eeh - eth z power system s laboratory ... digsilent powerfactory was used as a simulation...

eeh power systemslaboratory

Ganbayar Puntsagdash

Stability Analysis with DecentralizedControl of Photovoltaic Systems

Master’s ThesisPSL1215

EEH – Power Systems LaboratorySwiss Federal Institute of Technology (ETH) Zurich

Expert: Prof. Dr. Göran AnderssonSupervisors: Dr. Adrian Timbus (ABB), Matthias A.Bucher (ETH)

Zurich, January 25, 2013

Acknowledgement

First of all I want to thank my supervisor Dr. Adrian Timbus from ABBwho made this master’s thesis possible. I always appreciated your input andcommitment. I also want to give warmest thanks to my supervisor MatthiasBucher from ETH who helped me to stay focused and motivated throughoutthe entire project. In addition, I want to thank Matts Larsson from ABBfor many fruitful technical discussions and valuable perspectives. MariaVrakopoulou from ETH is another person who has given tireless supportin answering my questions in modelling. Thanks also to Prof. GöranAndersson for inspiration and new perspectives. Last but not least, I wantto express deep gratitude for my friend David Krammer and my sisterGereltuya Puntsagdash for encouragement, support and proofreading.

iii

Abstract

In this master’s thesis the frequency stability analysis with decentralizedphotovoltaic systems was done. Focus of the study was on two regulationsin Germany, the old DIN VDE 0126-1-1 and its replacement VDE-AR-N4105:2011-08, which force the photovoltaic systems to take control actionsin case of an overfrequency over 50.2 Hz. DIgSILENT PowerFactory wasused as a simulation environment. The IEEE 9 bus grid model with dif-ferent photovoltaic shares from 10% to 60% was used. In order to find arelation between the volume of primary frequency control reserve and thephotovoltaic share, the primary frequency control reserve of the system wasvaried. Overfrequency was triggered by a loss of load and photovoltaic con-trol reaction and frequency responses for the different regulations were ana-lyzed. The outcome of the study for the old regulation were numerical valuesof photovoltaic shares which could be withstand by the grid with differentsizes of primary frequency control reserves. Further, it was shown that in thesystem with the new regulation there is no stability problem anymore andthe system frequency can be stabilized. Moreover, the more photovoltaicsystems that are installed in the grid, the more they contribute to the pri-mary frequency control. A possibility for a higher potential of contributionto the frequency stability was shown as well.

v

Contents

List of Acronyms ix

1 Introduction 1

2 Regulations in Germany 32.1 Photovoltaic in Germany . . . . . . . . . . . . . . . . . . . . . 32.2 Regulations in Germany before November 2011 . . . . . . . . 5

2.2.1 Automatic Disconnection . . . . . . . . . . . . . . . . 52.2.2 50.2 Hertz Problem . . . . . . . . . . . . . . . . . . . . 6

2.3 Regulations in Germany after November 2011 . . . . . . . . . 82.3.1 Active Power . . . . . . . . . . . . . . . . . . . . . . . 82.3.2 Reactive Power . . . . . . . . . . . . . . . . . . . . . . 9

3 Modeling of Grid 133.1 Model of the Grids . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 IEEE 9 Bus Grid Model . . . . . . . . . . . . . . . . . 133.1.2 Distribution Grid Model of Västerås . . . . . . . . . . 13

3.2 Model of the Photovoltaic Systems . . . . . . . . . . . . . . . 153.2.1 Introduction to PV Systems . . . . . . . . . . . . . . . 153.2.2 Static Generator as Current Source Model . . . . . . . 183.2.3 Model of Photovoltaic Power Generating Systems . . . 19

4 Model of the Control Units 214.1 Frequency Control . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1.1 Inertia of the System . . . . . . . . . . . . . . . . . . . 214.1.2 Primary Frequency Control . . . . . . . . . . . . . . . 224.1.3 Secondary Frequency Control . . . . . . . . . . . . . . 24

4.2 Controlling of the PV-Generator . . . . . . . . . . . . . . . . 254.2.1 Active Power Reduction . . . . . . . . . . . . . . . . . 264.2.2 Active Power Control . . . . . . . . . . . . . . . . . . 264.2.3 Reactive Power Control . . . . . . . . . . . . . . . . . 28

vii

viii CONTENTS

5 Simulations and Results 315.1 PV units on the Grid . . . . . . . . . . . . . . . . . . . . . . . 315.2 Overfrequency Case Study and Parametrization . . . . . . . . 335.3 Automatic Disconnection DIN VDE 0126-1-1 . . . . . . . . . 35

5.3.1 Description of the Simulations . . . . . . . . . . . . . . 365.3.2 Results of the Simulations . . . . . . . . . . . . . . . . 36

5.4 Characteristic Curve VDE-AR-N4105:2011-08 . . . . . . . . . 405.4.1 Description of the Simulations . . . . . . . . . . . . . . 405.4.2 Simulation Results with Standard Parameters . . . . . 445.4.3 Variation of Parameters . . . . . . . . . . . . . . . . . 45

6 Conclusion 49

A Simulation Results 51A.1 Automatic Disconnection of PV System . . . . . . . . . . . . 51A.2 Characteristic Curve (40% per Hertz) . . . . . . . . . . . . . 59

A.2.1 Variation of Parameters . . . . . . . . . . . . . . . . . 65

Bibliography 67

List of Acronyms

RES Renewable energy sourcesPV PhotovoltaicTSO Transmission System OperatorDSO Distribution System OperatorDG Distributed GenerationSL Slack BusPV bus Active Power and Voltage Specified Bus (Not Photovoltaic Bus)PQ bus Active and Reactive Power Specified BusLV Low VoltageMV Middle VoltageHV High VoltageDSG Deutsche Gesellschaft für Sonnenenergie e.V

(German Society for Solar Energy)DSL DIgSILENT Simulation LanguageWSCC West System Coordination CouncilACE Area Control ErrorAGC Automatic Generation ControlPT1 First Order DelayPCR Primary Frequency Control ReserveENTSO-E European Network of Transmission System Operators for ElectricitySM Synchronous MachineRG Regional Group of ENTSO-ERG CE Regional Group Continental Europe of ENTSO-EPCR Primary Frequency Reserve

ix

x CONTENTS

List of Tables

2.1 Timeline for Retrofitting of PV Systems . . . . . . . . . . . . 8

3.1 Specifications of the Generators . . . . . . . . . . . . . . . . . 143.2 Maximal Demand of the Loads . . . . . . . . . . . . . . . . . 143.3 Specifications of the Lines . . . . . . . . . . . . . . . . . . . . 15

4.1 Typical values of inertia constant H for different types of syn-chronous machines [1] . . . . . . . . . . . . . . . . . . . . . . 21

4.2 Inertia Constants of the Synchronous Machines . . . . . . . . 224.3 Parameter values of Steam Turbine Governor TGOV1 for the

Machines G1 and G2 . . . . . . . . . . . . . . . . . . . . . . . 254.4 Parameter values of Hydro Turbine Governor HYGOV for the

Machines G3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.5 Parameter values of Secondary Frequency Control (AGC) . . 28

5.1 Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Automatic Disconnection of PV Systems . . . . . 38

5.2 Maximal Active Power Pmax and Controller Droop R [p.u] ofthe Synchronous Machines . . . . . . . . . . . . . . . . . . . . 42

5.3 Primary Frequency Control Reserves and Maximum Activa-tion Frequency [2] . . . . . . . . . . . . . . . . . . . . . . . . . 44

A.1 Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve . . . . . . . . . . . . . . . . 65

A.2 Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve with Speed Droop Charac-teristic starting from 50.15Hz . . . . . . . . . . . . . . . . . . 65

A.3 Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve with Speed Droop Charac-teristic starting from 50.10Hz . . . . . . . . . . . . . . . . . . 66

xi

xii LIST OF TABLES

List of Figures

2.1 Installed Capacity of PV’s in GW by Voltage Level. . . . . . 42.2 Maximal PV Power Production of Germany of the Year 2012

at 13:30 on March 25th [3]. . . . . . . . . . . . . . . . . . . . 52.3 An expample of disconnection and active power feed of an

aggregated PV system, which follows the DIN VDE 0126-1-1version Mai 2005 industry standard. . . . . . . . . . . . . . . 6

2.4 Frequency Pendulum caused by Disconnection and Reconnec-tion on Grid with high PV Power Penetration . . . . . . . . . 7

2.5 Decrease of active power feed at overfrequency between 50.2Hzand 51.5Hz [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 1. Provision of reactive power by a distributed generator withmaximum power 3.68 kAV <

∑SE max ≤ 13.8 kAV: the gray

zone [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.7 Provision of reactive power by a distributed generator with

maximum power∑SE max > 13.8 kAV [5]. . . . . . . . . . . . 11

2.8 Standard characteristic curve for cosφ(P ) [5]. . . . . . . . . . 11

3.1 IEEE 9-Bus System with 3 Synchronous Machines . . . . . . 143.2 Grid Model of Västerås, Sweden . . . . . . . . . . . . . . . . . 163.3 Simplified Diagram of an Equivalent Circuit for a Solar Cell [6] 173.4 Characteristic curves I = f(V ) and P = f(V ) of a monocrys-

talline silicon solar cell with a cell area of approximately 102cm2, irradiance amounting to 1 kW/m2 and 25C cell temper-ature [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5 Schematic Principle of a Grid-Connected PV System [7] . . . 173.6 Current Source Mode of Static Generator [8] . . . . . . . . . . 183.7 Input/Output Definition of a Static Generator (PV) in Cur-

rent Source Model [8] . . . . . . . . . . . . . . . . . . . . . . . 183.8 Model of PV Systems . . . . . . . . . . . . . . . . . . . . . . 20

4.1 Modified Steam Turbine Governor TGOV1 . . . . . . . . . . 234.2 Modified Steam Turbine Governor HYGOV . . . . . . . . . . 244.3 Model the Secondary Frequency Control of Single Area . . . . 27

xiii

xiv LIST OF FIGURES

4.4 Secondary Controller Block . . . . . . . . . . . . . . . . . . . 274.5 Active Power Reduction Block . . . . . . . . . . . . . . . . . . 274.6 Vdc Controller Block . . . . . . . . . . . . . . . . . . . . . . . 28

5.1 PV Systems on Low Voltage Level of Västerås Grid Model . . 325.2 Aggregated PV Power Plant on the Transmission Level of WCSS 335.3 Active Power Reduction of the Load A which is 10% of Total

Load and the Frequency Response of the System with Unlim-ited Primary Frequency Control Reserve . . . . . . . . . . . . 34

5.4 Primary and Secondary Control Part of the Thermal GovernorTGOV1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.5 Overfrequency Simulation: 10% of Load Reduction, 30% PVShare with Automatic Disconnection Function at 50Hz andunlimited Primary Frequency Control . . . . . . . . . . . . . 37

5.6 Automatic Disconnection DIN VDE 0126-1-1:(a) Unlimited Primary Control Reserve (PCR) (b) 20% PCR(c) 15% PCR (d) 10% PCR (e) 7.5% PCR (f) 5% PCR (g)2.5% PCR (h) 1% PCR . . . . . . . . . . . . . . . . . . . . . 39

5.7 Characteristic Curve for Active Power of PV systems accord-ing to VDE-AR-N4105:2011-08; P_M is Active Power of MPPTMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.8 Speed Droop Characteristic Curve Area of a PV System . . . 415.9 Speed Droop Characteristic Curves of Synchronous Machines

and PV Systems . . . . . . . . . . . . . . . . . . . . . . . . . 435.10 Maximal Frequency Response in Case of Overfrequency for

Different Primary Control Reserves and PV Shares . . . . . . 445.11 Frequency Response (a) 12.5% Primary Frequecy Reserve(PCR)

(b) 10% PCR (c) 7.5% PCR (d) 5% PCR (e) 2.5% PCR (f)1% PCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.12 Maximal Frequency Response in Case of Overfrequency forDifferent Primary Control Reserves and PV Shares with SpeedDroop Characteristic starting from 50.15Hz. . . . . . . . . . . 47

5.13 Maximal Frequency Response in Case of Overfrequency forDifferent Primary Control Reserves and PV Shares with SpeedDroop Characteristic starting from 50.10Hz. . . . . . . . . . . 47

A.1 Frequency Response, Automatic Disconnection, 10-50% PVShare, unlimited Primary Control Reserves . . . . . . . . . . 51

A.2 Frequency Response, Automatic Disconnection, 10-40% PVShare, 20% Primary Control Reserves . . . . . . . . . . . . . 52



LIST OF FIGURES xv

A.5 Frequency Response, Automatic Disconnection, 10-20% PVShare, 7.5% Primary Control Reserves . . . . . . . . . . . . . 53

A.6 Frequency Response, Automatic Disconnection, 10-20% PVShare, 5% Primary Control Reserves . . . . . . . . . . . . . . 54

A.7 Frequency Response, Automatic Disconnection, 10% PV Share,2.5% Primary Control Reserves . . . . . . . . . . . . . . . . . 54

A.8 Frequency Response, Automatic Disconnection, 10% PV Share,1% Primary Control Reserves . . . . . . . . . . . . . . . . . . 55

A.9 Frequency Response, Automatic Disconnection, 30% PV Share,Unlimited Primary Control Reserves . . . . . . . . . . . . . . 56

A.10 Frequency Response, Automatic Disconnection, 20% PV Share,5% Primary Control Reserves . . . . . . . . . . . . . . . . . . 57

A.11 Frequency Response, Automatic Disconnection, 30% PV Share,15% Primary Control Reserves . . . . . . . . . . . . . . . . . 58

A.12 Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, unlimited Primary Control Reserves . . . . 59

A.13 Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 10% Primary Control Reserves . . . . . . . 59

A.14 Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 7.5% Primary Control Reserves . . . . . . 60


A.16 Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 2.5% Primary Control Reserves . . . . . . 61


A.18 Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 7.5% Primary Control Reserves . . . . . . . . 62

A.19 Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 5% Primary Control Reserves . . . . . . . . . 63

A.20 Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 2.5% Primary Control Reserves . . . . . . . . 64

xvi LIST OF FIGURES

Chapter 1

Introduction

Nowadays the Renewable Energy Sources (RES) are becoming one of thecentral topics of energy supply and energy politics in developed and emergingcountries. Encouraged by subsidies in west European countries the capacityof solar and wind energy is increasing. Especially the installed capacity ofPhotovoltaic (PV) systems has grown rapidly in the last years. The leadingcountries in Europe are Germany, Italy and Spain. By the end of the year2012 Germany had a capacity of 32.8GWp of PV systems [9].

More than 75% of the installed capacity of PV systems in Germany isdecentralized. The decentralized PV systems are connected to the distribu-tion grid level. Since on good sunny days high injections of decentralized PVsystems are possible, the question how they influence the grid stability is ofinterest.

The decentralized PV systems are in general not controllable. In case ofa big fault in the grid the PV systems in Germany have to obey regulations.Currently the PV system inverters have settings corresponding to two regu-lations, the current one and the predecessor one. The new PV systems whichhave been installed after November 2012 have the setting corresponding tothe current regulation while the old PV systems have the setting correspond-ing to the predecessor regulation.

Goals and Structure of this Thesis

In this master’s thesis the frequency stability of a system in terms of high PVpenetration with both regulations was analyzed. Particularly the frequencyresponse of the system with different PV shares and different regulations wastested. Mainly, in this study the following questions were pursued:

• How much PV share can a system with the old regulation withstand?

• Is the system more stable with the new regulation?

• Which kind of stability problems could occur with the new regulation?

1

2 CHAPTER 1. INTRODUCTION

Further, the potential of the frequency stability support by decentralized PVsystems was analyzed and discussed.

This master’s thesis report is structured as follows:

• in Chapter 2 the German regulations for grid-connected decentralizedPV systems are introduced

• in Chapter 3 the methods of the study and the used models of electricpower grid are explained

• in Chapter 4 the implementation of the control units is presented

• in Chapter 5 the conducted simulations are described and the simula-tion results are discussed.

Chapter 2

Regulations in Germany

In this chapter the information about PV systems in Germany is given andthe regulations for grid-connected decentralized PV system and the problemsof it are introduced.

2.1 Photovoltaic in Germany

Germany is currently ranked among the world’s largest producers of elec-tricity from solar power [9, 10]. Energy production from PV in year 2011was 24.73 TWh[9], which was around 4.12 % of total electric energy demandof Germany [11]. With an installed PV capacity of 32.8GWp at the end of2012, Germany is the leading country by installed PV capacity [9]. If wecompare it with around 65GW peak demand of Germany the installed PVcapacity of 32.8GWp is notable substantial.

Comparing to all other power generating units PV systems have no ro-tating mass and do not contribute to the total system inertia. In case of afrequency disturbance the PV systems cannot absorb or release energy in anatural way like rotating masses [12]. Solar panels are connected throughpower inverters, which convert the direct current (DC) to alternating current(AC), with or without transformation to the public electric grid. Accord-ing to the German grid code all to the grid connected PV systems have tobe equipped with a mechanism, which contribute to the stabilization of thesystem in emergency situation [13, 14]. This is explained in Section 2.2. Interms of controllability we distinguish two kinds of PV systems:

• controllable

• and non-controllable.

The controllable PV system has to follow the reference signal, which issent by a central authority (TSO, DSO, energy producer). Communicationbetween (remote control) PV systems and a central authority is possible, so

3

4 CHAPTER 2. REGULATIONS IN GERMANY

that the central authority is informed about the current energy productionof the PV systems and can send a reference signal. In case of the control-lable PV systems active and reactive power control is possible. Usually thecontrollable PV systems are large scale PV parks installed on middle voltagelevel and operated by energy supply companies [7].

The non-controllable PV systems have no communication capabilities.They operate preferably at Maximum Power Point Tracking (MPPT) modeand do not provide or consume reactive power for local voltage control. Moredetails about MPPT mode is explained in Section 3.2.1. Usually the non-controllable PV systems have small power capacity and are installed on theroofs of residual houses and companies.

The controllable PV systems are usually installed on medium and highvoltage level (> 0.4 kV) and the non-controllable PV systems on a low voltage(≤ 0.4 kV). However 73 % of all installed capacity of PV systems are on lowvoltage level [15]. According to the data provided by Deutsche Gesellschaftfür Sonnenenergie e.V. (DGS), by the end of the year 2011 the 18.67GW oftotal installed PV capacity 24.46GW are on distribution voltage level andthe rest of 5.79GW on transmission voltage level [15]. The relation of voltagelevels are illustrated in Figure 2.1.

Figure 2.1: Installed Capacity of PV’s in GW by Voltage Level.

On the sunny days the injection of over 20GW power during the peakhours (12:00 - 14:00) is theoretically possible. In Figure 2.2 we can observethe PV power curve the day with maximum solar energy production of theyear 2012. At 13:30 of this day all PV generators of Germany produce21.1GW [3]. That would be 32.5 % of power demand, if we assume 65 GWof peak demand in Germany.

With the facts and data presented above we conclude that the non-controllable PV systems installed on low voltage levels levels can be signifi-cant for the stable and secure operation of the whole interconnected system.In the case of Germany, regulations for the secure operation were set. With arapid rise of installed PV systems capacity over the last years the regulationscontinuously were adjusted.

2.2. REGULATIONS IN GERMANY BEFORE NOVEMBER 2011 5

Figure 2.2: Maximal PV Power Production of Germany of the Year 2012 at13:30 on March 25th [3].

2.2 Regulations in Germany before November 2011

As mentioned in Section 2.1 the PV systems on the low voltage level areremotely not controllable, which is not the case for PV systems installed onthe transmission voltage level. Since 76.3 % of the total installed capacityin Germany is installed on the distribution grid level, in this master’s thesiswe focus on PV systems on the distribution grid level. From now when werefer to PV systems we mean always remotely non-controllable PV systemson distribution grid level.

In the year the 2001 installed capacity of PV system was negligibly smallcompared to other power generating units [9]. In the 4th edition of Regu-lation for Distributed Power Generation Systems on Low Voltage Level byVDEW [16], which was published in May 2001, there is no technical require-ments for PV systems to control frequency and voltage. The PV systemsoperated at MPPT-mode with power factor 1, which means there was noreactive power support for local voltage stability.

2.2.1 Automatic Disconnection

Caused by the increase of the PV systems in Germany between 2001 and2005, in May 2005 the regulations [16] were reviewed and supplemented withDIN VDE 0126-1-1 [13] industry standard. According to this standard all PVsystems should be able to disconnect automatically if voltage or frequencyreach certain operating points [13]. The new operations requirements, whichare relevant for this master’s thesis, are listed below:

• Automatic disconnection within 0.2 s from the grid if system frequencyis under 47.5Hz and over 50.2Hz

• Automatic disconnection within 0.2 s from the bus if bus voltage isunder 0.8 p.u. and over 1.15 p.u

• After a disconnection, which is caused by overfrequency, a reconnectionis allowed at least after 30 s if the system frequency is under 50.05Hz.


The increase of active power feed after the reconnection has to occurstepwise. Each step should not exceed 10 % of maximum power.

Almost instantaneous disconnection supposes to support the primarycontrol of the system to stop frequency increase. To avoid re-rise of thefrequency after the reconnection, the PV systems have to wait until the fre-quency is stabilized and increase the active power in-feed. In Figure 2.3 anexample of overfrequency and the active power feed of an aggregated PVsystem is illustrated. In Chapter 5 the simulations are described in detail,therefore we do not explain the details of the plot.

Figure 2.3: An expample of disconnection and active power feed of an ag-gregated PV system, which follows the DIN VDE 0126-1-1 version Mai 2005industry standard.

2.2.2 50.2 Hertz Problem

Advantaged through EEG (Erneuerbare-Energien-Gesetz: German Renew-able Energy Act) the installed capacity of PV power plants in Germany weregrowing continuously [4]. Already at the end of the year 2010 12.7GW cu-mulative capacity of PV systems were installed on the low voltage level [4].The regulation of the year 2005 on automatic disconnection was not suitableanymore. Theoretically, if the frequency goes over 50.2Hz the loss of 12.7GW generation was possible, which can lead to big stability problems. Apossible worst case scenario could occur as follows [17]:

• Germany exports 3 GW power to Italy over Switzerland

• For some reasons the transmission lines between Switzerland and Italyfail

• All other transmission lines to Italy are overloaded

• After certain time Italy is cut off (load shedding) from the synchronousarea

2.2. REGULATIONS IN GERMANY BEFORE NOVEMBER 2011 7

• Instantaneously Germany has overproduction, which leads to frequencyrise over 50.2Hz

• 9 GW of PV systems are disconnected from the grid, which leads tofrequency fall under 47.5Hz

• Following the regulations (disconnection at 47.5Hz, other decentral-ized power plants (wind energy, biogas, small hydro power plants) aredisconnected from grid, which leads to more frequency fall

• Primary control is not able to control the frequency and the systemcollapses

In the introduced worst case scenario are the automatic disconnectionof other decentralized power plants at frequency < 49.5Hz is considered.Even if we neglect this disconnection at underfrequency there could occuranother stability problem. After the disconnection at 50.2Hz the systemwill be stabilized. 30 s after the stabilization all disconnected PV systemswill be reconnected and start to increase the active power feeds. If theinjected active power after the reconnection is large and and if primary andsecondary control reserves are not sufficient, the frequency rise the frequencywill achieve repeatedly 50.2Hz and the decentralized PV systems will bedisconnected again. In this way we can have a frequency pendulum [17].In Chapter 5 this phenomenon is investigated. In Figure 2.4 such kind offrequency pendulum is illustrated.

Figure 2.4: Frequency Pendulum caused by Disconnection and Reconnectionon Grid with high PV Power Penetration

Under normal conditions the frequency deviation over 0.2Hz is unlikely.However, under unexpected large-scale disturbance big frequency deviationsare possible. For example the blackout in Italy in 2003 and the Europeanpower grid failure in 2006 [18, 19]. Increasing of fluctuating energy sourceslike wind and solar also influence the frequency deviation, for example sud-denly increase of wind or sun radiation. Newly, hourly traded energy causeshourly re-dispatch of power plants which leads to big frequency deviationsat each hour [20].


PV Systems Time DeadlineInstalled after mid. Nov. 2011 fulfill the new requirements

(retrofitting is not necessery)Installed before mid. Nov. 2011 August 31st 2013with rated power > 100 kWInstalled before mid. Nov. 2011 May 31st 2014with rated power between 30 kW and 100 kWInstalled before mid. Nov. 2011 December 31st 2014with rated power < 30 kW

Table 2.1: Timeline for Retrofitting of PV Systems

2.3 Regulations in Germany after November 2011

The German new technical requirements for power generation systems con-nected to the low-voltage distribution network (VDE-AR-N 4105:2011-08 [5])are valid from January 1st 2012. All new PV systems have to follow the newregulations and all old PV has to be retrofitted. According to [17] by theend of the year 2014 all PV systems on low voltage have to be retrofitted. InTable 2.1 the retrofitting time schedule for different PV systems are listed.

2.3.1 Active Power

Generation Management and Grid Safety

Power generation systems with maximum power of > 100 kW have to be ableto reduce the active power feed stepwise in maximal 10 % of maximum activepower. The power reduction reference signal is sent by Distribution SystemOperator (DSO) and the power generation system has to react immediately.The allowed maximum time delay is 1 minute. The DSO has no remoteaccess to the controller devices (inverter) of the power generation system.

Active Power Feed at Overfrequency

At frequencies between 50.2Hz and 51.5Hz all (decentralized) controllablepower generation systems have to decrease the momentary active power feedPM with gradient of 40 % per Hz during rise of the frequency and increaseduring the drop of the frequency. Following equation describes the activepower reduction for this case

∆P = 20 · PM ·50.2Hz− fGrid

50Hzfor 50.2Hz ≤ fGrid ≤ 51.5Hz (2.1)

where PM is momentary active power and the fGrid is the measuredgrid frequency. In Figure 2.5 power curve characteristic in dependence offrequency is presented.

2.3. REGULATIONS IN GERMANY AFTER NOVEMBER 2011 9

Figure 2.5: Decrease of active power feed at overfrequency between 50.2Hzand 51.5Hz [4].

If the system frequency reaches the point > 51.5Hz the power generatingsystem has to be disconnected from grid. Non-controllable power generationsystems in case of over frequency between 50.2Hz and 51.5Hz, alternativelyto decreasing of power, can be disconnected from grid. In this case theswitching-off frequency steps has to be maximum 0.1Hz.

Partly controllable power generation systems, for example controllableonly in the range from 70% to 100% of maximal installed power, has to followcharacteristic curve in the controllable region. Outside of the controllableregion the power generating systems have to be disconnected stepwise.

Active Power Feed at Underfrequency

At system frequency between 47.5Hz and 50.0Hz automatic disconnectionfrom grid is forbidden. At system frequency under 47.5Hz the power gener-ation system has to be disconnected from grid.

2.3.2 Reactive Power

The regulations concerning reactive power generation/absorption and sup-port of voltage stability depend on the installed maximal power of the PVsystems.

A small PV system on low voltage with total maximal power SE max ≤3.68 kVA has to follow the Requirements for the connection of micro-generatorsin parallel with public low-voltage distribution networks DIN EN 50438 [21].According to [21] this kind of small generation unit has to keep the powerfactor between 0.95 overexcited and 0.95 underexcited, if the power produc-tion is over 20% of the maximal power. There is no given specification byDSO as long as the tolerance of power factor is kept. In Figure 2.6 thepower factor area is presented. If the power production is below 20% of themaximal power, there are no restrictions for the power factor [21].

A PV system with total maximal power S between 3.68 kVA and 13.8 kVAhas to fulfill the requirements of VDE-AR-N 4105:2011-08 [5]. According to[5] the generation units in this range have to provide the reactive powerwith power factor between 0.95 overexcited and 0.95 underexcited, if thepower production is over 20% of the maximal power [5]. The power factorhas to follow a characteristic curve provided by the DSO. In case of power


production under 20% of the maximal power there is no restriction for thepower factor. In Figure 2.6 the power factor area is illustrated. In Figure2.8 a standard characteristic curve for power factory is shown.

A PV system with total maximal power SE max > 13.8 kVA has to fulfillthe requirements of VDE-AR-N 4105:2011-08 [5] as well. The regulationsfor generation units in this range are the same as for the generation unitswith maximal power S between 3.68 kAV and 13.8 kAV, which was describedahead. The only difference is, the power factor range is between 0.90 overex-cited and 0.90 underexcited. This power factor area is illustrated in Figure2.7.

Figure 2.6: 1. Provision of reactive power by a distributed generator withmaximum power 3.68 kAV <

∑SE max ≤ 13.8 kAV: the gray zone [5].

2.3. REGULATIONS IN GERMANY AFTER NOVEMBER 2011 11

Figure 2.7: Provision of reactive power by a distributed generator with max-imum power

∑SE max > 13.8 kAV [5].

Figure 2.8: Standard characteristic curve for cosφ(P ) [5].

Chapter 3

Modeling of Grid

In this chapter the modeling of the grid and the PV systems is presented.Further, the modeling environment is shortly introduced.

3.1 Model of the Grids

For the simulations of the dynamics the PowerFactory Version 14 by DIgSI-LENT was used. PowerFactory is one of the standard softwares for powersystems modeling, analysis and simulation, which is widely used in the elec-tric energy sector [22]. PowerFactory has a library with IEEE standardmodels for generation, transmission and distribution level, including renew-able energy sources like wind and solar. It has a graphical editor for blockdiagram definition as well as own programming language DSL (DIgSILENTSimulation Language).

3.1.1 IEEE 9 Bus Grid Model

For the study we use IEEE 9-Bus standard system, which represents thescaled West System Coordination Council (WSCC), the western states ofthe USA. The IEEE 9-Bus model has 3 synchronous generators, 3 cumulatedloads and 6 lines. In Figure 3.1 the grid model is illustrated. The mainparameters of the generators were adjusted and are listed in Table 3.1. Thesystem has peak demand of 315MW. Active and reactive peak demand ofeach load are listed in Table 3.2. The lines specifications were taken from thestandard model and are listed in Table 3.3. The model was chosen mainlyto investigate the frequency stability. The governors of the machines andcontrol systems of the model are introduced in Chapter 4.

3.1.2 Distribution Grid Model of Västerås

In order to consider besides the frequency stability also the voltage stabilityon the distribution grid level the IEEE 9-Bus model was extended with

13

14 CHAPTER 3. MODELING OF GRID

Figure 3.1: IEEE 9-Bus System with 3 Synchronous Machines

Smax [MVA] Vnom [kV] H [s]G1 192.00 16.50 6.50G2 192.00 18.00 6.50G3 128.00 13.80 2.50

Table 3.1: Specifications of the Generators

P [MW] Q [MVar]Load A 125.00 50.00Load B 90.00 30.00Load C 100.00 35.00

Table 3.2: Maximal Demand of the Loads

3.2. MODEL OF THE PHOTOVOLTAIC SYSTEMS 15

l [km] Imax [kA] Z [Ω] R [Ω] X [Ω] φ(Z) [deg] x/r-ratioLine1 1.00 1.00 45.275 5.290 44.965 83.290 8.500Line2 1.00 1.00 45.275 5.290 44.965 83.290 8.500Line3 1.00 1.00 38.353 4.497 38.088 83.267 8.471Line4 1.00 1.00 53.694 6.295 53.323 83.267 8.471Line5 1.00 1.00 92.266 20.631 89.930 77.079 4.359Line6 1.00 1.00 49.492 8.993 48.668 79.531 5.412

Table 3.3: Specifications of the Lines

detailed distribution grid. Consider the grid model in Figure 3.2. The modelrepresents one part of the city Västerås in Sweden. The middle voltage levelof the grid is 11 kV. The distribution grid is connected to the Bus 5 of biggerIEEE 9-Bus grid with two 11kV/230kV transformers. On middle voltage wehave a small PV park with the installed capacity of 5MW connected. ThePV park is similar to a real PV park by ABB in Totana in the south eastof Spain [23]. On the bottom of Figure 3.2 we have 2 low voltage partswith nominal voltage of 0.4 kV. On this part the residual PV systems areinstalled, which will be presented in Chapter 5. The x/r-ratios of the linesare between 1 and 3, which mean that the reactive power as well as activepower has influence to the bus voltages. Here, the r represents the resistanceand the x the reactance. With the x/r-ratio it can be determined whetherthe transmission losses are more real or reactive. The cumulative demand ofthe loads is 14.1248MW.

3.2 Model of the Photovoltaic Systems

3.2.1 Introduction to PV Systems

The basic component of the PV systems is a solar cell. The energy is pro-duced by solar cells using a photovoltaic effect. In Figure 3.3 the simplifieddiagram of an equivalent circuit for a solar cell is illustrated. Further infor-mation about solar cells and the photovoltaic effect can be found in Chapter3 of the [6].

Each type of solar cell has its own current-voltage (I-V) characteristiccurve. Depending on material, solar irradiation and temperature the I-Vcurve of a solar cell varies. The Maximum Power Point Tracking (MPPT) is acontrol method of an operation point that maximum power can be generated.The MPPT-controller sets optimal current and voltage for the operating I-Vcurve. In Figure 3.4 example of a I-V curve and according MPPT operationalpoint is illustrated.

We distinguish two types of PV systems application:

• stand-alone PV systems and


Figure 3.2: Grid Model of Västerås, Sweden


Figure 3.3: Simplified Diagram of an Equivalent Circuit for a Solar Cell [6]

Figure 3.4: Characteristic curves I = f(V ) and P = f(V ) of a monocrys-talline silicon solar cell with a cell area of approximately 102 cm2, irradianceamounting to 1 kW/m2 and 25C cell temperature [6]

• grid-connected PV systems [7].

The stand-alone PV systems have peak power up to several kilowattsand are not connected to the electric grid [7]. The generated power is usedlocally directly by the consumer. Usually the stand-alone PV systems havea local storage to store surplus energy. Further, the storage device supportscontrolled output power.

Figure 3.5: Schematic Principle of a Grid-Connected PV System [7]

The grid-connected PV systems are connected to the public electricitygrid through DC/AC inverter [7]. In Figure 3.5 a schematic principle ofa grid-connected PV system is illustrated. There are two kinds of grid-connected PV systems:

• central grid-connected PV systems and


• decentralized grid-connected PV systems [6].

The centralized grid-connected PV systems are big power plants in ruralareas. This kind of PV systems feed power directly to middle voltage or highvoltage level.

The decentralized grid-connected PV systems are usually small powerrange. Mostly they are installed on the roofs of residential houses and com-pany buildings [7]. This kind of PV systems are connected to the low voltagegrid. As mentioned in Chapter 2 75% of total installed PV capacity are de-centralized and connected to the low voltage level. In this master’s thesisthe focus will be on decentralized grid-connected PV systems. Further, theMPPT operation for all PV systems will be assumed.

3.2.2 Static Generator as Current Source Model

One of the standard models of DIgSILENT called Static Generator was usedfor the PV power plants. The Static Generator Model is suitable for non-rotating generators. For PV systems model buildup the current source modewas chosen. The circuit layout of the current source model is illustrated inFigure 3.6.

Figure 3.6: Current Source Mode of Static Generator [8]

Figure 3.7: Input/Output Definition of a Static Generator (PV) in CurrentSource Model [8]

Consider the input/output definition of the current source model in Fig-ure 3.7. To understand the relation between the Static Generators currentsource model and active and reactive power following derivations are pre-


sented. According to the model the current i1 is

i1 =(id_ref · cos(u)− iq_ref · sin(u)

)+

+ j ·(id_ref · sin(u)− iq_ref · cos(u)

)=

= id_ref · eju + j · iq_ref · eju(3.1)

and the output voltage u1 is

u1 = |u1| · cos(u) + j · |u1| · sin(u) = |u1| · eju (3.2)

with

cos(u) = cos ref and sin(u) = sin ref.

Consequently, the output power of the static generator is

S = U · I∗ = |u1| · id_ref − j · |u1| · iq_ref (3.3)

and the active and the reactive powers can be read out as follows

P = |u1| · id_ref (3.4)

Q = − |u1| · iq_ref. (3.5)

We conclude that the active power feed of PV power plant models canbe controlled with the reference signal id_ref and the reactive power feedwith reference signal −iq_ref, if we assume constant bus voltage u1. Bothreference signals are defined in per unit (p.u.).

3.2.3 Model of Photovoltaic Power Generating Systems

The composite frame of the PV systems is presented in Figure 3.8 and willbe denoted as PV Frame. The basic frame was provided by ABB ResearchCorporate Sweden. The PV Frame consists of

• PV Module Model

• Four blocks for measurement

• Static Generator block

• Active Power Reduction block

• Vdc Controller


Figure 3.8: Model of PV Systems

The Active Power Reduction and Vdc Controller was modified and ad-justed for this master thesis.

The PV Module Model block represents the PV panels itself. It has acertain maximal power and the signal p_pv corresponds to the MPPT modepower production. Since the run-time of the simulations only 200 s, in ourmodel the p_pv is constant.

In the PV Frame we have four blocks for measurement of bus voltage,local electric frequency, feed of active and reactive power, phases. Thismeasurement tools send signal to the controlling blocks of the PV Frame.

The Static Generator block represents the input slots of the Static Gen-erator Model, which was explained in Section 3.2.2. It receives referencesignals from Vdc Controller and adjusts the active and reactive power feedto the bus.

The Active Power Reduction Block is for controlling active power. Itreceives frequency measurement value, checks a certain conditions and sendsa reduction signal to the Vdc Controller. The active power condition refers toone of the used regulation, which are discussed in Chapter 2. The structureand the functionality of this block will be explained more detailed in thecontrolling part of this thesis in Chapter 4.

The Vdc Controller block is the main control block of the PV Frame.It processes all signals received from other blocks processes and sends thereference signals for the Static Generators. This block will be explained indetail as well in Chapter 4.

Chapter 4

Model of the Control Units

In this chapter the primary and the secondary control of the modeled grid aswell as the models of the PV control units are introduced.

4.1 Frequency Control

4.1.1 Inertia of the System

In our IEEE 9 bus grid model we have 3 generators with rotating mass. Un-der normal conditions all 3 machines operate synchronously. In case of dis-balance between the power generation and production the system frequencywill deviate from the nominal value (50Hz in Europe) and the machines willaccelerate or decelerate.

A reacting control mechanism almost instantaneously after disturbance isinertia of system. All machines with rotating mass (generators and motors)have inertia, which in case of frequency deviation can inject or absorb energy.The immediate reaction is called inertia response. Inertia response is natural.The inertia of a machine can be expresses with so called inertia constant.Typical inertia constants of synchronous machines are presented in Table4.1.

Types of Synchronous Machine Inertia Constant H(s)

Thermal Power• Steam Turbine 4-9• Gas Turbine 7-10Hydro Power

• Slow (< 200min−1) 2-3• Fast (≥ 200min−1) 2-4

Table 4.1: Typical values of inertia constant H for different types of syn-chronous machines [1]

21

22 CHAPTER 4. MODEL OF THE CONTROL UNITS

Generator Type Rated Power S [MVA] Inertia Constant H [s]G1 Steam 192 6.5G2 Steam 192 6.5G3 Hydro 128 2.5

Table 4.2: Inertia Constants of the Synchronous Machines

We consider the examples in Table 4.1 and set the reasonable values toinertia constants of the synchronous machines of our model. Since the G1and the G2 are steam generators and have the same rated power, we set theaverage of the typical values 6.5 s. The G3 is a slow hydro power plant. Weset there the value 2.5 s. In Table 4.2 the inertia constants are listed.

4.1.2 Primary Frequency Control

Large scale faults in the systems cause very fast frequency droop or rise.This could be for example generator outage, load shedding or outage of alarge transmission line. The fastest control action which will be activated isthe primary frequency control (inertia response is a natural reaction). Thepurpose of the primary frequency control is to keep the frequency within asuitable range. A primary frequency control consists of several power plants.All in primary control participating power plants have controllers, so calledgovernors, which measure local frequency and adapt the power productionwithin few seconds. The primary controllers are purely proportional (P-Controller) and follow the settled speed droop characteristic, which will bedenoted as Si. Typical speed droop characteristics are between 0.04 p.u.and 0.06 p.u. The gain of the P-Controllers has the following relation to thespeed droop characteristic

Kprim,i =1

Sii = 1, . . . , n (4.1)

where the index i denotes the number of the generator. If we assume a con-stant operational point of the generators, since the time constant of primarycontrol fairly small compared to the frequency dynamics of the system [1],we will have following dynamic characteristic of the primary control action,i.e. change of power production

∆Pi = −Kprim,i ·∆f = − 1

Si∆f (4.2)

and the total power generation response of the primary frequency control ofthe system is

∆P =

n∑i=1

∆Pi = −n∑

i=1

1

Si∆f. (4.3)

4.1. FREQUENCY CONTROL 23

Figure 4.1: Modified Steam Turbine Governor TGOV1

consequently we obtain the overall speed droop characteristic of the system

1

S=

n∑i=1

1

Si(4.4)

In our model all 3 synchronous machine participate in the primary fre-quency control. For both steam turbines IEEE governor model TGOV1 andfor the hydro turbine the IEEE governor model HYGOV were selected. Inorder to limit the primary control reserves of each synchronous machines thestandard structures of the governors were modified. In Figure 4.1 and 4.2the block diagrams of modified governor models are illustrated.

Consider the steam turbine governor model in Figure 4.1. The input1

on the slot 2 ω is the local frequency measurement and slot 3 ωref is theconstant nominal frequency. Consequently the sum of those two dω is localfrequency deviation. This frequency deviation signal goes to the gain-block1/K with lim. The parameter R corresponds to the speed droop characteris-tic S. The lower and upper bounds pmin and pmax are the limitation for theprimary reserve of the generator. The output of this gain-block o13 is theprimary frequency control response. This signal will be added to the sec-ondary frequency response, which will be explained in the next subsection,and will be sent to the turbine controller over several blocks.

The hydro turbine governor HYGOV’s primary controller has operationalprinciple like TGOV1 - local frequency measurement and gain-block withlimits. Consider Figure 4.2. The major difference is that the primary con-troller gain-block is in the loop.

1green slot = input, red slot = output


Figure 4.2: Modified Steam Turbine Governor HYGOV

4.1.3 Secondary Frequency Control

The primary frequency control consists of purely proportional controllers.The frequency measurement and control action occurs local at the generator.After the primary frequency action there will be still frequency deviation, socalled Area Control Error (ACE). To eliminate this ACE in addition to theprimary frequency controller a further controller is needed. The purpose ofthe secondary frequency controller is to bring the system frequency back tothe nominal value. The secondary frequency controller is coordinated cen-trally and responsible for balancing unscheduled power deviations within acertain control area. Usually it is performed by the Transmission SystemOperator (TSO). The controller measures the control area frequency. It con-sists of one central controller with Proportional-Integrator (PI-Controller).Let’s assume n generators are participating in the secondary control. Theoutput of the controller will be split to the n parts and will be sent to the gen-erators. Since there is only one central PI-Controller, there is no negativeinteraction between controllers and the ACE can be eliminated. The sec-ondary frequency controller balances the unscheduled inter-area exchanges.Since we have a single area system, this aspect is not of interest.

In our WSCC grid model two of three machines are providing secondarycontrol reserves, one steam (G2) and one hydro (G3) generator. For this pur-pose a secondary frequency controller was implemented. Consider Figure 4.3.Since we have a small scaled grid the frequency measurement was simplified.

4.2. CONTROLLING OF THE PV-GENERATOR 25

Parameter Description Value UnitT3 Turbine Delay Time Constant 2 [pu]T2 Turbine Derivative Time Constant 1 [pu]At Turbine power coefficient 1 [pu]Dt Frictional Losses Factor 0 [pu]R Controller Droop 0.05 [pu]K Secondary Gain 0.075 [pu]T1 Governor Time Constant 0.2 [s]PN Turbine Rated Power 192 [MW]Vmin Minimum Gate Limit 0 [pu]Vmax Maximum Gate Limit 1 [pu]pmin Lower Bound Primary Reserve 0 [pu]pmax Upper bound Primary Reserve 1 [pu]

Table 4.3: Parameter values of Steam Turbine Governor TGOV1 for theMachines G1 and G2

The measurement block Slow Frequency Measurment measures frequency onthe Bus 5 (PQ - Bus), which has no connected synchronous machine or PVsystem. The frequency measurement signal goes to the Secondary Controllerblock, where the ACE will be processed. The output signal delta_P is theresulting ACE, which will be split by the Spliter and sent to the generatorsG2 and G3. The Spliter has adjustable ratio of generators. The default ratiois set at 0.5:0.5, which means that the 50% of secondary reserve provision iscovered by G2 and 50% by G3.

Consider Figure 4.4, where the inner structure of the Secondary Con-troller block is illustrated. As mentioned above, the input is the frequencymeasurement Fmeas. The signal goes trough the first block, which is thefirst order delay (PT1). We need PT1 to ensure that the secondary controlis slower than the primary control. The block bias calculates the frequencydeviation from the nominal value and has a gain B, so called secondaryfrequency bias.

ACE = B ·∆f (4.5)

After the block bias we have a second PT1-element to ensure the smoothcurve, which will be sent to the next block K+1/sT. The last block is aPI-Controller. The main parameters of the secondary frequency controllerare listed in Table 4.5.

4.2 Controlling of the PV-Generator

The regulations for decentralized distributing generation on low voltage levelwere explained in Chapter 2. The inverters of PV units have to be able to fol-


Parameter Description Value Unitr Temporary Droop 0.1 [pu]Tr Governor Time Constant 10 [s]Tf Filter Time Constant 0.1 [s]Tg Servo Time Constant 0.5 [s]Tw Water Starting Time 1 [s]At Turbine Gain 1 [pu]Dturb frictional losses factor pu 0.01 [pu]qnl No Load Flow 0.01 [pu]R Permanent Droop 0.05 [pu]PN Turbine Rated Power 128 [MW]Gmin Minimum Gate Limit 0 [pu]Gmax Maximum Gate Limit 1 [pu]Velm Gate Velocity Limit 0.15 [pu]pmin Lower Bound Primary Reserve 0 [pu]pmax Upper bound Primary Reserve 1 [pu]

Table 4.4: Parameter values of Hydro Turbine Governor HYGOV for theMachines G3

low this operational requirements. In Chapter 3 the model of PV system wasintroduced. Consider Figure 3.8. The blocks Active Power Reduction andVdc Controller the most relevant part of the systems, which are importantfor the controlling issues.

4.2.1 Active Power Reduction

The block Active Power Reduction checks a certain frequency condition andsends the reduction signal to the Vdc Controller. In Figure 4.5 the structureof Active Power Reduction is illustrated. It receives the frequency measure-ment signal as input. After the PT1-element we have a Overfreuency PowerReduction block. In this unit the active power reduction conditions are in-tegrated. The conditions and the output were programmed in DSL. Twodifferent conditions were implemented which refers to the:

• Switch off at 50.2Hz (the old regulation)

• Reduce active power according to the characteristic at Figure 2.5 (thenew regulation)

4.2.2 Active Power Control

Consider the structure of the Vdc Controller block in Figure 4.6. The blockK(1+1/sT) controls the active power of PV power plant. This block will be


Figure 4.3: Model the Secondary Frequency Control of Single Area

Figure 4.4: Secondary Controller Block

Figure 4.5: Active Power Reduction Block

denoted as active power controller. It has two inputs. The dpd is changesignal of the active power and the pred is a power reduction factor. The activepower change signal change can be caused by solar radiation change, changeof the feeding bus voltage or manual settings of the active power. Since thesimulations will be done for a short time periods (up to 2 minutes), the solarradiation change will be neglected and the active power feed will be kept onconstant operational point. The bus voltage changes are reasonable duringthat short time. To keep the active power generation constant the d-axiscurrent will be adjusted by the active power control. The pred signal canbe between 0 and 1. The output of the active power controller id will be


Parameter Description Value UnitK gain of PI-Element 0.15 -T time constant of PI-Element 60 [s]T1 time constant of first PT1-Element 5 [s]T2 time constant of second PT1-Element 5 [s]f_nom nominal frequency value 50 [Hz]bias secondary frequency bias 1 -deltaf_down lower bound of PT1-Element -0.05 [Hz]deltaf_up upper bound of PT1-Element 0.05 [Hz]y_min minimal output ACE -20 [MW]y_max maximal output ACE 20 [MW]

Table 4.5: Parameter values of Secondary Frequency Control (AGC)

Figure 4.6: Vdc Controller Block

multiplied with pred.

4.2.3 Reactive Power Control

The block Reactive Power Support controls the reactive power. The maininputs are bus voltage deviation from the nominal value uac, current pro-ducing active power pist and the output of the active power control id. Theprogramming language DLS the reactive power provision in dependence ofactive power was implemented. As default the standard characteristic curveat Figure 2.8 was selected. However, with small modifications another char-


acteristic curves are easily adjustable.

Chapter 5

Simulations and Results

In this chapter the conducted simulations and their results are described. Inorder to test the frequency stability under different regulations, several anoverfrequency was simulated on the grid model.

5.1 PV units on the Grid

In Chapter 3 the grid model was introduced which was used in this master’sthesis. Since we want to analyze the behavior of the PV systems and itsinfluence to the grid stability PV power plants were connected to the differ-ent voltage levels of the model. Three different types of PV systems wereinstalled on the model:

• Small scale PV systems with installed capacity < 100 kW

• Medium size PV park with installed capacity of 5MW

• Large scale aggregated PV with installed capacity over 20MW

On the low voltage level of the Västerås grid model 11 PV systems withinstalled capacity between 30 kW and 70 kW were connected. The PV sys-tems on the low voltage level represent the residual’s and company’s PVsystems on the roofs or small commercial PV power plants. The maximalpower of this PV systems were chosen in a way that the line capacities couldbe used fully. The energy production is lager than the own consumption onthe nodes and the both low voltage levels result positive energy production.This configurations allow us to replicate the low voltage grid with high PVpenetration. In Figure 5.1 the PV systems installed on low voltage level areillustrated.

The medium size PV park was installed on Västerås grid model as well.This have installed capacity of 5MW and it is connected with 0.4 kV/11 kV-Transformer to the middle voltage level. The PV park represents a distri-

31

32 CHAPTER 5. SIMULATIONS AND RESULTS

bution generation unit, which is located close to the low voltage levels. InFigure 5.1 the connection point of the PV park is marked.

Figure 5.1: PV Systems on Low Voltage Level of Västerås Grid Model

On the Västerås grid model we have configurations which are close to thereal distribution grid. Since the x/r-ratios are between 1 and 3 the reactivepower flows are not neglectable comparing to the transmission level. Theinfluence of the reactive power on local voltage can be observed. On thispart of the model it is suitable to observe voltage stability.

In order to observe the influence of PV systems on the frequency stabilitywe need high PV energy penetration to the system. This was achievedwith an aggregated PV power plant, which was connected to the Bus 8

5.2. OVERFREQUENCY CASE STUDY AND PARAMETRIZATION 33

Figure 5.2: Aggregated PV Power Plant on the Transmission Level of WCSS

of the WCSS grid. The maximum power of the aggregated PV can be variedbetween 27MW and 192MW, which results the PV shares between 10%and 60% of total peak power consumption of the model. The aggregatedPV power plant represents all PV systems outside of the Västerås grid. InFigure 5.2 the model and the connection point of the aggregated PV plantis illustrated.

As mentioned in Section 3.2 the DIgSILENT model Static Generator wasused. The control components explained in Section 4.2 were used. In order toensure the regulations described in Chapter 2 different control configurationswere implemented in DLS programming language. In the following sectionsthe simulations with different PV controllers are described.

5.2 Overfrequency Case Study and Parametriza-tion

In order to analyze the frequency stability we have to trigger some faultsin the systems. The control actions of the PV systems, according to theregulations explained in Chapter 2, restrict to the frequency area over 50.2Hzand under 47.5Hz. Both regulations force the PV systems to instantaneouslydisconnect from the grid, when the frequency falls below under 47.5Hz.Therefore in this master’s thesis only cases with overfrequecy over 50.2Hzare of interest. This was achieved with load reduction (step). In Figure 5.3we see the frequency response in case of reduction 10% of load without anycontrol action of the PV systems. We conclude that in our grid model thatthe reduction of 10% of the load causes the overfrequecy over 50.2Hz. Inthe further simulations reduction of 10% of load will be held constant. Inreality this could be a loss of load area or load-shedding.


Figure 5.3: Active Power Reduction of the Load A which is 10% of TotalLoad and the Frequency Response of the System with Unlimited PrimaryFrequency Control Reserve

Each governor was modified so that the primary control reverse power ofthe system can be bounded. This allows us to observe the system behaviorfor different primary control reserves. The modification part of the DIgSI-LENT PowerFactory model is presented in Figure 5.4. The percentage ofthe primary control varies depending on size of the system. In the inter-connected continental European grid the primary frequency control of 1% ofpeak demand has to be ensured [24], which is 3000MW. In Nordic Grid thisis 3% and in Icelandic Grid 7% [25, 2]. This percentages are referring to theoutage of the largest generating unit [24]. In general we can assume that thebigger the grid is the smaller primary control reserve is needed. The primarycontrol reserve was varied between unlimited and 1% of the peak demand.Unlimited primary control reserve means that the synchronous machines areable to react from the operating point to the maximum and to minimumactive power. Primary control of 1% of peak demand is allocated at threesynchronous machines proportionally to the rated power.

Further, the power generation from the PV systems are varied. Thevariation allows us to estimate the system behavior both in poor sunny daywith less PV penetration and in good sunny day with high PV penetration.The PV share varied from 10% to 60%. This was achived through settingof the rated power and feeding active power of the aggregated PV System,which is connected to the Bus 8 of WCSS grid. Since we are interestedin frequency response right after the fault the active power feed of the PV

5.3. AUTOMATIC DISCONNECTION DIN VDE 0126-1-1 35

systems were held constant.

Figure 5.4: Primary and Secondary Control Part of the Thermal GovernorTGOV1

5.3 Automatic Disconnection DIN VDE 0126-1-1

As mentioned in Section 2.2 according to DIN VDE 0126-1-1 all PV sys-tems on low voltage level have to disconnect within 0.2 s at 50.2Hz. Asexplained in Chapter 2.2.2 there is a possible frequency stability problem,the so called 50.2Hz - problem, which could be caused by the disconnectionof PV systems. In case of an overfrequency the worst case could be that thedisconnection causes an underfrequency, which could cause a disconnectionof other generating units by reaching of lower operation limits. This willcause further underfrequency and possibly a load shedding or even a sys-tems collapse. To avoid this problem a new regulation for new PV systemswas introduced and the retrofitting of old PV systems started. In Tablet:retrofitting the time-plan for the retrofitting of the old PV systems is pre-sented. Since until end of 2014 there still will be PV systems with automaticdisconnection connected to the German public grid, simulation series withPV systems with automatic disconnection function according to DIN VDE0126-1-1 were conducted. The objectives of the simulations were

• to quantify the limit of the PV share which can be tolerated by thesystem,


• to observe and analyze the dynamics of the modeled system and

• to compare with the new regulation VDE-AR-N4105:2011-08.

5.3.1 Description of the Simulations

The active power control of the PV model was programmed according toDIN VDE 0126-1-1, i.e. automatic disconnection at 50.2Hz. The reactivepower was set constant to zero. This fulfills the power factor tolerance areabetween 0.95 underexcited and 0.95 overexcited.

The reconnection of the disconnected PV systems takes place if the fre-quency is under 50.05Hz for more than 30 s. After this 30 s the PV systemsstart to increase the active power linearly until MPPT. The time constantwas set to 60 s, i.e. after 30 s the PV systems feed in the maximal activepower.

The overfrequency was triggered with 10% load reduction according toFigure 5.3. 10 s after the start of the simulations the active power of theLoad A will be reduced from 125MW to 92MW. This loss is equal to 10%reduction of the total active power demand. As shown in Figure 5.3 this willcause an overfrequency greater than 50.2Hz.

In addition to the frequency response of the generated fault, in order toobserve the secondary frequency control, the reconnection of the PV systemsand their potential re-disconnection the simulation time was set to 200 s.We assume no big changes of the irradiation during this short time andset the MTTP active power of the PV systems as constant. The dynamicsimulation’s step size was set to 0.01 s which is small enough to observe theeffect of the primary control.

The series of the simulations consists of 35 simulations. The followingparameters were varied:

• the PV Share from 10% to 60% and

• the primary frequency control reserve from 1% to maximal available,i.e. from minimal to maximal production of the generating units.

5.3.2 Results of the Simulations

In order to understand the main key points of the simulation the dynamicsof an example result will be explained.

Consider Figure 5.5. We have there the simulation results of the systemwith 30% of PV share and unlimited primary frequency control reserve. Inthe Figure we have the plots of the active powers of the synchronous machinesG1, G2 and G3, the plot of the cumulative active power of all PV systems ofthe model and the plot of the frequency response over time. At the second10 we see the frequency rise which is caused by the 10% load reduction as


well as the negative primary control actions of the synchronous machines. Atthe point where the frequency reaches 50.2Hz we observe the disconnectionof all PV systems, which causes the underfrequency. After the PV systems’disconnections we observe the positve primary control action followed bypositive secondary control of G2 and G3. Until the second 42 we see thecontinuous reduction of the Area Control Error (ACE).

Since there is no overfrequency anymore after 30 s of waiting at second42 the PV systems will be reconnected to the grid and they start to increasethe active power. The increasing of the PV systems’ active power causesthe continuous frequency rise which is counter-regulated by the synchronousmachines. At the second 102 all PV systems feed in the maximal power byoperating in MPPT mode. The frequency rise stops at this point and theACE will be eliminated by the secondary control. In this case the system isstabilized.

Figure 5.5: Overfrequency Simulation: 10% of Load Reduction, 30% PVShare with Automatic Disconnection Function at 50Hz and unlimited Pri-mary Frequency Control

In Figure 5.6 the frequency responses of the simulations are illustrated.Each sub-figure corresponds to a system with different primary frequency


PCR PV Share10% 20% 30% 40% 50% 60%

unlim. fmax 50.2008 50.1995 50.1991 50.1986 50.1981 50.198fmin 49.9406 49.7256 49.4959 49.2629 49.0230 48.782

re-discon. no no no no no no

20% fmax 50.2008 50.1995 50.1991 50.1983 no conv. no conv.fmin 49.9406 49.7256 49.2913 45.1906 no conv. no conv.

rediscon. no no no yes - -

15% fmax 50.2008 50.1995 50.1991 - - -fmin 49.9406 49.7256 48.5002 - - -

rediscon. no no no - - -

10% fmax 50.2007 50.1998 50.2001 - - -fmin 49.9416 49.7257 44.7013 - - -

rediscon. no no yes - - -

7.5% fmax 50.1983 50.1994 - - - -fmin 49.9441 49.3726 - - - -

rediscon. no no - - - -

5% fmax 50.1988 50.2009 - - - -fmin 49.9437 48.5740 - - - -

rediscon. no yes - - - -

2.5% fmax 50.1979 50.2020 - - - -fmin 49.8721 47.057 - - - -

rediscon. no yes - - - -

1% fmax no conv. - - - - -fmin no conv. - - - - -

rediscon. - - - - - -

Table 5.1: Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Automatic Disconnection of PV Systems

control and includes frequency responses for different PV shares. In Ap-pendix A.1 the plots in higher resolution are presented. From the plots notshown, the PV shares either have an underfrequency below 47.5Hz or thesimulations have not converged.

In Table 5.1 the following characteristics of all simulations are listed:

• minimal and maximal frequency (Hz)

• re-disconnection of the PV systems (yes/no).

The critical values are marked in red. Obviously, the maximal frequencyof all simulations is around 50.2Hz since all PV systems will be disconnectedat this point. We classify the results according to the following 3 types:

• stable: the frequency does not pass the critical limits and the systemsis stabilized


(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 5.6: Automatic Disconnection DIN VDE 0126-1-1:(a) Unlimited Primary Control Reserve (PCR) (b) 20% PCR (c) 15% PCR(d) 10% PCR (e) 7.5% PCR (f) 5% PCR (g) 2.5% PCR (h) 1% PCR


• unstable: the frequency achieve the critical limit

• re-disconnection: the PV systems are re-disconnected which causes afrequency swing

5.4 Characteristic Curve VDE-AR-N4105:2011-08

5.4.1 Description of the Simulations

As mentioned in Chapter 2, to avoid the 50Hz-problem, a new regulationcame into effect. The requirements are valid since November 2012 and theretrofitting of the old PV systems will be finished by the end of 2014. Ac-cording to VDE-AR-N4105:2011-08 all decentralized PV systems on low andmiddle voltage levels have to reduce the active power with a gradient of40% per Hz between 50.2Hz and 51.5Hz [5]. This can be expressed by thefollowing equation

∆P = 20 · PM ·50.2Hz− fGrid

50Hzfor 50.2Hz ≤ fGrid ≤ 51.5Hz. (5.1)

where PM is the momentary active power (or MPPT). The equation can berewritten as

∆PPV = 0.4 · PM · (50.2Hz− fGrid) for 50.2Hz ≤ fGrid ≤ 51.5Hz. (5.2)

Further, at frequencies below 47.5Hz and over 51.5Hz the PV systems hasto be disconnected from the public electrical grid. The operation ranges canbe expresses by the characteristic curve in Figure 5.7.

Figure 5.7: Characteristic Curve for Active Power of PV systems accordingto VDE-AR-N4105:2011-08; P_M is Active Power of MPPT Mode

In the previous section it was shown that in some cases underfrequency orfrequency pendulum problem can occur. Obviously, from Equation 5.3 and

5.4. CHARACTERISTIC CURVE VDE-AR-N4105:2011-08 41

from Figure 5.7 it can be concluded that in the new regulation VDE-AR-N4105:2011-08 there is no underfrequency or pendulum problem like in theold regulation DIN VDE 0126-1-1. Moreover, the generation units operatingwith the new regulation can be considered as a special kind of primary controlprovider. If we rewrite Equation 5.3 to

∆PPV = 0.4 · PM ·∆fPV (5.3)

we get the similar form as in Equation 4.3 with speed droop characteristicand frequency deviation as follows

SPV =1

0.4 · PMand ∆fPV = 50.2Hz− fGrid. (5.4)

In order to visualize the speed droop characteristic area of the PV systems,Figure 5.7 can be redrawn as shown in Figure 5.8. The P_PV corresponds tothe actual cumulative active power production of all PV systems connectedto the grid.

Figure 5.8: Speed Droop Characteristic Curve Area of a PV System

From Equations 5.3 and 5.4 we see that the higher the active powerinjection PM by PV systems, the bigger the contribution to the primaryfrequency control. This interpretation about speed droop characteristic andprimary control shows that in case of overfrequency over 50.2Hz the systemswith more PV systems have lower frequency response than the systems withless PV systems. We expect this observations in the series of simulationswhich will be presented in the next section.

In order to understand the overall dynamics of the systems right afterthe fault the setting of primary frequency controls will be shortly explained.In Table 5.2 the maximal active power and the controller droop of the syn-chronous machines are listed. With Equation 5.5 the speed droop character-istic of the synchronous machines can be converted from p.u. to Hz/MW.


Generator Pmax [MW] R [p.u]G1 192.0 0.05G2 162.0 0.05G3 108.8 0.05

Table 5.2: Maximal Active Power Pmax and Controller Droop R [p.u] of theSynchronous Machines

S =f0 ·RPmax

(5.5)

Consequently the speed droop characteristics of the synchronous machinesare

S1 =1

76.8· HzMW

S2 =1

64.8· HzMW

S3 =1

43.52· HzMW

. (5.6)

With the following equation, which is already explained in Chapter 4, wecan calculate the overall speed droop of the synchronous machines1.

1

SSM=

n∑i=1

1

Si= 185.12 · MW

Hz(5.7)

This calculated value of the speed droop is also the overall speed droopcharacteristic value of the system, when the control area frequency is below50.2Hz. If the frequency is over 50.2Hz the PV systems will contribute totheir speed droop.

To clarify the dynamics of the simulation environment an example will beshown. We assume a system with 30% active power infeed by PV systems,which in our model is 98.7MW. The synchronous machines G1, G2 and G3are dispatched at 99.9MW, 80.64MW and 54.16MW respectively. We have3.5MW line losses, which is covered by the slack generator G1.

Considering Figure 5.9, the speed droop characteristic SSM on the rightside belongs to synchronous machines. The 234.7MW power is the sum ofthe initially dispatched values of all synchronous machines. Obviously, thispoint is located at the nominal frequency value of 50Hz, since at the beginof the simulation the system is balanced. The speed droop characteristic ofthe synchronous machines has a slope of −185.12MW per Hz, which wascalculated in Equation 5.7. The primary frequency control reserves will bevaried in the same way as in the simulation series in the previous section.The negative primary frequency control limit is shown with the red line. Thesynchronous machines are able to reduce the active power until this point.Variation of control reserve means shifting of this red line to right and left.

The speed droop characteristic SPV belongs to all PV systems connectedto the grid. The 98.7MW is the injected active power in MPPT mode. We

1the SM in SSM is for Synchronous Machines


Figure 5.9: Speed Droop Characteristic Curves of Synchronous Machinesand PV Systems

see that until 50.2Hz there is no droop, which is conform to the VDE-AR-N4105:2011-08. Beginning from 50.2Hz there is a droop with gradient of 40%per Hz. For this specific example the droop characteristic can be calculatedwith Equation 5.4.

SPV =1HZ

0.4 · 98.7MW=

1

39.48· HzMW

(5.8)

SPV =1

39.48· HzMW

(5.9)

The graph in Figure 5.9 can be divided into 3 frequency control intervalswhich are denoted in the graph as I, II and III:

I up to 50.2Hz: Primary control is covered by the synchronous machines,

II between 50.2Hz and the intersection-point of the primary control limit(red line) and SSM (y): the primary frequency control is supported bythe PV systems

III between the intersection-point of the primary control limit (red line)and SSM and 51.5Hz, where all PV systems disconnect: only PV sys-tems cover the primary control.

To get a comparison to real control areas in Table 5.3 the maximal pri-mary frequency control reserves and the maximal activation frequency ofsome synchronous areas of ENTSO-E are shown.

The content discussed in this section gives the background to understandthe dynamics and results of the simulations in the following subsection. We


PCR [MW] fmax [mHz]RG CE 3000 200RG Nordic 1800 500RG Ireland 560 500

Table 5.3: Primary Frequency Control Reserves and Maximum ActivationFrequency [2]

Figure 5.10: Maximal Frequency Response in Case of Overfrequency forDifferent Primary Control Reserves and PV Shares

have to keep in mind besides the primary control action there are other min-imal influences from system inertia, time delay of the synchronous machinesand secondary frequency control.

5.4.2 Simulation Results with Standard Parameters

In previous subsections the described simulations were conducted. As ex-pected we observe a significant difference between the new and the old reg-ulation:

• there is no underfrequency problem anymore like in the old regulation

• the PV systems support the primary frequency control.

In Figure 5.10 the maximal frequency responses of the systems with dif-ferent primary frequency control reserves and PV shares are shown. We see


that systems with lower primary frequency control have higher frequencyresponses, which means that the maximal activation frequency fmax will bereached sooner in the systems with lower PCRmax than in the systems withhigher PCRmax. From this point only the PV system’s speed droop charac-teristic controls the frequency. This frequency interval is denoted as IIIin Figure 5.9. In this frequency area we only have the frequency droop SPVfrom Equation 5.4. From the results in Figure 5.10 and Equation 5.4 we ob-serve that the higher the power injection by PV systems, the lower the speeddroop characteristic in the area III and accordingly low are the frequencyresponse.

The difference of primary frequency control support by the PV systemscan be observed more clearly in Figure 5.11. We see a clear difference be-tween the systems with 12.5% and 1% of primary frequency control reserves.In Figure 5.11(a) there are almost no differences between different PV shares,since there are enough primary control reserves and the part where only thePV systems control the frequency very low, while in Figure 5.11(f) are dif-ferences significant. In Appendix A.2.1 in Table A.1 the maximal frequencyresponses of the simulations are listed.

5.4.3 Variation of Parameters

In order to further estimate the influence of the new regulations on thefrequency stability the droop starting point was varied. Equation 5.3 can begeneralized as follows

∆PPV = 0.4 · PM · (fPV − f), (5.10)

where fPV is the starting point of the linear droop. The simulations fromthe previous subsection were repeated with values 50.15Hz and 50.10Hz forfPV. The maximal frequency responses are shown in Figure ?? and listed inAppendix A.2.1 in Tables A.2 and A.3.

If we compare the results of the simulations, we get the following numer-ical values:

• the maximal difference between fPV = 50.2Hz and fPV = 50.15Hzwas 0.1131Hz at 10% PV share and 1% PCR

• the maximal difference between fPV = 50.2Hz and fPV = 50.10Hzwas 0.1187Hz at 10% PV share and 1% PCR.

The differences between these results are more significant for systems withlow primary frequency control. When the primary control of synchronousmachines is fully activated, the starting point of the PV system’s droop couldmake a big difference.


(a) (b)

(c) (d)

(e) (f)

Figure 5.11: Frequency Response (a) 12.5% Primary Frequecy Reserve(PCR)(b) 10% PCR (c) 7.5% PCR (d) 5% PCR (e) 2.5% PCR (f) 1% PCR


Figure 5.12: Maximal Frequency Response in Case of Overfrequency forDifferent Primary Control Reserves and PV Shares with Speed Droop Char-acteristic starting from 50.15Hz.

Figure 5.13: Maximal Frequency Response in Case of Overfrequency forDifferent Primary Control Reserves and PV Shares with Speed Droop Char-acteristic starting from 50.10Hz.

Chapter 6

Conclusion

In this master’s thesis the influence of decentralized PV systems on the gridstability was analyzed. The focus was on frequency stability, but the voltagestability constraints were considered in all simulations. The scaled grid modelwas used with different shares of PV systems. The software environmentDIgSILENT was chosen in order to conduct the dynamical simulations.

The PV system’s settings were corresponding to 2 different regulationsin Germany, the actual one and the preceding one. The main question ofthis thesis was, how the electric grids are reacting in case of overfrequency.Frequency responses of the systems with different primary frequency controlreserves were analyzed.

In the grid with the preceding regulation the PV systems have to beautomatically disconnected from the grid at 50.2Hz. The numerical valuesof the PV share where the system’s primary control is able to withstandthe disconnection of PV systems and the systems frequency could be stabi-lized, were determined. As expected, a higher PV share needs more primaryfrequency control reserve.

In the actual regulation the PV systems have to reduce the active powerinfeed with a linear gradient of 40% in the case of an overfrequency greaterthan 50.2Hz. It was shown that there are no frequency stability problems.We conclude that in the overfrequency fault case the more PV share the lowerthe frequency response. The PV systems support the primary frequencycontrol. Further, it was shown that there is a bigger potential of supportingthe stability in case of overfrequency with shifting of the speed droop startingpoint from 50.2Hz to lower frequency.

The used model of the grid is a scaled IEEE 9 bus system with peakdemand of 315 MW and with longest line of 1 km. The local frequencymeasurement differences on the buses were negligible small. Studies on largergrid models with frequency measurement differences are reasonable. Further,the model has only two kind of generation units, the thermal synchronousmachines and PV systems. In future works other kind of power plants with

49

50 CHAPTER 6. CONCLUSION

tight constraints of minimal and maximal operation frequency should beconsidered. Studies about daily based ancillary services provision by PVsystems during peak hours with economical evaluation could be done aswell.

Appendix A

Simulation Results

A.1 Automatic Disconnection of PV System

Fixed Primary Control Reserves and Variation PV Shares

Figure A.1: Frequency Response, Automatic Disconnection, 10-50% PVShare, unlimited Primary Control Reserves

51

52 APPENDIX A. SIMULATION RESULTS

Figure A.2: Frequency Response, Automatic Disconnection, 10-40% PVShare, 20% Primary Control Reserves


A.1. AUTOMATIC DISCONNECTION OF PV SYSTEM 53


Figure A.5: Frequency Response, Automatic Disconnection, 10-20% PVShare, 7.5% Primary Control Reserves



Figure A.7: Frequency Response, Automatic Disconnection, 10% PV Share,2.5% Primary Control Reserves


Figure A.8: Frequency Response, Automatic Disconnection, 10% PV Share,1% Primary Control Reserves


Detailed Plots of Automatic Disconnection

Figure A.9: Frequency Response, Automatic Disconnection, 30% PV Share,Unlimited Primary Control Reserves

A.2. CHARACTERISTIC CURVE (40% PER HERTZ) 59

A.2 Characteristic Curve (40% per Hertz)

Figure A.12: Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, unlimited Primary Control Reserves

Figure A.13: Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 10% Primary Control Reserves


Figure A.14: Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 7.5% Primary Control Reserves



Figure A.16: Frequency Response, Characteristic Curve (40% per Hertz),10-60% PV Share, 2.5% Primary Control Reserves



Detailed Plots of the Characteristic Curve Regulation

Figure A.18: Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 7.5% Primary Control Reserves


Figure A.19: Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 5% Primary Control Reserves


Figure A.20: Frequency Response, Characteristic Curve (40% per Hertz),40% PV Share, 2.5% Primary Control Reserves


A.2.1 Variation of Parameters

PCR PV Share10% 20% 30% 40% 50% 60%

unlim. fmax 50.2287 50.2281 50.2276 50.227 50.2264 50.2259fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

10% fmax 50.2752 50.2627 50.2582 50.2539 50.2505 50.2475fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

7.5% fmax 50.4033 50.3545 50.3333 50.3175 50.3056 50.2959fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

5% fmax 50.6532 50.5118 50.4513 50.4117 50.3837 50.3629fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

2.5% fmax 51.0332 50.7247 50.6019 50.528 50.4782 50.4424fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

1% fmax 51.3106 50.8711 50.7027 50.6044 50.54 50.4939fmin 49.9813 49.9896 49.9903 49.991 49.9914 49.9918

Table A.1: Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve

PCR PV Share10% 20% 30% 40% 50% 60%

12.5% fmax 50.2252 50.2218 50.2186 50.2157 50.2129 50.2102fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

10% fmax 50.2603 50.2497 50.2406 50.2328 50.2268 50.2220fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

7.5% fmax 50.3725 50.3331 50.3072 50.2880 50.2733 50.2274fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

5% fmax 50.6015 50.4820 50.4173 50.3755 50.3511 50.3236fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

2.5% fmax 50.9624 50.6887 50.5627 50.4875 50.4356 50.3995fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

1% fmax 51.1975 50.8360 50.6614 50.5623 50.4956 50.4497fmin 49.9919 49.9901 49.9912 49.9902 49.9928 49.9923

Table A.2: Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve with Speed Droop Characteristic startingfrom 50.15Hz


PCR PV Share10% 20% 30% 40% 50% 60%

12.5%. fmax 50.2212 50.2143 50.2081 50.2025 50.1973 50.1925fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

10% fmax 50.2509 50.2338 50.2211 50.2116 50.2038 50.1973fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

7.5% fmax 50.3557 50.3093 50.2786 50.2573 50.2402 50.2274fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

5% fmax 50.5753 50.45 50.3815 50.3379 50.3116 50.2832fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

2.5% fmax 50.9271 50.6567 50.5215 50.4452 50.3116 50.3555fmin 50.0000 50.0000 50.0000 50.0000 50.0000 50.0000

1% fmax 51.1919 50.8035 50.6178 50.5181 50.4506 50.4040fmin 49.9917 49.9837 49.9888 49.9889 49.9907 49.9904

Table A.3: Maximal and Minimal Frequency Responses [Hz] at Overfre-quency and Characteristic Curve with Speed Droop Characteristic startingfrom 50.10Hz

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eeh - eth z power system s laboratory ... digsilent powerfactory was used as a simulation...

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