MODELLING OF THE POWER SYSTEM OF GOTLAND IN PSS/E WITH FOCUS ON HVDC LIGHT

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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

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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.

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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.

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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.

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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

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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

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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

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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.

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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.

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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.

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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.

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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 Z_fault 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

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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 . 10 53 24 3

10 2220

3 ³

6

U kA I S

base base

base =

⋅

= ⋅

=

Equation 2.1.1 The equation for the base current.

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( )

₀_.₂₅₉₄₆_[ _]

10 2220

10 24

6 3 2

2 = Ω

⋅

= ⋅

=

base base

base S

Z U

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.

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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] P_G [p.u.] Q_G [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.

) 2 (

1 ω

ω = − − ∆

∆ T T D

H ^m ^e

&

Equation 2.1.3 The differential equation for the speed deviation.

ω ω δ&= 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.

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• 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.]

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 X_l 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

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fault

Th Z Z Z Z

Z = ₁+ ₂+ ₀ +3

Equation 2.1.5 The equation for the Thévenin equivalent impedance.

where Z_Th 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 fault fault

fault fault

Z I U

I

I ₁ = ₂ = ₀ =

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 U_fault 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 impedances

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 .

2 0

1 =R =

R

32500 .

2 0

1 =X =

X

04875 . 0 3 ₁

0 = ⋅R =

R

97500 . 0 3 ₁

0 = ⋅X =

X

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

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2.1.7 Sequence components of the generator impedance

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 .

1=RA=0 R

2 .

1 =XD′′=0 X

03 . 0

2 =10⋅RA= R

2 .

2 =XD′′=0 X

0 =* R

144 . 0 9

.

0 =0 ⋅XA=

X **

* 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 53405

10 1 10

1

0 0

0 pu

I I Z U

base

=

Equation 2.1.7 The equation for the zero-sequence impedance.

.]

. [ 499998 .

5340 144

. 0 5 .

5340 ² ²

2 0 2 0

0 Z X pu

R = − = − =

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.

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2.2 Results

2.2.1 Power-flow simulation of the initial test system

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] P_G [p.u.] Q_G [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.

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 2.2.4 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 pu

U = and all voltage angles are ∠U =0[^o]^.

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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.

1 1.0 36 0.9 0.3

3 0.995 0 -0.9 -

2.2.2 Power-flow simulation of the final test system

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.

Bus U [p.u.] θ [^o] PG [p.u.] QG [p.u.]

1 1.0432 33.656 0.9000 0.3000

2 0.9755 17.238 0 0

3 0.9950 0 -0.8731 0.2376

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.

Bus U [p.u.] θ [^o] PG [p.u.] QG [p.u.]

1 1.0432 33.656 0.9000 0.3000

2 0.9755 17.238 0 0

3 0.9950 0 -0.8731 0.2376

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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] i_d [p.u.] i_q [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.

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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]

Voltage [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]

Voltage [p.u.]

Voltage bus 2

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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 0.5 30

40 50 60 70 80 90 100 110 120

Time [s]

Angle [o ]

Angle bus 1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0

5 10 15 20 25 30 35 40 45

Time [s]

Angle [o ]

Angle bus 2

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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]

Angle [o ]

Generator angle

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]

Speed [p.u.]

Generator speed

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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]

Angle [o ]

Generator angle

0 5 10 15

0.98 0.985 0.99 0.995 1 1.005 1.01 1.015 1.02

Time [s]

Speed [p.u.]

Generator speed

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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.

( )

⁰^.⁰⁵⁹⁵ ¹^.²⁰⁹^[ ^. ^.]

2220 3 . 1742 726

. 85

9755 .

0 ²

* 2

u p i i

S S Z U

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, S_baseis the base power and S_shunt 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

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Page 22 (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.

( ) ( )

( )

₀_.₀₆₁₉ ₁_.₁₇₅₈_[ _. _.]

6642 . 0 2442 . 0

174 . 17 sin 174 . 17 cos 8333 . 0

1 . 0 _

1 . 0

_ i pu

i I

Z U

fault fault shunt

own = +

−

= +

=

+ +

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.

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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]

Voltage [p.u.]

Voltage bus 1

Simpow detailed Simpow shunt Simpow own shunt 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 0.82

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

Time [s]

Voltage [p.u.]

Voltage bus 2

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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]

Angle [o ]

Angle bus 1

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]

Angle [o ]

Angle bus 2

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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]

Angle [o ]

Generator angle

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.9975

0.998 0.9985 0.999 0.9995 1 1.0005 1.001 1.0015 1.002 1.0025

Time [s]

Speed [p.u.]

Generator speed

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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]

Current [p.u.]

Real fault current

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]

Current [p.u.]

Imaginary fault current

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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]

Angle [o ]

Generator angle

0 5 10 15

0.9975 0.998 0.9985 0.999 0.9995 1 1.0005 1.001 1.0015 1.002 1.0025

Time [s]

Speed [p.u.]

Generator speed

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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 . 1791 295

. 1758 94 . 1 0619 . 0

2220 9755

.

0 ²

* 2

MVA i i

Z S S U

shunt own

base fault

shunt

own = +

−

= ⋅

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

In Equation 2.2.3 S_{own shunt} is the initial complex short-circuit power in the shunt, U_fault is the voltage in the faulted bus just before the fault is applied, Zown shunt is our own calculated shunt impedance, and S_base 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 . 3 1 . 1742 726

. 85

6 . 1791 295

. 94

/ =

+

= +

= i

i S

S S

shunt shunt own E

PSS in error

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 S_{own 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.

MODELLING OF THE POWER SYSTEM OF GOTLAND IN PSS/E WITH FOCUS ON HVDC LIGHT