voltage stability assessment in low- voltage...
TRANSCRIPT
Voltage Stability Assessment in Low-
Voltage DC-Grids
Kirill Rykov M.Sc.
Researcher
Eindhoven University of Technology
Contents
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
• Conclusions and Future Work
/ Electrical Engineering PAGE 120-10-2014
Outline
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
• Conclusions and Future Work
/ Electrical Engineering PAGE 220-10-2014
/ Electrical Engineering PAGE 320-10-2014
DC micro-grids: typical structure
Use of
sustainable
energy sources
Connection to
AC mains
Battery storage
Car charging
capabilities
Direct use of DC
power
/ Electrical Engineering PAGE 420-10-2014
DC grid architecture
5% less
power
consumption
7% cost
reduction
for solar power
State of the art AC power distribution architecture:
High efficiency DC power grid distribution architecture:
Stability Issues in DC-Grids
DC BUS
(cables)
/ Electrical Engineering PAGE 520-10-2014
Loads Sources
V
/ Electrical Engineering PAGE 620-10-2014
Voltage instabilities
Reasons:
• Interaction of non-linear components
• Feedback control loops
• Filters
• Various loads of different power levels
• Long interconnecting cables
Consequences:
• Inability to maintain voltage in the specified range
• Unexpected activation of protection devices
• Overheating and damage of components
Challenges:
• Lack of studies in the area of voltage stability in DC-grids
• Internal structure of converters is not provided by manufacturers
/ Electrical Engineering PAGE 720-10-2014
Main goals
• Develop an approach for small-signal voltage stability
analysis verified by the theoretical modeling
• Include a possibility of experimental impedance
identification of power modules and their aggregation in
the grid model
• Create a tool, which combines software and hardware
parts suitable for forecasting instabilities in complex grids
with multiple number of sources and loads
Outline
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
• Conclusions and Future Work
/ Electrical Engineering PAGE 820-10-2014
/ Electrical Engineering PAGE 920-10-2014
List of requirements
The tool should be capable of:
• Performing small-signal voltage stability analysis at any
point of the grid
• Verifying the fact of instability based on several criteria
• Handling big amount of power modules
• Obtaining impedance information of power modules
experimentally without knowing their internal structure
• Analyzing complex grids including the model of the DC-
grid at Fraunhofer IISB
/ Electrical Engineering PAGE 1020-10-2014
Tool structure
Software part, MATLAB + Simulink
Data Processing
Aggregated
System
Time-domain
simulation
PLECS
Hardware part
U [mV]
I [mA]
φ [rad]
Transfer
function
Theoretical modelling
Bode plot
Nyquist Plot
Data Analysis
Impedance
Z
/ Electrical Engineering PAGE 1120-10-2014
List of specifications: software part
Specification Description
Simulation software MATLAB + PLECS
Frequency range 50 – 3000 Hz
Number of input modules >2 (manual change of an admittance matrix needed)
Total simulation time
Sample time
Simulation model type
15 sec (limited by the simulation time in PLECS)
1e-6 sec
Discrete state-space
Required stability
conditions
• Nyquist stability
criterion
• Bode plot analysis
• Time-domain
simulations
System Nyquist plot encircles point (-1;0)
Equality of amplitudes and total phase shift of 180 ̊
Oscillation amplitude increases
Input for the tool Impedance Z(s) from measurements; Transfer function
G(s) from the theoretical modeling
/ Electrical Engineering PAGE 1220-10-2014
System instability
Bode plot:
• Equal magnitudes
• Phase shift is 180 ̊
Nyquist Diagram:
• System Nyquist plot
G(ω) encircles (-1:0)
Time-domain
simulations:
• Increasing amplitude
of oscillations
The system is
unstable if:
/ Electrical Engineering PAGE 1320-10-2014
Theoretical Modelling of Power Converters
• Average models with the switching process neglected,
enables the description of a DC-grid by means of
linearised transfer functions
• The dynamics of the actively controlled converters can be
modelled as equivalent impedances in frequency domain
using Thevenin or Norton Equivalents
/ Electrical Engineering PAGE 1420-10-2014
System instability
The transfer function of the PI controller is found to be
𝐺𝑠𝑙𝑎𝑐𝑘,𝑘 𝑠 = 𝐾𝑝 +𝐾𝑖𝑠.
The converter module may be represented by just a unity current gain,
including a propagation delay
𝐺𝑐𝑜𝑛𝑣,𝑘 𝑠 =𝑖𝑐𝑜𝑛𝑣,𝑘(𝑠)
𝑖𝑐𝑜𝑛𝑣,𝑘∗ 𝑠
=1
1 + (𝑛𝑇𝑠𝑤)𝑠.
Total transfer function of the slack module and the resulting converter
impedance:
𝐺𝑘 𝑠 = 𝐺𝑠𝑙𝑎𝑐𝑘,𝑘 𝑠 ∙ 𝐺𝑐𝑜𝑛𝑣,𝑘 𝑠 , 𝑍𝑠𝑙𝑎𝑐𝑘,𝑘 𝑠 = 1/𝐺𝑘 𝑠 .
The Norton equivalent representation of the interface converter:
𝐼𝑜,𝑘 𝑠 =𝑈𝑟𝑒𝑓,𝑘(𝑠)
𝑍𝑠𝑙𝑎𝑐𝑘,𝑘(𝑠), 𝑍𝑜,𝑘 𝑠 = 𝑍𝑠𝑙𝑎𝑐𝑘,𝑘(𝑠)// 1/𝑠𝐶𝑘 .
• Experimental Impedance Identification is based on injecting of
small-signal excitation AC-voltages (≈ 5 Vac)
• Equivalent impedances on the source 𝑍1 𝑠 and the load side
𝑍2 𝑠
Hardware part: set-up
𝑍1 𝑠 =∥ 𝑉1(𝑠) ∥
∥ 𝐼1(𝑠) ∥∠𝑉1 𝑠 + ∠𝐼1 𝑠 𝑍2 𝑠 =
∥ 𝑉2(𝑠) ∥
∥ 𝐼1(𝑠) ∥∠𝑉2 𝑠 − ∠𝐼1 𝑠
/ Electrical Engineering PAGE 1520-10-2014
Contents
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
• Conclusions and Future Work
/ Electrical Engineering PAGE 1620-10-2014
DC grid at Fraunhofer IISB
/ Electrical Engineering PAGE 1720-10-2014
DC grid at Fraunhofer IISB
/ Electrical Engineering PAGE 1820-10-2014
Linear representation of the grid
Impedance identification of main components
/ Electrical Engineering PAGE 1920-10-2014
Outline
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
Test Case: Complex Grid
Test Case: Parallel Operation of Two Modules
• Conclusions and Future Work
/ Electrical Engineering PAGE 2020-10-2014
Linear representation model – 6 modules (division at Node 4)
System admittance matrix
Stability analysis of the aggregated system,
Admittance matrix
𝑍𝑙𝑒𝑓𝑡 = 1/𝑌1,4 𝑍𝑟𝑖𝑔ℎ𝑡 = 1/𝑌4,6
𝑌6,6 =
𝑌11 𝑌12 𝑌13 𝑌14 𝑌15 𝑌16𝑌21 𝑌22 𝑌23 𝑌24 𝑌25 𝑌26𝑌31𝑌41𝑌51𝑌61
𝑌32𝑌42𝑌52𝑌62
𝑌33 𝑌34 𝑌35 𝑌36𝑌43𝑌53𝑌63
𝑌44 𝑌45 𝑌46𝑌54 𝑌55 𝑌56𝑌64 𝑌65 𝑌66
20-10-2014 PAGE 21/ Electrical Engineering
Equivalent impedance representation and instability
condition
• Equivalent impedance representation with 𝑍𝑙𝑒𝑓𝑡 and 𝑍𝑟𝑖𝑔ℎ𝑡
• Instability condition: Denominator of the system transfer function
𝐺 𝑠 =1
(1+𝑍𝑙𝑒𝑓𝑡/ 𝑍𝑟𝑖𝑔ℎ𝑡)equals to 0:
𝑍𝑙𝑒𝑓𝑡
𝑍𝑟𝑖𝑔ℎ𝑡= −1, or 𝑍𝑙𝑒𝑓𝑡 + 𝑍𝑟𝑖𝑔ℎ𝑡 = 0
Bode plot: Equality of amplitudes and total phase shift of 180 ̊;
Nyquist plot: Crossing critical point (-1: 0)
20-10-2014/ Electrical Engineering PAGE 22
Bode plot of the stable system
• Instability condition is not met:
System is stable
in the whole
frequency range
20-10-2014/ Electrical Engineering PAGE 23
Nyquist plot and time-domain simulation of the
parallel model system – stable system
Nyquist plot does not encircle
the point (-1;0)
Stable amplitude of oscillations
System is stable
20-10-2014/ Electrical Engineering PAGE 24
Outline
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
Test Case: Complex Grid
Test Case: Parallel Operation of Two Modules
• Conclusions and Future Work
/ Electrical Engineering PAGE 2520-10-2014
• Two modules working in parallel:
• Objective: Prove that system can be forced to instability
by making modifications in it
Test case: parallel operation of two modules
15kW Emerson
Network power
rectifier
1x 28W Philips DC
LED Driver
20-10-2014/ Electrical Engineering PAGE 26
Achieving system instability by impedance
shaping
• Ways to shape impedance (destabilize the system):
number of modules N (amplitude shaping)
extra cable length (phase and amplitude shaping)
20-10-2014/ Electrical Engineering PAGE 27
Use case – increased number of LEDs
System approaches instability with increased number of modules
Phase shift is not 180 ̊
20-10-2014/ Electrical Engineering PAGE 28
Addition of the cable to force instability for Nled =
60 and Nrec = 1
• For calculated by the tool parameters of the cable 𝑹𝒄 = 𝟖𝟒. 𝟖 𝒎𝑶𝒉𝒎
and 𝑹𝒄 = 𝟕𝟏. 𝟑 μ𝑯 Bode plot indicated instability at 𝒇𝟎 = 𝟓𝟖𝟑. 𝟓 𝑯𝒛
Instability
20-10-2014/ Electrical Engineering PAGE 29
Nyquist plot and time-domain simulation of the
parallel model system – unstable system
Nyquist plot crosses the point (-1;0)Increasing amplitude of
oscillations
System is
unstable
20-10-2014/ Electrical Engineering PAGE 30
Ways to stabilize the system
/ Electrical Engineering PAGE 3120-10-2014
Unstable
SystemStable System
• Addition of output
capacitors
• Rearranging cables
• Changing control
parameters
Outline
• Introduction
• Voltage Stability Assessment Tool
• DC-Grid Demonstrator at Fraunhofer IISB
• Voltage Stability Analysis
• Conclusions and Future Work
/ Electrical Engineering PAGE 3220-10-2014
Conclusions
/ Electrical Engineering PAGE 3320-10-2014
• DC micro grids technology is key for sustainability and energy
efficiency in power generation
• Voltage instabilities need to be managed
• Developed tool allows for:
Voltage stability analysis and forecast at any point of the grid
based on several criteria
Assessment of complex grids with big amount of power modules
(Fraunhofer IISB office building DC-grid demonstrator)
Experimental impedance identification of power modules with
unknown internal structure
• Extra cable length and increased number of load modules lead to
system instability
• When instability is detected, the system can be modified in such a
way, that it becomes stable (adding output capacitors, rearranging
cables, changing control parameters)
Conclusions
/ Electrical Engineering PAGE 3420-10-2014
Challenges:
• No standardization
• Lack of studies available
• Real large scale micro-grid analysis is needed
Future work:
• Approach verification at the grid-demonstrator at the
Fraunhofer Institute
• Commercial deployments will require a generalized
recyclable design
The end
/ Electrical Engineering PAGE 3520-10-2014
Thank you for attention!
Questions?