Paper proposes a control strategy based on virtual impedance design .... [2] L.N.Kanh,J.Seo,Y.Kim and D.Won, âPower management strategies for grid ...
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Simulation and Analysis of Modified Droop control Using Virtual Impedance to Improve Stability and Transient Response Presented by Md. Umar Hashmi, IIT Bombay Jayesh G. Priolkar, Goa College of Engineering
Objective • Paper proposes a control strategy based on virtual impedance design criteria and modification in conventional droop control • Proposed strategies improves transient response, stability and power sharing for parallel operated inverters interfaced with Distributed generation sources • The control technique does not require any communication and automatically compensates for parameter variations in network
• Mathematical analysis and simulation results are presented in the paper to prove the concept behind the control strategies
2
Inverter/UPS Parallel Operation
3
Introduction to Virtual Impedance Electrical Inverter
Controller Generating PWM
V
Electrical Load
Virtual Impedance
Controller uses impedance as number to make system perform in same way as if impedance exists in system, due to virtual characteristic of impedance, it incurs no actual power loss
• Virtual impedance to improve transient response and stability among parallel connected inverter interfaced DG sources. • Provides damping effect • Power decoupling, essential for implementation of droop control 4
Proposed Mathematical Model for Virtual Impedance
Under no load condition Z1||Zload = Z1 and Z2||Zload = Z2. Therefore it can be simplified as
5
Conventional vs Modified Droop Control Control Loops Inverter Current
Clock
Conventional Droop Control Freqref
X
P Voltage Current
Power Calculation
ω s+ω
SIN(X)
m
ω s+ω
n
Q
X
+
Kp + Ki/s
-
Inductor Current
Vref
R
Proposed Droop Control Inverter Current
Clock Freqref P Voltage Current
Kp
Power Calculation
Q
X
+
L
SIN(X)
m n
X Vref
Kp + Ki/s
+
-
Kp
-
Inductor Current 6
Conventional vs Modified Droop Control Control Response Comparison of Transfer Functions
System: Conventional Droop Control Gain Margin (dB): -96.4 At frequency (rad/sec): 49.6 Closed Loop Stable? No
150
Bode Diagram Modified Droop
100
Conventional Droop Control
Magnitude (dB)
50 System: Modified Droop Gain Margin (dB): 78.4 At frequency (rad/sec): 1.67e+003 Closed Loop Stable? Yes
0 -50 -100 -150 -200 270 System: Modified Droop Phase Margin (deg): 89.7 Delay Margin (sec): 3.14 At frequency (rad/sec): 0.499 Closed Loop Stable? Yes
Phase (deg)
180 90
Modified Droop Conventional Droop Control
0 -90 -180 -270 -1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Frequency (rad/sec)
7
Conventional vs Modified Droop Control Damping Provided for Sustained Oscillations & Transient Response Active Damping 6000
Active Power Transient Response 4500
5000
4000
4000 3000 2500
Watts
Active Power (Watt)
3500
2000
3000 2000
1500
1000
1000 Droop Control Modified Droop Proposed
500 0
0.1
0.15
0.2
0.25 Time(s)
0.3
0.35
Modified Droop Control Inverter 2 Active Power Shared Conventional Droop Control Inverter 2 Active Power Shared
0 0.4
-1000
0
1
2
3
4
5
Time
Settling Time (sec) Active Power overshoot (Watts)
Conventional Droop 0.1986 215.1708
Modified Droop 0.1737 127.4755
% Improvement 12.53776 40.75613
8
Individual Inverter Control
Inverter Control 9
Simulink Model
10
Simulation Parameters Parameters
Values
Inverter Rating Rated RMS Voltage Kpv Kiv Kpi m1 m2 n1 n2 Line Impedance LC Filter Inverter1 LC Filter Inverter2 Load 1 Load 2 Low Pass 1 (Power Calc) Low Pass 2 Virtual Impedance 1 Virtual Impedance 2 Zratio DC Link Voltage
6 kVA 222.7 Volt (Single phase) 1 100 10 1e-4 1e-6 0.009 2e-6 R=4e-3, L=1.9910e-005 Rl=0.2,L=1e-3, C=20e-6 Rl=0.2,L=0.8e-3, C=18e-6 8000 Watt +2000j VAR 2000 Watt +1800j VAR 5 Hz Cut off 200 Hz Cut off R=0.205 L=10.2078-004 R=0.205 L=10.2097-004 1.8 400 V 11
Simulation Results Linear Load Inverter 1 and 2 Voltage
Active Power Shared 6000
300
5000
200
100
3000
Volts
Watt
4000
0
2000
-100 Inverter 1 Active Power Inverter 2 Active Power
1000
-200 0 0
0.5
1 Time(s)
1.5
2
-300 0.9
0.95
Reactive Power Shared
1 Time(s)
1.05
1.1
Inverter 1 and 2 Current
1400
50
1200
40
Inverter 1 Current Inverter 2 Current
30
1000
20
800 Ampere
Vars
10
600
0 -10
400
-20
200 0 -200
-30
Inverter 1 Reactive Power Inverter 2 Reactive Power
0
0.5
1 Time(s)
1.5
-40
2
-50 0.9
0.95
1 Time(s)
1.05
1.1
12
Simulation Results Linear Load 10
3
Active Power Accuracy Reactive Power Accuracy
0
Net Circulating Current 2
-10
1
-30
Amperes
Watt/Var
-20
-40
0
-50 -1
-60 -70
-2
-80 -90
-3
0
0.5
1 Time(s)
1.5
2
0
0.5
1 Time(s)
1.5
2
13
Simulation Results Nonlinear Load Inverter 1 and 2 Current for Nonlinear Load
Inverter 1 and 2 Voltage for Nonlinear Load
8
300 Inverter 1 Voltage Inverter 2 Voltage
200
Inverter 1 Current Inverter 2 Current
6 4
100
Amperes
Volts
2 0
0 -2
-100
-4 -200
-6 -300 1.5
1.52
1.54
1.56 Time(s)
1.58
1.6
-8 1.5
1.52
1.54
1.56
1.58
1.6
Time(s)
Nonlinear load used in simulation
14
CONCLUSIONS • Paper proposes modification in conventional droop control • The control strategy enhances stability, improves transient response and provides damping for sustaining parameter mismatches which leads to flow of circulating current among power sources. •Mathematical model for virtual impedance design is also presented. •A systematic way to calculate virtual impedance for compensation of impedance mismatches has been explored.
•Simulation results validate the performance of the system. •Control analysis indicates inherent closed loop stability and improved transient response of the proposed modified droop control
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