voltage stability assessment in low- voltage...

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







DC micro-grids: typical structure

Use of

sustainable

energy sources

Connection to

AC mains

Battery storage

Car charging

capabilities

Direct use of DC

power


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)


Loads Sources

V


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


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







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


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


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


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:


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


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


Contents

• Introduction






DC grid at Fraunhofer IISB


DC grid at Fraunhofer IISB


Linear representation of the grid

Impedance identification of main components


Outline

• Introduction




Test Case: Complex Grid

Test Case: Parallel Operation of Two Modules



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


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


Outline

• Introduction




Test Case: Complex Grid

Test Case: Parallel Operation of Two Modules



• 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


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)


Use case – increased number of LEDs

System approaches instability with increased number of modules

Phase shift is not 180 ̊


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


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


Ways to stabilize the system


Unstable

SystemStable System

• Addition of output

capacitors

• Rearranging cables

• Changing control

parameters

Outline

• Introduction






Conclusions


• 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


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


Thank you for attention!

Questions?

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