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Contract No. DE-AC36-08GO28308

User Guide for PV Dynamic 

Model Simulation Written on 

PSCAD Platform

E. Muljadi, M. Singh, and V. Gevorgian

National Renewable Energy Laboratory

Technical Report

NREL/TP-5D00-62053

November 2014 
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

User Guide for PV Dynamic 

Model Simulation Written on 

PSCAD Platform

E. Muljadi, M. Singh, and V. Gevorgian

National Renewable Energy Laboratory

Prepared under Task No. SS13.2020

Technical Report

NREL/TP-5D00-62053

November 2014 
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

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iii

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Acknowledgements

This report was completed based on the generosity of many supporters and collaborators

interested in contributing to and expediting PV generation and deployment. Support was 

provided in the forms of technical discussion, advice and recommendations, and data and 

reference sharing. We would like to thank Kara Clark at the National Renewable Energy 

Laboratory; Abe Ellis and Mark Ralph at Sandia National Laboratories; Pouyan Pourbeik 

at the Electric Power Research Institute; Yuriy Kazachkov at Siemens Power 

Technologies International; Juan Sanchez Gasca from GE; Farbod Jahan at Quanta;

Xiaoyu Wang and Yue Meng at Brookhaven National Laboratory; Richard Bravo, Juan 

Castaneda, and Bob Yinger at Southern California Edison; Hassan Ghoudjehbaklou at 

San Diego Gas and Electric; Amy Carter and Jose Conto at the Electric Reliability 

Council of Texas; Professor Fernando Mancilla-David at the University of Colorado at 

Denver; Professor Emilio Gomez-Lazaro and Andres Honrubia Escribano at the 

Universidad de Castilla-La Mancha, Spain; Ryan McMorrow at Florida Power and Light;

Om Nayak, Aung Phyo That, and Chatura Pratabandi from Nayak Corporation; Vijay 

Bhavaraju at Eaton Corporation; Ken Christensen at SMA; and Antonio Ginart at 

SolarMax.
iv

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List of Acronyms

AC alternating current

CR-CSI current-regulated current-source inverter

CR-VSI current-regulated voltage-source inverter

CSI current-source inverter

DC direct current

HVRCM high-voltage reactive-current management

IEEE Institute of Electrical and Electronics 

Engineers

IGBT insulated-gate bipolar transistor

LLG line-to-line-to-ground

LVACM low-voltage active-current management

LVPL low-voltage power logic

PV photovoltaic

REEC renewable energy electrical controller

REGC renewable energy generator controller

REMTF Renewable Energy Modeling Task Force

REPC renewable energy plant controller

SLG single-line-to-ground

STATCOM static compensation

SVC static VAR compensator

VSI voltage-source inverter

WECC Western Electricity Coordinating Council
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Executive Summary

This document describes the dynamic photovoltaic (PV) model developed by the 

National Renewable Energy Laboratory and is intended as a guide for users of these 

models. It is divided into five sections.

Section 1 presents the overview, and Section 2 presents different types of power 

converters. We begin with a discussion of the basic PV inverter and the control 

philosophy adapted for a power electronics-based generator, which we then contrast to

the control philosophy for a conventional synchronous generator. A phasor diagram is 

used to represent the voltages and currents, including the magnitude and the phase angle; 

it is referred to throughout this application guide. Additional discussion is provided about

the deployment of synchrophasors (phasor measurement units) throughout the power 

system network, which in the future will make controlling and implementing PV 

inverters and PV power plants easier. Because most PV inverters that are available in the 

market are based on a current-source inverter, we discuss this type of converter in detail 

to understand its operation and components.

Section 3 presents the control implementation of a PV inverter and a PV plant. The 

Renewable Energy Modeling Task Force (REMTF) of the Western Electricity 

Coordinating Council (WECC) developed an excellent document titled Generic Solar 

Photovoltaic System Dynamic Simulation Model Specification. The control diagrams 

presented in Section 3 are based on the PSCAD implementation of the WECC-REMTF

control blocks derived from this document.

Section 4 gives examples of dynamic model validations using the data gathered from 

monitoring two PV plants. One of the two PV plants is a single-phase PV plant; the other 

is a three-phase PV power plant. When validating dynamic models, the input parameters 

are usually tuned and adjusted so that the output of the simulations matches the measured 

data. The tuned input parameters are documented and used to perform different 

simulations for the particular inverter and PV plant.

Finally, Section 5 presents the summary and conclusion, and the appendix presents the 

input parameters for the REMTF controllers. This input data is available from the 

WECC-REMTF document. Note that the PV inverter or PV plant is unique. The input 

parameters given in the appendix are generic typical input data. To ensure that the PV 

inverter and the PV plant dynamic models are well represented, the input data for the 

dynamic models provided by the PV inverter and PV plant owner/operator must be used.
vi

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Table of Contents

List of Figures............................................................................................................................................vii

List of Tables.............................................................................................................................................viii

1 Introduction ...........................................................................................................................................1

2 Basic Three-Phase PV Inverter............................................................................................................2

2.1 Basic Control of Real and Reactive Power in a Two-Bus Power System........................................2

2.1.1 Conventional Power System..............................................................................................3

2.1.2 Power-Converter-Based Power System.............................................................................4

2.2 Current-Source Inverter (CSI)—Average Model.............................................................................6

2.3 CSI—Detail Model.........................................................................................................................10

2.3.1 Power-Switching Control ................................................................................................10

2.3.2 Current-Regulated CSI....................................................................................................11

2.4 Voltage-Source Inverter (VSI)—Detail Model..............................................................................14

3 Controlling the Grid-Side Inverter and Power Plant........................................................................19

3.1 Device Level...................................................................................................................................20

3.2 Generator Level..............................................................................................................................20

3.2.1 REGC ..............................................................................................................................20

3.2.2 REEC...............................................................................................................................26

3.3 Plant Level......................................................................................................................................32

3.3.1 REPC...............................................................................................................................33

4 PV Dynamic Model Validation............................................................................................................38

4.1 Three-Phase PV Plant Validation...................................................................................................38

4.1.1 Detailed Model Implementation......................................................................................38

4.1.2 Average Model Implementation......................................................................................40

4.2 Single-Phase PV Plant Validation..................................................................................................42

5 Summary..............................................................................................................................................44

References .................................................................................................................................................45

Appendix: Control Blocks—REPC, REEC, and REGC...........................................................................46

REPC ....................................................................................................................................................46

REGC....................................................................................................................................................48

REEC ....................................................................................................................................................50
vii

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List of Figures

Figure 1. A typical three-phase PV inverter with IGBT power switches ................................................2

Figure 2. Illustration of a two-bus system demonstrating the voltage and reactive power 

flow in a synchronous generator ........................................................................................................3

Figure 3. Illustration of a two-bus system demonstrating real power control in a 

conventional synchronous generator.................................................................................................4

Figure 4. Illustration of a two-bus system in a PV inverter-based system with its 

corresponding phasor diagram...........................................................................................................5

Figure 5. Illustration of a phasor diagram to demonstrate real and reactive power control in 

a PV inverter ..........................................................................................................................................6

Figure 6. Illustration of an average model of a CSI synthesizing a PV inverter....................................6

Figure 7. Illustration of a PV inverter equivalent circuit representing a three-phase current 

source connected to the grid and the corresponding terminal voltage phasor, Vpv, and 

the output current phasor, Is, decoupled into Ip and Iq......................................................................7

Figure 8. Diagram illustrating the monitored voltage and current and the phase-locked 

loop to synchronize the reference frame to the terminal voltage....................................................8

Figure 9. Diagram illustrating the real and reactive power reference per unit to compute the 

peak of the actual reference currents Iq and Id...................................................................................8

Figure 10. Diagram illustrating the base value calculations to be used in the control blocks ...........9

Figure 11. Diagram illustrating the reference currents to generate the specified real power 

reference, Pgrid_pu, and the specified reactive power reference, Qgrid_pu...........................................9

Figure 12. Real current, Ipvd_ref, and reactive reference current, Ipvq_ref, signals in the 

synchronous reference frame ...........................................................................................................10

Figure 13. The three-phase reference signals—Ipvaref, Ipvbref, Ipvcref—in the stationary 

reference frame ...................................................................................................................................10

Figure 14. Diagram illustrating a three-phase CSI implementation with the actual six power 

switches (IGBTs).................................................................................................................................10

Figure 15. Diagram illustrating the logic circuits to turn the power switches in a CSI on and 

off in the correct order........................................................................................................................11

Figure 16. Diagram illustrating the real and reactive power references, per unit, to compute 

the peak of the reference currents, Iq and Id.....................................................................................11

Figure 17. Diagram illustrating the inverse Park and inverse Clarke transformations to 

convert the synchronous referenced current signals, Iq and Id, into the stationary 

reference frame current signals, Ia, Ib, and Ic....................................................................................12

Figure 18. Phase voltage, Vpva, monitored at the terminal of the power converter ............................12

Figure 19. Line-to-line voltage, Vpvab, monitored at the terminal of the power converter..................12

Figure 20. Line current output, Ia, of the power converter....................................................................13

Figure 21. The real and reactive power measured at the output of the power converter..................13

Figure 22. Three-phase line currents measured at the high side of the substation 

transformer..........................................................................................................................................13

Figure 23. Three-phase voltage measured at the high side of the substation transformer ..............14

Figure 24. Diagram illustrating the three-phase VSI implementation with the actual six 

power-switches (IGBTs).....................................................................................................................14

Figure 25. Diagram comparing the control philosophy of the CR-CSI to the CR-VSI ........................15

Figure 26. Diagram comparing the control philosophy of the CR-CSI to the CR-VSI ........................15

Figure 27. Diagram illustrating the three-phase voltage signal reference used to trigger the 

firing circuits of the VSI......................................................................................................................16

Figure 28. The transformation from Vpv (a,b,c) into Vpvd and Vpvq in the synchronous 

reference frame ...................................................................................................................................17

Figure 29. The transformation from Ipv (a,b,c) into Isd and Isq in the synchronous reference 

frame.....................................................................................................................................................17

Figure 30. The logic circuits to turn the power switches in the CSI on and off in the correct 

order.....................................................................................................................................................17

Figure 31. Per-phase voltage and line current of the CR-VSI ...............................................................18

Figure 32. Block diagram representing a PV power plant.....................................................................19
viii

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Figure 33. Phasor diagram illustrating commanded current and its real and reactive 

components.........................................................................................................................................20

Figure 34. Block diagram illustrating the HVRCM controller to inject additional inductive 

current during a high-voltage event..................................................................................................21

Figure 35. Block diagram illustrating the HVRCM controller to inject additional inductive 

current during a high-voltage event..................................................................................................22

Figure 36. Block diagram illustrating the LVACM controller to adjust the real current 

component (Ipcmd) during a low-voltage event .................................................................................23

Figure 37. Scaled voltage to adjust the Pord during a low-voltage event.............................................24

Figure 38. LVPL calculation to set the upper limit of Ipcmd during a low-voltage event......................25

Figure 39. Block diagram illustrating the computation of the reactive power input 

command Qin .......................................................................................................................................26

Figure 40. Reactive power and voltage control......................................................................................27

Figure 41. Identifying abnormal voltage to set Volt_dip .......................................................................28

Figure 42. Diagram illustrating an additional reactive current injection during an abnormal 

voltage event (Volt_dip = 1) ...............................................................................................................29

Figure 43. Block diagram illustrating a method to compute an additional reactive current 

injection during an abnormal voltage event (Volt_dip = 1).............................................................29

Figure 44. Block diagram illustrating a method to compute the real current component, 

Ipcmd .......................................................................................................................................................29

Figure 45. Block diagram illustrating a method to compute the current limits for the real 

and reactive current components .....................................................................................................30

Figure 46. Phasor diagrams illustrating the P-priority and Q-priority .................................................31

Figure 47. Block diagram illustrating a method to freeze the operating current during 

voltage dips .........................................................................................................................................32

Figure 48. Single-line diagram illustrating a PV plant with a single generator...................................33

Figure 49. Control block diagram illustrating voltage regulation for a remote bus ...........................34

Figure 50. Single-line diagram illustrating a method to accomplish different remote voltage 

regulations...........................................................................................................................................34

Figure 51. Control block diagram illustrating a method to regulate reactive power..........................35

Figure 52. Control block diagram illustrating a method to regulate real power.................................36

Figure 53. Single line diagram describing real power control in remote location..............................36

Figure 54. Graphical illustration of real power regulation during a frequency excursion.................37

Figure 55. Single-line diagram illustrating the dynamic model validation ..........................................38

Figure 56. Circuit diagram illustrating the dynamic model validation for a detailed model..............39

Figure 57. Real and reactive power output of the simulations.............................................................39

Figure 58. Voltage and current waveforms using a detailed model representation for (a) 

voltages measured, (b) currents measured, and (c) currents simulated......................................40

Figure 59. Circuit diagram illustrating the dynamic model validation of an average model.............40

(b) Three-phase voltages and currents ...................................................................................................41

Figure 60. Comparison of the simulation output to the measured output for an average 

model....................................................................................................................................................41

Figure 61. Diagram illustrating a single-phase PV plant circuit ...........................................................42

Figure 62. The voltage used to drive the simulation and the corresponding real and 

reactive power output.........................................................................................................................42

Figure 63. Output current waveforms and magnitude...........................................................................43

List of Tables

Table A-1. Parameters for the REPC........................................................................................................47

Table A-2. Parameters for the REGC .......................................................................................................49

Table A-3. Parameters for the REEC........................................................................................................51
1

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1 Introduction

The goal of the subtask on transient solar modeling (SS13-2020) is to develop and validate 

generic, open-source, flexible, three-phase, cycle-by-cycle models of photovoltaic (PV)

inverters, PV plants, and their associated controls in PSCAD and disseminate these models to 

industry via an application guide and technical papers and reports.

The term generic is used to describe a model that is not specific to any manufacturer, which 

means that a dynamic model should be able to represent PV inverters from different 

manufacturers and not be specific to only one manufacturer. Different editions of PV inverters

from the same manufacturer may implement similar control strategies but different ranges of 

settings. For example, various regional or market segments may have different grid codes, and a

PV inverter may be set to accommodate local grid codes. The input parameters of the dynamic 

model to represent the PV plant at this location must be adapted accordingly. The dynamic 

model is also an open source; thus, it is easy to modify. Only the original file will be kept 

unchanged. The model also needs to be flexible so that changes can be made and/or added to the 

control block diagram to suit the specific design of a PV inverter or a specific PV plant. Also, 

this model is based on three phases; thus, the three phases—a, b, and c—are represented, instead 

of positive sequences only. This means that all the symmetrical components—positive sequence, 

negative sequence, and zero sequence—can be represented. This is important for a PV inverter, 

because many PV inverters are single phase, and many PV inverters are installed in the 

distribution network, which is susceptible to unbalanced conditions (from the network or 

voltages).

The completed PV generation dynamic model developed in this subtask is built on the PSCAD 

platform. The PV industry lacks such a model, and this project proposed to fill that gap down to 

the switch details via PSCAD. PSCAD allows for the analysis of unbalanced faults, such as 

single-line-to-ground (SLG) or line-to-line-to-ground (LLG), a key characteristic distinguishing 

PSCAD models from other dynamic models that focus on positive sequence behavior (e.g., PSLF 

and PSS/E). This program is intended as a cycle-by-cycle model of PV inverters, and it is built 

with detailed circuitry of the power converter (including the power semiconductor switches);

thus, a detailed analysis of a PV inverter can be accomplished. For example, we can observe the

dynamic of the voltage on the direct-current (DC) bus during the transmission faults, or we can 

observe the dynamic of the output currents and powers when one of the power semiconductor 

switches is damaged or misfired. The model is also intended to include the collector system of 

the PV plants and other plant-level controllers. The control architecture is based on the one 

developed by the Renewable Energy Modeling Task Force of the Western Electric Coordinating 

Council (WECC). There are three major blocks: the (1) renewable energy plant controller

(REPC), (2) renewable energy electrical controller (REEC), and (3) renewable energy generator 

controller (REGC). The control block diagrams and their corresponding list of parameters are 

presented in the appendix.

In the previous report [1], we described the process of PV generation from the PV cell to the 

power converter, which includes the maximum power point tracker. In this report, we present 

different types of power converters (in Section 2), the control implementation (in Section 3), and 

the dynamic model validation (in Section 4). Finally, the summary and conclusion are presented 

in Section 5.
2

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2 Basic Three-Phase PV Inverter

A three-phase PV inverter is usually designed for a three-phase system with a large rating (10

kW–2 MW and above). Most PV inverters are current controlled. To understand a basic PV 

inverter, it is important to understand the module and PV inverter hardware. In general, a PV 

inverter consists of a DC bus and three pairs of power semiconductors, also called power 

electronic switches or power switches. The most common power switches presently used are

insulated-gate bipolar transistors (IGBT). An IGBT can be turned on and off very fast within 

microseconds (thus, the loss from power switching is low), and it has a low conduction loss.

Figure 1. A typical three-phase PV inverter with IGBT power switches

2.1 Basic Control of Real and Reactive Power in a Two-Bus Power 

System

In this section, we use a two-bus system to illustrate real and reactive power for conventional 

generation and generation based on power converter based generation. We assume that the 

generator, Vpv (Bus 1), is connected to an infinite bus, Vs (Bus 2). In a conventional power plant 

with a synchronous generator, the following quantities are usually used to control the output of 

the generator:

• The voltage magnitude is used to control the reactive power (or reactive current 

component, Iq by controlling the excitation winding, thus increasing the voltage of Vpv.

• The mechanical power is used to control the phase angle of the output voltage of the 

synchronous generator. The power angle, d, of the output voltage mostly corresponds to

the real current component, Ip, of the output current, Is, of the voltage source.

A similar method can be used for a PV inverter, except we attempt to control the current directly.
3

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2.1.1 Conventional Power System

2.1.1.1 Reactive Power Control

To understand a PV inverter and to simplify the analysis, let us consider an average model.

Because the relationship of the reactive power to the terminal voltage is very tight, either the 

reactive power control or the voltage control is generally used. The phasor diagram concept is 

very useful to visualize the real power, reactive power, voltage, and current. It is also timely, as 

the synchrophasor measurements to monitor these quantities are available and have been 

installed massively in the modern power system network. The fundamental understanding of 

power systems in references [2, 3] and the concept and applications of synchrophasor 

measurement can be found in the references [4, 6]. 

To describe the relationship between the reactive power flow and the voltage level, refer to the 

phasor diagram shown in Figure 2. It is assumed that the PV inverter (terminal voltage, Vpv) is 

connected to an infinite bus, Vs, through a reactance, Xs. The PV inverter (Vpv) generates an 

output current, Is. The equation describing the relationship of the voltage at the two buses and the 

corresponding voltage drop across the reactance, Xs, can be written as follows:

Vpp = Vs + j Xs Is

The reactive power losses (Is2 Xs) in the transmission line can be supplied from Bus 1 (Vpv) or 

Bus 2 (Vs), or they can be shared by both sides. Parallel compensation (e.g., capacitor banks) can 

be implemented on both sides. Reactive compensation can be implemented by controlling the 

generator itself (internal control), or it can be provided externally, such as from adjustable 

capacitor banks, synchronous condensers, and static power compensation (a static VAR 

compensator, SVC; or static compensation, STATCOM).

G1

XS

IS

Grid

PV POI

Inverter

a) PVP simplified equivalent circuit

VPV VS

jXSIS IS de

VS

f = 0.5 de

b) QE = QVs = 0.5 IS

2 XS

VPV

jXSIS de

VS

f = 0o

IS 

c) QVs =0; QE = IS

2 XS

VPV

jXSIS de

VS f < 0o

IS 

d) QVs = - VS IS cos f ; QE = IS

2 XS + |QVs|

VPV

Figure 2. Illustration of a two-bus system demonstrating the voltage and reactive power flow in a 

synchronous generator
4

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Consider Figure 2 (a), in which all the reactive power spent in the reactance, Xs, is supplied by 

Bus 1. As shown, the voltage Vpv > Vs, to make it possible for the reactive power to flow from 

Bus 1 to Bus 2. Similarly, as shown in Figure 2 (b), all the reactive power spent in the reactance,

Xs, is supplied by Bus 2. In this case, the relationship between the two voltages is Vpv < Vs. Now 

consider Figure 2 (c), in which the voltages at Bus 1 and Bus 2 are maintained constant, and 

there is equal magnitude at 1.05 p.u. The reactive power is supplied equally by both Bus 1 and 

Bus 2. The voltage Vpv = Vs requires that the source of the reactive power comes from both 

sides. Thus, the larger the contribution of the reactive power, the higher the voltage of the source 

of the reactive power.

2.1.1.2 Real Power Control

The equation describing the relationship of the voltage at the two buses to the corresponding 

voltage drop across the reactance, Xs, can be written as follows:

P = VPPVs

Xs

sin δ

IS δe

VS

φ=0.5 δe

jXSIS IS δe

VS

φ=0.5 δe

jXSIS

VPV

VPV

Figure 3. Illustration of a two-bus system demonstrating real power control in a conventional 

synchronous generator

Real power output can be increased in many ways. For example, increasing the real power output 

while maintaining equal voltage (Vpv = Vs) can be illustrated by the changes shown in the phasor 

diagrams in Figure 3. As mentioned above, in this equal-voltage condition both sides share the 

reactive power loss in the line reactance, Xs, equally. As the current, Is, increases, the power 

angle, de, also increases while equal voltage is maintained (Vpv = Vs).

2.1.2 Power-Converter-Based Power System

2.1.2.1 Reactive Power Control

Figure 4 illustrates the power converter based power system and its corresponding phasor 

diagram. The PV generator is connected to a grid through a reactance, Xs. The current, Is, is 

decoupled into real and reactive components (Ip1 and Iq1). Assuming that the grid is an infinite 

bus, Vs is constant. The impact of reactive power’s contribution on voltage regulation can be 

illustrated by the phasor diagrams shown in Figure 4 (b). As shown in Figure 4 (b), the phasor 

current, Is, is divided into the real current, Ip, (in phase with the voltage Vpv) and reactive 

current, Iq, (in quadrature with respect to the voltage, Vpv) components. 
5

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The voltage equation is rewritten as:

VP = Vs + j Xs (IP+IQ)

The real current component, Ip, is proportional to the real power generated, and the reactive 

current, Iq, is proportional to the reactive power generated. Doubling the reactive current, Iq, will 

double the voltage drop, Iq Xs, and directly increase the terminal voltage, Vpv, by an additional Iq

Xs. Thus, to increase reactive current, we need to increase the voltage, Vpv. The larger the value 

of Xs, the higher the voltage, Vpv, will increase as the same amount of the Iq current is increased. 

As can be expected, increasing the reactive component of the current, Iq, will directly impact the 

terminal voltage magnitude, Vpv, and increasing the real current component, Ip, will more 

directly impact the power angle, d, between Vpv and Vs. 

G1 G2

XS

IS

Grid

PV POI

Inverter

VPV VS

jXSIP

IS 

VS

IP 

jXSIQ (a) (b)

IQ 

VPV

Figure 4. Illustration of a two-bus system in a PV inverter-based system with its corresponding 

phasor diagram

In PV generation, two limits must be observed:

• The total resultant current, Is, is limited by the maximum current-carrying capability of 

the power converter (Imax). Thus, the power converter can increase its real or reactive 

current components (or both) only to a certain level, until the resultant current reaches its 

maximum (Is = Imax – current-carrying capability of the IGBT switches). At that point, 

the overcurrent protection will prevent the PV inverter from delivering more current.

• The maximum terminal voltage, Vpv, must be limited to the maximum voltage of the 

power converter. Thus, the power converter can increase its reactive current component, 

Iq, only so much, until the terminal voltage reaches its upper limit. At that point, the 

overvoltage protection will prevent the PV inverter unit from delivering more reactive 

current to the grid.

2.1.2.2 Real Power Control

Figure 5 (b) shows the size of the real current component increased to Ip2, while the size of the 

reactive current component, Iq1, is maintained. The additional voltage drop, jXs Ip2, is shown to 

increase by the same proportion. This affects the increase in the angle between Vpv1 and Vs.

Because the size of the infinite bus, Vs, is constant, the increase in Ip increases the voltage drop, 

but it decreases the voltage, Vpv2. The size of the reactive current component stays the same, and 

the resulting voltage drop, j Xs Iq2, also stays the same size. Note that the voltage, Vpv, decreases 

from Vpv1 to Vpv2 (indicated by the dashed line in Figure 5 (b)). To return Vpv2 to the same level 

as Vpv1, the reactive current component, Iq, is increased to Iq2. This is shown in Figure 5 (c), 
6

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which indicates the size of the voltage, Vpv1, and the size of the current, Ip2. The increase in the 

output power is proportional to the change from Ip1 to Ip2, and the reactive current contribution to 

cover Is

2 Xs loss are equally distributed between Vpv and Vs.

jXSIP

IS 

VS

IP1 

jXSIQ

IQ1 

jXSIP2

IS 

VS

IP2 

jXSIQ

IQ1 IS 

VS

IP2 

jXSIQ

IQ2 

jXSIS

VPV1 VPV2 VPV1

VPV2

IP1 VPV1

(a). Baseline:, Ip = Ip1, 

Iq = Iq1

(b). Increased: Ip = Ip2 (c). Ip = Ip2, Iq = Iq2

Figure 5. Illustration of a phasor diagram to demonstrate real and reactive power control in a PV 

inverter

2.2 Current-Source Inverter (CSI)—Average Model

Presently, most power converters are current-source inverters (CSIs). In the power drives, the 

current-control converter gives a very fast response to the torque required. In a grid-connected 

power converter, the current-control capability can give a quick response to the real and reactive 

power demand.

To understand a PV inverter, consider an average model, as shown in Figure 6. We consider an

average model one of an ideal power converter that can generate a sinusoidal current (with no 

harmonics). Thus, we simulate a PV inverter as a sinusoidal-current source. The output current is 

synthesized to give a sinusoidal output current that has a controllable magnitude and phase angle.

In a PV inverter, it is common to control the real (Ip) and reactive (Iq) components of the output 

currents.

Figure 6. Illustration of an average model of a CSI synthesizing a PV inverter

Eabc_hi

#1 #2

3.0 [MVA]

0.69 [kV] / 34.5 [kV]

0.001

Iabc

Vsource

V f Fsource R=0

Vpv Eabc

Ipv

Lrs

P = 0.7999

Q = 4.26e-005

V = 0.6911

V

A

Ipvaref Ipvbref Ipvcref

AB

C

1e-5 [H]

P = 0.7985

Q = 4.248e-005

V = 0.6899

V

A

Ppv, Qpv, Vpvrms

are defined in this block

Average Model

Current Source Inverter
7

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The one-line diagram shown in Figure 6 above illustrates a three-phase PV inverter (an ideal 

model of a three-phase current source) connected to the grid. The DC-AC (alternating current) 

inverter has two major functions: (1) to control the real power output of the PV strings and (2) to 

control the reactive power output. In actual PV generation, the control of the real power is very 

simply implemented by maintaining a constant DC bus voltage while the controlling the DC-DC 

converter to maximize the output power of the PV module.

The CSI is the block inside the rectangle marked by the dashed black lines. The first thing to 

consider when controlling a CSI is to find the reference frame at the point of measurement to 

which it is connected. In this case, the reference is the terminal voltage of the PV inverter. The 

voltage sensor is placed at node Vpv, as shown. Similarly, the real (Ppv) and reactive power (Qpv) 

sensors are inside the multi-meter at the Vpv node.

Figure 7 below shows a simplified equivalent circuit of the current source producing the output 

current, Is. Using the d-q axis synchronized to the phasor voltage, Vpv, we can decouple the 

current, Is, into its d-axis component (real current; Id = Ip component) and the q-axis, the reactive 

current component, Iq. The real current component, Ip, is used to control the output real power of 

the PV inverter. The control of the reactive current component, Iq, is used to control the reactive 

power output of the PV inverter. PV inverter generates reactive power into a regular (non-infinite 

bus) grid. The terminal voltage increases as the reactive power output of the PV inverter 

increases. Consequently, controlling the reactive current component, Iq, can be used to control 

the terminal voltage and vice versa.

VPV 

IS 

IP 

IQ 

− φο 

d-axis 

q-axis 

XS

VPV

PV IS

Inverter

VS

IS

Figure 7. Illustration of a PV inverter equivalent circuit representing a three-phase current source 

connected to the grid and the corresponding terminal voltage phasor, Vpv, and the output current 

phasor, Is, decoupled into Ip and Iq

The equation for the current can be expressed in a complex number.

Vpv = Vpv / 0o

Is = Is / -fο 

Based on the arrow direction, by definition (generator convention), the apparent power generated 

by the PV inverter can be written as:

Spv = Vpv Is

* = P + j Q

P = Vpv Is cos(fο)

Q = Vpv Is sin(fο)
8

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

The current conjugate of the output current is expressed as Is*. Thus, both the real power and the 

reactive power have positive values (generated from the PV inverter).

The phase-locked loop shown in Figure 8 (b) is the synchronizer that will latch the reference 

frame to the synchronous reference frame attached to the voltage phasor, Vpv, at the terminal of 

the PV inverter.

Note that after we found the reference frame of the terminal voltage, the real current component 

(Ip) and the reactive current component (Iq) can be oriented with respect to the “direct axis,” 

which has the same phase angle of the the terminal voltage, Vpv. Note that the subscript 

“p” indicates the real power component, and “q” indicates the reactive power component. The 

real power component, Ip, is represented by the “direct” axis component (in phase with the 

synchronous reference frame, “d”); thus, it is sometimes used to indicate Ip = Id; whereas the “q” 

also represents the “quadrature” axis component (in quadrature with respect to the direct axis,

“d”), thus Iq = Iq.

(a) Monitored voltage and current (b) Phase-locked loop to define the reference 

frame d-axis

Figure 8. Diagram illustrating the monitored voltage and current and the phase-locked loop to 

synchronize the reference frame to the terminal voltage

Vpva

Vpvb

Vpvc

1

2

3

Vpv

Ipva

Ipvb

Ipvc

1

2

3

Ipv

Va

Vb

Vc

PLL theta

phis

Relevant Voltage and Currents

Eabc_hi

3

2

1

Ec

Eb

Ea

Phase Lock Loop (PLL)

Vpvc

Vpvb

Vpva

Figure 9. Diagram illustrating the real and reactive power reference per unit to compute the 

peak of the actual reference currents Iq and Id

N

D

N/D Ipvq_ref_pu

Ipvd_ref_pu

0.0

Qgrid_pu Reference

Line side converter real and reactive power control

All reference values are in per unit.

1.0

Pgrid_pu Reference

B

-

D +

Qpv_pu

I

P

I

P

Ppv_pu

B

-

D + N

D

N/D

G

1 + sT

G

1 + sT

Vpv_pu

Vpv_pu

*

1.4142

*

*

Ibase

Ipvq_ref

Ipvd_ref

0.15 6.0 Tir Kpr
9

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

The diagram in Figure 9 shows a simple control to regulate the real and reactive power output of 

a PV inverter. The independent control is possible because the real and reactive currents are 

decoupled through the use of the synchronous reference frame calculation. 

To use the same controller for differently sized power converters, and to avoid performing very 

complicated parameter tunings, it is common to use per-unit quantities. Figure 10 shows the base 

value calculations for the voltage, power, and current.

After the real (Ipvd-ref) and reactive (Ipvq-ref) current components in the synchronous reference 

frame have been computed, as shown in Figure 9 above, the quantities Ipvd-ref and Ipvq-ref can be 

transformed into the three-phase currents in the stationary reference frame (the time domain 

sinusoidal forms Ipvaref, Ipvbref, and Ipvcref). These current signals are used to control the ideal 

current source to represent the CSI connected to the grid. Figure 12 and Figure 13 below show 

the reference current in the d-q axis using a synchronous reference frame and the three-phase 

reference currents in the time domain (the stationary reference frame), respectively.

Figure 11. Diagram illustrating the reference currents to generate the specified real power

reference, Pgrid_pu, and the specified reactive power reference, Qgrid_pu

Ppv

1.0

S_base (MVA)

N

D

N/D Ppv_pu N Qpv_pu

D

N/D Qpv

1.7321

sqrt(3)

N

D

N/D N

D

N/D

0.69

VLL_base (kV)

Ibase

Base Quantities

Sbase Sbase

VLLbase

Sbase

Ipvq_ref

Ipvd_ref Ipvaref

Ipvcref

Ipvbref

*

1

1

2

3

1 2 3

0.0

phis

Ppv

Qpv

Inverse Park

alfa angle

beta

d

q

Transform

0 0

Inverse Clarke

a

c

b

alfa

beta

0

Transform

Convert Ipvd-Ipvq reference in Synchronous Ref. Frame

into Ipvaref, Ipvbref, Ipvcref in Stationary Ref. Frame 

for the line side converter

Figure 10. Diagram illustrating the base value calculations to be used in the control blocks
10

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 12. Real current, Ipvd_ref, and reactive 

reference current, Ipvq_ref, signals in the 

synchronous reference frame

Figure 13. The three-phase reference 

signals—Ipvaref, Ipvbref, Ipvcref—in the stationary 

reference frame

Note that by using the average model, we can ignore the switching of the power switches, and 

we can assume that it has an infinite switching frequency—i.e., the resulting current is 

represented by the pure sinusoid generated by the controlled-current source to represent the 

practical CSI. One major advantage to this is that the simulations can be accomplished in a much 

shorter time, which allows us to perform many different types of dynamic simulations in power 

system studies.

2.3 CSI—Detail Model

A detailed model of a CSI is shown in Figure 14. The hardware of the power converter is 

represented by the real IGBT in parallel to its flywheel diode. The circuit driver is simulated by 

the real switching pattern commonly used in an actual power converter. The circuit is connected 

to the grid, as in the previous section. The only differences are that the ideal current source is 

replaced by an actual (hardware) power converter with six power switches and the firing control 

logic is implemented. The fundamental of power electronics converters, applications, and design 

can be found in reference [7] 

Figure 14. Diagram illustrating a three-phase CSI implementation with the actual six power

switches (IGBTs)

2.3.1 Power-Switching Control

The commanded sinusoidal reference three-phase currents are compared to the actual three-phase 

currents (see Figure 15), and the errors are compared to a triangular waveform with a peak-topeak value of +1. The currents are per-unitized by dividing the current errors by the base current.

The outputs of the comparators are used as the firing signals to drive the base of the IGBTs; thus,

they turn the IGBTs on and off.

Main : Graphs

x 20.000 20.010 20.020 20.030 20.040 20.050 20.060 20.070 

-1.00 

-0.75 

-0.50 

-0.25 

0.00 

0.25 

0.50 

0.75 

1.00 Ipvaref Ipvbref Ipvcref

P = 0.9957

Q = -0.05672

V

A

Eabc_hi

#1 #2

3.0 [MVA]

0.69 [kV] / 34.5 [kV]

P = 0.9972

Q = 0.006473

V = 0.6911

V

A

0.001

Iabc

Vsource

V f Fsource R=0

Eabc

BRK_DC R=0

I_chop 0.1 [ohm]

Vpv

Ipv

Lrs

0.0001 [H]

P = 0.9994

Q = 0.006473

V = 0.6917

V

A

Idc1

T4

T3

T6

T5

T4

T2

T5

T2

T6

T1 T3

T1

E_dc

100000.0 [uF]

Tch

Ppv, Qpv, Vpvrms

are defined in this block

Main : Graphs

x 19.990 20.000 20.010 20.020 20.030 20.040 20.050 20.060 20.070 20.080 

-1.50 

-1.00 

-0.50 

0.00 

0.50 

1.00 

1.50 

2.00 Ipvd ref Ipvq ref
11

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Figure 15. Diagram illustrating the logic circuits to turn the power switches in a CSI on and off in 

the correct order

The time delays are inserted in series with the firing signals to ensure that the top and bottom 

pairs of the IGBTs do not turn on at the same time to avoid short-circuiting the DC bus. This 

time delay is very small, in microseconds (modern IGBTs can turn on and off very fast). The 

detailed operation of the power converter is well-known technology that can be found in many 

power electronics textbooks.

2.3.2 Current-Regulated CSI

To regulate the real and reactive power output of the power converter, the same technique is 

used. The real (Id_ref) and reactive current (Iq_ref) components are computed in the synchronous 

reference frame to obtain the phasor quantities, as shown in Figure 5 and Figure 7 above. The 

rotating reference frame is attached to the phasor voltage, Vpv, and the rotating angle “phis” is 

found using the phase-locked loop. 

The real and reactive current components (Ipvd_ref, Ipvq_ref) in the synchronous reference frame 

(see Figure 16) are then transformed back to the three-phase sinusoidal current references (Ipvaref, 

Ipvbref, Ipvcref) in the stationary reference frame to drive the power switches of the IGBTs (see

Figure 17).

Figure 16. Diagram illustrating the real and reactive power references, per unit, to compute the 

peak of the reference currents, Iq and Id

Triang

Triang

D +

F

-

D +

F

-

D +

F

-

Ipv

1 2 3

A

B Comparator

A

B Comparator

A

B Comparator

Ipvaref

Ipvbref

Ipvcref

T1

T5

T4

T3

T6

T2

Delay

T

Delay

T

Delay

T

Delay

T

Delay

T

Delay

T

PWM and firing control for line side converter

N

D

N/D

Ibase

Ibase

N

D

N/D

Ibase

N

D

N/D

N

D

N/D Ipvq_ref_pu

Ipvd_ref_pu

0.0

Qgrid_pu Reference

Line side converter real and reactive power control

All reference values are in per unit.

1.0

Pgrid_pu Reference

B

-

D +

Qpv_pu

I

P

I

P

Ppv_pu

B

-

D + N

D

N/D

G

1 + sT

G

1 + sT

Vpv_pu

Vpv_pu

*

1.4142

*

*

Ibase

Ipvq_ref

Ipvd_ref

0.15 6.0 Tir Kpr
12

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 17. Diagram illustrating the inverse Park and inverse Clarke transformations to convert the 

synchronous referenced current signals, Iq and Id, into the stationary reference frame current 

signals, Ia, Ib, and Ic

Figure 18. Phase voltage, Vpva, monitored at the terminal of the power converter

Figure 19. Line-to-line voltage, Vpvab, monitored at the terminal of the power converter

The per-phase voltage and the line-to-line voltage monitored at the terminal of the power 

converter are shown in Figure 18 and Figure 19 above. As can be expected, the output of the 

pulse-width modulation contains a lot of harmonics at the specified switching frequencies (900 

Hz).

Ipvq_ref

Ipvd_ref Ipvaref

Ipvcref

Ipvbref

*

1

1

2

3

1 2 3

0.0

De-coupled Id-Iq control for line side converter

phis

Inverse Park

alfa angle

beta

d

q

Transform

0 0

Inverse Clarke

a

c

b

alfa

beta

0

Transform

Main : Graphs

x 3.0950 3.1000 3.1050 3.1100 3.1150 3.1200 3.1250 3.1300 3.1350 

-1.50 

-1.00 

-0.50 

0.00 

0.50 

1.00 

1.50 Ea

Main : Graphs

x 4.0900 4.0950 4.1000 4.1050 4.1100 4.1150 4.1200 4.1250 4.1300 

-2.50 

-2.00 

-1.50 

-1.00 

-0.50 

0.00 

0.50 

1.00 

1.50 

2.00 

2.50 Eab
13

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 20. Line current output, Ia, of the power converter

As shown in Figure 20, the line current in Phase A is closer to the sinusoidal current, although 

the higher harmonic content is still visible. Note that the actual current is synthesized to follow 

the sinusoidal reference signal, Ipva_ref. 

Figure 21. The real and reactive power measured at the output of the power converter

Figure 21 shows the measured real power and the reactive power at the terminal of the power 

converter. As the measurements are taken farther from the terminal of the PV inverter, the higher 

harmonic components of the currents are filtered out and the output voltage and currents look 

very sinusoidal.

Figure 22. Three-phase line currents measured at the high side of the substation transformer

Main : Graphs

x 4.0900 4.0950 4.1000 4.1050 4.1100 4.1150 4.1200 4.1250 4.1300 4.1350 

-2.00 

-1.50 

-1.00 

-0.50 

0.00 

0.50 

1.00 

1.50 

2.00 Ipva

Main : Graphs

x 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 

-0.20 

0.00 

0.20 

0.40 

0.60 

0.80 

1.00 

1.20 

1.40 

Qpv Ppv

Main : Graphs

x 19.9850 19.9900 19.9950 20.0000 20.0050 20.0100 20.0150 

-0.0200 

-0.0150 

-0.0100 

-0.0050 

0.0000 

0.0050 

0.0100 

0.0150 

0.0200 Ia Ib Ic
14

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Figure 23. Three-phase voltage measured at the high side of the substation transformer

Figure 22 and Figure 23 show the measurements of the line currents and voltages taken at the 

high side of the substation transformer. As shown, the filtering of the line impedance very 

effectively cancelled most of the higher harmonics in both the currents and the voltages. 

2.4 Voltage-Source Inverter (VSI)—Detail Model

A voltage-source inverter (VSI) synthesizes a voltage source connected to the grid. Because real 

and reactive power control is generally accomplished by controlling the reference currents, and 

controlling the voltage does not guarantee a direct response of the output currents, it is common 

practice to control the current indirectly by controlling the voltage output of the PV inverter. As 

shown below, the hardware for the VSI and the CSI are identical.

Figure 24. Diagram illustrating the three-phase VSI implementation with the actual six powerswitches (IGBTs)

Figure 25 shows a comparison of the current-regulated current-source inverter (CR-CSI) to the 

current-regulated voltage source inverter (CR-VSI). The CR-CSI uses the reference current to 

generate a current signal to trigger the base drivers of the IGBTs and uses the current feedback to 

compare and correct the current errors to make accurate syntheses of the PV inverter output 

current. Thus, the filter inductance (represented by the reactance, Xls) does not have to be 

included in the equations used to generate the output currents.

The CR-VSI indirectly controls the output current. It uses the voltage feedback Vpv and the 

corresponding voltage drop across the filter inductance, Xls Is, to synthesize the voltage feedback 

E that will produce the desired output currents (Is-reference). Thus, the filter inductance, Xls, must 

be included in the equations used to generate the voltage E.

Main : Graphs

x 19.9850 19.9900 19.9950 20.0000 20.0050 20.0100 20.0150 20.0200 20.0250 20.0300 

-30 

-20 

-10 

0 

10 

20 

30 Eabc

Eabc_hi

#1 #2

3.0 [MVA]

0.69 [kV] / 34.5 [kV]

P = 1.001

Q = 0.2208

V = 0.6904

V

A

0.001

Iabc

Vsource

V f Fsource R=0

Eabc

BRK_DC R=0

I_chop 0.1 [ohm]

Vpv

Ipv

Lls

0.001 [H]

P = 1.004

Q = 0.2208

V = 0.6926

V

A

Idc1

T4

T3

T6

T5

T4

T2

T5

T2

T6

T1 T3

T1

E_dc

100000.0 [uF]

Tch

Ppv, Qpv, Vpvrms

are defined in this block
15

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

VPV

PV CR-CSI

IS

Power 

Converter 

Controller _

+ IS-reference

IS-measured

Xls

VPV

IS

PV CR-VSI

E

Power 

Converter 

Controller _

+

IS-reference

IS-measured

Xls

Efiring logic IS-firing logic

IS

Figure 25. Diagram comparing the control philosophy of the CR-CSI to the CR-VSI

Consider Figure 26 (a), which shows the phasor diagram of the controller used to generate the 

voltage E in a CR-VSI. The single-line diagram of the power converter is enclosed in the dashed 

black lines. First, consider the voltage, Vs, as an input to the phase-locked loop; thus, the d-axis 

is aligned to the voltage, Vs. These phasor diagrams are shown in Figure 26 (b) and Figure 26

(c).

(b) Reference frame aligned to Eq (c) Reference frame aligned to Vpv

Figure 26. Diagram comparing the control philosophy of the CR-CSI to the CR-VSI

The equations governing the voltage can be written as:

E = Vpp + j Xl Is

jXSIq IS 

VPV

Id 

Iq 

E

G1

Xls

IS

E VPV

jXSId

jXSIq

IS 

VPVd

q axis

Iq 

E

jXSId

Id 

VPV VPVq

Ed

Eq

Iq 

Id d axis

d axis

Alligned to VPV

d axis 

Alligned 

to VPV

q axis

q axis in in

quadrature to 

VPV

Xs

VS

Ed

Eq

(a) Circuit diagram
16

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We can decouple the equation into its complex representation as:

Ed + jEq = (Vpp + jVpp ) + j Xl (Id − jIq)

Or, this can be decoupled into two equations:

Ed = Vpp + Xl Iq

Eq = Vpp + Xl Id

As shown in Figure 26 (b), the Clarke and Park transformations can be used to transform the 

terminal voltages (Vpva, Vpvb, Vpvc) in the stationary reference frame into the synchronous 

reference frame (Vpvd and Vpvq). When the Vpv is used as the input to the phase-locked loop, the 

d-axis is aligned to the phasor voltage, Vpv, and the phasor, Vpvq = 0, as represented by the 

phasor diagrams shown in the Figure 26 (c). Description about Clark and Park transformations 

can be found in references [1] and [8, 9].

Ed = Vpp + Xl Iq

Vpp = 0

The q-axis equation can be rewritten as:

Eq = Xl Id

Figure 27 shows the implementation of the voltage reference signals Ed and Eq. Additional input 

to make any corrections is also implemented using the PI controller to ensure that the reference 

real power and reactive power can be maintained.

Figure 27. Diagram illustrating the three-phase voltage signal reference used to trigger the firing 

circuits of the VSI

D +

F

- Ipvd_ref

D +

F

- Ipvq_ref

Isd

Isq

I

P

I

P B

+

D -

F

+

B

+

D +

F

+

Vpvd

Vpvq

Edref

Eqref

Inverse Clarke

a

c

b

alfa

beta

0

Transform

Inverse Park

alfa angle

beta

d

q

Transform

0 0

Earef

Ecref

Ebref

0.0

Isq

Isd

Xls

*

*

phis

De-coupled Vd-Vq control for line side converter

Del_Iq
17

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 28. The transformation from Vpv (a,b,c) into Vpvd and Vpvq in the synchronous reference

frame

Figure 29. The transformation from Ipv (a,b,c) into Isd and Isq in the synchronous reference frame

Figure 30. The logic circuits to turn the power switches in the CSI on and off in the correct order

Compute Vd-Vq at the terminal 

for line side converter in 

synchronous reference frame

phis

Vpvq

Vpvd

Vpvc

Vpvb

Vpva

Clarke

a

c

b

alfa

beta

0

Transform Park Transform

alfa angle

beta

d

q

0 0

phis

Park Transform

alfa angle

beta

d

q

0 0

Clarke

a

c

b

alfa

beta

0

Transform

Isd

Isq

Ipv

1

2

3

Compute Id-Iq at the terminal 

for line side converter in 

synchronous reference frame

A

B Comparator

A

B Comparator

A

B Comparator

Earef

Ebref

Ecref

T1

T5

T4

T3

T6

T2

Delay

T

Delay

T

Delay

T

Delay

T

Delay

T

Delay

T

PWM and firing control for line side converter

N

D

N/D

N

D

N/D

N

D

N/D

Vphbase_peak

Vphbase_peak

Vphbase_peak
18

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After the voltage reference signals of the Eqref and Edref have been computed in the synchronous 

reference frame, the three-phase voltage signals (Earef, Ebref, Ecref) in the stationary reference 

frame can be generated and fed into the firing circuit board (shown in Figure 30) of the power 

converter to turn the IGBTs on and off in the correct sequence. 

Figure 31. Per-phase voltage and line current of the CR-VSI

Figure 31 presents an example of the per-phase voltage and the line-current output of the CRVSI. Note that the current waveform is less sinusoidal compared to that of the CR-CSI, because

the power converter is not commanded to follow the reference currents; instead, it is commanded 

to synthesize the reference voltages, Earef, Ebref, and Ecref.

Main : Graphs

x 0.860 0.870 0.880 0.890 0.900 0.910 0.920 0.930 0.940 

-1.50 

-1.00 

-0.50 

0.00 

0.50 

1.00 

1.50 Ea

-1.00 

-0.50 

0.00 

0.50 

1.00 

Ipva
19

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

3 Controlling the Grid-Side Inverter and Power Plant

The PV inverter is the point of conversion from DC to AC power. In small residential 

applications, the PV inverter is usually single phase, converting DC to single-phase AC (60 Hz). 

The PV array is connected to the PV inverter via a maximum power point tracker to optimize 

energy conversion from sunlight to electrical power. A detailed discussion about this process is 

not included in this report. A PV inverter for large-scale installation usually comes in three-phase 

arrangements. The PV inverter combines the output of rows of PV strings in DC and converts 

them to AC. For example, an inverter can processes the output of a PV array with 500 PV 

modules. Three-phase output rated at 208 V or 480 V is commonly found in commercial PV 

inverters. Again, it must be emphasized that the topology described here is a single-stage 

topology, and controls for multi-level and multi-stage converters will require significant 

modifications from the ones described here.

In this chapter, we implement a controller based on the controllers developed and recommended 

by the WECC Renewable Energy Modeling Task Force (REMTF) [10]. A block diagram 

illustrating an overview of PV power plant control is shown in Figure 32. From left to right, the 

highest level of control is implemented first, by the control block REPC; to the REEC, with a

focus on the level of the PV inverter; then to the REGC, which is implemented to correct utility 

interface issues. The block diagrams and corresponding parameters are listed in the appendix.

Figure 32. Block diagram representing a PV power plant

• REPC—This supervisory control is implemented to control the real and reactive power of 

an entire PV power plant. Inputs may include the reference voltage (Vref), reference 

reactive power (Qref), reference real power (Pref), and reference frequency (Freqref).

Thus, the control block functions to control the real power output to respond to a 

frequency disturbance (and/or governor response) and to respond to a voltage regulation 

at a bus (at the point of interconnection or at the remote bus).

• REEC—This power-converter control is implemented to limit the currents based on the 

carrying capability of the power switches (i.e., IGBT and free-wheeling diode). Different 

types of reactive power control are implemented in this block as well.

• REGC—This generator control is implemented to the grid interface (under-/overvoltage 

scenarios) and enables nonlinear current control capability.
20

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3.1 Device Level

A PV inverter is a mature technology developed early on by the power drive industry for 

adjustable-speed drives, also known as adjustable-frequency drives, used to control the variablespeed operation of electric machines (e.g., induction motors) with torque or speed-control 

capabilities. Later, grid-interface technology was also developed extensively by the industry to 

provide uninterruptible power supply for the computer industry. Thus, the basic operations have 

been developed based on the experiences gained by the various industries. The details of the 

design, analysis, and protection at the device level can be found in many power electronics 

textbooks.

3.2 Generator Level 

At the generator level, the controller focuses on power-converter control and protection at the 

power-converter level. Two controllers to serve these functions have been developed by the 

WECC-REMTF. These controllers are meant to provide good grid integration to allow a PV 

converter to interface with the utility grid according to local standards and regulations. A PV 

controller can be set to provide fault ride-through capability, current limit protection, 

instantaneous and independent control of real and reactive power, and ancillary services to the 

grid.

3.2.1 REGC

The REGC is the first controller to be implemented and is directly connected to the power 

converter driver logic. As shown Figure 33, the inputs to this block are the commanded real 

power (P) current component (Ipcmd) in phase with the voltage (Vt), and the commanded reactive 

power (Q) current component (Iqcmd), the current component in quadrature (perpendicular) to the 

voltage Vt. The total current (Icmd) consists of the two components: Ipcmd and Iqcmd. The REGC is 

intended to ensure that the power converter has ride-through capability when exposed to local 

disturbances or transmission line faults.

Vt

Ipcmd

Iqcmd Icmd

Figure 33. Phasor diagram illustrating commanded current and its real and reactive components 

The outputs to this block are the commanded real power (P) current component (Ipord), the 

current component in phase with the voltage Vt, and the commanded reactive power (Q) current 

component (Iqord), the current component in quadrature (perpendicular) to the voltage Vt. Both of 

these quantities (Ipord and Ipord) are the adjusted input values during high- or low-voltage 

operation.

The REPG uses per-unit quantities and the generator base (PV inverter base; e.g., MBASE = 1.5 

MVA) instead of a system base or PV power plant base (e.g., SBASE = 60 MVA). However, if a 

single-generator representation is used, the REPG uses MBASE = SBASE.
21

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Figure 34. Block diagram illustrating the HVRCM controller to inject additional inductive current 

during a high-voltage event

As shown in the block diagram in Figure 34, the high-voltage reactive-current management 

(HVRCM) functions to alter the control behavior of the reactive power during high-voltage 

operation (e.g., higher than 1.2 p.u.), and the low-voltage active-current management (LVACM) 

functions to alter the control behavior of the active power during low-voltage operation (e.g.,

lower than 0.9 p.u.).

3.2.1.1 High-Voltage Region

The block diagram shown in Figure 35 below can be used to describe the control functions of the 

HVRCM. The term reactive current is used to describe both the inductive current and capacitive 

current. Inductive current is the current that causes a power converter to absorb reactive power,

and the capacitive current is the current that causes a power converter to produce reactive power.

The HVRCM has the control property to change the output reactive current command (Iqcmd) by 

providing an additional inductive current injection to decrease the reactive power output of the 

power converter, thus indirectly reducing the terminal voltage of the power converter. It also has 

a ramp-rate limiter to limit the rate of change in the reactive current output.

In analogy to the droop, in a power plant governor this HVRCM also functions to increase the 

inductive current to draw more reactive current from the grid, thus, in effect, reducing the 

terminal voltage.

Vt

Ipcmd

Iqcmd Ipord

Iqord

IQ Ramp Rate

Limiter 

999 1/sec

High Voltage 

Reactive Current Management

Vt > 1.2 p.u. Activate this controller

IQord

G

1 + sT

B

+

F

-

D +

F

-

d/dt

*

*

Vt

Iqcmd Iq

DeltVt

A

B

Ctrl

Ctrl = 1

1.2

Volim [pu]

BA

Compar- ator

Vt

0.0 IQord

IPord

Ipcmd

Iqcmd

Iqmin

Iqmax = Current Limit

for high voltage clamp

logic (p.u. on MBASE)

DeltQ

Volim

Volim

Volim

Tg 0.02

Tg [s]

999.9

IQRRlim [1/s] IQRRlim

Hi_V_flag

Khv

Khv 0.7

Khv

Vt

N

D

N/D

Iqcmd = commanded

reactive current input

Ipcmd = commanded active

current input

IQord= reactive current

Order to the Power

IPord= active current Order

to the Power Converter

Trigger during high voltage condition.

Reactive current injection to reduce

the high voltage condition

DeltIqMax 1.0

DeltIqMax

Qcmd0 Qcmd1

Iqmax Iqmax *

-1

Iqmax= max reactive current

computed in REEC
22

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Qcmd

∆V = Vt – Vo_lim

Qcmd_0

Qcmd_1

0.0 0.1 0.2 0.3

(p.u.)

∆Qcmd

Figure 35. Block diagram illustrating the HVRCM controller to inject additional inductive current 

during a high-voltage event

Figure 35 describes the changes in reactive power command if the terminal voltage (Vt) exceeds 

the threshold voltage (Volim). The slope of the line is specified as the constant (Khv).

Note that the additional current injection is not activated until the level of the terminal voltage 

passes the overvoltage limit (Volim). The sensor used to activate this function is embedded in the 

comparator with the logic output Hi_V_flag = 1.

Under normal circumstances (the logic output Hi_V_flag = 0):

∆Q = 0

Iqcmd1 = Iqcmd0

However, when the Hi_V_flag = 1, the inductive current injection is activated, and the following 

equations are used to govern the output of the inductive current injector:

∆Vt = Volim − Vt

∆Q = Qcmd0 − Qcmd1

∆Q = Khv ∆V

Iqcmd1 = Iqcmd0 − ∆Q

Vt

Take, for example, Volim= 1.2 p.u., Khv = 0.7, the initial Iqcmd = 0.1 p.u. at the terminal voltage of 

Vt = 1.0 p.u. The terminal voltage suddenly increases to Vt = 1.3 p.u. because of an external 

disturbance. The reactive power, which was initially Qcmd_0 = 0.1 p.u. during the high-voltage 

event, decreases to Qcmd_1 = (0.1 - 0.07) p.u. = 0.03 p.u. Note that the current limiter is placed to 

ensure that the Iqmax (computed in the REEC block) is not exceeded.

The choice of Khv is certainly determined by the local power system network. If the voltage in 

the local network varies a wide range above normal, the value of Khv can be adjusted 
23

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accordingly. The impact from a single PV inverter to suddenly change the voltage level may not 

be significant; however, the collective impact of hundreds of PV inverters connected to the grid 

following the same command will definitely be very effective. Also note that the current limits 

must be set to the limit of the reactive power capability of the power converter. These currents 

are limited before the commanded currents are passed to the power switches via the variable 

Iqord.

3.2.1.2 Low-Voltage Region

The block diagram shown in Figure 36 below can be used to describe the control functions of the 

LVACM. The term active current is used to describe the real or active power component (e.g.,

Ipcmd or Ipord).

In summary, the LVACM allows two choices determined by the low-voltage power logic, or 

LVPL (the upper limit of Ipcmd), switch. If LVPL = 1, the upper limit of the real power current 

component Ipcmd is governed by the nonlinear map LVPL compared to Vt. If LVPL = 0, the 

upper limit of the real power current component Ipcmd is governed by Ipmax computed in another 

controller block called REEC (discussed below).

Figure 36. Block diagram illustrating the LVACM controller to adjust the real current component 

(Ipcmd) during a low-voltage event

The block diagram in Figure 36 shows two quantities that should be computed. The first one is 

the scaled voltage (Vt_scaled), and the second one is the upper limit of the real current component 

(LVPL).

3.2.1.2.1 Computing Vt_scaled

Consider the Vt_scaled computation. Vt_scaled is computed from preprogrammed map shown in 

Figure 37. During a low-voltage event, the commanded power (Pord) must be scaled down to 

rrpwr and LVPL

Limits

Vt x mult

(Low Voltage Control)

Vt_Filtered

Tfltr = 0.02 s

Vt

G

1 + sT

G

1 + sT *

A

B

Ctrl

Ctrl = 1

d/dt

Vflt

Ipcmd

Pord

Lvplsw

LVPL

Filter Block

Tg = 0.02 s

0.02

Tfltr [s] Tfltr

Low Voltage

Active Current 

Management

Low Voltage

Power Logic (LVPL)

rrpwr

10.0

rrpwr [1/s]

Lvplsw

Lvplsw Lvplsw

Lvpl...

Lvplsw

0

OFF ON

0.9

Brkpt Brkpt

Zerox 0.4

Zerox

IPord

Vt

N

D

N/D

Low Voltage 

Active Current Management

IPord = f(V)

Choice between "Ipmax"

(Lvplsw=0) active power and

"scaled down" (Lvplsw=1)

active power during low voltage.

Pord = Vt x mult x Ip

(Low Voltage Control)

Limiting IPord during Low Voltage with

LVPL will give extra headroom to support

additional iQord to boost the votlage.

Ipmax Ipmax

Ipmax

Ipmax= max active current

computed in REEC

Ip_LVPL

Vt_scaled

Lvpl1

0.4

Lvpnt0 Lvpnt0

Lvpnt1 0.9

Lvpnt1
24

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accommodate the current-carrying capability of the power switches (IGBT and diodes). The Pord

should be scaled such that the resulting Ipord current will be within the allowable limit. 

Figure 37. Scaled voltage to adjust the Pord during a low-voltage event

For example, if the original commanded power Pord = 1.0 p.u., under normal voltage (Vt = 1.0 

p.u.), the commanded real power stays the same. Suppose during a grid disturbance the voltage 

drops to Vt = 0.6 p.u.; without scaling, the computed current command would be very high (Ipcmd

= Pord/Vt = 1.0/0.6 = 1.67 p.u.), which is much larger that the allowable current limit (Ipmax ~ 1.2 

p.u.). Thus, by scaling the voltage accordingly, the new Pord = Vt_scaled x 1.0 p.u. = 0.4 x 1.0, 

which gives the new Pord = 0.4 p.u. 

Note that when voltage is within the normal range (0.9 p.u.< Vt < 1.1 p.u.), the power converter 

must be capable of delivering Pord = 1.0 p.u.; thus, the voltage is scaled to 1.0 for voltages Vt > 

0.9 p.u. For example, at Vt = 0.9 p.u., the Pord = 1.0 p.u. and Ipcmd = 1.11 p.u., which is within the 

maximum current limit

3.2.1.2.2 Computing LVPL

The second quantity of interest is the LVPL. This quantity is actually the upper limit of the real 

power component. There are two options based on the position of the logical switch, LVPLsw. If 

LVPLsw = 0, the value of LVPL is set to Ipmax (computed in the REEC block and indicated by 

the thick, bold, black line shown in Figure 38); on the other hand, if LVPLsw = 1, the value of 

LVPL is computed by using the nonlinear map shown above.

Unlike using the map for the scaled voltage presented previously, using the LVPL map may or 

may not affect the outcome of the commanded output power Pord; instead, this map is applicable 

only to the commanded current output, Ipcmd. For example, under normal voltage (Vt = 1.0 p.u), 

Ipcmd = 0.2 p.u. If the voltage suddenly drops to 0.6 p.u., indicated by Point A on the map, the 

computed LVPL = 0.48 p.u.; thus, it does not affect the Ipcmd (i.e., at Vt = 0.6 p.u.) the Ipcmd is 

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Vt_Scaled (p.u.)

Voltage (p.u.)

Vt_Scaled

Vt-Scaled

Vt-orig
25

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not limited, and it is the same as the original value (Ipcmd = 0.2 p.u., indicated by Point A’). On 

the other hand, if the original Ipcmd = 0.8 p.u. (at Vt = 1.0 p.u., as indicated by Point B) and the 

voltage suddenly drops to Vt = 0.6 p.u., the commanded Ipcmd must be limited to Ip_LVPL = 0.48 

p.u., as indicated by Point B’ in the map. Note that within the normal voltage range, the current 

is limited to Ipmax. (Ipmax is set to 1.2 p.u. in this particular map for 0.9 p.u. < Vt < 1.1 p.u.)

Figure 38. LVPL calculation to set the upper limit of Ipcmd during a low-voltage event

If LVPLsw = 0, the value of LVPL is set to Ipmax. If the original Ipcmd = 0.8 p.u. (at Vt = 1.0 p.u.,

as indicated by Point B) and the voltage suddenly drops to Vt = 0.6 p.u.; the commanded Ipcmd

will stay the same as the upper limit of the Ip_LVPL = 1.2 p.u. Thus, the operating point will move 

from Point B at Vt = 1.0 p.u. to the new operating point at Vt = 0.6 p.u., then to a new operating 

point as indicated by Point B” in the map.

3.2.1.2.3 Revised Commanded Power Pord in the Low-Voltage Region

The revised commanded power Pord, computed based on the output of the Vt scaler and LVPL,

can be different for different power levels and different settings of the LVPLsw logic switch.

3.2.1.2.3.1 Example 1

Normal condition Pord_orig = 0.8 p.u.; Vt = 1.0 p.u.; and Ipcmd = 0.8 p.u

LVPLsw = 1. The voltage drops to Vt = 0.6 p.u., Pord_new = Vt_scaled x Ipcmd_limited = 0.4 x 0.48 = 

0.192 p.u., and the new Ipcmd = Ipord = 0.192/0.6 = 0.32 p.u.

LVPLsw = 0. The voltage drops to Vt = 0.6 p.u., Pord_new = Vt_scaled x Ipcmd_limited = 0.4 x 0.8 = 0.32 

p.u., and the new Ipcmd = Ipord = 0.32/0.6 = 0.533 p.u.

3.2.1.2.3.2 Example 2

Normal condition Pord_orig = 0.2 p.u.; Vt = 1.0 p.u.; and Ipcmd = 0.2 p.u

LVPLsw = 1. The voltage drops to Vt = 0.6 p.u., Pord_new = Vt_scaled x Ipcmd_limited = 0.4 x 0.2 = 0.08 

p.u., and the new Ipcmd = Ipord = 0.08/0.6 = 0.133 p.u.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

LVPL - Ip_max (p.u.)

Voltage (p.u.)

LVPL

LVPLsw = 0

LVPLsw = 1

A’

B

B’

A

B”
26

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LVPLsw = 0. The voltage drops to Vt = 0.6 p.u., Pord_new = Vt_scaled x Ipcmd_limited = 0.4 x 0.2 = 0.08 

p.u., and the new Ipcmd = Ipord = 0.08/0.6 = 0.133 p.u.

Thus, the impact of the controller on the outcome of the commanded active power component is 

significant for medium to rated power when the LVPLsw is activated. However, when the active 

power command is low, it makes no difference whether the LVPLsw is activated or not.

3.2.2 REEC

The REEC is designed to control the real and reactive power (under normal and transient 

conditions). The REEC uses per-unit quantities and the generator base (PV inverter base; e.g.,

MBASE = 1.5 MVA) instead of a system base or PV power plant base (e.g., SBASE = 60 

MVA). However, if a single-generator representation is used, the REPG uses MBASE = SBASE.

3.2.2.1 Control Implementation of Reactive Power and Voltage Control

The reactive power control block shown in Figure 39 illustrates the control mechanism of the 

reactive power control. Two stages are considered. This controller controls the reactive power to 

match the reactive power command, Qin. The Qin is the input to the PI controller to regulate the 

reactive power or voltage, as shown in Figure 40 (enclosed in the solid black line). For now, 

ignore the blocks NoFreeze and Freeze and assume that these blocks are shorted.

Figure 39. Block diagram illustrating the computation of the reactive power input command Qin

3.2.2.1.1 Logical Switch PF_flag 

If the controller is set to control the reactive power output of the power converter (Vflag = 1; see 

the description of Vflag below), two options are available to control the reactive power output. 

• PF_flag = 1 sets the reactive power input command to follow Qpf computed based on a 

constant power factor pfaref. The reactive power is commanded to be proportional to the 

actual real power Pe output; thus, it varies with the actual output power Pe as the output 

changes, except when the pfref = 1; however, in this case, the reactive power is 

commanded to be zero at all times. The Qpf calculation can be shown as 

Qpp = PP tan(cos−1(pppp p))

Pe

G=1

Tp=0.02

PF_flag

Tan

* G

Pe 1 + sT

pfaref

Qin

Qext

Qpf

A

B

Ctrl

Ctrl = 1

pfaref 0.9

pfaref

0.02

Tp [s] Tp

ArcCos

PF_flag - Choice between

constant PF (1) or external Q

control input (0) 

Constant PF (pfaref)

or Q control Qext

Pe - measured power

(to be controlled)
27

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• PF_flag = 0 sets the reactive power input command to follow the external reactive power 

command Qext. This input can be driven by supervisory control within the supervisory 

control domain (i.e., the REPC block diagram).

3.2.2.1.2 Logical Switch Vflag

The logical switch Vflag (shown in Figure 40) functions to control the reactive power output of 

the power converter. This block is inside the rectangle marked by the dashed red line. The input 

to this block is the output of the first block, and it may take two branches or directions,

depending on the Vflag set. Focus on the circuit enclosed in the rectangle marked by the thin red 

line. 

• Vflag = 1. The logical switch is set to A, then the reactive power control is chosen. The 

reactive power output will be controlled to match the reference Qin.

• Vflag = 0. The logical switch is set to B, then the voltage control is chosen. Note that the 

limiter placed before the Vstar will limit the value of Vstar (thus, the Vref1) within the 

acceptable voltage level (Vmin < Vstar < Vmax). The terminal voltage Vt will be controlled 

to match the reference voltage Vref1.

Figure 40. Reactive power and voltage control

3.2.2.1.3 Logical Switch Qflag

The output from the block enclosed in the red rectangle shown in Figure 40 will be the input A to 

the next logical switch (shown in the light blue ellipse) and to the next stage to calculate the 

commanded reactive current Iqcmd. The logical switch is activated by the Qflag. The logical 

switch Qflag functions to determine if the reactive power output will be controlled via the two PI

controllers (within the rectangles marked by the solid black line and the solid red line) or via the 

linear path (within the rectangle marked by the black dashes and dots).

• Qflag = 1 and Vflag = 1. The reactive power is accomplished via the PI controller inside 

the rectangle marked by the solid black line and the PI controller inside the rectangle 

marked by the dashed red line (two PI controllers in series).

• Qflag = 1 and Vflag = 0. The voltage is controlled by the PI controller shown inside the

rectangle marked by the dashed red line (a single PI controller).

Iqcmd

Iqmin and Iqmax

Computed

G = 1 , Tiq =

Iqmin and Iqmax

Computed

Iqinj

B

+

D +

Iqcmd

Qflag

Iqo_qflag

A

B

Ctrl

Ctrl = 1

Iqmin and Iqmax

-1.0 and 1.0 Kvp = 

Kvi =

I

P

N

D

N/D

B

+

D +

F

-

Vt_filt

Vstar

Vmin and Vmax

Qe

Vmin and Vmax Kqp = 

Kqi =

I

P

Qmin and Qmax

pu on MBASE

Q_ff

G

1 + sT

Qin D +

F

-

A

B

Ctrl

Ctrl = 1

Vvflag

Vflag

Qe Qe

Vref1

1.0

Vref1 [pu] Vref1

0.0

A

B

Ctrl

1 = Ctrl

0.0

Volt_dip *

-1

V_flag - Choice between

Qcontrol (1) or voltage P-I control (0) 

Reactive Power Control Block

(with or without) PI controller to

control Q

 

Q_flag - Choice between

linear Qcontrol (0) or (V

or Q) with P-I control (1) 

Volt_dip - Choice

between voltage boost

current injection (1) or No current injection (0) d i b l lt

Iqcmd = commanded

reactive current output

Qe = measured reactive

current in a branch

Qin

S / H

in

hold

* out

S / H

in

hold

* out NoFreeze Freeze

NoFreeze Freeze

Freeze

S / H

in

hold

out

*

online
28

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• Qflag = 0. The reactive power is controlled by a feed-forward linear loop without the PI 

controller (see the rectangle marked by the black dashes and dots). This loop will allow 

the reactive power to be controlled externally—for example, by supervisory control via 

the variable Qext to accomplish plant-level reactive control by paralleling the response of 

all the PV inverters within the PV plant (see the REPC block diagram).

3.2.2.1.4 Identifying Abnormal Voltage Range 

Another logical switch is the one encircled within the dashed green ellipse shown in Figure 40.

This logical switch enables the injection of additional reactive current, Iqinj, during abnormal 

voltage (either in the overvoltage condition when the voltage Vt > Vup or in the undervoltage 

condition when the voltage Vt < Vdip.

Figure 41. Identifying abnormal voltage to set Volt_dip

Figure 41 shows the logical switch Volt_dip. This logical switch will be operated based on the 

detection of the terminal voltage, Vt, as shown in the diagram.

• Volt_dip = 0 is a normal condition, and the injection current Iqinj = 0.

• Volt_dip = 1 is an abnormal condition, and the injection current is used based on the 

droop characteristic.

The output commanded reactive current, Iqcmd, is limited by its maximum, Iqmax, and its 

minimum, Iqmin. Calculating Iqmax and Iqmin will be shown in a later section.

3.2.2.1.5 Additional Reactive Current Injection, Iqinj

The additional reactive current injection is computed based on the size of the voltage deviation 

of the terminal voltage, Vt, from the reference voltage, Vref0.

Calculating an additional reactive current injection is done with the linear model shown in Figure 

42. This controller block includes the deadband db1 and db2 to disable the control from injecting 

the additional reactive current, Iqinj, when the voltage is within the normal range. In most cases, 

the reference voltage is assumed to be Vref0 = 1.0 p.u., and the normal voltage range 0.9 p.u. < Vt

< 1.1 p.u.; thus, the deadbands db1 = db2 = 0.1 p.u. The constant value Kqv is the slope affecting 

the aggressiveness of the current injection, Iqinj, to correct the voltage deviation. Note that the 

impact of the controller is dependent upon the stiffness of the grid, the availability of currentcarrying capability of the power converter to pass this additional current, and the control setting 

of the PQflag. However, db1, db2, Kqv, and Vref0 can be adapted to the new values to follow 

specific regional and/or local rules and regulations.

Vdip Vup 0.7

Vdip

1.3

Vup

If (Vt < Vdip ) or (Vt > Vup)

 Volt_dip = 1

else

 Volt_dip = 0

1.0

Vup

Vdip

Vt

0.0

A

B

Ctrl

Ctrl = 1

Volt_dip

A

B Comparator

A

B Comparator

Abnormal Voltage Range

to identify Over-voltage 

and Under-voltage

Vdip = 1 = flag to identify abnormal 

voltage range. Either over-voltage 

or under-voltage

Vdip = 0 = normal operating 

voltage

G

1 + sT
29

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∆V = Vref0 – Vt 

slope = Kqv 

-0.2 -0.1 0.0 0.1 0.2 0.3 (p.u.)

Iq-inj

DB1 DB2

Iqh1

Iql1

Figure 42. Diagram illustrating an additional reactive current injection during an abnormal voltage

event (Volt_dip = 1)

Figure 43. Block diagram illustrating a method to compute an additional reactive current injection 

during an abnormal voltage event (Volt_dip = 1)

Figure 43 above shows the control block diagram implementation of the additional current 

injection based on the voltage condition.

3.2.2.2 Real Power Control

Because the relationship of the reactive power to the terminal voltage is very tight, either the 

reactive power control or the voltage control is generally chosen. The reference real current 

component, Ipcmd, can be computed by dividing the reference power, Pref, by the terminal 

voltage.

Figure 44. Block diagram illustrating a method to compute the real current component, Ipcmd

Vt

G=1

Trv=0.02

Reactive Current 

Injection Gain (0-10)

Current Limit

Iql1 and Iqh1

D -

F

+ * Vt Iqinj

G

1 + sT Vt_filt

Deadband 

db1=db2=dbd

1.0

Kqv Trv Kqv 0.02

Trv [s] Vref0 1.0

Vref0 [pu]

Vref0 Kqv

Vt - voltage measured

(to be controlled)

Vt

Voltage Control Block

Pref Ipcmd

G=1

Tpord=0.02

Ipcmd

Freeze during

voltage dip

N

D

N/D

Vt_filt

Pref d/dt G

1 + sT

Feed-foward real power Pref control.

Linear control for Ipcmd (no P-I block) Ramp rates

Limiter 0.02

Tpord

Tpord

RampR_Lim 99.0

RampR_Lim Ipcmd = commanded active

current output

Pref = commanded active

power

Freeze

S / H

in

holdout

Pmax 1.2

Pmax

Pmin 0.0

Pmin Ipmax Ipmin

Computed based on

S / H

in

holdout

Freeze

Freeze during

voltage dip
30

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The block diagram shown in Figure 44 illustrates the following calculation.

Ipppp = Prr

Vt

The current limiter is used to limit the Ipcmd to the allowable Ipmax based on the setting of the 

PQflag (P-priority or Q-priority).

3.2.2.3 Calculating the Maximum and Minimum Current of Ipcmd and Iqcmd

To prevent the power switches (IGBTs and diodes) from conducting current higher than the 

current-carrying capability, the control block diagram shown in Figure 45 can be used to 

implement overcurrent protection.

Figure 45. Block diagram illustrating a method to compute the current limits for the real and 

reactive current components

Two type of priorities can be set through the PQflag.

• PQflag = 1 is also known as P-priority. The controller’s priority is to maximize the range 

of the real current component, Ipmax, and use the remaining current capability for the 

reactive current component, Iqcmd.

Ipppp = I Ipppp = 0

Iq = �I2 − Ipppp

2 Iq = −Iq

Iqmax

1.3

Imax

Imax

Current Limit Logic

Q Priority (Pqflag = 0)

Ipmax = (Imax^2 - Iqcmd^2)^(0.5) , Ipmin = 0

Iqmax = Imax, Iqmin = - Iqmax

P Priority (Pqflag = 1)

Ipmax = Imax, Ipmin = 0

Iqmax = (Imax^2 - Ipcmd^2)^(0.5) , Iqmin = -Iqmax

Ipmin

*

Iqmax -1

A

B

Ctrl

Ctrl = 1

Imax Iqmin

0.0 Imax

A

B

Ctrl

Ctrl = 0

PQVdipflag

X2 X Imax

Ipcmd

X2

D +

F

-

Ipmax

D +

F

-

X2 Iqcmd

Imax X2 X

PQVdipflag

PQflag

Volt_dip

Ipmax

Iqmax

Vflag

Qflag

Current limits to protect IGBTs

During faults or abnormal voltage

Iqmax = maximum

commanded Iq

Ipmax Ipmax

PQVdipflag

Ipmax = maximum

commaned Ip
31

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• PQflag = 0 is also known as Q-priority. The controller’s priority is to maximize the range 

of the reactive current component, Iqmax, and use the remaining current capability for the 

real current component, Ipcmd.

Ipppp = �I2 − Iq

2 Ipppp = 0

Iq = I Iq = −I

Figure 46 illustrates the operation in P-priority and Q-priority. During a normal condition, the 

terminal voltage is assumed to be Vt = 1.0 p.u., and the maximum current allowed is Imax = 1.3

p.u. We assume initially that the output real power P = 0.8 p.u. Ipcmd = 0.8 p.u., and the reactive 

power Q = 0.2 p.u., Iqcmd = 0.2 p.u.; thus, the initial current is shown as the phasor I1.

P-priority

Ipmax =1.28

Imax = 1.3

Iqcmd = 0.2

Ipcmd = 0.8

I1 I2

Q-priority

Imax = 1.3

Iqcmd = 0.2

Iqcmd = 0.4

Ipcmd = 0.8

I1

I3

I4 Iqmax = 1.02

(a) P-priority (b) Q-priority

Figure 46. Phasor diagrams illustrating the P-priority and Q-priority 

The operation of P-Priority and Q-Priority is triggered by the logic diagram shown inside the red 

ellipse. Unless stated differently for different projects, during normal operation the P-Priority is 

set to maximize the energy yield of the renewable energy resources; thus, P-Priority is enabled 

(PQflag = 1) during normal operation (when the logic Volt_dip = 0). Even during abnormal 

voltage (V_dip = 1), the P-Priority can be activated (PQflag = 1) under certain circumstances.

3.2.2.3.1 Operation in P-priority

The phasor diagram shown in Figure 46 (a) illustrates the operation when P-priority option is 

selected. When a disturbance in the transmission line occurs, the voltage drops to Vt = 0.5 p.u.

Using the P-priority, we can compute the maximum Ipmax = sqrt (1.32 – 0.22

) = 1.28 p.u. Because 

the operation is set to P-priority, the controller tries to maintain output power constant at P = 0.8 

p.u.; however, this requires Ipcmd = 0.8/0.5 = 1.6 p.u., which is higher than the allowable Ipmax = 
32

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1.28 p.u. Thus, we have to settle to Ipcmd = 1.28 p.u., and Iqcmd = 0.2 p.u. is frozen and must stay 

the same as the value before the voltage drop, and the output current changes from I1 to I2.

3.2.2.3.2 Operation in Q-priority

The phasor diagram shown in Figure 46 (b) illustrates the operation when the Q-priority option is 

selected. When a disturbance in the transmission line occurs, the voltage drops to Vt = 0.5 p.u.

Using the Q-priority, we can compute the maximum Iqmax = sqrt (1.32 – 0.82) = 1.02 p.u. Because 

the operation is set to Q-priority, the controller tries to maintain the output reactive power 

constant at Q = 0.2 p.u. Thus, the required Iqcmd = 0.2/0.5 = 0.4 p.u. This value is the maximum 

range of allowable Iqmax = 1.02 p.u. The phasor current I1 moves to I3. Note that the magnitude of 

the phasor I3 = 0.89 p.u., which is less than the maximum current limit Imax = 1.3 p.u.

Next, consider the additional current injection, Iqinj, to support the voltage during the voltage 

dips. In this case, assume that Kqv = 2.0 and Vref0 = 1.0 p.u. When the voltage, Vt, drops to Vt = 

0.5 p.u. The additional injection current is Iqinj = Kqv (Vref0 – Vt) = 2 (1 - 0.5) = 1.0 p.u.; thus, 

including the current injection, Iqinj, the total Iqcmd = 0.4 + 1.0 = 1.4 p.u. However, the Iqmax = 

1.02 p.u. In this case, we have to settle with Iqcmd = 1.02 p.u. and Ipcmd = 0.8, and the total current 

I4 = sqrt (1.022 – 0.82

) = 1.3 p.u.

3.2.2.4 Controlling the Freeze During Abnormal Voltage Conditions

It is common in a PV inverter to freeze the states that control the output of the reactive power.

This is done during the transients, so that the impact of the short disturbance does not exaggerate 

the situation and make the power system unstable when the disturbance is removed the grid. In 

some applications, the output current is frozen until the disturbance is over; however, this will 

only limit the output current contribution to the fault. The implementation is shown in Figure 47. 

Figure 47. Block diagram illustrating a method to freeze the operating current during voltage dips

3.3 Plant Level 

A PV plant consists of many large inverters connected in parallel by miles of AC cables (also 

known as a collector system). Supervisory control is implemented to the inverters within the 

power plant to achieve plant-level objectives. As the level of PV penetration increases, PV plants 

are required to provide low-voltage and high-voltage ride-through capabilities and different types 

of ancillary services (reactive power support, oscillation damping, inertial response, governor 

Volt_dip

Clear

1

sT

A

B Comparator

No_dip

deltaT

No_dip

1.0 TimeFreeze Freeze

If TimeFreeze < deltaT then

Freeze = 1

NoFreeze

deltaT

60.0

Freeze Control

Volt_dip

N

D

N/D 60.0

# of cycles

Volt_dip

offline online

NoFreeze
33

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control, spinning reserve, etc.) to the power system network. In large power system studies (such 

as WECC-wide studies), it is common to represent a wind power plant or PV plant as a single 

generator, as shown in Figure 48.

Figure 48. Single-line diagram illustrating a PV plant with a single generator 

As shown, the output of a PV inverter is usually 208 V or 480 V. In the example presented 

above, the output voltage of the 165-kVA, three-phase PV inverter is 480 V; this is a parallel 

combination of many inverters representing a PV plant.

The transformers (480 V/34.5 kV) are connected to a substation transformer. Several of these 

nodes are connected in a daisy-chain fashion, which is then connected to the substation 

transformer (66 MVA, three-phase, 34.5 kV/110 kV). It is customary for the utility meters to be 

connected at the high side of the substation transformer to measure the revenue of a PV plant.

3.3.1 REPC

The REPC module shown in Figure 49 is a very useful way to implement the ancillary service 

capabilities of a renewable energy generator as required by the system operator. The REPC 

control block can be used to implement supervisory control to both the real and reactive power.

Note the capability of the power converter to deliver the desired output and that the currentcarrying capability of the power switches (IGBTs) takes precedence over the objective function 

specified in the REPC. For example, if the current/voltage limit of the IGBT has been reached, 

and the REPC objective function has not been accomplished, the final outcome will be 

determined by the IGBTs current/voltage limit.

Like REPG and REEC, the REPC uses per-unit quantities; however, in the REPC, the base 

quantity used is the system base (a PV power plant base) instead of the generator base (a PV 

inverter base).

3.3.1.1 Voltage Control at a Remote Bus

As shown in Figure 50, the remote bus is defined as the bus farther from the terminal voltage.

The electrical distance from the terminal voltage is represented by the reactance Xbr, the current 

flowing through the branch is represented by Ibranch, and the reactive power flowing in the 

branch is represented by Qbranch.

66 MVA 3 phase

60Hz, 34.5kV/110kV)

66 MVA 3 phase

60Hz, 0.48kV/34.5kV)
34

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The regulated voltage is located in a remote bus from a monitored bus voltage Vreg. Two types of 

voltage compensation can be activated in the REPC block diagram:

• VcompFlag = 1—The voltage to be controlled is measured from the Vreg, bus and it is 

compensated by using the computed voltage drop I X.

A. Example 1—If you want to regulate V1 (high side of the transformer) and have

access only to the voltage Vt, then to control V1, the branch current Ibranch = Ixfrmr

and Xbr = Xxfrmr; voltage Vreg = Vt; and the voltage drop is computed from Ixfmr

Xxfmr.

B. Example 2—If you want to regulate V2 and monitor only the voltage V1, then to 

control V2, the branch current Ibranch = Ibranch1 and Xbr = Xs; the voltage Vreg = V1; 

and voltage drop is computed from Ibranch1 Xs.

• VcompFlag = 0—The voltage to be controlled is measured from the Vreg bus, and it is 

compensated by estimating the voltage drop by Kc Qbranch.

A. Example 1—If you want to regulate V3 and have access only to the voltage V2, 

then to control V3, the Qbranch = Qbranch1 and voltage Vreg = V2, and the voltage 

drop is estimated by Kc1 Qbranch1. 

B. Example 2—If you want to regulate V1 and you have access only to the voltage 

Vt, then to control V1, the Qbranch = Qout and voltage Vreg = Vt, and the voltage 

drop is estimated by Kcxfmr Qout.

Figure 49. Control block diagram illustrating voltage regulation for a remote bus

PV Power 

Plant

Vt

V1

V3

V2

Ibranch1

Qbranch1

Xs

Xxfmr

Ixfmr

Qout

Figure 50. Single-line diagram illustrating a method to accomplish different remote voltage 

regulations

G=1

Tfltr=0.02

G

1 + sT

Vref

D -

F

+

Vcomp2

0.02

Kc

VcompFlag

A

B

Ctrl

Ctrl = 1

Qbranch

D +

F

+ *

Vreg

VdRX

Xbr

* Vreg

X2

X

VregCmd

D +

F

+

X2 VdRX

VregCmd

Kc

Kc

Xbr 0.0

Xbr

Vcomp1 Vcomp3

VregCmd = voltage

command including

voltage drop IX

Voltage command including

voltage drop due to reactive

power flow Qbranch

VcompFlag - Choice between

compensation wih Voltage Drop IX (1)

or voltage drop Kc Qbranch (0)

Ibranch

Vcomp3 = reference

voltage command

including voltage drop

compensation

Voltage Control

(remote bus)
35

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Figure 51. Control block diagram illustrating a method to regulate reactive power

3.3.1.2 Reactive Power Control

The reactive power control is illustrated by the control block diagram shown in Figure 51. In this 

control block diagram, there is a logical switch called RefFlag that must be set to make the 

following choices:

• RefFlag = 1—Configure the controller to regulate the voltage based on the measured 

voltage Vreg. 

• RefFlag = 0—Configure the controller to regulate the reactive power flow in a specified 

branch (for example, the Qbranch1 in Branch 1 or Qout measured at the output of bus Vt) to 

follow the reference, Qref. Caution must be taken when controlling a branch from a PV 

power plant when the output is split into multiple branches. For example, we can control 

the reactive power flow in a particular branch to follow a certain reference Qbranch =

Qbranch1; however, the setup will let us control the reactive power flow only in a single 

branch, so if we control only the reactive power flow in Branch 1, we do not have any 

control over the power flow in Branch 2. Because the output of the power plant flows in 

both Branch 1 and Branch 2, the power plant may have reached its upper limit before 

Qbranch1 = Qref is reached.

The output of this controller is the Qext, which is an input to the next block, REEC, and will be 

used to compute the reactive current component, Iqcmd, that will generate the requested Qext.

Note that Qext is either the reference reactive power Qref (for RefFlag = 0) or the equivalent 

reactive power needed to regulate the voltage at a specified remote bus (for RefFlag = 1). 

3.3.1.3 Real Power Control

The real power control is illustrated by the control block diagram shown in Figure 52. The 

reference power is set by the reference power Plant_Pref. The single-line diagram shown in 

Figure 53 is as an example of how to use reference power Plant_Pref. For example, if the output 

power of a PV power plant is to be controlled to follow the reference Plant_Pref, then we can set 

Pbranch = Pout.

Caution must be taken when controlling a branch power flow from PV power plant when the 

output is split into multiple branches. For example, we can control the power flow in a particular 

branch to follow Plant_Pref by setting Pbranch = Pbranch23 or Pbranch = Pbranch1. However, the setup 

TstPt1 TestPoint1

Vcomp3

Qref

A

B

Ctrl

Ctrl = 1

RefFlag

G1 + sT1

1 + sT2

Local Q Regulator

Qmin and Qmax

Kqp= Kqi= Tqi=1/Kqi

Vdrop Limit

emin and emax

Qext

G

1 + sT D -

F

+

G=1

T1 = Tft=0.02

T2 = Tfv=0.15-5

G=1

Tfltr=0.02 Deadband

db1=db2=dbd=0.1

0.0

Tft

Tft

Tfv 0.075

Tfv

0.0

Tfltr

Tfltr

TestPoint2 TstPt2

Qmin

Qmax 0.436

Qmax

-0.436

Qmin

-0.1

emin

0.1

emax

emax

emin

I

P

Tqi 1.0 N

D

N/D

Kqi 5.0

Kqi

Kqp 1.8

Kqp=18

TstPt1

TstPt2

Qext Qbranch

RelFlag - Choice between Voltage

Drop compensation (1) or reactive

power set at Qref (0)

Reactive Power Control

*

1.0

Qext = commanded reactive

power output
36

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will let us control the power flow only in a single branch; thus, if we control only the power flow 

in Branch 1, we do not have any control over the power flow in Branch 2. The power plant may 

have reached its upper limit before Pbranch1 = Plant_Pref is reached. 

This control block diagram shows a logical switch called FreqFlag that must be set to make the 

following choices:

• FregFlag =1—Configure the controller to regulate the real power flowing in the specified 

branch Pbranch using the PI controller to include the reference Plant_Pref and the 

frequency response dP/dF. At this point, the only way to disable the frequency response 

dP/dF into the power command mix is to set the slope Ddn = Dup = 0.

• FreqFlag = 0—Configure the controller to regulate the reactive power flow in a specified 

branch Pbranch to follow the reference real power command Plant_Pref using the feedforward linear path (bypassing the PI controller) without the influence of frequency

response.

Figure 52. Control block diagram illustrating a method to regulate real power

PV Power 

Plant

Vt

V1

V3

V2

P Pbranch1 branch23

Xs

Xxfmr

Ixfmr

Pbranch2 Pout

Figure 53. Single line diagram describing real power control in remote location

The output of this controller is the Pref, which will be used as an input to the next block, REEC,

and to compute the real current component Ipcmd that will generate the requested Plant_Pref.

Deadband

fdb1=fdb2=fdbd=0.01

Freq

G

P_err 1 + sT

D -

F

+

G=1

B Tlag=0.15-5

+

D -

F

+

FreqFlag

A

B

Ctrl

Ctrl = 0

Pref

Droop Error Limits

femin and femax

I

P

Pmin and Pmax ; -999 and 999

Kpg = 0.1 Kig= 0.05 Tig = 1/Kig

G=1

Tp=0.02

G

Pbranch 1 + sT

*

dP_dF

1.0e-006

Dup

C

+

E

+

*

20.0

Ddn

Plant_Pref

Governor response with down regulation, only 

Ddn >0 ; Dup =0 ; Duplim=0b; Ddnlim = -0.2

Governor response with up and down regulation 

Ddn > 0 ; Dup >0 ; Ddnlim =0 ; Ddnlim = 0.2

Note: Droop (pu power/pu freq on mbase)

Ddn = 20.0 - 33.3

Governor response

limits

 

Tlag 0.0

Tlag

1.0

Kpg

Kpg

0.75

Kig

Kig

N

D

N/D 1.0 Tig

Tp 0.25

Tp

DdnMin -20.0

DdnMin

20.0

DdnMin

DupMax

Ddn

Dup

Ddn

Dup

-999.0

Pmin

999.0

Pmax

Pmax

Pmin -999.0

femin

999.0

femax

femax

femin

Pref

Freq_ref

Real Power Control

FreqFlag - Choice between

including governor control (1) or a

simple Pref control (0)

Plant_Pref

Pref = commanded active

power output
37

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The real power control following the path with the PI loop lies within rectangle marked by the 

blue dashes. The diagram within the red rectangle is the frequency response control, and the 

diagram within the black rectangle is the total control of real power to match the real power flow 

within the branch to match the reference Plant_Pref.

3.3.1.4 Additional Real Power Boost to Respond to Frequency Changes

The additional real power control to support frequency regulation is illustrated by the control 

block diagram shown within the red rectangle in Figure 52. The reference frequency is set by 

Freq_ref. The measured frequency is the Freq. The error ∆Freq is passed through the deadband 

block, and the slope is controllable via the parameters Ddn and Dup, and the output is limited by 

the limiter DdnMin and DupMax. Figure 54 shows a graphical illustration of this concept. Note 

that the characteristics can be made nonsymmetrical to perform governor control and frequency 

response.

∆Freq = Freqref – Freq

slope = Ddn 

-0.02 -0.01 0.0 0.01 0.02 0.03 (p.u.)

fdb2

slope = Dup 

fdb1

∆Freq/∆P

DdnMin 

DupMax 

Figure 54. Graphical illustration of real power regulation during a frequency excursion
38

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4 PV Dynamic Model Validation

Dynamic model validation is not an easy task to perform and includes many stages. Ideally, as 

much information as possible is needed. In a dynamic simulation, enough information may not 

be available to simulate an actual PV plant that we want to validate. In such a case, assumptions 

about the missing data have to be made; however, in some cases, the validation simply cannot be 

performed. On the other hand, having too much but inaccurate information may lead to a bad 

validation and an inaccurate representation of a PV inverter or PV plant.

A typical model validation will represent a PV plant as shown in Figure 55, in which a single PV 

inverter represents the total generation of an entire plant. The first step-up transformer 

connecting the PV inverter to the collector system is used to step up the voltage from low voltage 

to medium voltage (e.g., 480 V/34.5 kV). The collector system represents the lines or cables 

interconnecting the step-up transformer within the power plant to the substation transformer,

where all the output of the PV inverters within the PV plant are stepped up to the transmissionlevel voltage (e.g., 34.5 kV/230 kV) to be transmitted over long distances. This collector system 

can be aggregated into a single impedance represented by Zcollector.

The recorded voltage measured at the point of interconnection is used to drive the simulation as 

the infinite voltage source at the point of interconnection. The simulation output of the real and 

reactive power as well as the output currents were compared to the measured data.

Figure 55. Single-line diagram illustrating the dynamic model validation

4.1 Three-Phase PV Plant Validation

4.1.1 Detailed Model Implementation

A detailed model of the circuit implementation is shown in Figure 56 below. To prepare for 

dynamic validation, the data measured at the point of interconnection is used as the input to the 

detailed model; these are usually three-phase voltages and currents. The real and reactive power 

output can be computed, or it can be obtained from the data recorder. Note that the real and 

reactive power from the calculation may contain high-frequency noise, whereas the output data 

obtained from the measurement is usually filtered. For the purpose of the validation, we use a 

moving average filter for the real and reactive power output computed from the measured threephase voltages and currents.

PV

 PV 

Generator

 

 230kV/34.5kV

Input V and f

Zcollector

A B C

Compare P & Q (simulated vs measured)
39

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Figure 56. Circuit diagram illustrating the dynamic model validation for a detailed model

The initial condition (pre-fault) of the simulation is adjusted to match the pre-fault measured 

data. The measured values of the real and reactive power as shown in Figure 57 are used to 

adjust the commanded real and reactive power. The measured data is shown in blue, and the 

simulated results are shown in green. As shown, the simulation very closely follows the actual 

output measurement.

Figure 57. Real and reactive power output of the simulations

In a real set-up, ideally the solar irradiance should be the input; however, this information is 

seldom available, and—in addition to the transient model analysis, in which the duration of the 

observation is only a few seconds—this input is less important; thus, we assume that the solar 

irradiance is constant during the disturbance. The real and reactive power in the pre-fault 

condition is used to set the real and reactive power commands (reference real and reactive 

power). These reference values are considered to be constant for the duration of the fault. As 

shown in Figure 57, during the fault the result of the simulation indicates that the real and 

reactive power changes. That is a result of the control actions of the PV inverter, and it is not 

because of the reference values of the real and reactive power that are changing during the 

Main : Graphs

x 4.950 5.000 5.050 5.100 5.150 5.200 5.250 

-0.20 

0.00 

0.20 

0.40 

0.60 

0.80 

1.00 

1.20 

1.40 

1.60 Pmeasured Psimulated

-0.75 

-0.50 

-0.25 

0.00 

0.25 

0.50 

0.75 

1.00 

1.25 

1.50 Qmeasured Qsimulated

Real 

Power

Reactive 

Power
40

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disturbance. A comparison of the reference values to the measured values shows that the 

controller of the dynamic models functions properly, as indicated in Figure 57.

Figure 58. Voltage and current waveforms using a detailed model representation for (a) voltages 

measured, (b) currents measured, and (c) currents simulated

The voltage applied to drive the simulation is shown in the top row of Figure 58. The PV plant 

responded to this voltage, thus generating the current waveforms shown in the bottom row of 

Figure 58. A comparison of the measured current waveforms to the simulated waveforms 

indicates that the dynamic model and the controller represent the actual PV plant. Note that the 

output current, real power, and reactive power are determined by the voltage and the control 

parameter set for this particular PV plant or PV inverter. By comparing the output real and 

reactive power shown in Figure 57 to the output currents shown in Figure 58 (simulated versus 

measurement), we can conclude that the PV plant dynamic model very closely represents the 

actual plant.

4.1.2 Average Model Implementation

The average model of the circuit implementation is shown in Figure 59 below. The process to 

prepare for dynamic validation of the average model is the same as that described in the detailed

model representation.

Figure 59. Circuit diagram illustrating the dynamic model validation of an average model

Main : Graphs

x 4.950 5.000 5.050 5.100 5.150 5.200 5.250 

-40 

-30 

-20 

-10 

0 

10 

20 

30 

40 Va_measured Vb_measured Vc_measured

-0.050 

-0.040 

-0.030 

-0.020 

-0.010 

0.000 

0.010 

0.020 

0.030 

0.040 

0.050 Ia measured Ib measured Ic measured

-0.050 

-0.040 

-0.030 

-0.020 

-0.010 

0.000 

0.010 

0.020 

0.030 

0.040 

0.050 Iabc simulated

Line Voltages

Measured

Currents

Simulated

Currents

Main : Graphs

sec 4.950 5.000 5.050 5.100 5.150 5.200 5.250 

-0.050 

-0.040 

-0.030 

-0.020 

-0.010 

0.000 

0.010 

0.020 

0.030 

0.040 

0.050 Ia_flt Ib_flt Ic_flt
41

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(a) Real and reactive power

(b) Three-phase voltages and currents

Figure 60. Comparison of the simulation output to the measured output for an average model

Figure 60 (a) shows the real power compared to the reactive power, and Figure 60 (b) shows the 

voltage and current waveforms measured at the point of interconnection. This is the voltage used 

to drive the simulation. A comparison of Figure 57 to Figure 60 (a) shows that there is almost no 

difference between the detailed model and the average model. Also, a comparison of Figure 58 

to Figure 60 (b) shows that the current waveforms from the detailed model are very similar to the 

current waveforms from the average model. The only difference is the apparent harmonics 

shown in the output of the detailed model, but the fundamental components are very closely 

matched.

Main : Graphs

x 4.950 5.000 5.050 5.100 5.150 5.200 5.250 

-0.20 

0.00 

0.20 

0.40 

0.60 

0.80 

1.00 

1.20 

1.40 

1.60 Pmeasured Psimulated

-0.75 

-0.50 

-0.25 

0.00 

0.25 

0.50 

0.75 

1.00 

1.25 

1.50 Qmeasured Qsimulated

Main : Graphs

x 4.950 5.000 5.050 5.100 5.150 5.200 5.250 

-40 

-30 

-20 

-10 

0 

10 

20 

30 

40 Va_measured Vb_measured Vc_measured

-0.050 

-0.040 

-0.030 

-0.020 

-0.010 

0.000 

0.010 

0.020 

0.030 

0.040 

0.050 Ia_measured Ib_measured Ic_measured

-0.050 

-0.040 

-0.030 

-0.020 

-0.010 

0.000 

0.010 

0.020 

0.030 

0.040 

0.050 Iabc simulated
42

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

4.2 Single-Phase PV Plant Validation

In this section, a single-phase PV plant is validated against the measured data. This small-scale 

PV plant is illustrated in the circuit diagram presented in Figure 61.

Figure 61. Diagram illustrating a single-phase PV plant circuit

Figure 62 (a) shows the voltage waveforms measured at the point of interconnection. This is the 

voltage used to drive the simulation. The voltage dip is caused by a fault occurring in the 

transmission far away from the PV plant. 

(a) Voltage (b) Real and reactive power

Figure 62. The voltage used to drive the simulation and the corresponding real and reactive power 

output 

The real and reactive power output shown in Figure 62 (b) are the output of the simulation and 

the measured output. As mentioned previously, the measured data of the real power and the 

reactive power are filtered and the simulated output of the real and reactive power shows 120-Hz 

ripples, which is a typical characteristic of single-phase output power. 

Tch

100000.0 [uF]

E_dc

T1

T1 T3

T6

T4 T6

T3

T4

Idc1

P = 0.7634

Q = 0.02874

V = 0.6918

V

A

0.0001 [H]

Lls

Ipv

Vpv

0.1 [ohm] I_chop

R=0 BRK_DC

Eabc

V f

R=0 Fsource

Vsource

Iabc

P = 0.7587

Q = -0.03126

V = 34.5

V

A #1 #2

3.0 [MVA]

0.69 [kV] / 34.5 [kV]

0.001 Eabc_hi

Main : Graphs

x 1.50 2.00 2.50 3.00 3.50 4.00 

0 

50 

100 

150 

200 

250 

300 

350 

400 

450 Vpvrms

Main : Graphs

x 1.50 2.00 2.50 3.00 3.50 4.00 

0.0 

1.5k

3.0k

Ppv Ppv m

Main : Graphs

x 1.50 2.00 2.50 3.00 3.50 4.00 

0.0 

1.5k

Qpv Qpv m

Real Power

Reactive Power

Ppv_m - measured

Ppv - simulation

Qpv_m - measured

Qpv - simulation
43

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

The output currents are shown in Figure 63. The simulation output current waveform is shown in 

Figure 63 (a), and the measured output current waveform is shown in Figure 63 (b). A 

comparison of the output current magnitude from the simulation result to the measured data is 

shown in Figure 63 (c). 

Figure 63. Output current waveforms and magnitude

Main : Graphs

x 1.50 2.00 2.50 3.00 3.50 4.00 

0.00 

0.20 

0.40 

0.60 

0.80 

1.00 

1.20 Imagnitude Ifilt

Output Current Magnitude (p.u.)

Ifilt – measured filtered Imagnitude

Imagnitude - simulation

Main : Graphs

x 3.00 3.20 3.40 3.60 3.80 

-30 

-20 

-10 

0 

10 

20 

30 

40 Ipva

I – simulated 

I - measured
44

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

5 Summary

We have developed PSCAD modules to simulate a (three-phase and single-phase) PV inverter at 

the equipment level and at the network level. Detailed and average dynamic models have been 

completed. The detailed model can be used to simulate the impact of a grid disturbance on the 

power semiconductor switches and other power converter components; similarly, it can be used 

to simulate failures in the power semiconductor and the impact on the output currents, real 

power, and reactive power delivered to the grid. The average model can be used to simulate 

power system dynamics for various control algorithms implemented on the power converter.

The dynamic models were developed in the PSCAD platform and designed to simulate both 

normal and unbalanced conditions. This capability is not available in the commonly used 

positive-sequence power system planning software.

The advantage of the average model compared to the detailed model is that the simulation 

integration time step can be shortened significantly, thus shortening the simulation time. On the 

other hand, in the average model we lose the detail of the power converter model and are unable 

to simulate the malfunction of the power semiconductors or different sizes of power converter 

components.

We also developed the WECC-REMTF controllers REEC, REGC, and REPC. With minor 

modifications, these controllers can be set to perform fault ride-through capability and ancillary 

service functions, such as frequency and inertial response, governor droop control, reserve, and 

others.

Finally, we performed dynamic model validations using recorded data from two PV plants. In 

both cases, the results of the simulations very closely followed the measured data; thus, this is a 

good indication that the simulated dynamic models represent real PV plants. Because of a

confidentiality agreement, we are unable to disclose the location, size, and detail of the PV 

plants.
45

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References 

[1] Muljadi, E.; Singh, M.; Gevorgian, B. PSCAD Modules Representing PV Generator.

NREL/TP-5500-58189. Golden, CO: National Renewable Energy Laboratory, August 2013.

[2] Grainger, J.; Stevenson, Jr., W. Power System Analysis. ISBN-13: 978-0070612938, ISBN10: 0070612935. New York: McGraw-Hill, January 1, 1994.

[3] Bergen, A.R.; Vittal, V. Power Systems Analysis. 2nd edition. ISBN-13: 978-0136919902,

ISBN-10: 0136919901. Upper Saddle River, NJ: Prentice Hall, 1999. 

[4] Phadke, A.G.; Thorp, J.S. Synchronized Phasor Measurements and Their Applications 

(Power Electronics and Power Systems). ISBN-10: 0387765352, ISBN-13: 978-0387765358. 

New York: Springer Science Business Media, LLC, August 20, 2008.

[5] Wan, Y.H. Synchronized Phasor Data for Analyzing Wind Power Plant Dynamic Behavior 

and Model Validation. NREL/TP-5500-57342, NTIS/GPO Number: 1067916. Golden, CO: 

National Renewable Energy Laboratory, 2013.

[6] Allen, A.; Santoso, S.; Muljadi, E. Algorithm for Screening Phasor Measurement Unit Data 

for Power System Events and Categories and Common Characteristics for Events Seen in 

Phasor Measurement Unit Relative Phase-Angle Differences and Frequency Signals.

NREL/TP-5500-58611. Golden, CO: National Renewable Energy Laboratory, 2013. 

[7] Mohan, N.; Undeland, T.M.; Robbins, W.P. Power Electronics: Converters, Applications, 

and Design. 3rd edition. ISBN-13: 978-0471226932, ISBN-10: 0471226939. New York: 

Wiley, October 10, 2002. 

[8] Krause, P.C.; Wasynczuk, O.; Sudhoff, S.D.; Pekarek, S. Analysis of Electric Machinery and 

Drive Systems. 3rd edition. ISBN-13: 978-1118024294, ISBN-10: 111802429X. Piscataway, 

NJ: Institute of Electrical and Electronics Engineers, June 17, 2013.

[9] Ong, C.-M. Dynamic Simulations of Electric Machinery: Using MATLAB/SIMULINK. ISBN13: 978-0137237852, ISBN-10: 0137237855. Upper Saddle River, NJ: Prentice Hall, 

September 29, 1997. 

[10] WECC-REMTF. Generic Solar Photovoltaic System Dynamic Simulation Model 

Specification. Salt Lake City, UT: September 2012. 
46

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Appendix: Control Blocks—REPC, REEC, and REGC

The information on the control blocks presented here is as described in the Western Electricity 

Coordinating Council’s Renewable Energy Modeling Task Force report on Generic Solar 

Photovoltaic System Dynamic Simulation Model Specification (WECC 2012). 

REPC 
47

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Table A-1. Parameters for the REPC 
48

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

REGC 
49

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Table A-2. Parameters for the REGC 
50

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REEC 
51

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Table A-3. Parameters for the REEC 
52

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.