1
Comparison of Full and Reduced Scale Solar
PV Plant Models in Multi-Machine Power
Systems
Sachin Soni, George Karady, Mahesh Morjaria,
and Vladimir Chadliev
IEEE Transmission and Distribution Conference 2014
Chicago, Illinois
2
Presentation Outline
1.
2.
3.
4.
5.
6.
Grid Connected Solar PV Plants
Centralized PV plant model for load flow representation
PV Plant model components / subsystems
Modified IEEE 39 bus test system
Model Simulation results
Conclusions
3
Grid Connected PV Plant Topology
WECC Guide for Representation of Photovoltaic Systems in Large-Scale Load Flow Simulations, August 2010
4
Load Flow Representation
WECC Renewable Energy Modeling Task Force (REMTF) PV Plant Power Flow Model
•
Equivalent generator represents the total generating capacity of all inverters
•
Equivalent pad-mounted transformer represents aggregate effect of all step-up transformers
•
Equivalent collector system branch represents the aggregate effect of the PV plant collector
system
Model approximate PV plant load flow characteristics at the interconnection point
WECC Guide for Representation of Photovoltaic Systems in Large-Scale Load Flow Simulations, August 2010
5
Collection System Equivalent
𝑍𝑒𝑞 = 𝑅𝑒𝑞 + 𝑗𝑋𝑒𝑞 =
𝐼
2
𝑖=1 𝑍𝑖 𝑛𝑖
𝑁2
𝐵𝑒𝑞
𝑅𝑒𝑞
𝑋𝑒𝑞
𝐼
𝐵𝑒𝑞 =
𝐵𝑖
𝑖=1
E. Muljadi, C. P. Butterfield, A. Ellis, J. Mechenbier, J. Hochheimer, R. Young, N. Miller, R. Delmerico, R. Zavadil,
and J. C. Smith, "Equivalencing the Collector System of a Large Wind Power Plant," in IEEE PES General
Meeting, June 2006.
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Overall Model Structure for Central Station PV system
Overall model structure consists of the following •
Generator model (REGC_A) to provide current injections into the network solution
•
Electrical control model (REEC_B) for local active and reactive power control
•
Optional plant controller model (REPC_A) to allow for plant-level active and reactive power
control
WECC Generic Solar Photovoltaic System Dynamic Simulation Model Specification – September 2012
7
Generator /Converter Model Functional Block Diagram
Current regulator to inject inverter
current into external network in
response to real and reactive current
commands.
•
User settable reactive current
management during high voltage
events at the generator (inverter)
terminal
•
Active current management during
low voltage events to approximate
the response of the inverter PLL
controls during voltage dips
•
Power logic during low voltage
events to allow for a controlled
response of active current during
and immediately following voltage
dips
WECC Generic Solar Photovoltaic System Dynamic Simulation Model Specification – September 2012
8
Electrical Controller Model
Local Reactive Power Control
• Constant power factor,
based on the inverter
power factor
• Constant reactive
power, based either on
the inverter absolute
reactive power or,
plant controller model
Local Active Power
Control
•
•
Reference active
power from solved
power flow case or
from power plant
controller model.
Current Commands
subject to Converter
thermal ratings
WECC Generic Solar Photovoltaic System Dynamic Simulation Model Specification – September 2012
9
Multi-Machine Plant Model
POI
Utility Grid
230 kV Gen-Tie
R = 0.155760 Ohms/mile
X = 0.741302 Ohms/mile
Xc = 0.17320 Mohms/mile
Length = 1.0 Mile
230 kV Line A
R = 0.099560 Ohms/mile
X = 0.777181 Ohms/mile
Xc = 0.1817 Mohms/mile
Length = 2.1 Mile
230 kV Gen-Tie
Bus
230 kV Bus A
Y
Y
SUT-A
Size 54 MVA
Primary230 kV Wye Grounded
Sec 34.5 kV Wye Grounded
%Z = 9.000%
X/R = 43.7
34.5 kV
01-PVCS
25.20 MW
SUT-B
Size 54 MVA
Primary 230 kV Wye Grounded
Sec 34.5 kV Wye Grounded
%Z = 9.000%
X/R = 43.7
Y
•
Two Machine Model – Equivalenced
at 34.5 kV PVS buses
•
Five Machine Model – Equivalenced
at 34.5 kV medium voltage PVCS
collector system bus
SW-SWGR #B
34.5 kV Bus
Feeder 2
Feeder 3
R = 0.11670 Ohms/mile
X = 0.76658 Ohms/mile
Xc = 0.1776 Ohms/mile
2.1 mile
34.5 kV
02-PVCS
36.54 MW
Single Machine model Equivalenced at POI
Y
34.5 kV PVS Bus
34.5 kV Bus
R = 0.15100 Ohms/mile
X = 0.78052 Ohms/mile
Xc = 0.1819 Ohms/mile
1.4 mile
•
230 kV Bus B
SW-SWGR #A
Feeder 1
Possible Representations
230 kV Line B
R = 0.099560 Ohms/mile
X = 0.777181 Ohms/mile
Xc = 0.1817 Mohms/mile
Length = 2.3 Mile
R = 0.11670 Ohms/mile
X = 0.76658 Ohms/mile
Xc = 0.1776 Ohms/mile
2.1 mile
34.5 kV PVCS Bus
Feeder 4
Feeder 5
R = 0.11670 Ohms/mile
X = 0.76658 Ohms/mile
Xc = 0.1776 Ohms/mile
1.8 mile
34.5 kV
03-PVCS
30.24 MW
34.5 kV
04-PVCS
28.98 MW
R = 0.11670 Ohms/mile
X = 0.76658 Ohms/mile
Xc = 0.1776 Ohms/mile
2.2 mile
34.5 kV
05-PVCS
26.46 MW
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IEEE 39 Bus Test System
Modifications to IEEE 39 Bus System
•
Power output of generator 9 connected at Bus
38 is reduced to 100 MW.
•
In order to maintain same power injection at
Bus 29 as in actual system the load at Bus 29 is
disconnected.
•
Voltage regulator and power system stabilizer
of generator 9 were disconnected to expose PV
plant to more severe conditions.
PV Plant Model
•
Full scale model comprises of 117 inverters
•
Each inverter rated at 1350 kVA with power
factor operating range from 0.93 lead to 0.93
lag
•
9-cycles LLLG fault is applied at Bus 26
T. Athay, R. Podmore, and S. Virmani, "A Practical Method for the Direct Analysis of Transient Stability," in IEEE Transactions on Power
Apparatus and Systems, vol. PAS-98, pp. 573-584, 1979
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Feeder Impedance For Each Scenario
•
System equivalent impedance calculated using WECC power flow modeling guide
•
Collection system impedance for each scenario on 34.5 kV and 100 MVA base
Test Scenarios
Section
All Sections
Full Scale Model
Single-Machine model Full feeder
Two-Machines model
Five-Machines model
Section-I
Section-II
Section-I
Section-II
Section-III
Section-IV
Section-V
R (p.u.)
X (p.u.)
B (p.u.)
0.00504
0.00493
0.01226
0.00812
0.02189
0.02382
0.02314
0.00327
0.02841
0.00201
0.02681
0.06558
0.04488
0.09342
0.13667
0.13641
0.12009
0.14302
0.00022
0.03261
0.01432
0.01829
0.00534
0.00898
0.00692
0.00602
0.00565
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Response for One Machine and Full Scale Models
1.2
1.2
One Machine
Equivalent
BUS 40
0.8
0.6
Single Equivalent
Inverter rated 157.95
MVA, p.f. operating
range of +/- 0.93
0.4
0.2
0
1.15
2.33
3.53
4.73
5.93
7.13
8.33
105
75
45
15
-15
2.33
3.53
4.73
5.93
7.13
8.33
160
140
120
100
80
60
40
20
0
9.53
Full Scale Model
117 Inverters each rated 1.35 MVA
All capable of +/- 0.93 p.f.
0.00
1.15
2.33
3.53
4.73
Time (Sec.)
5.93
7.13
8.33
9.53
0.00
1.15
2.33
3.53
4.73
5.93
7.13
8.33
9.53
0.00
1.15
2.33
3.53
4.73
5.93
7.13
8.33
9.53
0.00
1.15
2.33
3.53
4.73
5.93
7.13
8.33
9.53
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
1.4
Active Power (MW)
Active Power (MW)
1.15
0.4
101
125
155
190
217
0
165
0.00
0.6
9.53
135
BUS
BUS
BUS
BUS
BUS
0.8
0.2
Reactive Power (MVAR)
Reactive Power (MVAR)
0.00
1
Voltage (p.u.)
Voltage (p.u.)
1
1.2
1
0.8
0.6
0.4
0.2
0
Time (Sec.)
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Response for Two Machine and Five Machine Models
1.2
Two Machine Equivalent
BUS 40
BUS 45
0.8
0.6
Equivalent Inverter 1 rated 66.15 MVA
1
Equivalent Inverter 2 rated 91.90 MVA
0.8
p.f. operating range of +/- 0.93
0.4
1.2
Voltage
(p.u.)
Voltage
(p.u.)
1
0.2
1.15
2.33
3.53
4.73
5.93
7.13
8.33
0
0.00
9.53
Reactive Power (MVAr)
70
50
30
10
1.15
2.33
3.53
4.73
5.93
7.13
8.33
Active Power
(MW)
2.33
3.53
4.73
5.93
7.13
8.33
1.15
2.33
3.53
4.73
5.93
7.13
8.33
1.15
2.33
3.53
4.73
5.93
Time (Sec.)
7.13
9.53
Five Machine Equivalent
Equivalent Inverter 1 rated 27.00 MVA
60
Equivalent Inverter 2 rated 39.15 MVA
Equivalent Inverter 3 rated 32.40 MVA
30
Equivalent Inverter 4 rated 31.05 MVA
Equivalent Inverter 5 rated 28.36 MVA
1.15
2.33
3.53
4.73 5.93
Time (Sec.)
7.13
8.33
9.53
35
25
15
5
-5
0.00
9.53
90
0
0.00
1.15
50
52
54
56
58
45
p.f. operating range of +/- 0.93
9.53
40
Active Power
(MW)
Reactive Power
(MVAr)
90
-10
0.00
0.6
0.4
0.2
0
0.00
BUS
BUS
BUS
BUS
BUS
30
20
10
0
0.00
8.33
9.53
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Steady State and Dynamic Simulation Results at POI
Measured Parameters at POI
Simulated Cases
Active Power
(MW)
Reactive Power
(MVAr)
Voltage
(p.u.)
Single Machine Equivalent
144.8
-23.5
1.062
Two Machine Equivalent
144.8
-23.7
1.061
Five Machine Equivalent
144.9
-23.7
1.061
Full Scale Model
144.9
-23.7
1.061
•
Root mean square (RMS) error for voltage
respectively.
•
Reduced order models are suitable for both
online (operation) and offline (stability)
studies
POI during steady-state analysis.
Ensures computational efficiency without loss
•
of any information about system behavior.
1
Voltage at POI (p.u.)
model are 0.06%, 0.28% and 0.357%
Active power, Reactive power and Voltage at
1.2
measured at POI for one-machine, twomachine and five-machine reduced scale
No significant change observed in measured
•
ONE MACHINE MODEL
TWO MACHINE MODEL
FIVE MACHINE MODEL
FULL SCALE MODEL
0.8
0.6
0.4
0.2
0
0.00
1.15
2.33
3.53
4.73
Time (Sec.)
5.93
7.13
8.33
9.53
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Conclusions
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RMS error calculated for measured voltage response is less than even 1%.
•
Ensures computational efficiency without loss of any information about system
behavior.
•
Reduced order model can represent the complete PV plant in similar manner as a
full scale model.
•
Reduced order models are suitable for both online (operation) and offline
(stability) studies
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Questions?