modelling of the power system of gotland in psse …

MODELLING OF THE POWER SYSTEM OF GOTLAND IN

PSS/E WITH FOCUS ON HVDC LIGHT

Bild: ABB

Martin Brask

Master Thesis Report

XR-EE-ES 2008:006

Abstract The purpose with this project is to develop a model of the whole power system of Gotland in the power system simulation software PSS/E. A model of the whole power system of Gotland has earlier been used in the power system simulation software Simpow but now there is a need to develop a model in PSS/E. In the power system of Gotland there are several components that need to be modelled such as lines, loads, transformers, shunt impedances, synchronous machines, asynchronous machines, an HVDC Classic link and an HVDC Light link. These components are modelled in the Simpow model and needs to be converted to the PSS/E model. The aim is to develop a model in PSS/E that is as equal as possible to the model in Simpow. Especially the HVDC Light link at Gotland has been investigated in the project. A problem with converting data from Simpow to PSS/E is that the models of several components differ in Simpow and PSS/E. Lines and shunt impedances can be modelled in the same way but the models for loads, transformers, synchronous machines, asynchronous machines, the HVDC Classic link, and the HVDC Light link differ in Simpow and PSS/E. The models in Simpow are converted to the models in PSS/E in an as equal way as possible. The results in PSS/E are analyzed and compared with the Simpow model. In the project we have also made a test of fault simulations in time-domain simulations in PSS/E. The aim with this test is to verify the PSS/E calculations when a three-phase or a single-phase fault is applied. The reason for that is that PSS/E only calculates using positive-sequence components and therefore only is able to calculate exact during circumstances of symmetrical loads and faults. The result shows that the calculations for both symmetrical and unsymmetrical faults in PSS/E are correct concerning the positive-sequence components. A drawback in PSS/E is, however, that we do not have any information concerning the negative- and zero-sequence components, which results in that we cannot calculate the three phase-quantities.

Sammanfattning Syftet med detta projekt är att utveckla en modell av hela Gotlands elnät i simuleringsprogrammet PSS/E. Tidigare har man använt en modell av hela Gotlands elnät i simuleringsprogrammet Simpow men nu finns det även ett behov av att utveckla en modell i PSS/E. Flertalet komponenter i Gotlands elsystem behöver modelleras som exempelvis ledningar, laster, transformatorer, shunt impedanser, synkronmaskiner, asynkronmaskiner, en klassisk HVDC länk och en HVDC Light länk. Dessa komponenter är modellerade i modellen i Simpow och behöver konverteras till modellen i PSS/E. Målet är att utveckla en modell i PSS/E som är så lik modellen i Simpow som möjligt. Modellen av HVDC Light länken på Gotland kommer att undersökas extra noga i detta projekt. Ett problem med att konvertera data från Simpow till PSS/E är att modellerna av flertalet komponenter skiljer sig från Simpow till PSS/E. Ledningar och shunt impedanser kan modelleras på samma sätt i Simpow och PSS/E men modellerna av laster, transformatorer, synkronmaskiner, asynkronmaskiner, den klassiska HVDC länken och HVDC Light länken skiljer sig från Simpow till PSS/E. Modellerna i Simpow konverteras därför till modellen i PSS/E på ett så likvärdigt sätt som möjligt. Resultatet i PSS/E analyseras och jämförs med resultatet från Simpow. I projektet har vi även gjort ett test av felsimuleringar i tidsdomänsimuleringar i PSS/E. Målet med testet är att verifiera PSS/E:s beräkningar när ett trefasfel eller enfasfel simuleras. Anledningen till detta är att PSS/E enbart utför beräkningar med plusföljdskomponenter och därför enbart kan beräkna korrekt vid symmetriska fel och laster. Resultatet visar att beräkningarna för både symmetriska och osymmetriska fel är korrekta beträffande plusföljdskomponenterna. En nackdel i PSS/E är dock att vi inte har någon information angående minusföljdskomponenterna och nollföljdskomponenterna vilket leder till att vi inte kan beräkna trefasstorheterna.

Preface This master thesis work was carried out at Vattenfall Research and Development AB and was approved by the division of Electrical Power Systems at the school of Electrical Engineering at the Royal Institute of Technology. My supervisor at Vattenfall Research and Development AB was Jonas Persson. At KTH my supervisor was Robert Eriksson and my examiner was Mehrdad Ghandhari. I want to thank the following persons and companies;

• Jonas Persson for guidance, discussions, and availability for all my questions.

• Urban Axelsson for coordination of the project and discussions.

• Robert Eriksson for reviewing my report and comments.

• Mehrdad Ghandhari for coordination of the project and suggestions.

• Per-Erik Björklund for guidance and support.

• Vattenfall Research and Development AB for hosting my thesis work.

• ABB for letting me use their model of an HVDC Light link in PSS/E.

Table of Contents Page

1 INTRODUCTION 1

1.1 Background 1

1.2 The power system of Gotland 1

1.3 Purpose 3

1.4 The simulated case of Gotland 4

1.5 Problem 4

1.5.1 The HVDC Light link 4

1.6 Report structure 5

1.6.1 Chapter 2 6

1.6.2 Chapter 3 6

1.6.3 Chapter 4 6

1.6.4 Chapter 5 6

1.6.5 Chapter 6 6

1.6.6 Chapter 7 6

2 TEST OF FAULT SIMULATIONS IN PSS/E 7

2.1 Method 7

2.1.1 Initial test system 8

2.1.2 Final test system 9

2.1.3 The dynamic of the swing bus in PSS/E 9

2.1.4 The dynamic of the generator 10

2.1.5 Simulations of faults in PSS/E 11

2.1.6 Sequence components of the power line impedances 12

2.1.7 Sequence components of the generator impedance 13

2.2 Results 14

2.2.1 Power-flow simulation of the initial test system 14

2.2.2 Power-flow simulation of the final test system 15

2.2.3 Dynamic simulation without fault 16

2.2.4 Three-phase fault simulation 16

2.2.5 Single-phase fault simulation 21

2.3 Discussion about symmetrical components of voltages 30

2.4 Conclusions 32

3 POWER-FLOW SIMULATION OF GOTLAND 33

3.1 Setup 33

3.1.1 Grid structure 33

3.1.2 Transformers 35

3.1.3 Machines 37

3.1.4 Shunt impedances 37

3.1.5 Loads 37

3.1.6 “Standard PSS/E model” 41

3.1.7 “ABB’s Open PSS/E model” 45

3.1.8 Lines 46

3.1.9 The HVDC Classic link 46

3.2 Simulation 46

3.3 Conclusions 48

4 TEST OF THE DYNAMIC OF THE HVDC LIGHT LINK 51

4.1 Grid structure 51

4.2 Setup for the power-flow simulation 51

4.3 Setup for the dynamic simulations 52

4.3.1 The “Simpow model” 52

4.3.2 The “Standard PSS/E model” 53

4.3.3 “ABB’s Open PSS/E model” 54

4.4 Results 57

4.4.1 Power-flow calculation 57

4.4.2 Dynamic simulations 58

4.5 Conclusions 62

5 DYNAMIC SIMULATIONS OF GOTLAND 63

5.1 Setup 63

5.1.1 The HVDC Light link 63

5.1.2 The HVDC Classic link 63

5.1.3 Machines 63

5.1.4 Regulators 63

5.2 Setup of the loads 64

5.2.1 Voltage part 65

5.2.2 Frequency part 65

5.2.3 Example 66

5.3 Simulations 68

5.3.1 Basic simulation 68

5.3.2 Simulation with priority on active power in Simpow 75

5.3.3 Simulation with the default settings of the AC voltage regulators in

“ABB’s Open PSS/E model” 76

5.3.4 Simulation of frequency regulation 78

5.4 Conclusions 78

6 CONCLUSIONS 81

6.1 Conclusions from the test of fault simulations in PSS/E 81

6.2 Conclusions from the simulations of Gotland 81

7 PROPOSAL FOR FUTURE WORK 85

8 REFERENCES 87

9 APPENDICES 89

9.1 Test of fault simulations in PSS/E 89

9.2 Power-flow simulation of Gotland 89

9.3 Test of the dynamic of the HVDC Light link 89

9.4 Dynamic simulations of Gotland 90

9.4.1 70 [kV] three-phase fault simulation 90

(96)

1 Introduction

1.1 Background

Power systems are an important part of today’s society. A reliable electricity supply is necessary for a large part of the society and a power cut can result in serious consequences. To increase the reliability in the power system, reinforcements of the weakest parts of the grid are needed. To locate the weaknesses in the power system, power system simulation software are used. With a model of the power system, in a simulation software, we can locate the weaknesses in the grid and investigate how different reinforcements should affect the power system. Simulation software are also used to investigate where new power plants are going to be built and which capacity they can have. With a model of the power system, with the power plants included, we can see how the power plants should affect the power system. We can also investigate how different power plants should affect the power system and which part of the power system that needs to be reinforced for different power plants.

1.2 The power system of Gotland

Gotland is an island located about 90 [km] east of the mainland of Sweden. The power system of Gotland is isolated from the mainland except for an HVDC Classic link between Ygne (close to Visby) at the island of Gotland and Västervik at the mainland of Sweden. Gotland consists of voltage levels between 0.4 [kV] and 70 [kV] and there is also an HVDC Light link installed between Bäcks (close to Visby) at the northern part of Gotland and Näs at the southern part of Gotland, see Figure 1.2.1. The largest loads in Gotland are the city Visby and the Cementa factory. The total power consumption varies between 40 [MW] and 155 [MW]. The total electricity consumption for one year is about 1 [TWh]. The power generation in Gotland consists today (December 14, 2007) mainly of 160 wind power plants. The wind power plants are located in the northern part and in the southern part of the island with the largest wind farm situated in Näs (NAS), see Figure 1.2.1. The maximum total power production from the wind power plants is 88.5 [MW] and the production for one year is about 200 [GWh], see GEAB Homepage [1]. The HVDC Light link is installed to transmit power from the wind power plants in Näs to the large load in Visby. In parallel with the HVDC Light link there is also a 70 [kV] AC power line transmitting power from the south of Gotland to the load in Visby, see Figure 1.2.1. In Gotland there is also a synchronous machine, which can produce up to 8 [MW], at the Cementa factory and gas turbines are installed as reserve power plants in Slite. To get higher inertia in the system, which results in a more stable grid, three synchronous machines are also

installed without generation in Visby. system of Gotland for the function of the HVDC Classic link. A simplified scheme of the 70 [kV] grid together with the HVDC Classic link and the HVDC Light link is shown in Figure 1.2

Figure 1.2.1 A simplified scheme of the 70 [kV] grid at

Page 2 (96)

installed without generation in Visby. It is necessary to have a rotating mass in the power system of Gotland for the function of the HVDC Classic link.

e 70 [kV] grid together with the HVDC Classic link and the HVDC 1.2.1.

ed scheme of the 70 [kV] grid at Gotland together with the HVDC Classic link

and the HVDC Light link.

It is necessary to have a rotating mass in the power

e 70 [kV] grid together with the HVDC Classic link and the HVDC

the HVDC Classic link

(96)

1.3 Purpose

The purpose of this project is to develop a model of the whole power system of Gotland in the power system simulation software PSS/E. A model of the whole power system of Gotland has earlier been used in the power system simulation software Simpow but now there is a need to develop a model in PSS/E. In the power system of Gotland there are several components that need to be modelled such as lines, loads, transformers, shunt impedances, synchronous machines, asynchronous machines, an HVDC Classic link and an HVDC Light link. These components are modelled in the Simpow model and needs to be converted to the PSS/E model. The aim is to develop a model in PSS/E that is as equal as possible to the model in Simpow. The focus of the project is the model of the HVDC Light link between Bäcks and Näs at Gotland, see Figure 1.2.1. The model of the HVDC Light link in Simpow is detailed and corresponds to the existing control system of the HVDC Light link at Gotland. In PSS/E there are the following two models that we can choose between;

• The standard model of an HVDC Light link in PSS/E called “Voltage Source Converter (VSC) Dc Line Data” in the power-flow setup and “VSCDCT” in the dynamic setup, see PSS/E-manual [2], POM, 4-25 and PSS/E-manual [2], POM, L-41.

• ABB’s model of an HVDC Light link “HVDC Light Open model Version 1.1.3-3” which can be imported into PSS/E, see Björklund [3].

In the rest of the report these models are called as following: • The model of the HVDC Light link in Simpow is called “Simpow model”. • The standard model of the HVDC Light link in PSS/E, called “Voltage Source

Converter (VSC) Dc Line Data” in the power-flow setup and “VSCDCT” in the dynamic setup, is called “Standard PSS/E model”.

• ABB’s model of the HVDC Light link in PSS/E “HVDC Light Open model Version 1.1.3-3” is called “ABB’s Open PSS/E model”.

The “Standard PSS/E model” is based on version 0 of “ABB’s Open PSS/E model” and is not recommended to be used by ABB, see Björklund [3], p.4 and Björklund [4]. “ABB’s Open PSS/E model” is delivered together with their sold HVDC Light links today (March 13, 2008) and is verified by comparison with identical test cases in PSCAD/EMTDC, see Björklund [3], p.1. By comparing the two models in PSS/E with the model in Simpow we can investigate how reliable the models are in PSS/E, concerning the HVDC Light link on Gotland. In the project we start with a test of fault simulations in time-domain simulations in PSS/E. The aim with this test is to verify the PSS/E calculations when a three-phase or a single-phase fault is applied. The reason for that is that PSS/E only calculates using positive-sequence components and therefore only is able to calculate exact during circumstances of symmetrical loads and faults.

(96)

1.4 The simulated case of Gotland

The studied model of the power system of Gotland in Simpow is a high load case and the total power consumption is 155 [MW]. The 0.4 [kV] voltage level in the power system of Gotland is not modelled and all loads are therefore modelled at the 10 [kV] voltage level. The power production in the model is at its maximum level and the total power production from the asynchronous machines (wind power plants) is 96 [MW]. One synchronous machine is also producing 8 [MW] in the model. The HVDC Light link in the model is transmitting 20 [MW] from Näs to Bäcks at Gotland and the HVDC Classic link is transmitting 54 [MW] from the mainland of Sweden to Ygne at Gotland, see Figure 1.2.1.

1.5 Problem

A problem with converting data from Simpow to PSS/E is that the models of several components differ in Simpow and PSS/E. Lines and shunt impedances can be modelled in the same way in Simpow and PSS/E but the models for loads, transformers, synchronous machines, asynchronous machines, the HVDC Classic link, and the HVDC Light link differ in Simpow and PSS/E and have to be treated with accuracy. The models in Simpow need to be converted to the models in PSS/E in an as equal way as possible.

1.5.1 The HVDC Light link

The HVDC Light link consists of two AC/DC converters, two filters, two transformers, and two DC cables, see Figure 1.5.1.

Figure 1.5.1 The HVDC Light link.

The converter in Näs controls the AC voltage on the AC-side in Näs and the active power drawn from the 70 [kV] grid. The inverter in Bäcks controls the DC voltage on the DC cables and the AC voltage on the AC-side in Bäcks. The two filters and the two transformers are not included in the models of the HVDC Light link and have to be modelled separately both in Simpow and in PSS/E.

(96)

In the power-flow setup the “Simpow model” consists of two PWM converters and one DC cable (this DC cable is representing the two DC cables in the HVDC Light link at Gotland). The “Standard PSS/E model” consists of two voltage source converters and one DC cable while “ABB’s Open PSS/E model” consists of two synchronous machines. We need to investigate how the two synchronous machines in “ABB’s Open PSS/E model” affect the power-flow setup and if the differences between the three models affect the power-flow simulation. In the dynamic setup, the “Simpow model” includes two AC voltage regulators, one DC voltage regulator, and one active power regulator. The active power regulator controls the active power on the power line between Näs (NAS) and Stenbro (STEN), see Figure 1.2.1. Both models in PSS/E include an active power regulator but we cannot control the active power on a specific power line with any of the PSS/E models. All regulators in Simpow have PI-regulator characteristic except for one special case; when the DC current becomes too high, then a temporary blocking is included in the “Simpow model”, see Björklund [4]. The “Simpow model” also includes a transient response, when the controlled AC voltages become lower than 0.8 [p.u.], which results in that the reactive power output becomes 90 [%] of its maximum value within 50 [ms], see Axelsson [5]. The transient response and the temporary blocking are not included in any of the PSS/E models. The “Standard PSS/E model” includes in the dynamic setup two AC voltage regulators and one active power regulator. All regulators have PI-regulator characteristic but are not as detailed as the regulators are in Simpow. Whether a DC voltage regulator is included in the model is not stated in the manual but there are no parameters that can be chosen for a DC voltage regulator in the model, see PSS/E-manual [2], POM, L-41. “ABB’s Open PSS/E model” includes two AC voltage regulators, one DC voltage regulator, and one active power regulator in the dynamic setup. As for the “Standard PSS/E model” all regulators have PI-regulator characteristic but are not as detailed as the regulators are in Simpow. “ABB’s Open PSS/E model” is delivered with the source code, which results in that we are able to make changes of parameters inside the code. The task here is to investigate if any of the models in PSS/E can be used to simulate the HVDC Light link at Gotland.

1.6 Report structure

The report is structured as shown below.

(96)

1.6.1 Chapter 2

Chapter 2 contains the test of fault simulations in PSS/E.

1.6.2 Chapter 3

Chapter 3 contains the power-flow simulation of Gotland. The models of the HVDC Light link in PSS/E are described in section 3.1.6 and section 3.1.7.

1.6.3 Chapter 4

Chapter 4 contains a test of the dynamic of the HVDC Light link. Both the “Standard PSS/E model” and “ABB’s Open PSS/E model” are included and compared with the “Simpow model”.

1.6.4 Chapter 5

Chapter 5 contains dynamic simulations of Gotland. The results from the two models in PSS/E are compared with the results from the model in Simpow.

1.6.5 Chapter 6

Chapter 6 contains conclusions from both the power-flow simulation and the dynamic simulations.

1.6.6 Chapter 7

Chapter 7 contains proposal for future work.

(96)

2 Test of fault simulations in PSS/E

2.1 Method

To simulate an unsymmetrical single-phase fault in a time-domain simulation, PSS/E makes the following approximation: It calculates a Thévenin equivalent using the positive-, negative-, and zero-sequence impedances seen from the node where the fault is applied and then calculates the positive- sequence current and voltage, see PSS/E-manual [2], POM, 5.35. The equivalent is equal to the positive-, negative-, and zero-sequence impedances in series with three fault impedances, see Figure 2.1.1.

Figure 2.1.1 Thévenin equivalent for unsymmetrical fault.

In Figure 2.1.1, Z1, Z2, and Z0 are the positive-, negative-, and zero-sequence impedances respectively and Zfault is the fault impedance. This equivalent is later used as a shunt which aim is to model the unsymmetrical fault. Here we have to remember that we can only study how the positive-sequence component is responding to the connection and disconnection of the shunt, see section 2.1.5. The main task here is to investigate how good this approximation is. By comparing fault calculations in PSS/E with calculations in another software, which includes negative- and zero-sequence components in time-domain simulations, we can see how reliable the approximation is in PSS/E. Vattenfall Research and Development has long experience in using Simpow and therefore Simpow is used as a reference. Unlike PSS/E, Simpow makes calculations with all three sequences and we can assume that these calculations are correct. Both types of faults can be simulated in Simpow and PSS/E, however in Simpow the modelling includes negative- and zero-sequence components and how they develop with time, which is not included in PSS/E. By constructing the small power system in Figure 2.1.2, consisting of one generator, two power lines, one generator bus, one load bus and one swing bus, we can compare the two

(96)

power-system simulation software and investigate the modelling in PSS/E and Simpow. The results will also be checked analytically.

Figure 2.1.2 The test system consisting of one single machine and one swing bus.

2.1.1 Initial test system

To verify our system we have initially used the same parameters, for power-flow calculations, as in Kundur [6], p.732. The parameters are shown in Table 2.1.1 - Table 2.1.3.

Table 2.1.1 Data for the setup of the power-flow calculation of the initial test system. The elements in

the table marked as “-” are later calculated by the two software.

Bus Model Ubase [kV] Sbase [MVA] U [p.u.] θ [o] PG [p.u.] QG [p.u.] 1 Generator bus 24 2220 1.0 - 0.9 - 2 Load bus 24 2220 - - 0 0 3 Swing bus 24 2220 0.995 0 - -

Table 2.1.2 Data for the lines in the initial test system.

Line From bus To bus R [p.u.] X [p.u.] 1 1 2 0 0.325 2 2 3 0 0.325

Table 2.1.3 Load-flow data for the generator in the initial test system.

Generator U [p.u.] PG [p.u.] 1 1 0.9

The system frequency is 50 [Hz]. In Kundur the system frequency is set to 60 [Hz]. The base current and base impedance can be calculated according to Söder [7], p.44, see Equation 2.1.1 and Equation 2.1.2.

][405.5310243

102220

3 3

6

kAU

SI

base

basebase =

⋅⋅⋅==

Equation 2.1.1 The equation for the base current.

(96)

( )][25946.0

1022201024

6

232

Ω=⋅

⋅==base

basebase S

UZ

Equation 2.1.2 The equation for the base impedance.

The power-flow calculation of the initial test system can be found in section 2.2.1.

2.1.2 Final test system

The parameters in section 2.1.1 are not appropriate for dynamic simulations and therefore we have decided to change the resistance of the lines, to 5 [%] of the reactance, in order to get more damping in the power system. We have also changed the voltage at bus 1 to 1.04318 [p.u.], in order to get the same production of reactive power in the generator at bus 1. The parameters for the final test system are shown in Table 2.1.4 - Table 2.1.6. For power-flow calculation of the final test system, see section 2.2.2.

Table 2.1.4 Data for the setup of the power-flow calculation of the final test system. The elements in

the table marked as “-” are later calculated by the two software.

Bus Model Ubase [kV] Sbase [MVA] U [p.u.] θ [o] PG [p.u.] QG [p.u.] 1 Generator bus 24 2220 1.04318 - 0.9 - 2 Load bus 24 2220 - - 0 0 3 Swing bus 24 2220 0.995 0 - -

Table 2.1.5 Data for the lines in the final test system.

Line From bus To bus R [p.u.] X [p.u.] 1 1 2 0.01625 0.325 2 2 3 0.01625 0.325

Table 2.1.6 Load-flow data for the generator in the final test system.

Generator U [p.u.] PG [p.u.] 1 1.04318 0.9

2.1.3 The dynamic of the swing bus in PSS/E

In PSS/E the swing bus in bus 3 have to be modelled as a synchronous machine with an infinite inertia in the dynamic simulations, as shown in Figure 2.1.3.

(96)

Figure 2.1.3 The test system in PSS/E with the swing bus in bus 3 modelled as a synchronous

machine.

The type of generator that is used in PSS/E for dynamic simulations for an infinite bus is the classical generator model, “GENCLS”, with the settings shown in Table 2.1.7.

Table 2.1.7 Data for the infinite bus in the test system.

Swing generator U [p.u.] θ [o] PG [p.u.] QG [p.u.] H [p.u.] 1 0.995 0 - - ∞*

* This is carried out by putting H = 0 in the input data of PSS/E.

2.1.4 The dynamic of the generator

The dynamic model of the generator in bus 1 is modelled with a “Type 1A” model in Simpow and a “GENROU” model in PSS/E, both models without saturation. These models are similar and contain among others two accelerating equations, see Equation 2.1.3 and Equation 2.1.4.

)(21 ωω ∆−−=∆ DTTH em&

Equation 2.1.3 The differential equation for the speed deviation.

ωωδ ∆= 0

&

Equation 2.1.4 The differential equation for the machine angle derivative.

The models also contain two equations describing the field current and the time-derivative of the flux in the field winding respectively. In addition to that, two damper windings are included in the q-axis and one damper winding is included in the d-axis, see Johansson [8], p.3-5. The two models contain in total six state variables. Nevertheless there are some differences between the two models:

• In PSS/E the rotor speed have to be included in the stator voltage equation. This is not the case in Simpow where it is possible to modify the generator model such that the rotor speed is not included. However, in this research the speed is included in the stator voltage equation in Simpow, as it is done in PSS/E.

(96)

• The stator fluxes are calculated in different ways. In Simpow the fluxes are calculated from the terminal voltage and the stator current but in PSS/E the fluxes are calculated from the stator current and the exciter voltage, see Slootweg [9], p.4.

Comparisons between the two models have earlier been investigated in Slootweg [9]. The settings of the generator in bus 1 are shown in Table 2.1.8.

Table 2.1.8 Dynamic parameters for the generator in bus 1 in the test system.

Parameters Value Unit Description TD0’ 6.000 [s] D-axis transient open-circuit time constant. TD0’’ 0.060 [s] D-axis subtransient open-circuit time constant. TQ0’ 0.500 [s] Q-axis transient open-circuit time constant. TQ0’’ 0.060 [s] Q-axis subtransient open-circuit time constant. H 2.000 [MWs/MVA] Inertia constant. D 0 [p.u.] Damping constant. XD 1.000 [p.u.] D-axis synchronous reactance. XQ 0.900 [p.u.] Q-axis synchronous reactance. XD’ 0.300 [p.u.] D-axis transient reactance. XQ’ 0.650 [p.u.] Q-axis transient reactance. XD’’ = ZX 0.200 [p.u.] D-axis subtransient reactance. * XQ’’ 0.200 [p.u.] Q-axis transient reactance. ** RA = ZR XA = X l

0.003 0.160

[p.u.] [p.u.]

Stator resistance. *** Stator reactance. ***

* Both parameters XD’’ and ZX are used in PSS/E but only XD’’ is used in Simpow, see Lindström [10].

** XQ’’ is only used in Simpow. XQ’’ is automatically set equal to XD’’ in PSS/E.

*** RA and XA is used in Simpow while ZR and Xl is used in PSS/E, see Lindström [10].

For dynamic simulation with no fault, see section 2.2.3.

2.1.5 Simulations of faults in PSS/E

In the system in Figure 2.1.3 we will simulate three-phase and single-phase faults at bus 2 and then see if the results in PSS/E and Simpow are equal. One restriction in PSS/E is that only one unsymmetrical fault can be calculated at one instant, see PSS/E-manual [2], POM, 5.35. In order to investigate the approximation in PSS/E, we will simulate the single-phase fault in Simpow in two ways. First we will make an exact calculation with all three sequences. Later we will make the calculation as it is done in PSS/E, using the PSS/E-approximation. We assume that the Thévenin equivalent used for the unsymmetrical one-phase fault in PSS/E is

(96)

faultTh ZZZZZ 3021 +++=

Equation 2.1.5 The equation for the Thévenin equivalent impedance.

where ZTh is the Thévenin-equivalent impedance, Z1, Z2, and Z0 are the positive-, negative-, and zero-sequence impedances respectively and Zfault is the fault impedance. This equivalent is mentioned in the PSS/E-manual [2], PAG, 10-40 and derived in Söder [7], p.133-134. The equivalent is mentioned in the short-circuit-part of the PSS/E-manual but not in the time-domain-part and therefore we assume this. The equations for the sequence currents in the fault becomes according to Kundur [6], p.897

Th

faultfaultfaultfault Z

UIII === 021

Equation 2.1.6 The equation for the sequence currents.

where Ifault1, Ifault2 and Ifault0 are the positive-, negative-, and zero-sequence currents respectively and Ufault is the positive-sequence voltage in the node just before the fault is applied. The three-phase fault simulation can be found in section 2.2.4 and the single-phase fault simulation can be found in section 2.2.5.

2.1.6 Sequence components of the power line impedan ces

To make an unsymmetrical fault simulation we need to include the negative- and zero-sequence components for the two power lines. Both lines have the same values. Calculations and values are shown in Table 2.1.9

Table 2.1.9 Calculations and values for sequence components of the two power lines.

Parameter [p.u.]

01625.021 == RR

32500.021 == XX

04875.03 10 =⋅= RR

97500.03 10 =⋅= XX where R1, R2, R0, X1, X2, and X0 are the positive-, negative-, and zero-sequence resistances and reactances respectively.

(96)

2.1.7 Sequence components of the generator impedanc e

Calculations and values for sequence components for the generator in bus 1 are shown in Table 2.1.10

Table 2.1.10 Sequence component data for the generator in bus 1.

Parameter [p.u.] 003.01 == RAR

2.01 =′′= DXX

03.0102 =⋅= RAR

2.02 =′′= DXX

*0 =R 144.09.00 =⋅= XAX **

* For calculation see Equation 2.1.7 and Equation 2.1.8.

** The value for XA can be found in Table 2.1.8. where R1, R2, R0, X1, X2, and X0 are the positive-, negative-, and zero-sequence resistances and reactances respectively, RA and XA are the stator resistance and reactance, and XD’’ is the D-axis subtransient reactance. Z0 is adjusted in Simpow so that the current I0 becomes 10 [A] when U0 is equal to 1 [p.u.] according to Lindquist [11], see Equation 2.1.7 and Equation 2.1.8. The same setting is used in PSS/E.

.].[5.5340

5340510

110

1

0

00 up

II

UZ

base

====

Equation 2.1.7 The equation for the zero-sequence impedance.

.].[499998.5340144.05.5340 2220

2

00 upXZR =−=−=

Equation 2.1.8 The equation for the zero-sequence resistance.

In Equation 2.1.7 and Equation 2.1.8 U0 is the zero-sequence voltage, I0 is the zero-sequence current, Z0 is the zero-sequence impedance, and Ibase is the base current.

(96)

2.2 Results

2.2.1 Power-flow simulation of the initial test sys tem

A power-flow simulation of the initial test system in PSS/E with a flat start1 generates the data in Table 2.2.1 and Table 2.2.2. In the calculation only positive-sequence components are used.

Table 2.2.1 Calculated variables for our initial test system with PSS/E.

Bus U [p.u.] θ [o] PG [p.u.] QG [p.u.] 1 0.9998 36.019 0.9000 0.3000 2 0.9485 18.054 0 0 3 0.9950 0 -0.9000 0.2852

Table 2.2.2 Power-flow in our initial test system with PSS/E.

From bus To bus P [p.u.] Q [p.u.]

1 2 0.9000 0.3000

2 1 -0.9000 -0.0074

2 3 0.9000 0.0074

3 2 -0.9000 0.2852

A power-flow simulation in Simpow generates the data in Table 2.2.3 and Table 2.2.4.

Table 2.2.3 Calculated variables for our initial test system with Simpow.


Table 2.2.4 Power-flow in our initial test system with Simpow.


1 2 0.9000 0.3000

2 1 -0.9000 -0.0074

2 3 0.9000 0.0074

3 2 -0.9000 0.2852

1 Flat start is an initial state of the power-flow calculation, which is that all voltage magnitudes are

.].[0.1 upU = and all voltage angles are ][0 oU =∠ .

(96)

According to Kundur [6], p. 732 the power-flow calculations are correct. As can be seen, the results are identical in PSS/E and Simpow. For values from Kundur see Table 2.2.5.

Table 2.2.5 Values from Kundur [6], p. 732. The element in the table marked as “-” is not calculated in

Kundur.

Bus U [p.u.] θ [o] PG [p.u.] QG [p.u.] 1 1.0 36 0.9 0.3 3 0.995 0 -0.9 -

2.2.2 Power-flow simulation of the final test syste m

A power-flow simulation of the final test system in PSS/E generates the data in Table 2.2.6 and Table 2.2.7.

Table 2.2.6 Calculated variables for our final test system with PSS/E.


Table 2.2.7 Power-flow in our final test system with PSS/E.


1 2 0.9000 0.3000

2 1 -0.8866 -0.0312

2 3 0.8866 0.0312

3 2 -0.8731 0.2376

A power-flow simulation in Simpow generates the data in Table 2.2.8 and Table 2.2.9.

Table 2.2.8 Calculated variables for our final test system with Simpow.


(96)

Table 2.2.9 Power-flow in our final test system with Simpow.


1 2 0.9000 0.3000

2 1 -0.8866 -0.0312

2 3 0.8866 0.0312

3 2 -0.8731 0.2376

As can be seen in Table 2.2.6 - Table 2.2.9, the results are identical in PSS/E and Simpow.

2.2.3 Dynamic simulation without fault

A simulation of the final test system with dynamics included generates the data in Table 2.2.10 and Table 2.2.11.

Table 2.2.10 Dynamic data from the “GENROU” generator model simulated with PSS/E.

Generator δ [o] id [p.u.] iq [p.u.]

1 64.389 0.6881 0.5946

Table 2.2.11 Dynamic data from the “Type 1A” generator model simulated with Simpow.

Generator δ [o] id [p.u.] iq [p.u.]

1 64.389 0.6881 0.5946

In Table 2.2.10 and Table 2.2.11 we can see that the steady-state situation of the two models is similar. Later in sections 2.2.4 and 2.2.5 we will see the dynamical behaviour of the two models.

2.2.4 Three-phase fault simulation

A simulation of the system with a 0.1 seconds three-phase fault, applied in bus 2 after 0.1 second, generates the data in Figure 2.2.1 - Figure 2.2.8. The PSS/E simulation is done both with 10 [ms] and 1 [ms] time steps, in order to see if it influences the result. In Simpow, the actual time step is varied automatically during the simulation and adjusted according to the behaviour of the system.

(96)

Figure 2.2.1 Voltage at bus 1 (positive-sequence) simulated with Simpow and PSS/E.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Time [s]

Vol

tage

[p.

u.]

Voltage bus 1

Simpow

PSS/E 10ms

PSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time [s]

Vol

tage

[p.

u.]

Voltage bus 2

Simpow

PSS/E 10ms

PSS/E 1ms

(96)

Figure 2.2.3 Angle at bus 1 (positive-sequence) simulated with Simpow and PSS/E.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.530

40

50

60

70

80

90

100

110

120

Time [s]

Ang

le [

o ]

Angle bus 1

Simpow

PSS/E 10msPSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

Time [s]

Ang

le [

o ]

Angle bus 2

Simpow

PSS/E 10msPSS/E 1ms

(96)

Figure 2.2.5 The generator angle simulated with Simpow and PSS/E.

Figure 2.2.6 The generator speed simulated with Simpow and PSS/E.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

40

60

80

100

120

140

160

180

Time [s]

Ang

le [

o ]

Generator angle

Simpow

PSS/E 10msPSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.985

0.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Time [s]

Spe

ed [

p.u.

]

Generator speed

Simpow

PSS/E 10ms

PSS/E 1ms

(96)

Figure 2.2.7 The generator angle simulated during 15 seconds with Simpow and PSS/E.

Figure 2.2.8 The generator speed simulated during 15 seconds with Simpow and PSS/E.

0 5 10 15

30

40

50

60

70

80

90

100

110

120

130

Time [s]

Ang

le [

o ]

Generator angle

Simpow

PSS/E 10msPSS/E 1ms

0 5 10 15

0.98

0.985

0.99

0.995

1

1.005

1.01

1.015

1.02

Time [s]

Spe

ed [

p.u.

]

Generator speed

Simpow

PSS/E 10ms

PSS/E 1ms

(96)

So far, the fault has been symmetrical which means that the approximation has not yet been used. In Figure 2.2.1 - Figure 2.2.6 we can see that before, during and immediately after the fault the simulations in PSS/E and Simpow correspond well to each other. This shows that the software calculates equal during a symmetrical fault. The angle in bus 2 during the fault in Figure 2.2.4 should not be analysed further since the voltage in bus 2 is equal to zero. After the fault has been removed and when t > 0.5 [s] we can see that the Simpow curve and the PSS/E curves begin to differ. This shows that the dynamical behaviours of the two models differ, however in Figure 2.2.7 - Figure 2.2.8 we can see that both models return to the same initial conditions. If we compare the two simulations in PSS/E, with different time steps, we can see that there is a small difference in Figure 2.2.1 - Figure 2.2.3 and Figure 2.2.6. The simulation with 1 [ms] time steps becomes more correct. The difference is however negligible and do not result in any difference in long-term simulations.

2.2.5 Single-phase fault simulation

A simulation of the system with a 0.1 seconds single-phase fault, applied in bus 2 after 0.1 second, generates the data in Figure 2.2.9 - Figure 2.2.18. In the simulation PSS/E calculates only the positive-sequence components using the approximation described in section 2.1. By reading the PSS/E-manual [8] we are not fully convinced about how this approximation is applied. We have assumed that a shunt which we think represents the positive-, negative- and zero-sequence impedances, is connected in the fault bus. This shunt impedance consumes, according to PSS/E, S = 85.726 + i1742.3 [MVA] which is the short-circuit power shown in the terminal window in PSS/E immediately after the fault has been applied. With this data we can calculate an equivalent shunt impedance, see Equation 2.2.1.

( ) .].[209.10595.0

22203.1742726.85

9755.0 2

*

2

upii

SS

UZ

base

shunt

fault

shunt +=−==

Equation 2.2.1 The equation for the equivalent shunt impedance.

In Equation 2.2.1 Zshunt is the shunt impedance, Ufault is the voltage at the faulted bus just before the fault is applied, Sbase is the base power and Sshunt is the initial complex short-circuit power through the shunt. In order to run a Simpow simulation using the same approximation as in PSS/E, this shunt will be connected in the fault bus in a Simpow simulation. Such Simpow simulation will be

(96)

symmetrical as in PSS/E since the shunt is connected symmetrical, see the graphs marked as “Simpow shunt” in the following figures. However, in the Simpow simulations using Zshunt we have seen that the result not becomes as the PSS/E simulation, see for instance Figure 2.2.15 where the blue graph indicates the Simpow simulation using Zshunt. Therefore we have tried to calculate a new shunt to get as close as possible to the PSS/E simulation. If we use the voltage and current in PSS/E and/or “Simpow detailed” at the time just after the fault is applied (t = 0.1+ [s]) we can calculate the shunt impedance Zown shunt in Equation 2.2.2.

( ) ( )( ).].[1758.10619.0

6642.02442.0

174.17sin174.17cos8333.0

1.0_

1.0_ upiiI

UZ

fault

faultshuntown +=

−+==

+

+

Equation 2.2.2 The equation for the “self-calculated” shunt impedance.

In Equation 2.2.2 Zown shunt is a “self-calculated” shunt impedance, Ufault_0.1+ is the voltage at the fault bus just after the fault is applied, and Ifault_0.1+ is the current in the fault just after the fault is applied. In the following result we can see the difference between the shunt impedance stated in PSS/E Zshunt and our self-calculated shunt impedance Zown shunt. The graphs with our self-calculated shunt impedance are marked as “Simpow own shunt” in the following figures. In the following graphs we have made three Simpow simulations and two PSS/E simulations:

• “Simpow detailed”. A single-phase fault simulation in Simpow using all three symmetrical components. Only the positive-sequence component is plotted.

• “Simpow shunt”. A symmetrical fault simulation in Simpow with the shunt impedance Zshunt from Equation 2.2.1 modelled as a symmetrical load at the fault.

• “Simpow own shunt”. A symmetrical fault simulation in Simpow with the shunt impedance Zown shunt from Equation 2.2.2 modelled as a symmetrical load at the fault.

• “PSS/E 10ms”. A single-phase fault simulation, with 10 [ms] time-steps, in PSS/E using the approximation described in section 2.1.

• “PSS/E 1ms”. A single-phase fault simulation, with 1 [ms] time-steps, in PSS/E using the approximation described in section 2.1.

The Simpow simulation with the correct value of the shunt should give the same result for the positive sequence as the simulation with all three components. The PSS/E simulation is done both with 10 [ms] and 1 [ms] time steps, in order to see if the time step influences the result.

(96)



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Time [s]

Vol

tage

[p.

u.]

Voltage bus 1

Simpow detailed

Simpow shunt

Simpow own shuntPSS/E 10ms

PSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

Time [s]

Vol

tage

[p.

u.]

Voltage bus 2

Simpow detailed

Simpow shunt


PSS/E 1ms

(96)



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

31

32

33

34

35

36

37

38

39

Time [s]

Ang

le [

o ]

Angle bus 1

Simpow detailed

Simpow shunt


PSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

16

16.5

17

17.5

18

18.5

19

19.5

Time [s]

Ang

le [

o ]

Angle bus 2

Simpow detailed

Simpow shunt


PSS/E 1ms

(96)

Figure 2.2.13 The generator angle simulated with Simpow and PSS/E.

Figure 2.2.14 The generator speed simulated with Simpow and PSS/E.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

60

62

64

66

68

70

Time [s]

Ang

le [

o ]

Generator angle

Simpow detailed

Simpow shunt


PSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.9975

0.998

0.9985

0.999

0.9995

1

1.0005

1.001

1.0015

1.002

1.0025

Time [s]

Spe

ed [

p.u.

]

Generator speed

Simpow detailed

Simpow shunt


PSS/E 1ms

(96)

Figure 2.2.15 The real part of the fault current (positive-sequence) simulated with Simpow and PSS/E.

Figure 2.2.16 The imaginary part of the fault current (positive-sequence) simulated with Simpow and

PSS/E.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

0.05

0.1

0.15

0.2

0.25

Time [s]

Cur

rent

[p.

u.]

Real fault current

Simpow detailed

Simpow shunt


PSS/E 1ms

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Time [s]

Cur

rent

[p.

u.]

Imaginary fault current

Simpow detailed

Simpow shunt


PSS/E 1ms

(96)

Figure 2.2.17 The generator angle simulated during 15 seconds with Simpow and PSS/E.

Figure 2.2.18 The generator speed simulated during 15 seconds with Simpow and PSS/E.

0 5 10 15

60

62

64

66

68

70

Time [s]

Ang

le [

o ]

Generator angle

Simpow detailed

Simpow shunt


PSS/E 1ms

0 5 10 150.9975

0.998

0.9985

0.999

0.9995

1

1.0005

1.001

1.0015

1.002

1.0025

Time [s]

Spe

ed [

p.u.

]

Generator speed

Simpow detailed

Simpow shunt


PSS/E 1ms

(96)

As we can see in Figure 2.2.9 - Figure 2.2.16 the simulations in PSS/E and Simpow corresponds well to each other except for the simulation with the shunt Zshunt stated in PSS/E. Before, during, and immediately after the fault the curves are almost equal, except for Simpow shunt. This means that the calculation in PSS/E, with the approximation, is correct concerning the positive-sequence components, which is the only component we can study in PSS/E. In Figure 2.2.17 and Figure 2.2.18 we can also in this simulation see that the dynamic of the generators in PSS/E and Simpow differ but both simulations returns to the same initial state. If we compare the two simulations in PSS/E, with different time steps, we can see that there is a small difference in Figure 2.2.9 - Figure 2.2.14. The simulation with 1 [ms] time steps becomes more correct. The difference is however negligible and do not result in any difference in long-term simulations. In the project we have not understood the complex power for the shunt stated in PSS/E. With our own shunt Zown shunt the power should be as in Equation 2.2.3.

][6.1791295.941758.10619.0

22209755.0 2

*

2

MVAiiZ

SUS

shuntown

basefault

shuntown +=−

⋅=⋅

=

Equation 2.2.3 The equation for the initial complex short-circuit power in our “self-calculated” shunt.

In Equation 2.2.3 Sown shunt is the initial complex short-circuit power in the shunt, Ufault is the voltage in the faulted bus just before the fault is applied, Zown shunt is our own calculated shunt impedance, and Sbase is base power. With this value for the complex short-circuit power we can calculate how erroneously the complex short-circuit power stated in PSS/E is, see Equation 2.2.4.

0285.13.1742726.85

6.1791295.94/ =

++

==i

i

S

SS

shunt

shuntown

EPSSinerror

Equation 2.2.4 The equation for the error in the stated initial complex short-circuit power in PSS/E.

In Equation 2.2.4 Sown shunt is our self-calculated initial complex short-circuit power in the shunt, Sshunt is the initial complex short-circuit power in the shunt stated in PSS/E, and Serror in

PSS/E is the error in the stated initial complex short-circuit power in PSS/E. The initial complex short-circuit power stated in PSS/E is therefore 2.85 [%] incorrect. In order to check the result analytically we will here investigate the initial result when the fault is applied. In order to do this we have to calculate the Thévenin equivalent. The Thévenin-equivalent impedance for a single-phase fault in bus 2 in the test system can be calculated with Equation 2.2.5 - Equation 2.2.8.

(96)

( )( )( ) .].[2007.00090.0

2.0003.0325.001625.02

2.0003.0325.001625.0325.001625.0

2

)(

11

1111 upi

ii

iii

ZZ

ZZZZ

GL

GLL +=+++

++++=+⋅+=

Equation 2.2.5 The equation for the positive-sequence impedance.

( )( )

( ) .].[2008.00130.02.003.0325.001625.02

2.003.0325.001625.0325.001625.0

2

)(

22

2222 upi

ii

iii

ZZ

ZZZZ

GL

GLL +=+++

++++=+⋅+=

Equation 2.2.6 The equation for the negative-sequence impedance.

( )( )

( ) .].[9750.00489.0144.05.5340975.004875.02

144.05.5340975.004875.0975.004875.0

2

)(

00

0000 upi

ii

iii

ZZ

ZZZZ

GL

GLL +=+++

++++=+⋅+=

Equation 2.2.7 The equation for the zero-sequence impedance.

.].[3765.10709.0021 upiZZZZTh +=++=

Equation 2.2.8 The equation for the Thévenin-equivalent impedance.

In Equation 2.2.5 - Equation 2.2.8 ZL1, ZL2, and ZL0 are the sequence-component impedances in Table 2.1.9 for the two power lines. ZG1, ZG2, and ZG0 are the sequence-component impedances in Table 2.1.10 for the generator. Z1, Z2, and Z0 are the positive-, negative-, and zero-sequence impedances respectively for the test system seen from the faulted bus and ZTh is the Thévenin-equivalent impedance. If we compare Equation 2.2.6 and Equation 2.2.7 with Equation 2.2.2 we can see that Zown shunt in Equation 2.2.2 is equal to Z2 + Z0 in Equation 2.2.6 and Equation 2.2.7, see PSS/E-manual [2], PAG, 10.54. With the Thévenin impedance in Equation 2.2.8 we can calculate the initial fault current, see Equation 2.2.9.

( ) ( )( ).].[6642.02442.0

3765.10709.0238.17sin238.17cos9755.0

upii

i

Z

UI

Th

faultfault −=

++==

Equation 2.2.9 The equation for the fault current.

In Equation 2.2.9 Ifault is the fault current and Ufault is the voltage in the node just before the fault is applied. As we can see in Figure 2.2.15 and Figure 2.2.16, for t = 0.1+ [s], the calculated initial fault current is correct. It is the same as calculated in Simpow detailed, Simpow own shunt and in the two PSS/E simulations. In the simulation “Simpow shunt” the current is not as calculated

(96)

in Equation 2.2.9. The calculated current Ifault in Equation 2.2.9 is therefore the same as the current Ifault_0.1+ earlier used in Equation 2.2.2.

2.3 Discussion about symmetrical components of volt ages

As stated earlier, a drawback in PSS/E is that we do not have the information concerning the negative- and zero-sequence components, which results in that we cannot calculate the correct phase quantities. When we get the result from an unsymmetrical fault, the result appears as a symmetrical fault in PSS/E and it is easy to misunderstand and think that the three phase-quantities are equal to the result of the positive-sequence voltage. For example, the voltage in the single-phase faulted bus in Figure 2.2.10 appears as a voltage in a three-phase fault. It is therefore easy to think that the phase-voltages are equal to that result as shown in Figure 2.3.1. The voltages in Figure 2.3.1 are shown at the time just after the fault is applied (t = 0.1+ [s]).

Figure 2.3.1 Phase voltages as it appears in a single-phase fault in PSS/E.

-1.5 -1 -0.5 0 0.5 1-1.5

-1

-0.5

0

0.5

1

Real voltage [p.u.]

Imag

inar

y vo

ltage

[p.

u.]

Bus 2 fault voltage

Ua

Ub

Uc

(96)

However, in Simpow2 we have full information about the negative- and zero-sequence components and with all three symmetrical components we can calculate the correct phase voltages as shown in Figure 2.3.2.

Figure 2.3.2 Phase-voltages and symmetrical component voltages for a single-phase fault in Simpow.

In Figure 2.3.2 Ua, Ub and, Uc are the phase-voltages at t = 0.1+ [s]. U1, U2 and U0 are the positive-, negative-, and zero-sequence voltages respectively. The differences between Figure 2.3.1 and Figure 2.3.2 are that Ua is indeed equal to 0 in Figure 2.3.2 and we can also see that the phase voltages Ub and Uc are having a larger magnitude and a phase shift ≠ 120o. With the positive-sequence voltage and the voltage in phase c from Simpow we can calculate the difference, if we think that the positive-sequence voltage is equal to the phase-voltage, see Equation 2.3.1.

6016.15374.06090.0

4573.02178.1

1=

+−+−

==i

i

U

UcU difference

Equation 2.3.1 The equation for the difference between the positive-sequence voltage and the

voltage in phase c.

2 Here we mean the Simpow simulation indicated as “Simpow detailed”.

-1.5 -1 -0.5 0 0.5 1-1.5

-1

-0.5

0

0.5

1

Real voltage [p.u.]

Imag

inar

y vo

ltage

[p.

u.]

Bus 2 fault voltage

UaUb

Uc

U1

U2U0

Ua=0Ua=0Ua=0Ua=0

UbUbUbUb

UcUcUcUc

(96)

In Equation 2.3.1 Uc is the voltage in phase c, U1 is the positive-sequence voltage, and Udifference is the difference between the positive-sequence voltage and the voltage in phase c. The difference in magnitude between the positive-sequence voltage and the voltage in phase c is 60 [%]. This is only shown in the detailed Simpow simulation. In Figure 2.3.1 the result can be misleading and it is easy to think that Ua ≠ 0 and that the phase-shift = 120 [o].

2.4 Conclusions

As we can see in section 2.2.4 and section 2.2.5 the simulations in PSS/E and Simpow corresponds well to each other except for the simulation in Simpow with the shunt Zshunt stated in PSS/E. The shunt is in our case 2.85 [%] incorrect. The remaining curves are before, during, and immediately after the fault almost equal. This means that the calculations for both symmetrical and unsymmetrical faults in PSS/E are correct concerning the positive-sequence components. Later in the simulations we can see that the dynamical models in PSS/E and Simpow differ. This dynamic is however not focused in this research. Both simulations return to the same steady-state. If we compare the two simulations in PSS/E, with different time steps, we can see that there is a small difference between the curves in some figures. The simulations with shorter time steps becomes more correct but the difference is negligible and do not result in any difference in long-term simulations. A drawback in PSS/E is that we do not have any information concerning the negative- and zero-sequence components in a time-domain simulation, which results in that we cannot calculate the correct three phase-quantities. When we get the result from an unsymmetrical fault, the result appears as a symmetrical fault in PSS/E and it is easy to think that the phase-quantities are equal to the result of the positive-sequence voltage.

(96)

3 Power-flow simulation of Gotland

3.1 Setup

3.1.1 Grid structure

The transmission network at Gotland consists of a 70 [kV] grid together with the HVDC Classic link from the mainland of Sweden and the HVDC Light link. The HVDC Classic link transmits power from the mainland of Sweden to Gotland and is connected to Västervik at the mainland and to Visby at the island of Gotland. The HVDC Light link transmits power from the wind power plants in the southern part of Gotland to the load in Visby at the northern part of Gotland and is connected between Näs and Bäcks. A scheme of the 70 [kV] grid at Gotland together with the HVDC Classic link and the HVDC Light link is shown in Figure 3.1.1. The HVDC Light link is in Figure 3.1.1 modelled with the “Standard PSS/E model”.

Figure 3.1.1 A scheme of the 70 [kV] grid at Gotland together with the HVDC Classic link and the

HVDC Light link. Here, the HVDC Light link is modelled with the “Standard PSS/E model”.

The HVDC Light link contains the nodes BACKAC.78 and NASAC.78 where the base voltage is 78.2 [kV]. To easily see a difference between the 78.2 [kV] nodes and the rest of

(96)

the 70 [kV] network, which have 75 [kV] as base voltage, the 78.2 [kV] nodes have been indicated as “.78”. The 70 [kV] grid in Gotland is connected via transformers to 30, 20, 10, and 6 [kV] voltage levels, where all loads are connected. There are also two synchronous machines installed at two other voltage levels, namely 13.8 and 12.4 [kV], in Ygne and one synchronous machine is connected at 6 [kV] at the Cementa factory. The distribution network is later transformed to a 0.6 [kV] voltage level where all wind power plants are connected. There are also several shunt capacitors installed at 0.6 [kV]. The transmission network and the distribution network together with the 0.6 [kV] voltage level in the northern part of the power system are shown in Figure 3.1.2.

Figure 3.1.2 The northern part of the power system of Gotland.

The nodes in the power system of Gotland have been numbered to fit in the enumbering standard of Svenska Kraftnät’s data bank. The number starts at 36900 and ends at 36999 with the highest voltage level at the lowest number and the lowest voltage level at the highest number. 4 free numbers are still available between 36906 and 36909 for future use. The power system of the mainland of Sweden has been modelled with an equivalent consisting of a 130 [kV] grid with among other things 3 swing buses, see Adielson [12], p.7. All buses, except the swing buses are numbered according to Svenska Kraftnät’s data bank. However, the values of the lines and loads are different compared to the complete model of the mainland because of the calculated equivalent, see Figure 3.1.3. For example, the value of the resistance for the line between Kimsta.130 and Farhul.130 is negative, i.e., the line is producing active power. To not mistake any of the swing buses for being a bus in the Swedish power system they have been numbered as 800001, 800002, and 800003, which are not used in the data bank of Svenska Kraftnät. If we later would like to connect Gotland to the

complete model of the mainland then we should remove the equivalentmainland to node 34019, see Sweden used in the thesis together with the HVDC Classic link is shown in

Figure 3.1.3 The equivalent of the mainland of Sweden

3.1.2 Transformers

There are a total of 63 transformers in the grid model. 62 transformers are twotransformers and one transformer is a threevoltage control function of which 2 transformers have been modelled with 17 steps and 27 transformers have been modelled with infinite number of steps. A problem with converting the transformers with infinite number of steps is that the maximum number of steps in PSS/E is 9999. This results in a small differencecalculations in PSS/E compared to the results from Simpow Another difference between the transformer models in Simpow and PSS/E is that the tapside is on different windings in the two softwarecontrolled bus (second bus in the Simpow text file) but in PSS/E the tapside is at the uncontrolled bus (first bus in the Simpow text file). Therefore the transformer sides have to be exchanged from Simpow to PSS/E, i.e., the transformer has to be turned around. The parameters in the two programs are shown in transformer. The parameters in Simpow for thand NAS.70 with stepped voltage regulation

Page 35 (96)

complete model of the mainland then we should remove the equivalentmainland to node 34019, see Figure 3.1.3. A scheme of the equivalent of the mainland of

together with the HVDC Classic link is shown in

The equivalent of the mainland of Sweden used in the thesis together with the HVDC

Classic link.

There are a total of 63 transformers in the grid model. 62 transformers are twotransformers and one transformer is a three-winding transformer. 29 transformers have a

on of which 2 transformers have been modelled with 17 steps and 27 transformers have been modelled with infinite number of steps. A problem with converting the transformers with infinite number of steps is that the maximum number of steps in PSS/E

This results in a small difference in the fourth decimal of the voltage in powercompared to the results from Simpow.

Another difference between the transformer models in Simpow and PSS/E is that the tapside in the two software. In Simpow the tapside is at the voltage

controlled bus (second bus in the Simpow text file) but in PSS/E the tapside is at the uncontrolled bus (first bus in the Simpow text file). Therefore the transformer sides have to be

nged from Simpow to PSS/E, i.e., the transformer has to be turned around. The parameters in the two programs are shown in Table 3.1.1 and Table 3.1

w for the two-winding transformer between the nodes NASAC.78 with stepped voltage regulation are shown in Table 3.1.1.

complete model of the mainland then we should remove the equivalent and connect the valent of the mainland of

together with the HVDC Classic link is shown in Figure 3.1.3.

together with the HVDC

There are a total of 63 transformers in the grid model. 62 transformers are two-winding winding transformer. 29 transformers have a

on of which 2 transformers have been modelled with 17 steps and 27 transformers have been modelled with infinite number of steps. A problem with converting the transformers with infinite number of steps is that the maximum number of steps in PSS/E

in the fourth decimal of the voltage in power-flow

Another difference between the transformer models in Simpow and PSS/E is that the tapside . In Simpow the tapside is at the voltage-

controlled bus (second bus in the Simpow text file) but in PSS/E the tapside is at the uncontrolled bus (first bus in the Simpow text file). Therefore the transformer sides have to be

nged from Simpow to PSS/E, i.e., the transformer has to be turned around. The 3.1.2 for one certain

between the nodes NASAC.78

(96)

Table 3.1.1 Data in Simpow for the two-winding transformer in Näs.

Parameter Value Unit Description N NASAC.78 NAS.70 The first and second bus name SN 70 [MVA] Base power UN1 75 [kV] Nominal voltage at winding 1 UN2 75 [kV] Nominal voltage at winding 2 U 75 [kV] Voltage at the controlled bus FI 0 [o] Phase shift angle ER12 0 [p.u.] Resistance between bus 1 and bus 2 EX12 0.08 [p.u.] Reactance between bus 1 and bus 2 CNODE NAS.70 Voltage controlled bus +NSTEP 16 Increasing steps -NSTEP 0 Decreasing steps STEP 0.01875 [p.u.] Tap step size The parameters in PSS/E for the two-winding transformer between the nodes NASAC.78 and NAS.70 with stepped voltage regulation are shown in Table 3.1.2.

Table 3.1.2 Data in PSS/E for the two-winding transformer in Näs.

Parameter Value Unit Description I 36933 (NAS.70) Number of bus 1 J 36903 (NASAC.78) Number of bus 2 R1-2 0 [p.u.] Resistance between bus 1 and bus 2 X1-2 0.08 [p.u.] Reactance between bus 1 and bus 2 SBASE1-2 70 [MVA] Winding 1 to 2 base power WINDV1 1 [p.u.] Winding 1 off-nominal turn ratio NOMV1 75 [kV] Nominal voltage at winding 1 ANG1 0 [o] Phase shift angle CONT1 36933 (NAS.70) Number of voltage controlled bus RMI1 - RMA1 1 - 1.3 [p.u.] Turn ratio VMI1 - VMA1 0.990625 – 1.009375 [p.u.] Voltage at the controlled bus NTP1 17 Number of steps WINDV2 0.959079 [p.u.] Winding 2 off-nominal turn ratio NOMV2 75 [kV] Nominal voltage at winding 2 In the example above we can see that the first node in Simpow (NASAC.78) is bus number 2 in PSS/E.

(96)

3.1.3 Machines

The total production from the generators in the model is 105 [MW]. There are about 160 wind power plants in the power system, which have been modelled as 23 asynchronous machines in Simpow. The asynchronous machines should control active power but not the voltage. The reactive power of the machines should vary as a function of the active power. A problem with this is that there is no such model for power-flow simulations in PSS/E. The generator model in PSS/E has to control either voltage or reactive power. To get a correct power-flow simulation we have therefore chosen to control the reactive power according to the result of the power-flow simulation in Simpow3, see section 1.4. There is also an asynchronous machine connected at the Cementa factory. This machine has been modelled in Simpow as a mechanical load with a torque. The torque should vary as a function of the frequency, which results in a varying power consumption. Also here there is no corresponding model in PSS/E and we have therefore chosen to control the active and reactive power according to the result in Simpow3, see section 1.4. In Ygne there are two synchronous machines installed at the nodes NG.14 and NG.13 and at the Cementa factory there is one synchronous machine installed at the node NG.11. NG.11 and NG.13 are generator nodes and the machines have fixed active and reactive power production. NG.14 is a swing bus and the machine is controlling the voltage and angle. A problem with the machine in node NG.14 is that in Simpow it is controlling the voltage in another node namely YGNE.70. In PSS/E a machine in a swing bus has to control the voltage in its own bus. To solve this problem the machine in NG.14 is controlling the voltage in NG.14 according to the result of the power-flow simulation in Simpow, see section 1.4.

3.1.4 Shunt impedances

There are 47 shunt impedances included in the grid model. Most of them are installed at the 0.6 [kV] voltage level and close to wind farms to compensate the reactive power consumption in the power plants. There are 3 shunt impedances installed at the 70 [kV] voltage level in Gotland to compensate the reactive power consumption from the HVDC Classic link and at the Cementa factory.

3.1.5 Loads

There are 45 loads in the grid model and the total power consumption is 155 [MW]. A problem with converting the loads from Simpow to PSS/E is that the modelling of the loads differs in Simpow and PSS/E. The model for a load in Simpow is shown in Equation 3.1.1.

3 Here it has to be emphasized that a disadvantage with these solutions is that if we want to make a change in the

network model, then it might lead to that we have to change the reactive power of all asynchronous machines in

the network model.

(96)

( ) ( )MQMPLS UjQUPS 00 +=

Equation 3.1.1 The model for a load in Simpow.

In Equation 3.1.1 SLS is the complex power for the load. P0 is the active power and Q0 is the reactive power at 1 [p.u.] voltage. U is the voltage at the load in [p.u.] of the base voltage of the node and MP and MQ are voltage exponents. MP and MQ do not have to be integers, they can have any arbitrary value. The model for a load in PSS/E is shown in Equation 3.1.2.

( ) ( )( )2321

2321 UQUQQjUPUPPSLP +++++=

Equation 3.1.2 The model for a load in PSS/E.

In Equation 3.1.2 SLP is the complex power for the load. The sum of P1, P2, and P3 is the active power at 1 [p.u.] voltage and the sum of Q1, Q2, and Q3 is the reactive power at 1 [p.u.] voltage. U is the voltage at the load in [p.u.] of the base voltage of the node. To be able to convert the loads from Simpow to PSS/E we have to put SLS = SLP and then identify P1, P2, P3, Q1, Q2, and Q3 to model the load in PSS/E. Since the voltage exponents in Simpow do not have to be equal to any of the voltage exponents (0, 1, 2) in the PSS/E model, the equation system, SLS = SLP, may be unsolvable. The solution to this problem is to solve the equation system numerical. The numerical solution will not be absolutely correct but it will be close to the correct solution in a chosen interval of voltages. We have here chosen the voltage interval 0.8 < U < 1.2 [p.u.] since we do not have any voltages below 0.8 [p.u.] and over 1.2 [p.u.] in the power system of Gotland in the studied cases. To make the numerical identification we have used Gaussian elimination in Matlab. To make the Gaussian elimination we have to write our equation system on a matrix form, see Equation 3.1.3.

[ ] [ ] [ ]bxA =⋅

Equation 3.1.3 Matrix form for doing Gaussian elimination of equation systems in Matlab.

In Equation 3.1.3 A is a matrix and x and b are vectors. The equation system for the active power is shown in Equation 3.1.4.

(96)

⋅

⋅⋅

=

⋅

⋅⋅⋅

⋅⋅⋅||||

0

3

2

1

210 MPUP

P

P

PUUU

Equation 3.1.4 The equation system for the active power in matrix form.

In Equation 3.1.4 U is a vector with values between 0.8 [p.u.] and 1.2 [p.u.] so that the first row of the A-matrix is 0.80 0.81 0.82 and the last row is 1.20 1.21 1.22. In Equation 3.1.4 it is P1, P2, and P3 that shall be identified. The equation system for the reactive power is written in the same way, see Equation 3.1.5.

⋅

⋅⋅

=

⋅

⋅⋅⋅

⋅⋅⋅||||

0

3

2

1

210 MQUQ

Q

Q

QUUU

Equation 3.1.5 The equation system for the reactive power in matrix form.

The Gaussian elimination of the equation system is done with the command for Gaussian elimination in Matlab, see Equation 3.1.6.

bAx \=

Equation 3.1.6 The command for solving a system of equations in Matlab with Gaussian elimination.

As an example we have here chosen load 1 at the node PILH.10 in the grid of Gotland. The equation in Simpow for that load is shown in Equation 3.1.7.

( ) ( ) ][22 9.158.0 MVAUjUSLS +=

Equation 3.1.7 The equation in Simpow for load 1 at node PILH.10.

The numerical solution for load 1 at the node PILH.10 is shown in Figure 3.1.4 and Figure 3.1.5 and the identified equation from Matlab to be used in PSS/E is shown in Equation 3.1.8. The results are very similar between Simpow and PSS/E and therefore the blue graph is behind the red graph in Figure 3.1.4 and Figure 3.1.5.

( ) ( )( ) ][7106.13774.00880.02462.06552.15909.0 22 MVAUUjUUSLP ++−+−+=

Equation 3.1.8 The equation in PSS/E for load 1 at node PILH.10.

(96)

Figure 3.1.4 Active power in load 1 at bus PILH.10.

Figure 3.1.5 Reactive power in load 1 at bus PILH.10.

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.21.75

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

2.25

Voltage [p.u.]

Act

ive

pow

er [

MW

]

Active power in load

Simpow

PSS/E

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Voltage [p.u.]

Rea

ctiv

e po

wer

[M

var]

Reactive power in load

Simpow

PSS/E

(96)

In these figures we can see that the load’s voltage dependence in PSS/E is almost equal to the load’s voltage dependence in Simpow when the voltage is varied between 0.8 and 1.2 [p.u.] Therefore the difference between the two models should not be a problem during simulations.

3.1.6 “Standard PSS/E model”

The “Standard PSS/E model” contains two converters and one DC cable in the power-flow setup of the HVDC Light link. The converter in Näs controls the active power drawn from the 70 [kV] grid and the AC voltage in node NASVAC.78. The inverter in Bäcks controls the AC voltage in node BACKVAC.78 and the DC voltage on the DC cable, see Figure 3.1.1. There are the following three problems with converting data, for the HVDC Light link, from the “Simpow model” to the “Standard PSS/E model”:

1. In the “Simpow model” the DC cable is modelled as a resistance and a capacitance but in the “Standard PSS/E model” the DC cable can only be modelled as a pure resistance. We have not found any solution to this problem, which not will affect the power-flow simulation because of the constant voltage on the DC cable. However, the capacitance could affect dynamic simulations in case of voltage variations on the DC cable. The model of the DC cable in the “Simpow model” is shown in Figure 3.1.6.

Figure 3.1.6 The model of the DC cable in the “Simpow model”.

2. The models of the converters in the “Simpow model” and the “Standard PSS/E

model” are different. In the “Simpow model” the resistance and the reactance of the converters are stated but this is not possible to do in the “Standard PSS/E model”. To solve this problem we have inserted an additional line in PSS/E between the filters and the converters with the impedance stated for the converters in the “Simpow model”. This solution results in that we need to reduce the power demand for the converter in Näs in the “Standard PSS/E model” because of that some internal losses in the converter is transferred to the added line, see Figure 3.1.8. The model of the converters in the “Simpow model” is shown in Figure 3.1.7. The same converter exists in Näs (shown in Figure 3.1.7) and in Bäcks.

(96)

Figure 3.1.7 The model of the converters in the “Simpow model”.

The model of how we have decided to model the converters in the “Standard PSS/E model” is shown in Figure 3.1.8. The same converter exists in Näs (shown in Figure 3.1.8) and in Bäcks.

Figure 3.1.8 The model of the converters in the “Standard PSS/E model, with the added line.

3. The two filters between the transformers and the converters in the HVDC Light link

are modelled as a series reactance and a shunt impedance in Simpow, see Figure 3.1.9. We can model the shunt impedance in PSS/E but there is no model in PSS/E for a series reactance. This problem is solved by modelling the series reactance as a line with the same impedance. The model of the filter in Simpow is shown in Figure 3.1.9. The filter arrangement exists both in Näs (shown in Figure 3.1.9) and in Bäcks.

Figure 3.1.9 The model of the filters between the converters and the transformers in Simpow.

The parameters for the DC cable in the “Simpow model” are shown in Table 3.1.3.

Table 3.1.3 The parameters in the “Simpow model” for the DC cable.

Parameter Value Unit Description R 13 [Ω] DC line resistance C 11.5 [µF] DC line capacitance

The parameters for the DC cable in the “Standard PSS/E model” are shown in Table 3.1.4.

(96)

Table 3.1.4 The parameters in the “Standard PSS/E model” for the DC cable.

Parameter Value Unit Description RDC 13 [Ω] DC line resistance

The parameters in the “Simpow model” for the converter in Näs are shown in Table 3.1.5.

Table 3.1.5 The parameters in the “Simpow model” for the converter in Näs.

Parameter Value Unit Description N NASVAC.78 Bus name P -20 [MW] Power demand U 72 [kV] AC voltage

CNODE NASVAC.78 Voltage controlled bus SN 65 [MVA] Base power R 0.012 [p.u.] Converter resistance X 0.14 [p.u.] Converter reactance

The parameters in the “Standard PSS/E model” for the converter in Näs are shown in Table 3.1.6.

Table 3.1.6 The parameters in the “Standard PSS/E model” for the converter in Näs.

Parameter Value Unit Description IBUS 36905 (NASVSC.78) Bus number

DCSET -19.89 [MW] Power demand ACSET 0.920716 [p.u.] AC voltage* REMOT 36904 (NASVAC.78) Voltage controlled bus

* The AC voltage is set to 72 [kV] and gets with the base voltage 78.2 [kV] 0.920716 [p.u.].

The parameters in PSS/E for the converter impedance in Näs modelled as a line are shown in Table 3.1.7

Table 3.1.7 The parameters in PSS/E for the converter impedance in Näs modelled as a line.

Parameter Value Unit Description I 36905 Bus 1 J 36904 Bus 2 R 0.1845 [p.u.] Line resistance* X 2.1527 [p.u.] Line reactance*

* The reason for different values in Simpow (see Table 3.1.5) and PSS/E (see Table 3.1.7) is that the base power

is 65 [MVA] in Simpow while it is 1000 [MVA] in PSS/E.

(96)

The parameters in the “Simpow model” for the inverter in Bäcks are shown in Table 3.1.8.

Table 3.1.8 The parameters in the “Simpow model” for the inverter in Bäcks.

Parameter Value Unit Description N BACKVAC.78 Bus name

UD 121.5 [kV] DC voltage U 71.2 [kV] AC voltage

CNODE BACKVAC.78 AC voltage controlled bus SN 65 [MVA] Base power R 0.012 [p.u.] Inverter resistance X 0.14 [p.u.] Inverter reactance

The parameters in the “Standard PSS/E model” for the inverter in Bäcks are shown in Table 3.1.9.

Table 3.1.9 The parameters in the “Standard PSS/E model” for the inverter in Bäcks.

Parameter Value Unit Description IBUS 36902 (BACKVSC.78) Bus number

DCSET 121.5 [kV] DC voltage ACSET 0.910486 [p.u.] AC voltage* REMOT 36901 (BACKVAC.78) AC Voltage controlled bus

* The AC voltage is set to 71.2 [kV] and gets with the base voltage 78.2 [kV] 0.910486 [p.u.].

The parameters for the inverter impedance in Bäcks modelled as a line in PSS/E are shown in Table 3.1.10.

Table 3.1.10 The parameters in PSS/E for the inverter impedance in Bäcks modelled as a line.

Parameter Value Unit Description I 36902 Bus 1 J 36901 Bus 2 R 0.1845 [p.u.] Line resistance* X 2.1527 [p.u.] Line reactance*

* The reason for different values in Simpow (see Table 3.1.8) and PSS/E (see Table 3.1.10) is that the base

power is 65 [MVA] in Simpow while it is 1000 [MVA] in PSS/E.

(96)

3.1.7 “ABB’s Open PSS/E model”

“ABB’s Open PSS/E model” contains two synchronous machines in the power-flow setup. The synchronous machines represent the two converters in Figure 3.1.7 and the series reactance in the filters in Figure 3.1.9 and are connected to the nodes NASAC.78 and BACKAC.78. This setup results in that the nodes NASVSC.78, NASVAC.78, BACKVSC.78, and BACKVAC.78 in the setup of the “Standard PSS/E model” have to be removed, see Figure 3.1.1 and Figure 3.1.10. A scheme of the 70 [kV] grid in Gotland together with the HVDC Classic link and “ABB’s Open PSS/E model” is shown in Figure 3.1.10.

Figure 3.1.10 A scheme of the 70 [kV] grid in Gotland together with the HVDC Classic link and “ABB’s

Open PSS/E model”.

The impedances in the series reactors are included in the machines with the parameter ZSOURCE. The machines control the active power and the voltages in their own nodes to the result of the power-flow simulation in Simpow. Compared to the setup of the “Standard PSS/E model” in section 3.1.6, this setup results in that all problems listed in section 3.1.6 are omitted. The parameters for the synchronous machines are shown in Table 3.1.11 and Table 3.1.12.

(96)

Table 3.1.11 The parameters for the synchronous machine in node BACKAC.78.

Parameter Value Unit Description I 36900 (BACKAC.78) Bus number

PG 18.6675 [MW] Active power output VS 0.910043 [p.u.] AC Voltage

ZX (ZSOURCE) 0.14 [p.u.] Complex machine impedance

Table 3.1.12 The parameters for the synchronous machine in node NASAC.78.

Parameter Value Unit Description I 36903 (NASAC.78) Bus number

PG -20.8385 [MW] Active power output VS 0.921204 [p.u.] AC Voltage

ZX (ZSOURCE) 0.14 [p.u.] Complex machine impedance

3.1.8 Lines

There are 54 lines in the model of the network of which 15 lines are on the mainland and 39 lines are on Gotland. Most of the lines on Gotland are at the 70 [kV] voltage level but there are also lines at the 30, 10, and 6 [kV] voltage levels. Most of the lines are considered being medium long lines. For medium long lines the shunt susceptance cannot be negligible and therefore they have been modelled with the pi-equivalent model, see Söder [7], p.27. The pi-equivalent model consists of a resistance connected in series with an inductive reactance between two nodes and at the ends of the line a susceptance is connected to ground.

3.1.9 The HVDC Classic link

The HVDC Classic link between Ygne and Västervik consists of 2 poles and has been imported from Kostina [13], appendix 2. The active power from the inverters in Ygne has been changed according to the power-flow result of the Simpow simulation, see section 1.4.

3.2 Simulation

By including all the analysis from section 3.1 we have arrived to two power-flow simulations in PSS/E, one with the “Standard PSS/E model” and one with “ABB’s Open PSS/E model”. These simulations in PSS/E are equal and almost the same as calculated in Simpow. This shows that there is almost no difference between the “Standard PSS/E model” and “ABB’s Open PSS/E model” in power-flow simulations. Therefore both models can be used in power-flow simulations. A small difference between the simulation in Simpow and the simulations in PSS/E is the reactive power produced or consumed by the HVDC converters. This can depend on that the

(96)

imported HVDC Classic model in PSS/E is not equal to the model used in Simpow. The two power-flow simulations in PSS/E, which are equal, and the power-flow simulation in Simpow for the HVDC converters are shown in Table 3.2.1. The power-flow simulation in Simpow is marked with brackets. The converters in buses YGNE.70 and VVIK.130 are HVDC converters of the HVDC Classic link.

Table 3.2.1 Power-flow in both PSS/E and Simpow for the HVDC converters. The simulation in

Simpow is marked with brackets.

Converter bus number P [MW] Q [Mvar] BACKAC.78 18.7 (18.7) -2.9 (-2.6) NASAC.78 -20.8 (-20.8) 4.3 (4.4) YGNE.70 26.7 (26.7) -9.9 (-9.7) YGNE.70 26.7 (26.7) -9.9 (-9.7) VVIK.130 -26.8 (-26.9) -9.6 (-7.9) VVIK.130 -26.8 (-26.9) -9.6 (-7.9)

The difference in the reactive power-flow from the HVDC converters results in a difference in the voltage in the 130 [kV] buses, the 70 [kV] buses, and some parts of the lower voltage levels where we do not have voltage-regulating transformers. Here we should also have in mind that we cannot model a transformer with infinite number of steps in PSS/E and therefore we can get a difference in the fourth decimal of the voltage in nodes where we have voltage-regulating transformers. An example of this is the node SLIT.0.6, see Table 3.2.2. The two power-flow simulations in PSS/E, which are equal, and the power-flow simulation in Simpow for the nodes VVIK.130, FARHUL.130, YGNE.70, BACK.70, ROMA.70, NAS.70, MART.0.6, and SLIT.0.6 are shown in Table 3.2.2. The power-flow simulation in Simpow is marked with brackets.

Table 3.2.2 Power-flow result in both PSS/E and Simpow. The result from Simpow is marked with

brackets.

Bus U [p.u.] θ [o] VVIK.130 1.0124 (1.0134) -35.7 (-35.7)

FARHUL.130 1.0126 (1.0133) -34.7 (-34.7) YGNE.70 1.0008 (1.0000) -0.02 (0.00) BACK.70 0.9978 (0.9973) -1.89 (-1.88) ROMA.70 0.9935 (0.9929) -1.00 (-0.99) NAS.70 1.0009 (1.0008) 2.68 (2.69)

MART.0.6 1.0000 (1.0000) -4.21 (-4.20) SLIT.0.6 0.9997 (1.0000) -3.81 (-3.79)

(96)

The difference in the reactive power-flow from the HVDC converters also results in a difference in the reactive power production in the swing buses. The two power-flow simulations in PSS/E, which are equal, and the power-flow simulation in Simpow for the swing buses NG.14, FARHULI.130, ATVIDBI.130, and KIMSTAI.130 are shown in Table 3.2.3. The power-flow simulation in Simpow is marked with brackets.

Table 3.2.3 Power-flow result for the swing buses in both PSS/E and Simpow. The result from

Simpow is marked with brackets.

Bus U [p.u.] θ [o] PG [MW] QG [Mvar] NG.14 0.9999 (0.9999) 0.00 (0.00) 0.2 (0.0) -0.6 (-0.1)

FARHULI.130 1.0133 (1.0133) -32.00 (-32.00) 55.0 (55.2) -6.1 (-7.0) ATVIDBI.130 0.9985 (0.9985) -36.90 (-36.90) -44.6 (-44.6) -1.0 (-1.2) KIMSTAI.130 1.0370 (1.0370) -28.90 (-28.90) 149.6 (149.8) 22.0 (21.5)

3.3 Conclusions

The two power-flow simulations in PSS/E (one with the “Standard PSS/E model” and one with “ABB’s Open PSS/E model”) are equal and almost the same as calculated in Simpow. This shows that there is almost no difference between the “Standard PSS/E model” and “ABB’s Open PSS/E model” in power-flow simulations. Therefore both models can be used in power-flow simulations. The result from the two power-flow simulations in PSS/E is almost correct except for the reactive power produced or consumed by the HVDC converters. This can depend on that the imported HVDC Classic model in PSS/E is not corresponding perfectly to the model in Simpow. The difference in the reactive power flow from the HVDC converters results in a difference in the voltage magnitudes in the 70 [kV] voltage level. This results also in a difference in some parts of the lower voltage levels where we do not have voltage-regulating transformers. Here we should also have in mind that we cannot model a transformer with infinite number of steps in PSS/E and therefore we can get a difference in the fourth decimal of the voltage in nodes where we have voltage-regulating transformers. A disadvantage with the setup of the power-flow calculation is the control of the asynchronous machines, i.e., their reactive power consumption. The asynchronous machines should control active power but not voltage or angle and the reactive power of the machines should vary as a function of the active power. In PSS/E there is no such model for power-flow simulations. The generator model in PSS/E has to control either voltage or reactive power. To get a correct power-flow calculation we have chosen to control the reactive power according to the result of the power-flow calculation in Simpow. Here it has to be emphasized that the problem with this solution is that if we want to make a change in the network model, then it

(96)

might lead to that we have to change the reactive power consumption of all asynchronous machines in the model.

(96)

4 Test of the dynamic of the HVDC Light link

4.1 Grid structure

To analyse the dynamic of the HVDC Light link we have created a small power system consisting of a part of the 70 [kV] grid in Gotland together with the HVDC Light link, the node STEN.10, and the swing bus NG.14, see Figure 4.1.1. In this test system we have removed all voltage levels below 70 [kV] except for the node STEN.10 and the swing bus NG.14. The susceptances for all power lines have also been removed. This resulted in that all loads and asynchronous machines were disconnected. To get loads in the test system we inserted one load in the bus STEN.70 and one load in the bus SLIT.70. Since we have got an isolated AC network in Näs we had to insert the swing bus STNASI.70. STNASI.70 is connected to the bus STNAS.70 with a power line that has the same characteristics as the power line that connects the bus BACK.70 via the nodes SKRU.70 and PILH.70 to YGNE.70. A scheme of the test system including the “Standard PSS/E model” of the HVDC Light link is shown in Figure 4.1.1.

Figure 4.1.1 The test system for the HVDC Light link.

In this test system we can simulate the model of the HVDC Light link in Simpow (“Simpow model”) and the two models of the HVDC Light link in PSS/E (“Standard PSS/E model” and “ABB’s Open PSS/E model”). By comparing these simulations we can see how reliable the models of the HVDC Light link are in PSS/E.

4.2 Setup for the power-flow simulation

In the setup for the power-flow simulation we have modelled the loads in the buses STEN.70 and SLIT.70 as constant power loads. The machine in the swing bus STNASI.70 is

(96)

controlling the voltage amplitude to 1 [p.u.] and the angle to 0 [o] in its own bus. The machine in the other swing bus NG.14 is modelled as in section 3.1.3. The “Standard PSS/E model” of the HVDC Light link is modelled as in section 3.1.6 and “ABB’s Open PSS/E model” of the HVDC Light link is modelled as in section 3.1.7. The parameters for the loads are shown in Table 4.2.1.

Table 4.2.1 The parameters for the loads.

Bus P [MW] SLIT.70 20 STEN.70 18

The power-flow simulation can be found in section 4.4.1.

4.3 Setup for the dynamic simulations

The synchronous machine in the swing bus NG.14 is modelled as a “Type 2” model with saturation only in the d-axis in Simpow. In PSS/E the machine has been modelled as a “GENSAL” model, which is similar to the “Type 2” model in Simpow according to Persson [14], p.12. To include dynamic for the swing bus STNASI.70 we have used a copy of the machine data for the other swing bus NG.14 to the bus STNASI.70. The loads in STEN.70 and SLIT.70 are modelled as constant impedance loads in the dynamic simulations.

4.3.1 The “Simpow model”

The “Simpow model” of the HVDC Light link is a non-standard model in total and written in the dynamic simulation language DSL in Simpow. The model includes two AC voltage regulators, one DC voltage regulator, and one active power regulator. The inverter in Bäcks controls the AC voltage in the node BACK.70 and the DC voltage on the DC cable, see Figure 4.1.1. The converter in Näs controls the AC voltage in the node NAS.70 and the active power drawn from the grid in the Näs area. The active power drawn from the grid is regulated in order to keep the active power on the power line between the nodes NAS.70 and STNAS.70 constant, see Figure 4.1.1. All regulators in Simpow have PI-regulator characteristic except for one special case; when the DC current becomes too high, then a temporary blocking is included in the “Simpow model”, see Björklund [4]. The “Simpow model” also includes a transient response, when the controlled AC voltages become lower than 0.8 [p.u.], which results in that the reactive power output becomes 90 [%] of its maximum value within 50 [ms], see Axelsson [5]. The reactive power limits are as in the following for the two converters in the “Simpow model”:

(96)

• The minimum reactive power output for the converter in Näs is -48.75 [Mvar] and the maximum reactive power output for the converter in Näs is 48.75 [Mvar].

• The minimum reactive power output for the converter in Bäcks is -65 [Mvar] and the maximum reactive power output for the converter in Bäcks is 52 [Mvar].

The AC voltage regulators, the DC voltage regulator, and the active power regulator in the “Simpow model” are based on an AC current control (in Swedish “inre strömregulator”). The commands from the four regulators are realized via the AC current control, which generates the three-phase voltage reference for the converter AC voltage, see Häfner [15], p.21.

4.3.2 The “Standard PSS/E model”

The “Standard PSS/E model” includes two AC voltage regulators and one active power regulator. The inverter in Bäcks controls the AC voltage in the node BACK.70. The converter in Näs controls the AC voltage in the node NAS.70 and the active power drawn from the grid. All regulators have PI-regulator characteristic but are not as detailed as the regulators are in the “Simpow model”. There are the following problems for the “Standard PSS/E model”:

1. There is no DC voltage regulator included in the model. It is, however, not clearly stated in the manual that a DC voltage regulator is not included, but there are no parameters that can be chosen for a DC voltage regulator in the model, see PSS/E-manual [2], POM, L-41.

2. The minimum reactive power output from the converters in Bäcks and Näs cannot be lower than -0.5 [p.u.] and the maximum reactive power output from the converters in Bäcks and Näs cannot be higher than +0.5 [p.u.] in the model. In the “Simpow model” the minimum reactive power output for the converter in Näs is -0.75 [p.u.] and the maximum reactive power output for the converter in Näs is +0.75 [p.u.]. The minimum reactive power output for the converter in Bäcks is -1 [p.u.] and the maximum reactive power output for the converter in Bäcks is +0.8 [p.u.]. The base power in the “Simpow model” is 65 [MVA]. In this work we have tried to solve this problem by changing the base power for the “Standard PSS/E model” to 130 [MVA], which results in that we can have the same limits in the “Standard PSS/E model” as in the “Simpow model” for the reactive power output. This attempt to solution resulted, however, in an unstable system in the dynamic simulations and therefore we have not solved this problem.

3. The temporary blocking of the HVDC Light link, when the DC current becomes too high, which is included in the “Simpow model”, is missing in the “Standard PSS/E model”, see the second paragraph in section 4.3.1.

4. The transient response of the reactive power, which is included in the “Simpow model”, is missing in the “Standard PSS/E model”, see the second paragraph in section 4.3.1.

5. The active power regulator cannot regulate the active power in order to keep the active power on the power line between NAS.70 and STNAS.70 constant, as in the “Simpow

(96)

model”. The active power regulator regulates instead the active power in order to keep the active power consumed by the converter in Näs constant.

4.3.3 “ABB’s Open PSS/E model”

“ABB’s Open PSS/E model” includes two AC voltage regulators, one DC voltage regulator, and one active power regulator. The inverter in Bäcks controls the AC voltage in the node BACK.70 and the DC voltage on the DC cable. The converter in Näs controls the AC voltage in the node NAS.70 and the active power drawn from the grid. All regulators have PI-regulator characteristic but are not as detailed as the regulators are in the “Simpow model”. An advantage with “ABB’s Open PSS/E model” is that we have the source code of the model. This results in that we are able to make changes of the parameters in the code. There are, however, the following problems for “ABB’s Open PSS/E model”:

1. The AC current control, that the two AC voltage regulators, the DC voltage regulator, and the active power regulator are based on, in the “Simpow model”, is ideal in “ABB’s Open PSS/E model” according to Björklund [4].

2. The second problem is the same as problem number 2 in the list in section 4.3.2. We have solved this problem by changing the base power for “ABB’s Open PSS/E model” to 100 [MVA] and changing the value for the parameter AcvcIntLim in the source code from 0.6 to 1.6. The solution results in correct limits of the reactive power output from the converter in Näs but we still have a small error in the limits of the reactive power output from the converter in Bäcks. This depends on that we have different limits of the reactive power output in the converter in Näs and in the converter in Bäcks and at the same time we cannot have different base powers in the two converters. We have not fully understood why we cannot have different base powers in the converter in Näs and in the converter in Bäcks and why the limits of the reactive power output are fixed to ±0.5 [p.u.].

3. The third problem is the same as problem number 3 in the list in section 4.3.2. 4. The fourth problem is the same as problem number 4 in the list in section 4.3.2. 5. The fifth problem is the same as problem number 5 in the list in section 4.3.2. 6. The increase of the reactive power output from the AC voltage regulators is to fast in

the model. We have solved this problem by changing the parameters for the AC voltage regulators in the source code of “ABB’s Open PSS/E model” to the values of similar parameters in the “Simpow model”. For the AC voltage regulator in Näs the value of the gain AcvcKp has been changed from 0.6 to 0.9, the value of the parameter AcvcIntLim has been changed from 0.6 to 1.6, and the value of the parameter AcvcTi has been changed from 0.01 to 0.028. For the AC voltage regulator in Bäcks the value of the parameter AcvcKp has been changed from 0.6 to 1.6, the value of the parameter AcvcIntLim has been changed from 0.6 to 1.6, and the value of the parameter AcvcTi has been changed from 0.01 to 0.013.

(96)

7. The increase of the active power consumption from the active power regulator in Näs is too slow in the model. For the active power regulator there are 10 parameters that can be varied. However by doing sensitivity analysis it has been shown that only two of them have an impact on the dynamic simulations. These are a gain Kp and a time constant Ti. First we selected to change the time constant Ti to the value of 0.02 in order to reach the same steady-state as in Simpow in a shorter time. A simulation of the test system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the active power consumed by the HVDC Light converter in Näs shown in Figure 4.3.1. “ABB’s Open PSS/E model” has been simulated with both the default value of Ti (0.08) and Ti = 0.02. The results are compared with the results from the “Simpow model”. Now we want to adjust Kp in “ABB’s Open PSS/E model” to have a better matching with the active power in the “Simpow model”. A simulation of the test system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the active power consumed by the HVDC Light converter in Näs shown in Figure 4.3.2. “ABB’s Open PSS/E model” has here been simulated

0.05 0.1 0.15 0.2 0.25 0.3 0.3515

16

17

18

19

20

21

22

23

24

25

Time [s]

Act

ive

pow

er [

MW

]

Active power NAS.70 - NASAC.78

Simpow model

ABB's Open PSS/E model Ti=0.08 (default)

ABB's Open PSS/E model Ti=0.02

Figure 4.3.1 Active power consumed by the HVDC Light converter in Näs simulated

with Simpow and “ABB’s Open PSS/E model” in PSS/E.

(96)

with Ti = 0.02 and the following values of Kp; Kp = 0.3 (default), Kp = 1.5, Kp = 1.7, and Kp = 1.9. The vertical axis in Figure 4.3.2 is focused compared to Figure 4.3.1.

Here we have chosen to use Kp = 1.7, which generates the simulation in PSS/E that is closest to the results from the “Simpow model”. To verify that we have chosen the most appropriate value of Ti (0.02), we have also changed the value of Ti to 0.015 and 0.025. A simulation of the test system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the active power consumed by the HVDC Light converter in Näs shown in Figure 4.3.3. “ABB’s Open PSS/E model” has therefore been simulated with Kp = 1.7 and the following values of Ti; Ti = 0.015, Ti = 0.020, and Ti = 0.025.

0.05 0.1 0.15 0.2 0.25 0.3 0.3518

18.5

19

19.5

20

20.5

21

21.5

22

Time [s]

Act

ive

pow

er [

MW

]


Simpow model

ABB's Open PSS/E model Kp=0.3 (default)

ABB's Open PSS/E model Kp=1.5ABB's Open PSS/E model Kp=1.7

ABB's Open PSS/E model Kp=1.9



(96)

In Figure 4.3.3 we can see that Ti = 0.02 generates the simulation in PSS/E that is closest to the simulation in Simpow and therefore we have chosen to use Ti = 0.02 for “ABB’s Open PSS/E model”.

4.4 Results

4.4.1 Power-flow calculation

The power-flow calculation of the test system in Simpow and the two power-flow calculations of the two test systems in PSS/E are equal and generate the data in Table 4.4.1.

0.05 0.1 0.15 0.2 0.25 0.3 0.3518

18.5

19

19.5

20

20.5

21

21.5

22

Time [s]

Act

ive

pow

er [

MW

]Active power NAS.70 - NASAC.78

Simpow model

ABB's Open PSS/E model Ti=0.015ABB's Open PSS/E model Ti=0.020

ABB's Open PSS/E model Ti=0.025



(96)

Table 4.4.1 Power-flow calculation of the test system in Simpow and the two calculations in PSS/E.

Bus U [p.u.] θ [o] YGNE.70 1.0000 -0.13 BACK.70 1.0003 -0.22 NAS.70 0.9918 -3.25 STEN.70 0.9959 -2.25

BACKAC.78 0.9100 1.14 NASAC.78 0.9212 -4.74

4.4.2 Dynamic simulations

In this section we compare the dynamic simulations from the “Simpow model”, the “Standard PSS/E model”, and “ABB’s Open PSS/E model”. The parameters of “ABB’s Open PSS/E model” have been modified as described earlier in section 4.3.3. A simulation of the test system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the data in Figure 4.4.1 - Figure 4.4.6.

Figure 4.4.1 Voltage at NAS.70 simulated with Simpow and both models in PSS/E.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Time [s]

Vol

tage

[p.

u.]

Voltage NAS.70

Simpow model

Standard PSS/E model

ABB's Open PSS/E model

(96)

Figure 4.4.2 Reactive power produced by the HVDC Light converter in Näs simulated

with Simpow and both models in PSS/E.


with Simpow and both models in PSS/E. Focused part of Figure 4.4.2.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

60

70

80

90

Time [s]

Rea

ctiv

e po

wer

[M

var]

Reactive power NASAC.78 - NAS.70

Simpow model



0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.425

30

35

40

45

50

55

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model



(96)





0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



0.05 0.1 0.15 0.2 0.2515

16

17

18

19

20

21

22

23

24

25

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



(96)

As we can see in Figure 4.4.1 the simulations with the “Simpow model” and “ABB’s Open PSS/E model” correspond well to each other, for the controlled AC voltage, during the fault. This depends on that the generated reactive power in Figure 4.4.2 is similar in the “Simpow model” and “ABB’s Open PSS/E model” during the fault. The “Standard PSS/E model” cannot generate enough reactive power as shown in Figure 4.4.2, which results in that the AC voltage shown in Figure 4.4.1 becomes too low. The reason for this is that the maximum reactive power output from the converter in the “Standard PSS/E model” cannot be higher than +0.5 [p.u.], see the second point in the list in section 4.3.2. After the fault in Figure 4.4.2 we can see that we have a difference in the generated reactive power in both the “Standard PSS/E model” and in “ABB’s Open PSS/E model” compared to the “Simpow model”. We have not fully understood what this depends on and we have not found any solution to solve this problem. In Figure 4.4.3 and Figure 4.4.6 we can see that we have a numerical error in the “Standard PSS/E model”, see the red curve for 0.28 < t < 0.40 [s] in Figure 4.4.3 and the red curve for 0.85 < t < 0.92 [s] in Figure 4.4.6. The active power output and the reactive power output from the “Standard PSS/E model” change for each time step and this results in the thick red

0.85 0.9 0.95 1 1.0516

17

18

19

20

21

22

23

24

25

26

Time [s]

Act

ive

pow

er [

MW

]Active power NAS.70 - NASAC.78

Simpow model





(96)

line in Figure 4.4.2 for 0.28 < t < 0.90 [s] and the thick red line in Figure 4.4.4 for 0.28 < t < 0.90 [s]. We have not fully understood what causes this oscillation and we have not found any solution to solve this problem. In Figure 4.4.4, Figure 4.4.5, and Figure 4.4.6 we can see that we have a small deviation during the transient in the consumed active power in both the “Standard PSS/E model” and in “ABB’s Open PSS/E model” compared to the “Simpow model”. The active power is increasing too fast in the “Standard PSS/E model” and in “ABB’s Open PSS/E model”, just after the fault is applied. Just after the fault is removed, the active power is decreasing too fast in the “Standard PSS/E model” and in “ABB’s Open PSS/E model”. All models consume, however, almost constant active power during the simulation. We intended to calculate the eigenvalues for the two test systems in PSS/E and the eigenvalues for the test system in Simpow to analyze small-signal stability. We did, however, not have access to the needed module in PSS/E and therefore we could not make these calculations.

4.5 Conclusions

The simulations with the “Simpow model” and “ABB’s Open PSS/E model” correspond well to each other, for the controlled AC voltage in Näs, during the fault. This depends on that the generated reactive power is similar in the “Simpow model” and “ABB’s Open PSS/E model” during the fault. There is a small deviation in the active power just after the fault is applied and just after the fault is removed in “ABB’s Open PSS/E model” compared to the “Simpow model”. Both models transmit, however, almost constant power during the simulation. This shows that “ABB’s Open PSS/E model” can be used to simulate the HVDC Light link at Gotland in the test system. Two disadvantages with “ABB’s Open PSS/E model” are that we cannot simulate the temporary blocking or the transient response, which are included in the Simpow model, see section 4.3.1. The “Standard PSS/E model” cannot generate enough reactive power in the simulations, which results in that the AC voltage becomes too low. The reason for this is that the maximum reactive power output from the converter in the “Standard PSS/E model” cannot be higher than 0.5 [p.u.]. We have also a small deviation in the active power, which is increasing too fast just after the fault is applied and decreasing too fast just after the fault is removed in the “Standard PSS/E model”. This shows that it is preferable to use “ABB’s Open model” instead of the “Standard PSS/E model”.

(96)

5 Dynamic simulations of Gotland

5.1 Setup

5.1.1 The HVDC Light link

The HVDC Light link is here modelled with both the “Standard PSS/E model” and “ABB’s Open PSS/E model”. The setups of the models are the same as in section 4.3. The results are compared with the “Simpow model”.

5.1.2 The HVDC Classic link

The model of the HVDC Classic link has been imported from appendix 3 in Kostina [13].

5.1.3 Machines

The synchronous machines in the nodes NG.14, NG.13, and NG.11 are modelled as “Type 2” models with saturation only in the d-axis in Simpow. In PSS/E the machines have been modelled as “GENSAL” models. The “GENSAL” model in PSS/E is similar to the “Type 2” model in Simpow according to Persson [14], p.12. The 24 asynchronous machines, which are representing the wind power units, are modelled with “Asynchronous machine” models in the dynamic setup in Simpow. There is no equivalent model in PSS/E to the “Asynchronous machine” model in Simpow and we have instead chosen to use the induction generator model “CIMTR3” in PSS/E. The model “CIMTR3” do not take the stator flux (dφ/dt) in consideration, which can result in differences in the dynamic simulations in Simpow and PSS/E, see Öberg [16], p.2. The asynchronous machines are equipped with over- and under-voltage as well as frequency protection in Simpow. There is no model for over- and under-voltage protection in our version of PSS/E (version 30) and therefore no over- and under-voltage protection model has been used for the asynchronous machines. This problem is therefore solved by manually disconnecting the asynchronous machines in the dynamic simulations in PSS/E according to the result of the dynamic simulations in Simpow. In version 31 of PSS/E there are models for over- and under-voltage protection, which needs to be included in future work, see Lindström [10].

5.1.4 Regulators

The three synchronous machines in the nodes NG.14, NG.13, and NG.11 are equipped with voltage regulators. The regulators for the machines in the nodes NG.14 and NG.13 are modelled with “Type 15” models in Simpow. There is no equivalent model in PSS/E to the

(96)

regulator model “Type 15” in Simpow but the model “BUDCZT” in PSS/E is similar to the model in Simpow. Therefore the regulator model “BUDCZT” is used in PSS/E for the synchronous machines in the nodes NG.14 and NG.13. The regulator model for the machine in the node NG.11 in Simpow is written in the dynamic simulation language DSL and called “”STEX”. There is no regulator model in PSS/E that is equal or similar to the regulator model “STEX” in Simpow and therefore no regulator model has been used for the machine in the node NG.11.

5.2 Setup of the loads

The characteristics of the loads in Gotland were detailed identified in a project described in Adielson [12]. It is of a great interest to keep this detailed level of modelling the loads. Therefore the following adaptation of the loads from Simpow to PSS/E has been made. The dynamic model for a load in the dynamic setup in Simpow is shown in Equation 5.2.1.

( ) ( )NQ

MQ

NP

MPLS f

fUjQ

f

fUPS

⋅+

⋅=

00

00

Equation 5.2.1 The equation for a load in the dynamic simulations in Simpow.

In Equation 5.2.1 SLS is the complex power for the load. U is the actual voltage in [p.u.] of the calculated voltage from the corresponding power-flow calculation. f is the actual frequency in [Hz] and f0 is equal to 50 [Hz]. P0 and Q0 are the active and reactive power respectively from the corresponding power-flow calculation. MP and MQ are voltage exponents and NP and NQ are frequency exponents. MP, MQ, NP, and NQ do not have to be integers, they can have any arbitrary value. The dynamic model for a load in PSS/E that is as equal as possible to the dynamic load model in Simpow is the model “IEELBL”. The model “IEELBL” is shown in Equation 5.2.2.

( )( ) ( )( )favavavajQfavavavaPS nnnLoad

nnnLoadLP ∆++++∆+++= 86547321 11 654321

Equation 5.2.2 The equation for the dynamic load model “IEELBL” in PSS/E.

In Equation 5.2.2 SLP is the complex power for the load. PLoad and QLoad are the active and reactive power respectively from the corresponding power-flow calculation. v is the actual voltage at the load in [p.u.] of the calculated voltage from the corresponding power-flow calculation. ∆f is the frequency deviation in [Hz]. a1, a2, a3, a4, a5, a6, a7, a8, n1, n2, n3, n4, n5, and n6 are parameters that can have any arbitrary value.

(96)

5.2.1 Voltage part

The voltage parts of the model of the load in Simpow (P0(U)MP and Q0(U)MQ in Equation 5.2.1) have already been converted to PSS/E-format in the power-flow setup, see section 3.1.3. This result in that we need to make the voltage part of Equation 5.2.2 equal to Equation 3.1.2 instead of equal to the voltage parts of Equation 5.2.1, see Equation 5.2.3.

( ) ( ) ( ) ( )( )2321

2321654321

654321 UQUQQjUPUPPvavavajQvavavaP nnnLoad

nnnLoad +++++=+++++

Equation 5.2.3 The voltage parts of Equation 5.2.2 equal to Equation 3.1.2.

Because of that we can separate each load in Equation 3.1.2 into three loads P1+jQ1, P2U+jQ2U, and P3(U)2+jQ3(U)2 we can make the voltage parts of Equation 5.2.2 equal to Equation 3.1.2 by putting a1 and a4 equal to one (=1) and n1 and n4 equal to the voltage exponents, see Equation 5.2.4, Equation 5.2.5, and Equation 5.2.6.

414111

nLoad

nLoad vajQvaPjQP +=+

Equation 5.2.4 The constant power part of the load as a separate load in PSS/E.

41

4122n

Loadn

Load vajQvaPUjQUP +=+

Equation 5.2.5 The constant current part of the load as a separate load in PSS/E.

( ) ( ) 4141

23

23

nLoad

nLoad vajQvaPUjQUP +=+

Equation 5.2.6 The constant impedance part of the load as a separate load in PSS/E.

5.2.2 Frequency part

The frequency parts of Equation 5.2.1 and Equation 5.2.2 are not possible to make equal. By letting the straight lines of the frequency in Equation 5.2.2 be the derivatives of the frequency parts of Equation 5.2.1, for the frequency 50 [Hz], we will have a solution in PSS/E with a small difference to Simpow when the frequency is not equal to 50 [Hz]. For calculations see Equation 5.2.7, Equation 5.2.8, and Equation 5.2.9. In Equation 5.2.7 and Equation 5.2.8 the frequency derivatives at 50 [Hz] is calculated.

1

00

0

1

00

0

−−

=

=

NQNQNPNP

f

fNQ

f

f

f

fd

d

f

fNP

f

f

f

fd

d

Equation 5.2.7 The derivatives of the frequency parts of Equation 5.2.1.

(96)

NQNQNPNPNQNP

=

=

−− 11

50

50

50

50

Equation 5.2.8 The derivatives of active and reactive power when the frequency is 50 [Hz].

fNQfafNPfa ∆+=∆+∆+=∆+ 1111 87

Equation 5.2.9 The equations for the straight lines of the frequency in Equation 5.2.2 equal to the

derivatives of the frequency parts of Equation 5.2.1 when the frequency is 50 [Hz].

In Equation 5.2.9 we can identify the parameters a7 and a8 as a7 = NP and a8 = NQ.

5.2.3 Example

As an example we have here chosen load 1 at the node PILH.10. The equation in Simpow for load 1 at the node PILH.10 is shown in Equation 5.2.10.

( ) ( ) ][50

250

23.1

9.13.1

58.0 MVAf

Ujf

USLS

−

⋅+

⋅=

Equation 5.2.10 The equation in Simpow for load 1 at node PILH.10.

The load in Simpow in Equation 5.2.10 is represented in PSS/E as the three loads in Equation 5.2.11, Equation 5.2.12, and Equation 5.2.13.

( ) ( ) ][3.110880.03.115909.0 MVAfjfSLP ∆−−∆+=

Equation 5.2.11 The constant power part of the load in Simpow as a separate load in PSS/E.

( ) ( ) ][3.113774.03.116552.1 MVAfUjfUSLP ∆−+∆+=

Equation 5.2.12 The constant current part of the load in Simpow as a separate load in PSS/E.

( ) ( ) ( ) ( ) ][3.117106.13.112462.0 22 MVAfUjfUSLP ∆−+∆+−=

Equation 5.2.13 The constant impedance part of the load in Simpow as a separate load in PSS/E.

The complex power for load 1 at the node PILH.10 with varying voltage was earlier shown in Figure 3.1.4 and Figure 3.1.5. The complex power for load 1 at the node PILH.10 with varying frequency is shown in Figure 5.2.1 and Figure 5.2.2. The voltage in Figure 5.2.1 and Figure 5.2.2 is equal to 1 [p.u.].

(96)

Figure 5.2.1 Active power in load 1 at bus PILH.10.

Figure 5.2.2 Reactive power in load 1 at bus PILH.10.

47.5 48 48.5 49 49.5 50 50.5 51 51.5 52 52.51.85

1.9

1.95

2

2.05

2.1

2.15

2.2

Frequency [Hz]

Act

ive

pow

er [

MW

]

Active power in load

Simpow

PSS/E

47.5 48 48.5 49 49.5 50 50.5 51 51.5 52 52.51.85

1.9

1.95

2

2.05

2.1

2.15

2.2

Frequency [Hz]

Rea

ctiv

e po

wer

[M

var]

Reactive power in load

Simpow

PSS/E

(96)

5.3 Simulations

Here we perform simulations of the whole Gotland network.

5.3.1 Basic simulation

A simulation of the system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the data in Figure 5.3.1 – Figure 5.3.10.

At t = 0.30 [s], t = 0.70 [s], and t = 0.71 [s] three asynchronous machines are disconnected close to the fault. This can be observed in Figure 5.3.1 and Figure 5.3.2 where the voltage increases at these instances. At t = 0.39 [s] the tap-changer of the transformer in Bäcks in the HVDC Light link is changing position. This can be seen in the “Simpow model” in Figure 5.3.1. At t = 1.00 [s] the tap-changer of the transformer in Näs in the HVDC Light link is changing position. This can be seen in the “Simpow model” in Figure 5.3.2. There are no dynamic models of tap-changers included in PSS/E.

Figure 5.3.1 Voltage at BACK.70 simulated with Simpow and both models in PSS/E.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

Time [s]

Vol

tage

[p.

u.]

Voltage BACK.70

Simpow model



(96)

Figure 5.3.2 Voltage at NAS.70 simulated with Simpow and both models in PSS/E.



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Time [s]

Vol

tage

[p.

u.]

Voltage NAS.70

Simpow model



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

60

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



(96)





0.05 0.1 0.15 0.2 0.25 0.3 0.3515

16

17

18

19

20

21

22

23

24

25

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



0.85 0.9 0.95 1 1.0515

20

25

30

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



(96)

In Figure 5.3.3 and Figure 5.3.4 we can see that we have a difference in the active power, consumed by the HVDC Light converter in Näs during the fault, in both models in PSS/E compared to Simpow. The HVDC Light converter in Näs consumes almost constant active power, during the fault, in both models in PSS/E while the HVDC Light converter in Simpow is decreasing the consumed active power at the time t = 0.22 [s], see Figure 5.3.3 and Figure 5.3.4. The “Simpow model” is decreasing the active power at the time (t = 0.22 [s]) when the reactive power almost is at its maximum level, see Figure 5.3.4 and Figure 5.3.7. This depends on that the “Simpow model” has priority on the reactive power. When the produced reactive power is reaching its maximum level the “Simpow model” is decreasing the active power to be able to produce a higher amount of reactive power. This have been verified by changing the priority in the “Simpow model” to active power, see section 5.3.2.

For 0.0 < t < 0.1 [s] in Figure 5.3.6 we can see that we have different steady-states in Simpow and PSS/E. The reason for this is that the steady-state changes in the pre-simulation in Simpow. We have not found any solution to solve this problem.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

60

70

80

90

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model





(96)

In Figure 5.3.6 we can see that the produced reactive power is decreasing during the fault in “ABB’s Open PSS/E model”. It decreases from when the reactive power has reached its maximum level until the fault has been removed, see the green curve in Figure 5.3.6 for 0.23 < t < 0.9 [s]. To verify that this problem do not depends on the changes of the AC voltage regulators in the source code of “ABB’s Open PSS/E model” (see problem number 6 in section 4.3.3) we have made a simulation with the default values of the AC voltage regulators in the source code, see section 5.3.3.

The “Standard PSS/E model” cannot generate enough reactive power during the fault as shown in Figure 5.3.6, which results in that the AC voltage shown in Figure 5.3.2 becomes too low. The reason for this is that the maximum reactive power output from the converter in the “Standard PSS/E model” cannot be higher than 0.5 [p.u.] of the rated power. In Figure 5.3.5 and Figure 5.3.6 we can see that we have a numerical error in the “Standard PSS/E model”, see the red curve for 0.9 < t < 0.95 [s] in Figure 5.3.5 and the red curve for 0.9 < t < 0.95 [s] in Figure 5.3.6. The active power output and the reactive power output from the “Standard PSS/E model” change for each time step and this results in the thick red line in Figure 5.3.3 for 0.9 < t < 0.95 [s]. We have not fully understood what causes this oscillation and we have not found any solution to solve this problem.

0.15 0.2 0.25 0.345

50

55

60

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model





(96)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Time [s]

Vol

tage

[p.

u]

Voltage NNAS2A.0.6

Simpow model



Figure 5.3.8 Voltage at the asynchronous machine node NNAS2A.0.6 simulated with

Simpow and both models in PSS/E.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 28

9

10

11

12

13

14

15

16

Time [s]

Act

ive

pow

er [

MW

]

Active power NNAS2A.0.6 - NNAS2A.10

Simpow model



Figure 5.3.9 Active power produced by the asynchronous machine in node

NNAS2A.0.6 simulated with Simpow and both models in PSS/E.

(96)

The model of the asynchronous machines “CIMTR3” do not take the stator flux (dφ/dt) in consideration, which can result in differences in the dynamic simulations in Simpow and PSS/E, see section 5.1.3. In Figure 5.3.9 we can see the produced active power by the asynchronous machine in the node NNAS2A.0.6 and in Figure 5.3.10 we can see the produced reactive power by the asynchronous machine and the shunt impedance in the node NNAS2A.0.6. The voltage at NNAS2A.0.6 is shown in Figure 5.3.8.

In Figure 5.3.9 and Figure 5.3.10 we can see that we have a difference in the active power and the reactive power, produced by the machine in the node NNAS2A.0.6, with both models in PSS/E compared to Simpow. We have not further investigated from where these differences between the models occur, but what is most important here is that it is of major importance to include a detailed model representing real installations of wind power units in PSS/E, as a suggestion Chalmers induction generator model. Differences in the dynamic simulations in PSS/E compared to Simpow in Figure 5.3.1 - Figure 5.3.7 can also depend on the following;

1. The model of the HVDC Classic link to the mainland of Sweden in PSS/E has not been verified, see section 5.1.2 and section 5.3.4.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-12

-10

-8

-6

-4

-2

0

2

4

6

8

Time [s]

Rea

ctiv

e po

wer

[M

var]

Reactive power NNAS2A.0.6 - NNAS2A.10

Simpow model



Figure 5.3.10 Reactive power produced by the asynchronous machine and the shunt

impedance in node NNAS2A.0.6 simulated with Simpow and both models in PSS/E.

(96)

2. The regulator model for the machine in the node NG.11, called “STEX” in Simpow, is missing in PSS/E, see section 5.1.4.

5.3.2 Simulation with priority on active power in S impow

A simulation of the system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the data in Figure 5.3.11 and Figure 5.3.12. The “Simpow model” is now simulated with priority on active power.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

60

Time [s]

Act

ive

pow

er [

MW

]


Simpow model




with priority on active power in Simpow and both models in PSS/E.

(96)

By comparing Figure 5.3.11 and Figure 5.3.12 with Figure 5.3.3 and Figure 5.3.4 we can see that the “Simpow model” is not decreasing the active power during the fault when the priority is set to active power. In both models of the HVDC Light link in PSS/E we have priority on active power which results in that the active power stays at a constant level when the produced reactive power reaches its maximum level, see Figure 5.3.4 and Figure 5.3.7. We are not able to change the priority from active power to reactive power in any of the models in PSS/E and therefore we have not found any solution to solve this problem and to have the same priority as in the original “Simpow model”. However, when the “Simpow model” is changed, the results are as in Figure 5.3.11 and Figure 5.3.12.

5.3.3 Simulation with the default settings of the A C voltage regulators in “ABB’s Open PSS/E model”

In order to check if the behaviour of the reactive power in “ABB’s Open PSS/E model” in section 5.3.1 is a result of our parameter settings, the network is here simulated with the default settings of the AC voltage regulators in “ABB’s Open PSS/E model”, see problem

0.05 0.1 0.15 0.2 0.25 0.3 0.3515

16

17

18

19

20

21

22

23

24

25

Time [s]

Act

ive

pow

er [

MW

]


Simpow model




with priority on active power in Simpow and both models in PSS/E. Focused part of

Figure 5.3.11.

(96)

number 7 in section 4.3.3. The “Simpow model” is here simulated with priority on the reactive power. A simulation of the system with a 0.8 seconds three-phase fault with Z = 0.5 + j0.5 [Ω] in the fault, applied in STEN.10 after 0.1 second, generates the data in Figure 5.3.13. “ABB’s open PSS/E model” is now simulated with the default values of the AC voltage regulator in the source code.

In Figure 5.3.13 we can see that the produced reactive power also here is decreasing, during the fault in “ABB’s Open PSS/E model”, with the default values of the AC voltage regulators in the source code. The reactive power is decreasing during the fault, from when it has reached its maximum level until the fault is removed, see the green curve in Figure 5.3.13 for 0.15 < t < 0.9 [s]. The reason for this slow ramping in the reactive power in “ABB’s Open PSS/E model” has not been found. This should be investigated further.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

0

10

20

30

40

50

60

70

80

90

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model



Figure 5.3.13 Reactive power produced by the HVDC Light converter in Näs

simulated with Simpow and both models in PSS/E. “ABB’s open PSS/E model” is

simulated with the default values of the AC voltage regulator in the source code.

(96)

5.3.4 Simulation of frequency regulation

In the model of the power system of Gotland in Simpow frequency regulation is included in the model of the HVDC Classic link. In our model of the HVDC Classic link in PSS/E frequency regulation is missing. The absence of frequency regulation in PSS/E results in that our system becomes unstable after changes in the system. This can clearly be seen in appendix 9.4.1 where we have simulated a 0.3 seconds three-phase fault with Z = 15 + j15 [Ω] in the fault, applied in STEN.70 after 0.1 second. In the simulations a majority of the wind power units are disconnected in the Näs area. In Figure 9.4.11 and Figure 9.4.12 the speed of the synchronous machine in the node NG.14 is plotted, which is the same as the frequency at Gotland. In Figure 9.4.11 and Figure 9.4.12 we can clearly see a difference in the frequency between Simpow and PSS/E after the fault has been removed. The frequency simulated with the model in Simpow is returning to 50 [Hz] while the frequency simulated with the model in PSS/E is decreasing after the fault has been removed. In Figure 9.4.9 and Figure 9.4.10 we can see that the active power in the HVDC Classic link in PSS/E is constant while the active power in the HVDC Classic link in Simpow varies. This variation of the active power in the HVDC Classic link in Simpow depends on the frequency regulation that is included in the model of the HVDC Classic link in Simpow. The disconnected power, which was produced by the wind power units in the Näs area and other areas, is in Simpow replaced by a higher import to Gotland from the mainland in the HVDC Classic link, see Figure 9.4.9 and Figure 9.4.10. In PSS/E this is not the case since the imported power from the mainland is not regulated. In our previous simulations in chapter 5 the absence of frequency regulation has not been seen clearly since we have simulated a less powerful fault than in appendix 9.4.1.

5.4 Conclusions

In both the “Standard PSS/E model” and in “ABB’s Open PSS/E model” we have a difference in the transmitted active power during the fault compared to the “Simpow model”. This depends on that the “Simpow model” has priority on the reactive power, which results in that the model reduces the active power during the fault to be able to produce a higher amount of reactive power. Both models in PSS/E have priority on active power which results in that the transmitted active power almost is constant during the fault. We have also a difference in the reactive power produced by the HVDC Light converter in Näs in both models in PSS/E compared to Simpow. The “Standard PSS/E model” cannot generate enough reactive power during the fault, which results in that the controlled AC voltage becomes too low. The produced reactive power during the fault simulated with “ABB’s Open PSS/E model” is decreasing from when the reactive power has reached its

(96)

maximum level until the fault is removed. This results in that the controlled AC voltage is decreasing during the fault. From the simulations shown in section 5.3 it is recommended to use “ABB’s Open PSS/E model” instead of the “Standard PSS/E model” of three reasons; a) “ABB’s Open PSS/E model” is possible to modify, b) there is a numerical error in the “Standard PSS/E model”, and c) the results from “ABB’s Open PSS/E model” shows less deviation from the results provided by the “Simpow model”. Improvements are however recommended in the dynamic part of “ABB’s Open PSS/E model”, see future work in section 7. Without the improvements, “ABB’s Open PSS/E model” should be used with a critical eye. In case of scepticism when analysing results from PSS/E simulations, comparable Simpow simulations should be made in order to control the results.

(96)

6 Conclusions The conclusions are here separated in two subsections.

6.1 Conclusions from the test of fault simulations in PSS/E

In the test of fault simulations in PSS/E in chapter 2 the simulations in PSS/E and Simpow corresponds well to each other. The curves in PSS/E and Simpow are before, during, and immediately after the fault almost equal. This means that the calculations for both symmetrical and unsymmetrical faults in PSS/E are correct concerning the positive-sequence components. A drawback in PSS/E is that we do not have any information concerning the negative- and zero-sequence components in a time-domain simulation, which results in that we cannot calculate the correct three phase-quantities. When we get the result from an unsymmetrical fault, the result appears as a symmetrical fault in PSS/E and it is easy to think that the phase-quantities are equal to the result of the positive-sequence voltage. If we compare the two simulations in PSS/E, with different time steps, we can see that there is a small difference between the curves in some figures. The simulations with shorter time steps becomes more correct but the difference is negligible and do not result in any difference in long-term simulations.

6.2 Conclusions from the simulations of Gotland

In the power-flow simulation of Gotland in chapter 3 the two power-flow simulations in PSS/E (one with the “Standard PSS/E model” and one with “ABB’s Open PSS/E model”) are equal and almost the same as calculated in Simpow. This shows that there is almost no difference between the “Standard PSS/E model” and “ABB’s Open PSS/E model” in power-flow simulations. Therefore both models can be used in power-flow simulations. The result from the two power-flow simulations in PSS/E is almost correct except for the reactive power produced or consumed by the HVDC converters. This can depend on that the imported HVDC Classic model in PSS/E is not corresponding perfectly to the model in Simpow. The difference in the reactive power flow from the HVDC converters results in a difference in the voltage magnitudes in the 70 [kV] voltage level. This results also in a difference in some parts of the lower voltage levels where we do not have voltage-regulating transformers. Here we should also have in mind that we cannot model a transformer with infinite number of steps in PSS/E and therefore we can get a difference in the fourth decimal of the voltage in nodes where we have voltage-regulating transformers when comparing the calculations with Simpow.

(96)

In the test of the dynamic of the HVDC Light link in chapter 4 the simulations with the “Simpow model” and “ABB’s Open PSS/E model” correspond well to each other, for the controlled AC voltage, during the fault. This depends on that the generated reactive power is similar in the “Simpow model” and “ABB’s Open PSS/E model” during the fault. There is a small difference in the active power just after the fault is applied and just after the fault is removed in “ABB’s Open PSS/E model” compared to the “Simpow model”. Both models transmit, however, almost constant power during the simulation. This shows that “ABB’s Open PSS/E model” can be used in the test system to simulate the HVDC Light link at Gotland. Two disadvantages with “ABB’s Open PSS/E model” are that we cannot simulate the temporary blocking or the transient response, which are included in the Simpow model, see section 4.3.1. The “Standard PSS/E model” cannot generate enough reactive power in the simulations, which results in that the AC voltage becomes too low. The reason for this is that the maximum reactive power output from the converter in the “Standard PSS/E model” cannot be higher than 0.5 [p.u.]. We have also a small deviation in the active power, which is increasing too fast just after the fault is applied and decreasing too fast just after the fault is removed in the “Standard PSS/E model”. This shows that it is preferable to use “ABB’s Open PSS/E model” to simulate the HVDC Light link at Gotland. In the dynamic simulations in chapter 5 of the whole Gotland network we have a difference in the transmitted active power during the fault compared to the “Simpow model” in both the “Standard PSS/E model” and in “ABB’s Open PSS/E model”. This depends on that the “Simpow model” has priority on the reactive power, which results in that the model reduces the active power during the fault to be able to produce a higher amount of reactive power. Both models in PSS/E have priority on active power which results in that the transmitted active power almost is constant during the fault. We have also a difference in the reactive power produced by the HVDC Light converter in Näs in both models in PSS/E compared to Simpow. The “Standard PSS/E model” cannot generate enough reactive power during the fault, which results in that the controlled AC voltage becomes too low. The produced reactive power during the fault simulated with “ABB’s Open PSS/E model” is decreasing from when the reactive power has reached its maximum level until the fault is removed. This results in that the controlled AC voltage is decreasing during the fault. From the simulations shown in section 5.3 it is recommended to use “ABB’s Open PSS/E model” instead of the “Standard PSS/E model” of three reasons; a) “ABB’s Open PSS/E model” is possible to modify, b) there is a numerical error in the “Standard PSS/E model”, and c) the results from “ABB’s Open PSS/E model” shows less deviation from the results provided by the “Simpow model”.

(96)

Improvements are however recommended in the dynamic part of “ABB’s Open PSS/E model”, see future work in section 7. Without the improvements, “ABB’s Open PSS/E model” should be used with a critical eye. In case of scepticism when analysing results from PSS/E simulations, comparable Simpow simulations should be made in order to control the results.

(96)

7 Proposal for future work 1. The imported model of the HVDC Classic link in PSS/E, in both the power-flow setup

and the dynamic setup, needs to be investigated, see section 3.1.9 and section 5.1.2. The imported model generates probably the differences in the power-flow simulations in PSS/E compared to Simpow and contributes to differences in the dynamic simulations of Gotland, see section 3.2 and section 5.3.

2. Frequency regulation needs to be included in the HVDC Classic model in PSS/E, see section 5.3.4. Frequency regulation is missing in the dynamic setup of the HVDC Classic link in PSS/E.

3. A model representing real installations of wind power units is needed, as a suggestion Chalmers induction generator model. The model of the induction generator machines in the dynamic setup in PSS/E “CIMTR3” contributes to differences in PSS/E compared to Simpow in the dynamic simulations of Gotland, see section 5.1.3 and section 5.3.1. The model “CIMTR3” do not take the stator flux (dφ/dt) in consideration, which can result in differences in the dynamic simulations, see Öberg [16], p.2.

4. A model of the voltage regulator for the synchronous machine in the node NG.11 needs to be developed in PSS/E. The voltage regulator for the synchronous machine in the node NG.11, called “STEX” in Simpow, is missing in the dynamic setup in PSS/E, see section 5.1.4.

5. Over- and under-voltage as well as frequency protection for the asynchronous machines needs to be modelled in the dynamic setup in PSS/E. There is no model for over- and under-voltage protection for machines in our version of PSS/E (version 30) but there are models for over- and under-voltage protection for machines in version 31 of PSS/E. Therefore, the model of Gotland in PSS/E needs to be converted from version 30 to version 31 of PSS/E and then the over- and under-voltage protections needs to be modelled.

6. Tap-changers for the transformers in Bäcks and Näs in the HVDC Light link need to be modelled in the dynamic setup in PSS/E. Tap-changers for the transformers in Bäcks and Näs in the HVDC Light link are missing in the dynamic setup in PSS/E, see section 5.3.1.

7. The priority of reactive power, which is included in the dynamic setup in the “Simpow model”, needs to be developed in “ABB’s Open PSS/E model”, see section 5.3. The transmitted active power is reduced in the “Simpow model” when the reactive power production in the converter in Näs reaches its maximum level. This priority of reactive power is missing in “ABB’s Open PSS/E model”.

(96)

8. The regulation of the active power on the power line between the nodes NAS.70 and

STNAS.70, which is included in the dynamic setup in the “Simpow model”, needs to be developed in “ABB’s Open PSS/E model”, see section 4.3.1 and section 4.3.3. The active power drawn from the grid in Näs is regulated in the “Simpow model” in order to keep the active power on the power line between the nodes NAS.70 and STNAS.70 constant. This regulation is missing in “ABB’s Open PSS/E model”.

9. The transient response, which is included in the dynamic setup in the “Simpow model”, needs to be developed in “ABB’s Open PSS/E model”, see section 4.3.1 and section 4.3.3. The transient response in the “Simpow model” is activated when the controlled AC voltages become lower than 0.8 [p.u.] and results in that the reactive power output becomes 90 [%] of its maximum value within 50 [ms]. This response is missing in “ABB’s Open PSS/E model”.

10. The temporary blocking of the HVDC Light link when the DC current becomes too high, which is included in the dynamic setup in the “Simpow model”, is missing in “ABB’s Open PSS/E model” and needs to be developed, see section 4.3.1 and section 4.3.3.

11. The limits of the reactive power in “ABB’s Open PSS/E model” need to be changed, without changing the base power, in order to have the same base power as in the dynamic setup in the “Simpow model”, see section 4.3.1 and section 4.3.3.

12. A blocking of the HVDC Light converter in Bäcks and its consequences need to be simulated and analyzed according to Axelsson [5].

(96)

8 References 1. GEAB Homepage, “Elnätet – ryggraden i din elanvändning”,

http://www.gotlandsenergi.se/elnat/index.php, December 14, 2007. 2. Shaw Power Technologies, Inc. “PSS/E 30 Manual”, Online documentation, 2004. 3. Per-Erik Björklund, “User guide for the PSS/E implementation of the HVDC Light

Open model Version 1.1.3-3”, ABB Power Technologies AB, Ludvika, Sweden, 2007.

4. Per-Erik Björklund, Discussion, ABB Power Technologies AB, Ludvika, Sweden, 2008.

5. Urban Axelsson, Discussion, Vattenfall Research and Development AB, Råcksta,

Sweden, 2008.

6. Phabha Kundur, “Power System Stability and Control”, The EPRI POWER System Engineering Series, McGraw-Hill, Reprint ISBN: 7-5083-0817-4, 2001.

7. Lennart Söder, “Static Analysis of Power Systems”, Compendia used at Royal

Institute of Technology, Stockholm, Sweden, 2004.

8. E. Johansson, J. Persson, L. Lindkvist, L. Söder, “Location of Eigenvalues Influenced by Different Models of Synchronous Machines”, in Proceedings of the 6th IASTED International Multi Conference on Power and Energy Systems, Paper 352-145, Marina del Rey, USA 2002.

9. J.G. Slootweg, J. Persson, A.M. van Voorden, G.C. Paap, W.L. Kling, “A Study of the

Eigenvalue Analysis Capabilities of Power System Dynamics Simulation Software”, in Proceedings of the 14th Power Systems Computation Conference 2002, Paper 26-3, Sevilla, Spain 2002.

10. Per-Olof Lindström, Discussion, Vattenfall Power Consultant AB, Råcksta, Sweden,

2007.

11. Lars Lindquist, Discussion, STRI AB, Ludvika, Sweden, 2007.

12. Ture Adielson, “Analys av Elleveranssäkerhet för Gotland”, Vattenfall Transmission, Råcksta, Sweden, 1989.

13. Natalja Kostina, “Modellering av Gotland Light i PSS/E”, Vattenfall Power

Consultant AB, Råcksta, Sweden, 2007.

(96)

14. Jonas Persson, “Conversion of PSS/E-files to SIMPOW-format focusing on dynamic models”, ABB Power Systems, Västerås, Sweden, 1999.

15. Ying Jiang Häfner, “Functional Description for HVDC Light Control – Gotland

Project”, ABB Power Systems, Ludvika, Sweden, 2001.

16. Öyvind Öberg, “Referat från PSS/E norden möte hos Birka Nät”, Vattenfall Sveanät AB, Stockholm, 2002.

(96)

9 Appendices

9.1 Test of fault simulations in PSS/E

1. Power-flow data file for the initial test system, Testsystem_initial.raw, v:\exjobb\Martin Brask\PSSE filer\Testsystem\

2. Power-flow data file for the final test system, Testsystem.raw, v:\exjobb\Martin Brask\PSSE filer\Testsystem\

3. Dynamic data file for the test system, Testsystem.dyr, v:\exjobb\Martin Brask\PSSE filer\Testsystem\

4. Sequence data file for the test system, Seqdata.txt, v:\exjobb\Martin Brask\PSSE filer\Testsystem\

9.2 Power-flow simulation of Gotland

5. Power-flow data file for the power system of Gotland with the “Standard PSS/E model”, Gotland_Standard.raw, v:\exjobb\Martin Brask\PSSE filer\Gotland\

6. Power-flow data file for the power system of Gotland with “ABB’s Open PSS/E model”, Gotland_Open_model.raw, v:\exjobb\Martin Brask\PSSE filer\Gotland\

9.3 Test of the dynamic of the HVDC Light link

7. Power-flow data file for the HVDC Light test system with the “Standard PSS/E model”, HVDC Light test system Standard.raw, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

8. Dynamic data file for the HVDC Light test system with the “Standard PSS/E model”, HVDC Light test system Standard.dyr, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

9. Power-flow data file for the HVDC Light test system with “ABB’s Open PSS/E model”, HVDC Light test system.raw, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

10. Dynamic data file for the HVDC Light test system with “ABB’s Open PSS/E model”, HVDC Light test system.dyr, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

(96)

11. Dynamic data files for “ABB’s Open PSS/E model”, chvdob_O-V1_1.obj,

chvdon_O_V1_1.obj, CONEC.OBJ, CONET.OBJ, dc_hl2_V1_1.obj, DSUSR.DLL, DSUSR.exp, DSUSR.lib, DSUSR.MAP, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

12. Source code for “ABB’s Open PSS/E model”, chvdob_O-V1_1.f, chvdob_O-V1_1-data-insert.f, chvdol_O-V1_1-declar-insert.f, chvdol_O-V1_1-logfile-insert.f, chvdol_O-V1_1-logfile-insert-AUTO.f, chvdol_O-V1_1-logfile-insert-Meta_AUTO.f, chvdon_O-V1_1.f, chvdon_O-V1_1-data-insert.f, conec.flx, conet.flx, dc_hl2_V1_1.f, dc_hl2_V1_1-logfile-insert.f, dc_hl2_V1_1-logfile-insert-AUTO.f, dc_hl2_V1_1-logfile-insert-Meta_AUTO.f, v:\exjobb\Martin Brask\PSSE filer\HVDC Light test system\

9.4 Dynamic simulations of Gotland

13. Dynamic data file for the power system of Gotland with the “Standard PSS/E model”, Gotland_Standard.dyr, v:\exjobb\Martin Brask\PSSE filer\Gotland\

14. Dynamic data file for the power system of Gotland with “ABB’s Open PSS/E model”,

Gotland_Open_model.dyr, v:\exjobb\Martin Brask\PSSE filer\Gotland\

15. Dynamic data files for “ABB’s Open PSS/E model”, chvdob_O-V1_1.obj, chvdon_O_V1_1.obj, CONEC.OBJ, CONET.OBJ, dc_hl2_V1_1.obj, DSUSR.DLL, DSUSR.exp, DSUSR.lib, DSUSR.MAP, v:\exjobb\Martin Brask\PSSE filer\Gotland\

16. Source code for “ABB’s Open PSS/E model”, chvdob_O-V1_1.f, chvdob_O-V1_1-data-insert.f, chvdol_O-V1_1-declar-insert.f, chvdol_O-V1_1-logfile-insert.f, chvdol_O-V1_1-logfile-insert-AUTO.f, chvdol_O-V1_1-logfile-insert-Meta_AUTO.f, chvdon_O-V1_1.f, chvdon_O-V1_1-data-insert.f, conec.flx, conet.flx, dc_hl2_V1_1.f, dc_hl2_V1_1-logfile-insert.f, dc_hl2_V1_1-logfile-insert-AUTO.f, dc_hl2_V1_1-logfile-insert-Meta_AUTO.f, v:\exjobb\Martin Brask\PSSE filer\Gotland\

9.4.1 70 [kV] three-phase fault simulation

A simulation of the system in chapter 5 with a 0.3 seconds three-phase fault with Z = 15 + j15 [Ω] in the fault, applied in STEN.70 after 0.1 second, generates the data in Figure 9.4.1 - Figure 9.4.12. The simulation with the “Standard PSS/E model” resulted in a non-convergent system and therefore the “Standard PSS/E model” is not included in the data.

(96)

0 1 2 3 4 5 6 7 8 9 100.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Time [s]

Vol

tage

[p.

u.]

Voltage NAS.70

Simpow model


Figure 9.4.1 Voltage at NAS.70 simulated with Simpow and “ABB’s Open PSS/E

model” in PSS/E.

Figure 9.4.2 Voltage at NAS.70 simulated with Simpow and “ABB’s Open PSS/E

model” in PSS/E. Focused part of Figure 9.4.1.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Time [s]

Vol

tage

[p.

u.]

Voltage NAS.70

Simpow model


(96)

0 1 2 3 4 5 6 7 8 9 10-80

-60

-40

-20

0

20

40

60

80

Time [s]

Act

ive

pow

er [

MW

]


Simpow model




0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-80

-60

-40

-20

0

20

40

60

80

Time [s]

Act

ive

pow

er [

MW

]


Simpow model



with Simpow and “ABB’s Open PSS/E model” in PSS/E. Focused part of Figure 9.4.3.

(96)

0 1 2 3 4 5 6 7 8 9 10-40

-20

0

20

40

60

80

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model




0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-20

-10

0

10

20

30

40

50

60

70

80

Time [s]

Rea

ctiv

e po

wer

[M

var]


Simpow model



with Simpow and “ABB’s Open PSS/E model” in PSS/E. Focused part of Figure 9.4.5.

(96)

0 1 2 3 4 5 6 7 8 9 10-100

-80

-60

-40

-20

0

20

40

60

80

Time [s]

Act

ive

pow

er [

MW

]

Active power NAS.70 - STNAS.70

Simpow model


Figure 9.4.7 Active power transmitted between the nodes NAS.70 and STNAS.70

simulated with Simpow and “ABB’s Open PSS/E model” in PSS/E.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-80

-60

-40

-20

0

20

40

60

80

Time [s]

Act

ive

pow

er [

MW

]

Active power NAS.70 - STNAS.70

Simpow model


Figure 9.4.8 Active power transmitted between the nodes NAS.70 and STNAS.70

simulated with Simpow and “ABB’s Open PSS/E model” in PSS/E. Focused part of

Figure 9.4.7.

(96)

0 1 2 3 4 5 6 7 8 9 10-50

0

50

100

150

200

250

Time [s]

Act

ive

pow

er [

MW

]

Active power VVIK.130 - YGNE.70

Simpow model


Figure 9.4.9 Active power produced by both HVDC Classic converters in Ygne

simulated with Simpow and “ABB’s Open PSS/E model” in PSS/E.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250

Time [s]

Act

ive

pow

er [

MW

]

Active power VVIK.130 - YGNE.70

Simpow model


Figure 9.4.10 Active power produced by both HVDC Classic converters in Ygne

simulated with Simpow and “ABB’s Open PSS/E model” in PSS/E. Focused part of

Figure 9.4.9.

(96)

0 1 2 3 4 5 6 7 8 9 1030

32

34

36

38

40

42

44

46

48

50

Time [s]

Spe

ed [

Hz]

Synchronous machine speed NG.14

Simpow model


Figure 9.4.11 The speed of the synchronous machine in the node NG.14 simulated


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 243

44

45

46

47

48

49

50

Time [s]

Spe

ed [

Hz]

Synchronous machine speed NG.14

Simpow model


Figure 9.4.12 The speed of the synchronous machine in the node NG.14 simulated

with Simpow and “ABB’s Open PSS/E model” in PSS/E. Focused part of Figure

9.4.11.

modelling of the power system of gotland in psse …

Documents