of 49.0Hz (or below).

The electrical grids of several countries within the scope of the ReGrid project - Morocco, Alge-ria and Tunisia - are synchronous with ENTSO.

Frequency Deviation Actions

50Hz 0 Nominal frequency

49.98Hz / 50.02Hz ± 20mHz Activation of primary control

49.95Hz / 50.05Hz ± 50mHz Disturbed operation

48.8Hz / 50.2Hz 200mHz Maximum steady-state frequency deviation

49.2Hz / 50.8Hz 800mHz Maximum instantaneous frequency deviation

49Hz / 51Hz > 1000mHz Load shedding frequency criterion

Table 4: Maximum thresholds of grid frequency for safe operation. Source: ENTSO-E (Draft Network Code on Load-Frequency Control and Reserves, Jan. 2013)

4.2 Provision of ancillary services in electrical grids

Apart from frequency and voltage regulation, there are further ancillary services needed to guarantee stable operation of electrical grids. (System) ancillary services are “services neces-sary for the operation of an electric power system provided by the system operator and/or by power system users” according to IEC 60050-617. Some examples of ancillary services are:

Black start: includes all the services and activities necessary for a transition from the restoration state explained in section 0 (gradual re-energising, re-synchronising of the power system, restoration of unsupplied load, etc.).

Islanded operation, which is also part of the above mentioned power system restora-tion process as a follow up to the black start.

Reduction and compensation for active power losses in the transmission system, since the transportation of active or reactive power in the network leads to active power losses. These power losses must be compensated, either by producing or supplying power in addition to the power delivered to end consumers.

5 Electrical system frequency and active power regulation

28


As already described in previous sections, imbalances between electricity supply and demand for active power lead to increases or drops in grid frequency. Disturbances in this balance, causing a deviation of the system frequency from its set-point values, will be offset initially by the kinetic energy of the rotating generating sets and motors. In practice, the grid frequency almost never equals the nominal grid frequency, as can be observed in Real-time frequency

graph of Continental Europe. Source: ENTSO-E.

Figure 18: Real-time frequency graph of Continental Europe. Source: ENTSO-E

Tthe tolerance ranges for grid frequency are kept strictly small. Consequently, in order to com-pensate imbalances, synchronous electrical systems need rapid responses in order to follow variability of demand as well as respond to sudden mismatches between active power genera-tion and consumption, such as during system faults.

5.1 Frequency control in power systems

Frequency stability involves responses from generators over different time scales. Fig. 19 illus-trates the behaviour of a synchronous electrical power system after a disturbance. In undis-turbed conditions, the system frequency is maintained within strict limits. At some point in time a contingency occurs, which in this example provokes an excess of consumption com-pared to generation. Fig. 19 indicates two magnitudes used to quantify the rate at which the frequency drops after the contingency. The first one is the dynamic frequency deviation, which is governed mainly by the following12:

The amplitude and development over time of the disturbance affecting the balance be-tween power output and consumption.

The kinetic energy of rotating machines in the system.

The number of generators subject to primary control, the primary control reserve and its distribution between these generators.

The dynamic characteristics of the machines (including controllers).

The dynamic characteristics of the loads, particularly the self-regulating effect of the loads.

The second one is the quasi-steady-state frequency deviation, which is mainly influenced by the following:

12 ENTSO-E’s Continental Europe Synchronous Area Operation Handbook. Available at: https://www.entsoe.eu/resources/publications/system-operations/

29


The drop of all generators subject to primary control in the synchronous area.

The sensitivity of consumption to variations in system frequency.

The frequency control structure of synchronous interconnected electrical systems performs three levels of control, called primary, secondary and tertiary frequency control. After a dis-turbance, as soon as the frequency exceeds a predefined threshold value, a control mecha-nism is activated within 15 to 30 seconds. This is denoted as primary frequency control and aims to restore the balance between generated and consumed active power at a certain fre-quency level.

Figure 19: Frequency behaviour after a grid disturbance. Source: Adapted from ENTSO-E Operation Handbook

Conventional power plants usually have primary frequency or droop controllers installed. In the case of conventional fossil fuelled generators, the steam flow from the boiler to the tur-bine is regulated by a valve. The control signal to open or close the valve is provided by a gov-ernor, which measures the rotational speed of the generator, compares it to the reference value (50 or 60Hz) and, based on the error signal, opens or closes the steam valve. This pro-portional control is the droop of the generator, expressed as:

𝒔𝑮 =−∆𝒇

𝒇𝒏⁄

∆𝑷𝑷𝑮𝒏⁄

(4.1)

30


fn and PGn are the nominal frequency and nominal power of the generator, ΔP is the decay in generator power when the increase in frequency Δf in the system takes place. Fig 20 shows a diagram of variations in the generating output of two generators (a and b) with different droop under equilibrium conditions. The droop of the generator is the slope of the P/f (pow-er/frequency) characteristic of a generator. The contribution of generator a (which has the controller with the smaller droop) to correcting the disturbance will be greater than that of generator b, which has the controller with the greater droop. The frequency offset (Δfa) at which the primary control reserve of generator a will be exhausted (i.e. where the power gen-erating output reaches its maximum value Pmax) will be smaller than that of generator b (Δfb)

13.

Figure 20: Frequency power characteristics of two different generators equipped with a governor. Source: ENTSO-E Operation Handbook

The second step is to bring the system frequency back to the set-point value. This task is ac-complished by the secondary frequency control, which delivers reserve power at short notice. Secondary reserves must be able to increase active power output within 15 seconds and be able to maintain the response for a further 30 minutes. Hydropower and pumped storage plants are commonly used as secondary reserves.

Beyond primary and secondary reserves, power systems have tertiary reserves (also called minute reserves). The tertiary frequency control involves a manual or automatic change in the dispatching of power. Changes may be achieved by14:

Connecting and tripping power (gas turbines, reservoir and pumped storage power sta-tions, increasing or reducing the output of generators in service).

Redistributing the output from generators participating in secondary control.

Changing the power interchange programme between interconnected undertakings.

13 ENTSO-E’s Continental Europe Synchronous Area Operation Handbook. Available at: https://www.entsoe.eu/resources/publications/system-operations/ 14 ENTSO-E’s Continental Europe Synchronous Area Operation Handbook. Available at: https://www.entsoe.eu/resources/publications/system-operations/

31


Load control (e.g. centralised tele-control).

Overall, the combined action of primary, secondary and tertiary frequency control must guar-antee that the variations in frequency caused by the contingency are rapidly decreased. The response time and the return of the system frequency to its initial value are monitored by us-ing what is called the “trumpet method”15. In order to assess the quality and compliance of frequency control, trumpet-shaped curves of the type:

𝑯(𝒕) = 𝒇𝟎 ± 𝑨 ∙ 𝒆−𝒕/𝑻 (4.2)

have been defined on the basis of values obtained from experience and the monitoring of sys-tem frequency over a period of years. In equation (4.2), A is an experimental value, which is equal to 1.2* Δf2 (Δf2 being the maximum frequency deviation expected –f0 is the set frequen-cy value. The system frequency must be restored to within a margin of d = ± 20mHz of the set-point frequency by 900 seconds (15 minutes) after the start of an incident. Hence, the time constant T of the trumpet curve results from the relation:

𝑻 =𝟗𝟎𝟎

𝒍𝒏(𝑨 𝒅⁄ )𝒇𝒐𝒓𝑻 ≤ 𝟗𝟎𝟎𝒔𝒂𝒏𝒅|𝒅| = 𝟐𝟎𝒎𝑯𝒛 (4.3)

Figure 21: Frequency variation during a fault in a power network. Source: ENTSO-E Operation Handbook

15 UCTE Operation Handbook. Available at: https://www.entsoe.eu/resources/publications/system-operations/

32


5.2 Excerpt: electrical system frequency as a communication link for active power sharing

The droop properties of conventional generators introduced in section 5.1 can be used as a load sharing scheme in interconnected electric power systems with multiple generators.

Figure 22: Two generators connected to a load. Source: RENAC

Fig. 22 hows two generators connected to a load through two transmission lines. As listed the X/R ratio for medium and high voltage lines is rather high, and so the transmission line is pre-dominantly inductive. Therefore, for the purposes of simplified analysis, the transmission lines will be represented by pure inductances.

The complex power provided to the load by the generator i is given by:

𝑺𝒊 = 𝑷𝒊 + 𝒋𝑸𝒊 = 𝑽 ∙ 𝑰𝒊∗ (4.4)

where 𝑰𝒊∗ is the complex conjugate of the generator i current, which can be expressed as a

function of the line voltages using Kirchoff ’s voltage law:

𝑰𝒊∗ = (

𝑬𝒊∠𝜹𝒊−𝑽∠𝟎

𝑿𝒊∠𝟗𝟎°)∗

(4.5)

Substituting (4.5) into (4.4) and using Euler’s formula to break the total power into real and imaginary:

𝑺𝒊 = 𝑽 ∙ 𝑰𝒊∗ = 𝑽 ∙ (

𝑬𝒊

𝑿𝒊∠(𝜹𝒊 − 𝟗𝟎°) −

𝑽

𝑿𝒊∠ − 𝟗𝟎°)

∗

= 𝑽 ∙ (𝑬𝒊

𝑿𝒊𝒔𝒊𝒏𝜹𝒊 + 𝒋

𝑽

𝑿𝒊− 𝒋

𝑬𝒊

𝑿𝒊𝒄𝒐𝒔𝜹𝒊) (4.6)

33


The former relation gives us the active and reactive power flowing from the ith generator:

𝑷𝒊 =𝑽𝑬𝒊

𝑿𝒊𝒔𝒊𝒏𝜹𝒊 (4.7)

𝑸𝒊 =𝑽𝟐

𝑿𝒊−

𝑽𝑬𝒊

𝑿𝒊𝒄𝒐𝒔𝜹𝒊 (4.8)

Relations (4.7) and (4.8) are important in power systems technology as they describe the flow of active and reactive power in grid-connected synchronous generators. Equation (4.7) states that real power flow (Pi) is mostly influenced by the phase shifts of the power generators (𝜹𝒊). Equation (4.8) shows that the reactive power flow (Qi) between the generator i and the load depends on the difference between the load voltage (V) and the voltage at the generator I (Ei).

Therefore, the flow of active power (P) and reactive power (Q) in an electrical power system can be regulated by altering the voltage magnitudes and power angles. While the power phase deviation angles can be controlled by altering the system frequency. It is for these rea-sons the droop method uses frequency instead of phase to control the active power flows and the share of loads between the generators connected to an electrical system.

34


6 Reactive power and voltage control

There are several definitions of voltage stability. The IEEE defines voltage stability as the ability of a power system to maintain steady voltages after a disturbance (IEEE-CIGRE, 2004)16. Volt-age disturbances are commonly associated with reactive power deficiencies.

6.1 Effects of active and reactive power flows on voltage

Expression (1.4) obtained in section 2.1:

∆𝐔𝐫𝐞𝐚𝐥 =𝐏𝐑 +𝐐𝐗

𝐔

provides a method to estimate the voltage drops in transmission and distribution lines. Ac-cording to this expression, both active and reactive power flows over distribution and trans-mission lines will affect the voltage profiles of the different nodes in the network. Which com-ponent – active power flow or reactive power flow – affects voltage stability more strongly depends upon whether the corresponding lines are predominantly resistive (RL>XL) or reactive (XL>RL). In the event that the line is predominantly resistive, the term 𝐏𝐑 will generally be more important in the relation than 𝐐𝐗 , and therefore voltage nodes will be affected by ac-tive power flow due to voltage drops at the resistive part of the line impedance. The opposite happens when the line is predominantly reactive. The line parameters are different for distri-bution/low voltage lines and for transmission/medium and high voltage lines:

Distribution lines are predominantly resistive. Consequently voltage in distribution lines is affected by active power flow rather than by reactive power flow.

The higher the voltage of the line, the stronger the reactive character of the line im-pedance. Therefore, in medium and especially in high voltage lines, voltage profiles are affected more by the flow of reactive power.

6.2 Load flow calculations

The equations obtained in section 5.2 can also be applied to a transmission line linking two buses as depicted in Fig. 23

16 P. Kundur, J. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. V. Custem, V. Vittal: ‘Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions’ in “IEEE Transactions on Power Systems”. Vol. 19, No. 2, August 2004. p. 1388

35


Figure 23: Transmission line linking two nodes. Source: RENAC

The equations can be generalised for the transmission line as follows17:

0 = PL −V1V2XL

sinδ

0 = QL −V2

2

XL−V1V2XL

cosδ

0 = QG −V1

2

XL+V1V2XL

cosδ

There are several variables associated with each transmission line linking nodes of the electri-cal grid: active and reactive power injected or extracted at the bus; bus voltage; and voltage phase angle. These equations are not linear since they contain products of variables and trigo-nometric functions. Electrical power systems have thousands of interconnected nodes, and the equations listed above need to be solved for all the nodes simultaneously. These are the types of calculations that are carried out by power system simulation packages.

6.3 Mitigation of voltage stability problems/reactive power management

Voltage, unlike frequency, is not the same in all the nodes of an electrical power system. Equipment used to mitigate voltage stability problems behaves with certain time constants that need to be taken into consideration, and as such different time windows need to be con-sidered. The simplest differentiation is between short-term and long-term voltage stability. Short-term voltage stability (with a time frame of several seconds) comprises the time be-tween voltage digression after a disturbance occurs and the activation of a transformer tap changer close to loads. Short-term voltage stability dynamics are associated with the behav-iour of induction motors after a voltage disturbance. So, for example, a short circuit on the distribution/transmission grid will slow induction motors, which in turn leads to high currents

17 Leonard L. Grigsby (2007): “Power System Stability and Control”. CRC Press.

36


of the order of the starting currents and voltage sags. If voltages at the nearby buses drop by more than a certain threshold value below their pre-disturbance voltage, a cascade of motor stalling will occur within a few seconds. This will lead to a sudden loss of load. In order to avoid incumbent voltage instability, corrective actions are taken through automatically controlled power system equipment.

The following fast acting devices can act over several cycles to guarantee voltage stability with-in the timeframe18:

Synchronous condensers.

Automatic switched shunt capacitors.

Serial compensation devices.

Shunt reactors.

Static VAR compensators.

Flexible AC transmission system (FACTS) devices.

Voltage-dependent loads.

Induction motor dynamics.

Long-term voltage stability is associated with the topology of the concrete electrical power system. Due to large distances in transmission lines and their electrical properties (reactances, etc.) there is a need for voltage regulation. The main components employed for long-term voltage regulation are tap changers close to loads with a time constant of tens of seconds to minutes.

6.3.1 Static compensators

The first group of devices used for short-term voltage stability regulation are static compensa-tors (capacitors, serial compensation devices, shunt reactors and static VAR compensators). All these devices compensate reactive power using a similar operating principle.

The connection of shunt capacitors or reactances is probably the simplest and most widely used form of power factor correction and therefore also widely used for reactive power man-agement. Switchable capacitors or inductors are distributed in the transmission network to compensate reactive power under varying load conditions. Their capacitive or inductive char-acter is controlled in steps; mechanically through switches or relays, or electronically using electronic switches. The usage of power electronics in VAR compensators enables finer con-trol, allowing for infinite steps in the amount of positive or negative reactive power provided by capacitors or inductors. Static VAR compensators are voltage-controlled shunt compensa-tion devices.

Typically, the electronic switches used are thyristors. So, for example, in a thyristor-controlled series capacitor, a variable number of capacitor units are connected to the transmission line 18 G. Morison, B. Gao, and P. Kundur: ‘Voltage stability analysis using static and dynamic approaches’ in “IEEE Transactions on Power Systems”. Vol. 8, No. 3, August 1993. pp. 1159 – 1171

37


using thyristors as switches. Additionally, these devices can be used to filter resonances in a certain frequency range.

Figure 24: Static compensators a) shunt reactor, b) serial compensation device, c) static VAR compensator. Source:

adapted from Prof. Dr.-Ing. habil. I. Erlich, University of Duisburg-Essen, Germany

6.3.2 FACTS (flexible AC transmission system)

FACTS are defined by the IEEE as "power electronic based systems and other static equipment that provide control of one or more AC transmission system parameters to enhance controlla-bility and increase power transfer capability"19. FACTS devices can be classified into series and shunt compensation devices:

Series compensation: FACTS devices are connected in series with the power systems. As mentioned in previous sections, medium and high voltage transmission lines are characterised by high X/R values, that is to say, their character is reactive rather than resistive. On long distance lines, the flow of high currents provokes significant voltage drops in the inductances. In order to compensate, capacitors are connected in series, decreasing the effect of the inductances.

Shunt compensation: in this case, the power factor correction system is connected in shunt to the transmission line. Compared to series compensation devices, which act as a voltage source, shunt compensation devices act as a current source.

Fig. 24 shows the simplified principle of compensation. The transmission line a) shows a low power factor due to the connection of an inductive load to the transmission line and due to the inductive character of the transmission line itself. The inductance consumes reactive pow-er (Q). Consequently, the ratio of the real power flowing through the transmission line (P) to the apparent power (S) is rather low.

19 ‘Proposed terms and definitions for flexible AC transmission system (FACTS)’ in “IEEE Transactions on Power Delivery”. Vol. 12, Issue 4, October 1997. pp. 1848–1853

38


Figure 25: Shunt compensation principle. Source: RENAC

In order to compensate the inductive character of the transmission line with an inductive load connected, a capacitive element is connected to the transmission line (Xc). Capacitive ele-ments deliver reactive power (QC). Therefore, the overall reactive power consumed in the line is reduced (Q-QC). For the same amount of apparent power (S) for which the transmission line, transformers, etc. have been dimensioned, more useful real power (P1 > P2) can be trans-ferred. As such, the power factor improves.

A very common FACTS device used for compensation and dynamic voltage support through reactive power management is the static synchronous compensator (STATCOM). This device is usually composed of a voltage converter that produces a line voltage with variable magnitude and phase. The DC voltage for the voltage converter is supplied by a DC capacitor. STATCOMs are interfaced in shunt to the transmission line through a coupling transformer. When the feeder voltage (Vp) is larger than the voltage of the converter (Vsh), the STATCOM generates reactive power. When the converter voltage is higher than the feeder voltage, the STATCOM absorbs reactive power20. Fig. 26 shows the components and shunt connection of a STATCOM device to the transmission line.

20 HF. Wang, M. Jazaari, JY. Cao (2005): ‘Operating M and control interaction analysis of unified power flow controller’ in “IEEE proceedings (Generation, Transmission, Distribution)”. Vol. 152, No. 2. pp. 264-270

39


Figure 26: STATCOM interfaced in shunt to a transmission line. Source: RENAC (adapted from Erlich and [7])

V1 δ1 and V2 0° are the generator voltages, X1 and X2 the reactances of the transmission

lines, and VP β the voltage at the node where the compensator has been connected. Both the active and reactive power components are given by21:

PSh =VSh−VPXSh

sin(θ − β)

QSh =VSh2 − VShVPcos(θ − β)

XSh

To summarise, a STATCOM can act either as a source or a sink of reactive power and, there-fore, can dynamically support voltage stability in the electrical network. Furthermore, network losses are reduced and adequate power quality is provided to the electric energy end-users.

21

R. Strzelecki, B. Benysek (2008): “Power Electronics in Smart Electrical Energy Networks”. Springer. pp. 221-222

40


6.3.3 Tap changers

Transformers are indispensable devices in electrical power networks. Transformers transfer electrical energy between different transmission lines through inductively coupled conductors. The induced voltage in the secondary winding (Vs) is in proportion to the primary voltage (Vp), and is given by the ratio of the number of turns in the secondary coil (Ns) to the number of turns in the primary coil (Np) as follows:

VsVp

=Ns

Np

Transformers equipped with tap changers are equipped with connection points (taps) to the windings. The number of effective windings can be changed, allowing the voltage ratio to be continuously adapted. These are the most widely used devices for voltage control in electrical networks nowadays.

41


7 Integration of renewable energy generation in power systems

The use of renewable energy generation (wind turbines, solar power plants, etc.) is continu-ously increasing. Renewable energy generation often takes place with decentralised units con-nected to the distribution network, and is not centrally planned or dispatched. Also, renewa-ble energy generation is increasingly being implemented on a utility scale, with generation units with a capacity comparable to conventional generators being directly connected to the transmission network.

The question of grid stability and distributed generation is not straightforward. Supporters of renewable energy generation claim that distributed generation contributes to the improve-ment of power quality. So, for example, in areas with a weak grid and where voltage support is non-existent, distributed generation can improve the voltage profile and correct the power factor. Detractors of renewable energy generation claim that large-scale introduction of decen-tralised power generating units may lead to grid instability. The next section will deal with some aspects of renewable energy generation and grid integration and try to throw some light on this controversial issue.

7.1 Voltage effects

Larger amounts of distributed generation affect the load flow in distribution systems, but also the load flow in transmission systems. The connection of a distributed generator usually has the effect of raising the voltage at the point of connection, and this can lead to over-voltages for nearby customers22. The voltage profile in a distribution line can be calculated using rela-tion (1.4) obtained in section 2.1:

∆𝐔 =𝐏𝐑 +𝐐𝐗

𝐔 (6.1)

In the case of a distribution line with only consumption and no generation, the active (P) and reactive (Q) power is negative. ∆U in equation 6.1 will therefore be negative. The voltage in the distribution line predominantly exhibits a decaying profile (see upper black line in Fig. 27). With an increasing amount of distributed generation, the active power P might become posi-tive and the voltage profile tend to increase through the distribution line. The voltage increase would be more pronounced the higher the impedance of the distribution lines, and the longer they are. Through compensation measurements and flexible power factor control of the dis-tributed generation sources, the amount of distributed energy sources that can be connected to a distribution line can be significantly increased (orange lines). The variability of the voltage at the nearest transformer connected to the voltage line can change the starting point of the voltage profiles. Furthermore, the connection of heavily inductive loads to the distribution line leads to a higher consumption of reactive power, further leading to a steeper decay of the voltage profiles, as shown in the lower part. Overall, distribution network operators must en-

22 Leon Freris, David Infield (2008): “Renewable Energy in Power Systems”. John Wiley & Sons, New York, NY.

42


sure that maximum and minimum acceptable limits for voltage are not exceeded (red lines in Fig. 27). The ability of distributed generation units to inject reactive power increases the amount of renewable energy that can be connected to a distribution line.

Figure 27: Voltage profiles in distribution line. Source: RENAC

7.2 Active and reactive power from renewable energy generators

The approaches introduced in the last sections for active and reactive power generation from conventional generators are not directly applicable to renewable energy generators. Renewa-ble energy generators rely more heavily on the use of power electronics for active and reactive power management. As an example, the active and reactive power management of solar pho-tovoltaic generators is examined below:

Active power management can be accomplished easily in solar PV systems by forcing operation from the maximum power point towards operation points of the solar PV generator where energy delivered is less than the maximum power point.

Regarding reactive power management, PWM (pulse width modulated) power elec-tronic inverters used in solar PV systems can control reactive power injection and ex-traction. PWM inverters are devices that convert DC power delivered by the solar PV generator into AC power delivered to the grid. By adjusting the switching times of the four switches S1 to S4, a sinusoidal AC waveform is generated. The phase shift of the waveforms can also be adjusted and, as has been seen in previous sections, this means that the amount of reactive power being consumed or injected in the grid can conse-

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quently be adapted.

Figure 28: PWM inverter. Source: RENAC

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7.3 Codes and regulations

An increasing number of countries are already continuously connecting significant amounts of renewable energy generation to the grid. As a consequence, transmission system operators increasingly require an active contribution of distributed generators towards power system frequency and voltage stability during contingencies. In systems that aim for a high penetra-tion of renewable energies, it is essential that renewable sources contribute to grid control and stability.

There are two categories of required behaviour determined by grid codes:

Static grid support: regulates performance under normal operation, where response times are not of paramount importance.

Dynamic grid support: defines behaviour in critical situations, where equipment must react quickly to ensure grid stability.

Compliance rules regarding power factor requirements are an example of static grid support. An example of these rules is the German Static Voltage-Var Requirements. The red line in Fig.

29 sets the limits for the operation of renewable energy generating units. The shape and limits of the curve are determined by the grid layout and operating parameters.

Figure 29: German Static Voltage-Var Requirements. Source: Prof. Dr.-Ing. habil. I. Erlich, University of Duisburg-

Essen, Germany

One example of dynamic grid support is fault ride-through capabilities. Wind generators in Germany at the beginning of 2000 and photovoltaic systems even today are required to shut down immediately in the event of significant disturbances on the grid (e.g. a voltage drop higher than 20% or significant frequency deviations). The rationale behind this has been to avoid islanding. A generator is said to be islanded if it continues to supply a local load after

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being disconnected from the main network23. Islanding is a dangerous situation when mainte-nance works are performed since utility workers may not realise that a circuit is still powered. However, as more renewable generation units come online, if a widespread disturbance across the network occurs, it would cause a large number of renewable energy generation units to trip simultaneously. This would be highly undesirable in the context of controlling the voltage and frequency of the overall power system. Therefore, in 2003, German grid opera-tors were the first to introduce new requirements including fault ride-through. Fault ride-through describes the ability of renewable sources to remain grid-connected for a specified time span in the event of voltage drops. Fig. 30 displays fault ride-through characteristics as proposed by CENELEC, the European Standardisation Organisation.

Figure 30: Fault ride-through voltage profile for dynamic grid support of RE generation units. Source: E. Troester:

“German Grid Codes for Connecting PV Systems to the Medium Voltage Power Grid”, Second IWCPPP Proceeding

The red line defines the most serious fault generators have to withstand, which means they have to ride through a fault of 0.5 seconds where voltage drops down to 30% and doesn’t reach 90% of nominal value until 1.5 seconds after the disruption. Generators are allowed to disconnect if voltage drops below the line.

The details of the different grid code requirements for renewable energy generation differ from one country to the next, and to a certain extent may be somewhat arbitrary.

23 Leon Freris, David Infield (2008): “Renewable Energy in Power Systems”. John Wiley & Sons, New York.

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Summary

System reliability in terms of voltage and frequency is absolutely crucial for the opera-tion of modern electrical power systems.

Power generation – either in electricity pool markets or centrally dispatched markets – is allocated according to economic criteria (cost optimisation) as well as supply reliabil-ity (by guaranteeing a necessary amount of reserve capacity available for reliable sys-tem operation).

Frequency stability is mainly related to the balance between generation and consump-tion in an interconnected electrical system.

Voltage stability in medium and high voltage layers is mainly related to power reactive flows.

Renewable energy generation units are usually interfaced to the grid through power conditioning devices with a fair degree of flexibility in terms of active and reactive power compensation.

The increasing amount of renewable energy generation introduces further generation fluctuations and uncertainties; the technical solutions for a reliable integration of re-newable energy generation into electrical grids are already available.

Clear and adequate formulation of grid codes is essential to guarantee a smooth inte-gration of renewable energy generation units.

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References and recommended further reading

[1] Danish Wind Industry Association: “Guided Tour on Wind Energy”. Available at: http://www.vindselskab.dk/en/tour

[2] Leon Freris, David Infield (2008): “Renewable Energy in Power Systems”. John Wiley & Sons, New York, N.Y.

[3] Alexander Kusko and Marc T. Thompson (2007): “Power Quality in Electrical Systems”. McGraw-Hill Professional. ISBN: 0071470751. DOI: 10.1036/0071470751

[4] Angelo Baggini (2008): “Handbook of Power Quality”. John Wiley & Sons, New York, N.Y. ISBN: 978-0-470-06561-7 760pp

[5] T.E. Dy Liacco: ‘The adaptive reliability control system’ in “IEEE Transactions on Power Ap-paratus and Systems”. PAS-86(5). May 1967. pp. 517–531,.

[6] Antonio Gómez-Expósito, Antonio Conejo, Claudio Cañizares (2009): “Electric Energy Sys-tems Analysis and Operation”. CRC Press. ISBN: 978-0-8493-7365-7

[7] R. Strzelecki, B. Benysek (2008): “Power Electronics in Smart Electrical Energy Networks”. Springer. pp. 221-222

[8] G. M. Masters (2004): “Renewable and Efficient Electric Power Systems”. John Wiley & Sons.

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Glossary

Active Power - A term used for power when it is necessary to distinguish between apparent power, complex power and its components, or active and reactive power.

Alternating Current (AC) - An electric current that reverses direction at regular intervals, with a magnitude that varies continuously in a sinusoidal manner.

Alternator - An electromechanical device that converts mechanical energy to electrical energy in the form of alternating current.

Apparent Power (volt-amps) - The product of the applied voltage and current in an AC circuit. Apparent power, or volt-amps, is not the true power of the circuit because the power factor is not considered in the calculation.

Bus - A conductor, which may be a solid bar or pipe, normally made of aluminium or copper, used to connect one or more circuits to a common interface. An example would be the bus used to connect a substation transformer to the outgoing circuits.

Capacitance - 1) The ratio of an impressed charge on a conductor to the corresponding change in potential. 2) The ratio of the charge on either conductor of a capacitor to the potential dif-ference between the conductors. 3) The property of being able to collect a charge.

Capacitor - An electrical device with capacitance.

Direct Current (DC) - Electric current flowing in only one direction.

European Network of Transmission System Operators for Electricity (ENTSO-E) - Association of Europe's transmission system operators (TSOs) for electricity. It is a successor of ETSO, the association of European Transmission System Operators founded in 1999 in response to the emergence of the internal electricity market within the European Union.

Flexible Alternating Current Transmission System (FACTS) - A system composed of static equipment used for the AC transmission of electrical energy. It is meant to enhance controlla-bility and increase the power transfer capability of the network. It is generally a power elec-tronics-based system.

Frequency - In AC systems, the rate at which the current changes direction, expressed in hertz (cycles per second); a measure of the number of complete cycles of a waveform per unit of time.

Grid - A term used to describe an electrical utility distribution network.

Impedance - 1) The total opposing force to the flow of current in an AC circuit. 2) The combi-nation of resistance and reactance affecting the flow of an alternating current, generally ex-pressed in ohms.

http://en.wikipedia.org/wiki/Generator_%28device%29

http://en.wikipedia.org/wiki/Alternating_current

http://en.wikipedia.org/wiki/Transmission_system_operator

http://en.wikipedia.org/wiki/European_Union


http://en.wikipedia.org/wiki/Electric_power_transmission

http://en.wikipedia.org/wiki/Power_electronics


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Inverter - A device that converts DC electricity into single- or multi-phase AC electricity.

Load - 1) The amount of electrical power required by connected electrical equipment. 2) The total impedance of all the items in the output circuit.

Load Shedding - The act or process of disconnecting the electric current on certain lines when the demand becomes greater than the supply.

Maximum Power Point - The point on an I-V curve that represents the largest rectangle area that can be drawn under the curve. Operating a PV array at that voltage will produce maxi-mum power.

Nominal Voltage - A nominal value assigned to a circuit or system for the purpose of conven-iently designating its voltage class.

Power Factor - The ratio of energy consumed (watts) versus the product of input voltage (volts) times input current (amps). In other words, power factor is the percentage of energy used compared to the energy flowing through the wires.

Pulse Width Modulation (PWM) - A commonly used technique for controlling power to iner-tial electrical devices, made practical by modern electronic power switches.

Reactance - The opposition of inductance and capacitance to alternating current equal to the product of the sine of the angular phase difference between the current and voltage.

Reactive Power - A component of apparent power (volt-amps) which does not produce any real power (watts). It is measured in VARs (volt-amps reactive).

Resistance - The opposition to current flow, expressed in ohms.

Shunt - A device that allows electric current to pass around another point in the circuit. The term is also widely used in photovoltaics to describe an unwanted short circuit between the front and back surface contacts of a solar cell, usually caused by wafer damage.

Static Synchronous Compensator (STATCOM) - A regulating device used on alternating current electricity transmission networks. It is based on a power electronics voltage-source converter and can act as either a source or sink of reactive AC power to an electricity network. If con-nected to a source of power it can also provide active AC power. It is a member of the FACTS family of devices.

Static Var Compensator - A device that supplies or consumes reactive power comprised solely of static equipment. It is shunt-connected on transmission lines to provide reactive power compensation.

Three-Phase - Three-phase refers to one circuit consisting of three conductors where the cur-rent and voltage in each conductor (phase) is 120° out of phase with each other phase.

Thyristor – A solid-state semiconductor device with four layers of alternating N- and P-type material. They act as bistable switches, conducting when their gate receives a current pulse and continuing to conduct while they are forward biased (that is, while the voltage across the device is not reversed).

http://en.wikipedia.org/wiki/Electric_current

http://en.wikipedia.org/wiki/Electrical_network

http://en.wikipedia.org/wiki/Photovoltaics

http://en.wikipedia.org/wiki/Solar_cell

http://en.wikipedia.org/wiki/Wafer_%28electronics%29



http://en.wikipedia.org/wiki/AC_power

http://en.wikipedia.org/wiki/AC_power

http://en.wikipedia.org/wiki/Flexible_AC_transmission_system

http://en.wikipedia.org/wiki/Solid_state_%28electronics%29

http://en.wikipedia.org/wiki/Semiconductor_device

http://en.wikipedia.org/wiki/N-type_semiconductor

http://en.wikipedia.org/wiki/P-type_semiconductor

http://en.wikipedia.org/wiki/Bistable

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Transformer - An electromagnetic device used to change the voltage in an alternating current electrical circuit.

Transmission System - Normally, the highest voltage network of an electric utility system. This is the portion of the system that carries high power over the longest distances. Typically oper-ating at voltages in excess of 100kV, and most usually at 200kV and above.

Transmission System Operator (TSO) - An entity entrusted with transporting energy in the form of natural gas and/or electrical power on a national or regional level, using fixed infra-structure.

Winding - Material (as wire) wound or coiled about an object (as an armature); also: a single turn of the wound material.

http://en.wikipedia.org/wiki/Natural_gas

http://en.wikipedia.org/wiki/Infrastructure

http://en.wikipedia.org/wiki/Infrastructure

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Renewables Academy (RENAC) AG

Schönhauser Allee 10-11

10119 Berlin (Germany)

Tel: +49 (0) 30-52 689 58 70

Fax: +49 (0) 30-52 689 58 99

E-Mail: [email protected], June 2013

http://www.renac.de/en/projects/regrid/

frequency and voltage regulation in electrical grids

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