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Department of Industrial Electrical Engineering and AutomationLund University

Coordinated Voltage Control

CODEN:LUTEDX/(TEIE-5158)/1-35/(2002)

Fredrik Roos

i

Abstract The main scope of the Master’s project presented in this report is to investigate what can be achieved in terms of reduced tap operations by relatively simple means. For this purpose, a coordinated tap changer control method, based on fuzzy set manipulation, has been derived. No attention is paid to optimisation issues. A centralized coordinated tap changer controller of course requires extensive communication infrastructure to enable remote coordinated control. In the test system under consideration, six out of twelve substations are equipped with remote control facilities for the tap changers. Thus, six tap changers take part in the coordinated tap changer control. For the evaluation of the derived coordinated tap changer control, a model of the test system has been developed. The test system model has been run twice using load curves and voltage curves recorded 19 September 2001. During the first run, conventional tap changer control, based on local automatic controllers, was applied, and during the second run, the derived coordinated tap changer control, realized in the form of a fuzzy rule based controller, replaced the conventional tap changer control. In evaluating the derived coordinated tap changer control, the conventional tap changer control is used as a reference. By comparing the numbers of tap operations resulting from the two runs, it has been concluded that the derived coordinated tap changer control reduces the total number of tap operations by 15 %. Furthermore, an attempt has been made to show that this reduction has not been achieved at the cost of deterioration in voltage quality. The simulation results have not been validated through field tests.

ii

Preface Lars-Åke Wahlqvist, at Sydkraft Elnät Syd AB, has for many years been concerned with the effect of poorly coordinated voltage control actions on the number of tap operations. In [Wahlqvist, 2000], Lars-Åke concludes from voltage measurements, recorded at a 50 kV substation busbar in Horsaryd, that it is desired to coordinate the manual voltage control actions and the automatic voltage control actions. In [Wahlqvist, 2000], he also takes the opportunity to bring up the idea of a centralized voltage controller. The results in [Larsson, 1997] show a significant reduction in the number of tap operations thanks to coordinated tap changer control. After Mats Larsson’s excellent work, comprising a radial system, Lars-Åke would like to have the effect of coordinated voltage control, applied to a system comprising a meshed 130 kV subtransmission system and several 130, 50 and 20 kV distribution radials, investigated. Lars-Åke initiated the Master’s project in October 2000 by formulating the problem. Almost a year later, in September 2001, I accepted the assignment. It was clear right from the beginning that I would continue on the road already marked out by Mats Larsson. Thus, my assignment was to extend Mats Larsson’s fuzzy rule based control method to also include the overlying meshed 130 kV subtransmission system with its shunt capacitors. In addition, the performance of the extended method was to be evaluated in terms of the achieved reduction in the number of tap operations. At the moment, Sydkraft Elnät Syd AB is managing the operation of the transmission system in the south of Sweden on Svenska Kraftnät’s behalf. Thereby, Sydkraft Elnät Syd AB is able to utilize shunt capacitors and reactors that are available in the transmission system, to facilitate the voltage control at lower levels. However, in the future, Svenska Kraftnät will take over the operation of the transmission system. It is highly likely, that after having lost the control of the transmission system operation, Sydkraft Elnät Syd AB will have to put some more effort into the voltage control of the subtransmission systems and the distribution systems. Sydkraft Elnät Syd AB will have to treat all events in the transmission system as disturbances, though, coordination of the two operators is expected to some extent. In the light of these expected changes in the operating conditions, subtransmission system voltage control and distribution system voltage control have become pressing issues for Sydkraft Elnät Syd AB.

iii

Acknowledgements This report presents the Master’s project I have carried out at the department of Industrial Electrical Engineering and Automation, Lund University. First, I would like to thank Lars-Åke Wahlqvist for giving me such a pleasant start of the project by organising field trips to the substations in Sege, Trelleborg and Fotevik and to the system operation centre in Malmö. He also made contact with ElectroSandberg AB and arranged an appointment for me to attend tap changer maintenance work. Both Alf Larsen and Lars-Åke Wahlqvist, at Sydkraft Elnät Syd AB, have been most helpful in providing data for the model development. They have also given some useful advice during the three project meetings that were held. Special thanks go to Olof Samuelsson and Sture Lindahl at the department. Olof, who has been my supervisor, has given me guidance throughout the whole project and Sture has helped me with modeling issues. My most grateful thanks go to Mats Larsson, who received his PhD at the department in 2001 and is currently working for ABB Cooperate Research in Baden, Switzerland. With great patience, he has answered questions about the modeling language Modelica and about the simulation tool Dymola. I sincerely appreciate the additional instructions on how to work with Dymola in practice, which I got from Per Karlsson and Jörgen Svensson, both working at the department. Also, Torsten Brönmark, at Sydkraft Elnät Syd AB, deserves a special thanks for introducing me to the operators’ way of reasoning for the manual voltage control from the system operation centre in Malmö. Before the Christmas holidays, I had the pleasure to discuss my work with a group of people working at Sydkraft Elnät Syd AB. The feedback I received at this meeting is also gratefully acknowledged. Last, but certainly not least, I would like to thank the people at the department for all the enjoyable conversations during both spontaneous and scheduled breaks. Thank you all, ever so much, for your support.

Lund, March 15, 2002

Fredrik Roos

Contents Abstract .............................................................................................................................. i Preface ............................................................................................................................... ii Acknowledgements .......................................................................................................... iii 1 Introduction................................................................................................................1

The Voltage Control Problem..........................................................................................1 Conventional Tap Changer Control.................................................................................2 Fuzzy Control ..................................................................................................................3

2 The Test System .........................................................................................................6 3 Test System Modeling................................................................................................8

Lines ................................................................................................................................8 TCUL Transformers ........................................................................................................8 Loads..............................................................................................................................10 Thévenin Equivalents ....................................................................................................10 The Modeling Language................................................................................................11 Model versus Real System.............................................................................................11

4 The Control Method ................................................................................................14

Inputs and Outputs of the Controller .............................................................................14 Coordinated Voltage Control Actions ...........................................................................15 Additional Advantages of a Centralized Voltage Control Approach ............................16

5 Control Method Evaluation ....................................................................................17

Simulation Results .........................................................................................................18 6 How to Continue the Work .....................................................................................21

Further Evaluation .........................................................................................................21 Further Development .....................................................................................................21 When the Time is Ripe ..................................................................................................21

7 Conclusions...............................................................................................................22 A Conventional Tap Changer Control Parameters..................................................23

B Definition of Primitive Fuzzy Operations..............................................................24 C Definition of Membership Functions .....................................................................25 D Test System Model Data..........................................................................................26 E Modeling of the Three Winding Transformer in Tomelilla.................................27

Per unit equivalent circuit ..............................................................................................27 Desired Model ...............................................................................................................28 Simplified Model Used in the Simulations....................................................................29

F Load Model Parameters and Profiles ....................................................................30 G Fuzzy Rule Base .......................................................................................................31 H References.................................................................................................................34

1

1 Introduction The Voltage Control Problem The purpose of voltage control in distribution systems is to compensate for load variations and events in the transmission system, in such a way that all customer supply voltages are kept within certain bounds. However, while keeping the system within operating constraints, it is also desired to minimise the power loss or power demand (sum of power loss and power consumption) and the number of control actions. Thus, a voltage control system should be able to select the optimal set of control actions. Common tools used for solving these optimisation problems are power flow analysis and sensitivity analysis. In addition, security issues can be incorporated in the voltage control problem. Most often, the operating situation requires a trade-off between different control objectives, such as economics versus keeping the system voltages within specified limits. In addition to generator voltage control, there are many kinds of reactive power sources, which can be used to control the voltage in power systems. Adjusting transformer tap positions and switching shunt capacitors and shunt reactors are the most common substation voltage control actions. Several methods for global optimisation are available. A vast amount of these methods divides the optimisation problem into a set of decoupled sub problems, forcing implementation to be based on several independent control systems. However, since coordination of control actions is an important issue, this is not a successful approach. A better approach is to structure, with respect to different time scales, the control system into several hierarchical levels, which communicate with each other. This structuring approach is adopted in the French transmission voltage control system, [Larsson, 1998]. Conventional voltage control is based on local automatic controllers, which use only local voltage measurements. Since conventional voltage control does not take requirements of the whole system into account, it is only possible to achieve local operating goals with conventional voltage control. To achieve global operating goals a centralized control approach needs to be adopted. To fully understand the importance of voltage control, one has to keep in mind that voltage control is accomplished by managing reactive power flows in the power system. For example, a shunt capacitor increases the voltage at the bus to which it is connected by injecting reactive power and thereby reducing voltage drops caused by transport of reactive power to that particular bus. Thus, different kinds of devices that can either consume or produce reactive power, or both, are used for the voltage control. Voltage control and reactive power control are closely related but have different objectives: Voltage control aims at keeping the voltage within certain limits, while the objective of reactive power control is to maximise transmission capabilities, minimise power losses or to minimise the amount of reactive power supplied by generators. Thus, voltage control and reactive power control are justified by the following reasons:

2

• Voltages must be kept within an acceptable range for both customer equipment and power system equipment to function properly.

• Transport of reactive power uses transmission capacity, which is better used for transport of real power.

• Transport of reactive power results in real power losses. • When generators supply excessive amounts of reactive power, their production of

real power is curtailed. A simple example illustrates why customer voltages should be kept at appropriate levels: At a too low voltage level, a light bulb provides less illumination, whereas at a too high voltage level, the lifetime of the light bulb is shortened. Thus, in general, equipment is designed to operate within a certain voltage range. Furthermore, the transmission system itself adds to the complexity of the control problem. At light loading it produces reactive power, while at heavy loading it consumes reactive power. Thus, changes in the transmission system configuration, due to some kind of fault, in turn reconfigure power flows and thereby loading conditions. This will call for rapid reactive power compensations. More details on the basic physical phenomena that create the need for voltage control can be found in Section 2.1 of [Larsson, 1997]. Conventional Tap Changer Control Transformer tap position changes, and shunt capacitor and shunt reactor switching cause rapid voltage changes, which propagate down in the system towards lower voltage levels. Figure 1.1 shows how the voltage at a low voltage transformer bus is controlled by a local automatic controller. As long as the voltage remains within the dead-band, no action is taken by the controller. The voltage has to violate the dead-band during a certain period of time, Td, before the controller will initiate a tap position change. In the figure, the increase in the voltage reference value, which occurs at 6 am, causes an upward tap operation. Similarly, the decrease in the voltage reference value, which occurs at 10 pm, causes a downward tap operation. Thus, only two tap position changes occur during the particular day. Consequently, the origin of the majority of the rapid voltage changes, which can be seen in the figure, is from events occurring higher up in the system. Slow voltage variations are on the other hand caused by the hourly load variations. The conventional tap changer control is characterized by following control parameters: Vref: Reference voltage value DB: The dead-band specifies the allowed voltage deviation from the reference voltage

value. Td: The controller time delay is the time the voltage has to violate the dead-band

before the controller will request a tap position change.

3

Td0: Time constant used in the expression for the controller time delay. Tm: The mechanical time delay is the time it takes for the tap changer to take one step,

once a step request from the controller has been received. The conventional tap changer controllers, used in the simulations of this work, are set to use inverse time characteristics. In this case, Td is inversely proportional to �dev ��which is the absolute value of the voltage deviation from the voltage reference value:

1060

1

2 −+⋅⋅=u

TTdev

dd

DB

0 5 1 0 1 5 2 0 2 51 . 0 2

1 . 0 4

1 . 0 6

1 . 0 8

1 . 1

1 . 1 2

T im e o f d a y ( h o u r s )

Vol

tage

(p.

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Figure 1.1 A local automatic tap position controller controls the voltage at a low-voltage transformer bus. The voltage reference value is plotted with a thick solid line, the controlled voltage is plotted with a thin solid line and the dashed lines show the dead-band.

The control parameter values used in the simulations of this work are presented in Table A.1. More details on the functioning of the local automatic tap changer controller can be found in Section 3.2 of [Larsson, 1997]. Fuzzy Control A fuzzy rule based controller consists mainly of two elements, the rule base and the inference engine. The control method is formulated as a collection of linguistic rules, which are stored in the rule base. Each rule in the rule base corresponds to a certain control action. By means of these rules, the values of the physical process variables and defuzzification threshold, the inference engine derives the most urgent control action. In other words, the inference engine judges how well each rule matches the actual process condition. The inference engine transforms the value of each physical process variable into a fuzzy variable, by means of a membership function, in such a way that each fuzzy variable

4

assumes a value between zero and one. Each fuzzy variable corresponds to a certain property, such as high or very high, and its value describes to what extent the physical process variable possesses this property. Figure 1.2 shows a membership function that is used for determining to what extent a certain voltage is very high with respect to its reference value. In the rule base of the fuzzy rule based controller presented in this report, three primitive operations are applied to fuzzy variables to form the rules. These operations have such properties that each rule itself can be considered as a fuzzy variable, describing to what extent a certain control action needs to be done. This enables rules to depend on each other, which will be used in this work to coordinate tap operations. How these three primitive operations are defined is made clear in Appendix B. The requirements on the membership functions are few, e.g. they can assume a variety of different shapes. Thus, not only can the function parameters be adjusted, but also the function itself can be replaced with another. It might even be so, that one specific function makes the controller perform particularly well. Thus, the performance of a fuzzy rule based controller can be improved mainly by adopting proper membership functions, adjusting the membership function parameters and deleting, adding and completing rules in the rule base. There is a variety of different membership functions, of which Section 2.1 in [Jantzen, 1991] mentions a few. The most characteristic property of a fuzzy membership function is that it only assumes values between zero and one. Appendix C presents the membership functions used in the fuzzy rule based controller presented in this report.

-0.04 -0.02 0 0.02 0.04 0.06 0.08

0

0.2

0.4

0.6

0.8

1

voltage deviation from reference value (p.u.)

grad

e of

mem

bers

hip

Figure 1.2 A membership function that is used for determining to what degree a certain voltage is very high with respect to its reference value.

According to [Jantzen, 1991], fuzzy control is most appropriate to use when one has some heuristic knowledge that can improve the control. The task then lies in transforming

5

the human expertise into a rule base. In [Jantzen, 1991], the major advantages and drawbacks of fuzzy control are brought up. The major advantages are:

• The fuzzy controller is simple in that is does not require the use of sophisticated mathematics.

• The rules in the rule base are formulated in terms of daily language use, which simplifies the utilization of human expertise.

• The fuzzy controller does not rely on a system model. The major drawback is:

• The controller is difficult to analyse in the usual mathematical fashion. Thus, stability is difficult to predict and an optimal parameter setting is difficult to achieve.

For further reading on fuzzy control, Section 3.4 in [Larsson, 1997] and Chapter 1 and 2 in [Jantzen, 1991] are recommended as a start.

6

2 The Test System The test system covers an area in the very south of Sweden. Figure 2.1 shows a map of the Swedish province Skåne, which describes the geographical location of each of the twelve substations included in the test system. Since the 130 kV line between Tomelilla and Åhus is a part of the test system, Åhus can also be found on the map, however, this substation is not a part of the test system. In addition, the city of Malmö is located on the map. All the substations of the test system, except Fotevik and Järrestad, are part of a 130 kV slightly meshed subtransmission system. Fotevik and Järrestad, on the other hand, are substations in radial distribution systems starting at Trelleborg and Tomelilla respectively.

Figure 2.1 Map of Skåne: The geographical locations of the substations that are included in the test system are indicated. In Trelleborg there are two TCUL transformers, which can be switched to manual remote control. However, today only the tap changer of one of these is remotely controlled.

The test system is connected to the 400 kV transmission system at Barsebäck and Sege. Two 400 kV transmission lines connected between Barsebäck and Sege and between Sege and Arrie, respectively, are included in the test system.

7

Today, all the tap changers of the test system, except the one in Sege and one of the tap changers in Trelleborg, which are controlled manually from the system operation centre in Malmö, are controlled exclusively based on local criteria. Besides the two manually controlled tap changers in Sege and Trelleborg, there are another five tap changers, which can be switched to manual remote control. These tap changers are located in Arrie, Trelleborg, Fotevik, Tomelilla and Järrestad. Since the manually controlled tap changer in Trelleborg is at position 0 most of the time, this tap changer does not take part in the coordinated tap changer control. Consequently, this makes six tap changers that take part in the coordinated tap changer control presented in this report. All the other tap changers in the test system continue to be controlled based on local criteria exclusively. Table 2.1 presents the reactive power compensation resources available in the test system. X-SEE is a shunt reactor, while the other units are shunt capacitors. All of these reactive power compensation resources are controlled manually from the system operation centre in Malmö, except C-SHM, which has a time based control.

designation location rate (MVAr)

nominal voltage (kV)

X-SEE Sege 150 415 CA-SEE Sege 90 142 CB-SEE Sege 90 142 CA-TBG Trelleborg 48 142 CB-TBG Trelleborg 32 142 C-TLA Tomelilla 60 142 C-SHM Stjärneholm 8 22.2

Table 2.1 Reactive power compensation resources available in the test system.

8

3 Test System Modeling Figure 3.2 shows the structure of the test system model and provides each bus with a unique number. Line data and transformer data are given in Table D.1. In order to isolate the test system from its surroundings, Thévenin equivalents and load models have been used. Load variations for the load models and voltage variations for the Thévenin equivalents, were recorded 19 September 2001 and represent the operating condition in the model. Lines Lines were modelled as a pi-link equivalent with G set to zero. Figure 3.1 shows a schematic of the pi-link equivalent.

Figure 3.1 Pi-link equivalents represent lines in the test system model.

TCUL Transformers A TCUL (Tap Changing Under Load) transformer model, which represents the discrete nature of the tap changer mechanism, was used. This model is characterized by the following parameters: minpos: The lowest tap position, (usually equal to –9) maxpos: The highest tap position, (usually equal to 9) tappos: Current tap position of the discrete tap changer,

(minpos, …, 0, …, maxpos) n0: Nominal transformer turns ratio at tap position 0 stepsize: Change in transformer turns ratio caused by one step up or down n: Current transformer turns ratio, (n = n0 + tappos · stepsize) R: Leakage Resistance X: Leakage Reactance The transformer turns ratio is here defined as the voltage at the low-voltage side of the transformer divided by the voltage at the high-voltage side of the transformer. A more detailed description on the functioning of the tap changer mechanism can be found in Section 2.1 of [Larsson, 1997].

9

Figure 3.2 Test system model structure: In order to isolate the test system from its surroundings, Thévenin equivalents and load models have been used.

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Loads For the modeling of the loads the dynamic exponential recovery load model, according to [Karlsson and Hill, 1994], has been used. The actual load at a bus in the system, [Pl, Ql], depends on the connected load, [P0, Q0], and the voltage V at that bus. The connected load is the sum of the rated W and VAr of all connected devices. The model is fed with the recorded load, which is assumed to be the connected load. The actual load, [Pl, Ql], is given by:

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where �s is the steady-state active-power voltage-dependency exponent, �t is the transient active-power voltage-dependency exponent,

Tp is the active-power recovery-time constant, s is the steady-state reactive-power voltage-dependency exponent, t is the transient reactive-power voltage-dependency exponent,

Tq is the reactive-power recovery-time constant and xp is a dynamic internal state. Thévenin Equivalents Thévenin equivalents represent the interconnection with the external system at Barsebäck, Sege and Åhus. The ideal independent generator of the Thévenin equivalent introduces an infinite bus by keeping its terminal voltage equal to the recorded voltage. For the modeling of the impedance of the Thévenin equivalent, a pi-link equivalent with B and G set to zero is used. R and X are calculated from three-phase short-circuit currents.

11

The Modeling Language For the development of the test system model, a freely available (http://www.modelica.org/library/library.html, 11 March 2002) power system component library, called ObjectStab, has been used. This component library is intended for the simulation of voltage stability and transient stability in power systems, and is written in Modelica, which is a multi-formalism, multi-domain, general-purpose, object-oriented language for modeling of physical systems. All component models written in Modelica are transparent and can easily be modified or extended. To make the ObjectStab components useful, a few component models had to be extended. For example, the circuit breaker model had to be extended to enable shunt capacitor switching and shunt reactor switching. In addition, the introduction of voltage reference values to the conventional tap changer control, and the replacement of the local automatic controllers with a centralized controller, resulted in some modifications and extensions. Since Modelica is not a domain-specific modeling language, the efficiency of the modeling is suffering, and thereby the ability to model large systems in Modelica is limited. The simulation of one day’s operation of the moderately sized test system model used in this work took approximately two hours. Model versus Real System A model mimics the true behaviour of the modelled system. The more accurate model, the better results. For the simulation results to be relevant, the model has to be sufficiently accurate. For future refinement of the model, it is suggested that the following issues should be considered:

• The external systems are represented by Thévenin equivalents and load models with a few exceptions:

o The influence of the Baltic Cable and the filter and shunt capacitor in

Kruseberg is not represented in the model. o The influence of the two 130 kV lines connected between Sege and Svalöv

and between Sege and Södra Sandby, respectively, is neglected. o The loads at MMÖ SJ, ÖKL, GRD, SOF, BGY and VKA are neglected. o The interconnection with the external system at VKA is not represented by a

Thévenin equivalent.

• The load variation at bus 29 is recorded 16 October 1996. • The load variation at bus 15 equals three times the load variation at bus 29.

• The generator of the Thévenin equivalent, connected to bus 6, is not fed with

recorded voltage variation. Instead, it is fed with a constant voltage value, which constitutes the average value of the voltage variation recorded at bus 5.

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• The parameter values of the pi-link equivalent representing the 400 kV line between bus 5 and 6, equal three times the corresponding parameter values of the pi-link equivalent representing the 400 kV line between bus 4 and 5.

• A constant impedance model has been used. Especially for the under load tap

changing transformer this weakness is apparent, since, in practice, the transformer impedance varies with the tap position. In the model, the transformer impedances correspond to the nominal tap positions. Furthermore, it has been assumed for some of the transformers, that the transformer impedance is purely inductive.

• The initial tap positions, i.e. the tap positions at the instant when the recording of

the load curves and feeding voltage curves started, are unknown. Hopefully this will only induce differences in the transient behaviour of the model and the real system.

• In reality, the tap changer in Sege is controlled manually from the system

operation centre in Malmö, whereas, in the model, due to lack of information about tap positions, the tap changer is provided with conventional tap changer control.

• Since the data sheet of the transformer in Önneslöv is missing, parameter values

for this transformer are roughly estimated.

• For the 130/50/20 kV tap changing transformer in Tomelilla, a simplified model has been used. The desired model comprises one 130/50 kV transformer and one 130/20 kV transformer with the tap changers controlled in parallel with respect to the 20 kV voltage. However, the simplified model comprises two 130/50 kV transformers connected in parallel, with the 20 kV load of the three-winding transformer applied to the secondary side. Appendix E describes step by step how this simplified model has been derived.

• In Trelleborg there are two 130/50 kV tap changing transformers T1 and T2. In

reality, the tap changer of T1 is exclusively controlled from the system operation centre in Malmö, though very occasionally, whereas, in the model, the tap changer of T1 is blocked at its nominal position by assigning the dead-band of the controller a considerably greater value.

• The load model parameter values are roughly estimated by using one of the three

load profiles denoted FVK, SLA and TLA for each load:

o FVK, characterizing a villa area where electric space heating dominates, has been derived by calculating the average of the parameter values presented in Section 3.3.2 of [Karlsson, 1992] for each of the six parameters.

o SLA, characterizing a town area with industries, has been derived by calculating the average of the parameter values presented in Section 3.3.2 of [Karlsson, 1992] for each of the six parameters.

13

o TLA, characterizing a rural town area, is the same load profile used in [Larsson, 1997].

Tables F.1 and F.2 summarize the parameter values used for the three load profiles and associate each load bus in the test system model, with a load profile, respectively.

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4 The Control Method The purpose of the voltage control method presented in this report is to explore the potential in coordinating control actions in the test system, and does not deal with optimisation of any kind. The basic idea of coordination is to consider the whole system, i.e. make use of system-wide information in the control. Furthermore, the derived voltage control method is intended for normal operating conditions. Thus, it is not capable of dealing with voltage stability issues. In this work, the coordinated tap changer control is realized in the form of a fuzzy rule based controller. The choice of controller is motivated by referring to the work presented in [Larsson, 1997], where three approaches to coordinated tap changer control in a radial distribution system are proposed. One of these approaches has the advantage of not requiring any new equipment. It simply offers a new tuning methodology for the existing local tap changer controllers. The other two approaches are dependent on both communications and a centralized control method. One of these two centralized control approaches, the optimal control method, showed the best simulation results. However, according to Section 3.5 in [Larsson, 1997], this control method relies on a system model, which has to be accurate in order to avoid stationary control errors. Consequently, the model has to be satisfactorily updated on-line. The major advantages of the other centralized control approach are that it does not rely on a system model and it is computationally simple. The latter advantage becomes increasingly important as the size of the controlled system increases. Although not explicitly stated in [Larsson, 1997], it is apparent that the author favoured this so-called fuzzy rule based controller because of its robustness and simplicity. It was not without any reasons that the fuzzy rule based controller was chosen to be implemented for the field tests in [Larsson, 1997]. Section 3.4 in [Larsson, 1997] first introduces the basics of fuzzy control and then goes on describing the fuzzy rule based controller used in [Larsson, 1997]. This controller has a rule base consisting of six rules, while the coordinated voltage control presented in this report is based on a fuzzy rule based controller that has a rule base consisting of fourteen rules. These fourteen rules can be found in Appendix G. The coordinated voltage control aims at reducing the number of unnecessary tap operations in the test system by coordinating the voltage control actions. An example of unnecessary tap operations has been recorded at the 50 kV substation in Horsaryd [Wahlqvist, 2000]: First an automatic upward tap operation is made, shortly followed by a manual connection of a shunt capacitor higher up in the system, after which the tap changer is forced to return to its previous position. Thus if the tap changer control system had waited for the shunt capacitor to switch, two tap operations could have been avoided. Inputs and Outputs of the Controller Table 4.1 specifies the input voltage signals of the derived fuzzy rule based controller. Each input voltage signal in Table 4.1 is accompanied by an input voltage reference value signal.

15

The fuzzy rule based controller has six transformer turns ratio output signals, one for each TCUL transformer participating in the coordinated tap changer control.

designation measured at bus

V20_FVK 25 V20_JSD 29 V50_TBG 20 V50_TLA 27 V130_AIE 8 V130_SEE 9 V130_TBG 17 V130_TLA 26

Table 4.1 Input voltage measurement signals of the fuzzy rule based controller. Each input voltage measurement is accompanied by an input voltage reference value. The designations refer to the process variables used in the rules of the rule base in Appendix G and the bus numbers refer to Figure 3.2.

Coordinated Voltage Control Actions The derived coordinated voltage control involves the six tap changers and the five shunt capacitors, which are available for manual remote control in the test system. The tap operations of these six tap changers are coordinated both mutually and to the manual switching of the five shunt capacitors. The latter has been accomplished by surrounding every shunt capacitor switching instant with an interval and blocking tap changers within these intervals. Of course in a practical application the shunt capacitor switching instants are unknown. However, since the scope of the Master’s project is to explore the potential in coordinating voltage control actions in the test system, the tap changer blocking approach is both relevant and illustrative. The shunt reactor at the 400 kV bus in Sege is not involved in the coordinated voltage control. Consequently, the shunt reactor switching constitutes a major disturbance to the coordinated voltage control. Table 4.2 specifies how the control of the six tap changers is coordinated to the switching of the five shunt capacitors.

shunt capacitor switching CA-SEE CB-SEE CA-TBG CB-TBG C-TLA tap operation

on off on off on off on off on off tapSEEdown

tapSEEup tapAIEdown

tapAIEup tapTLAdown

tapTLAup tapTBGdown

tapTBGup tapJSDdown

tapJSDup tapFVKdown

tapFVKup

Table 4.2 Each tap operation is blocked two minutes before and one minute after the indicated shunt capacitor events. The notations of the capacitors refer to Table 2.1 and the tap operations refer to Appendix G.

16

How the control of the six tap changers is mutually coordinated is explained below by means of the two rules from the rule base (Appendix G). tapSEEdown =

[high(V130_TLA) and high(V130_TBG) and high(V130_SEE)]

or

[veryhigh (V130_SEE)] tapAIEdown =

[high(V130_TLA) and high(V130_TBG) and high(V130_AIE) and not tapSEEdown]

or

[veryhigh (V130_AIE)]

Each rule is formulated by using the primitive fuzzy operations (Appendix B) on fuzzy variables. This results in a fuzzy variable, which can be used in another rule. Additional Advantages of a Centralized Voltage Control Approach Since the control parameter values of the local automatic controllers cannot be remotely changed, one has to visit the substations in person. This is also the case for changes in the voltage reference values. A centralized voltage control approach makes it easier to change the values of control parameters. In due time, this might lead to voltage control systems that will be able to use alternative control strategies for different operating conditions and thereby be able to manage even stressed operating conditions.

17

5 Control Method Evaluation For the evaluation of the coordinated tap changer control, a model of the test system has been developed and two test system model simulations have been run. During one run, the conventional tap changer control is applied to the model, whereas during the other run the derived coordinated tap changer control was applied to the model. The run of the model with the conventional tap changer control is considered as a reference in the evaluation of the coordinated tap changer control. During the two runs, the same manual shunt capacitor switching pattern was used. Figure 5.1 shows the manual switching of the five remotely controlled shunt capacitors, during the simulated day (19 September 2001). In addition, the switching of the shunt reactor at the 400 kV bus in Sege is shown in the figure. The shunt capacitor at the 20 kV bus in Stjärnehom is constantly connected during the two runs. Furthermore, the same voltage reference values were used during the two runs (Table A.1).

0 10 200

0.5

1

1.5

Time of day (hours)0 10 20

0

0.5

1

1.5

Time of day (hours)

0 10 200

0.5

1

1.5

Time of day (hours)11 11.5 120

0.5

1

1.5

Time of day (hours)

0 10 200

0.5

1

1.5

Time of day (hours)0 10 20

0

0.5

1

1.5

Time of day (hours)

a) CASEE b) CBSEE

c) CATBG d) CBTBG

e) CTLA f) XSEE

Figure 5.1 Manual switching of the remotely controlled reactive power sources, which are available in the test system (Table 2.1), on = 1, off = 0: a) switching of CA_SEE. b) switching of CB_SEE. c) switching of CA_TBG. d) switching of CB_TBG. e) switching of C_TLA. f) switching of X_SEE.

Tap operations of a tap changer are coordinated to the connections of a particular shunt capacitor by prohibiting upward tap operations of the tap changer two minutes before and one minute after connections of the shunt capacitor. Similarly, tap operations of a tap

18

changer are coordinated to the disconnections of a particular shunt capacitor by prohibiting downward tap operations of the tap changer two minutes before and one minute after disconnections of the shunt capacitor. Since every single tap operation gives rise to a sudden change in the voltage, which propagates all the way down to the customer supply voltages, a reduction in the number of unnecessary tap operations is expected to improve the voltage quality and reduce maintenance costs. There are many ways of measuring the voltage quality:

• Average value, minimum value and maximum value of the voltage deviation from the reference value computed over a certain time interval.

• Standard deviation of the voltage computed over a certain time interval. • The number of voltage steps during a certain time interval, where a voltage step is

defined as a voltage change of 1 % or more in less than 1 second. According to [Wahlqvist, 2000], the Swedish standard [SS 421 18 11, 1989], titled EMC levels in low voltage distribution systems, allows repeated occurrence of a stepwise voltage change of 3 %, at the maximum, every second minute.

In this report, the influence of the derived coordinated tap changer control on the voltage quality is evaluated by comparing the voltage standard deviation value at 12 buses in the test system model, resulting from the two test system model runs. Simulation Results The test system model has been run twice using load curves and voltage curves recorded 19 September 2001. During the first run, conventional tap changer control was applied to all the thirteen tap changers included in the test system, and during the second run, the derived fuzzy rule based controller replaced the conventional tap changer control at six of the twelve substations. Table 5.1 makes clear which TCUL transformers participate in the coordinated tap changer control. The control of the other seven tap changers was remained unchanged during the second run. The simulation results were obtained using a sample period of the fuzzy rule based controller of 20 seconds. Before both test system model simulations, the tap positions were initialised to yield voltage deviations within the dead-bands at the start of the simulation. The simulation results indicate that, by controlling six of the thirteen tap changers with the fuzzy rule based controller, the total number of tap operations made is reduced by 15 %. Diagram 5.1 presents the number of tap operations made at each substation, whereas Diagram 5.2 presents the standard deviations of the voltages at the low-voltage side of the transformers located at the twelve substations. As can be seen in Diagram 5.1, the introduction of the coordinated tap changer control in the test system, led to an increased number of tap operations only in Stjärneholm (SHM).

19

By inspection of Diagram 5.2, it can be concluded that a severe deterioration in voltage quality occurred in Stjärneholm (SHM) and Tomelilla (TLA), while a more modest deterioration in voltage quality was detected in Arrie (AIE) and Trelleborg (TBG). Improved or unchanged voltage quality has been shown in the remaining eight substations. For the results to be completely comparable, the two test system model runs should yield the same voltage standard deviations for each substation bus. However, this is not the case here, and it is difficult to make a comment on how the detected differences in voltage standard deviation for each substation bus influence the simulation results.

from bus

to bus

conventional control

coordinated control

4 8 5 9 6 10 11 14 12 15 13 16 17 19 17 20 18 21 22 24 23 25 26 27 28 29

Table 5.1 During the second run, the derived coordinated tap changer control replaced the conventional tap changer control at six substations. The bus numbers refer to Figure 3.2. The shaded tap changer is blocked at its nominal tap position by assigning the dead-band of the local automatic controller a considerably greater value.

20

0

2

4

6

8

10

12

14

16

BBK SEE ÖLV VBD SJB TLA JSD AIE SLA TBG FVK SHM

Substation

Nu

mb

er o

f T

ap O

per

atio

ns

Conventional TapChanger Control

Coordinated TapChanger Control

Diagram 5.1 The number of tap operations for each substation included in the test system

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

BBK SEE ÖLV VBD SJB TLA JSD AIE SLA TBG FVK SHM

Substation

Sta

nd

ard

Dev

iati

on

of

Vo

ltag

es (

%)

Conventional TapChanger Control

Coordinated TapChanger Control

Diagram 5.2 Standard deviations of the voltages at the low-voltage side of the transformers located at the twelve substations included in the test system.

21

6 How to Continue the Work Since time has limited the extent of this work, there are still many questions to be answered concerning centralized automatic voltage control. In this section, there are two kinds of questions. One kind of questions concerns further evaluation, while the other kind of questions concerns further development. Further Evaluation The coordinated tap changer control method presented in this report has been evaluated by simulating one day’s operation. This does not answer how well this method is suited for different kinds of operating conditions. Thus, one question that needs to be answered is how robust the method is with respect to varying operating conditions. In addition, the robustness of the method with respect to various system configuration changes (power system faults) needs to be examined. It is claimed in this report that the proposed method is especially well suited for large systems, as it is computationally simple. However, this has not been proved in any way and therefore an investigation of the computer power required by the method would be appropriate. Such an investigation should emphasize the computation time and memory required. Prior to a future implementation of a centralized automatic voltage control system, the costs of such a system should be weighed against the benefits. Further Development Further development of the method might include introduction of automatic shunt capacitor switching. A user interface would facilitate adjustments of the rule base. In addition, strategies for how to handle different kinds of control system errors that might appear, such as communication errors, should be developed. When the Time is Ripe When the method is considered sufficiently evaluated and developed, it is suggested to continue the evaluation of the method by carrying out a field test using a prototype of the control system. At an early stage of the field test, it is appropriate to let the controller work in an open loop. The controller should then be considered as a support for decision-making. Through the user interface, the operators should be able to enhance the performance of the controller by working with the rules in the rule base. However, it is recommended that default values for membership function parameters will be used.

22

7 Conclusions In this report, a coordinated tap changer control method, realized in the form of a fuzzy rule based controller, is presented. The rule base of the controller consists of a set of rules, which are formulated in such a way that tap operations are coordinated both to each other and to manually switched shunt capacitors. By means of simulations of a single day’s normal operation, it is shown that the coordinated tap changer control reduces the total number of tap operations, made in the test system, by 15 % compared to conventional tap changer control. In addition, the simulation results indicate that the coordinated tap changer control deteriorates the voltage quality at four out of the twelve substations included in the test system.

23

A Conventional Tap Changer Control Parameters

from bus

to bus

Td0 (s)

Tm (s) Time of the day Vref

(p.u.) DB

(p.u.) 4 8 120 8 1.0615 0.0261 5 9 120 8 1.0615 0.0350 6 10 120 6 1.0615 0.0400

11 14 120 6 1.0700 0.0269 00.00-06.00 1.0850 06.00-22.30 1.1050 12 15 120 6 22.30-24.00 1.0850

0.0323

13 16 120 6 1.0750 0.0234 17 19 120 6 1.1700 0.3230*

00.00-06.00 1.0400 06.00-22.00 1.0500 17 20 120 6 22.00-24.00 1.0400

0.0271

00.00-05.00 1.0700 05.00-06.00 1.0850 06.00-21.00 1.1000 21.00-23.00 1.0850

18 21 120 6

23.00-24.00 1.0700

0.0323

22 24 120 3 1.0750 0.0269 00.00-05.00 1.0750 05.00-23.30 1.0900 23 25 120 6 23.30-24.00 1.0750

0.0269

00.00-06.00 1.0620 06.00-22.00 1.0820 26 27 120 3 22.00-24.00 1.0620

0.0271

00.00-06.00 1.0650 06.00-22.00 1.0850 28 29 120 8 22.00-24.00 1.0650

0.0385

Table A.1 Parameters of the local automatic tap changer controllers, 19 September 2001. *The tap changer between bus 17 and 19 is blocked at its nominal tap position by assigning the dead-band of the controller a considerably greater value. The bus numbers refer to Figure 3.2.

24

B Definition of Primitive Fuzzy Operations function fuznot�

input Real x; output Real y;

algorithm y := (1 - x); end fuznot; function fuzand input Real x; input Real y; output Real z; algorithm z := min(x,y); end fuzand; function fuzor input Real x; input Real y; output Real z; algorithm z := max(x,y); end fuzor;

25

C Definition of Membership Functions function increase� input Real x; “physical process variable” input Real a; “membership function parameter” input Real b; “membership function parameter” output Real y; “fuzzy variable” constant Real pi=3.14159; algorithm y := if x > a then 1 else if x < (a - b) then 0 else 0.5 + 0.5*cos((x - a)/b*pi); end increase; function decrease input Real x; “physical process variable” input Real a; “membership function parameter” input Real b; “membership function parameter” output Real y; “fuzzy variable” constant Real pi=3.14159; algorithm y := if x < a then 1 else if x > (a + b) then 0 else 0.5 + 0.5*cos((x - a)/b*pi); end decrease;

26

D Test System Model Data

from bus

to bus

R (p.u.)

X (p.u.) B (p.u.) n0 (p.u.) stepsize

(p.u.) maxpos minpos

1 5 0.0023 0.0316 2 6 0.0006 0.0134 3 7 0.0193 0.1178 4 5 0.0002 0.0031 0.0010 4 8 0.0206 1.0882 0.0182 9 -9 5 6 0.0006 0.0092 0.0031 5 9 0.0212 1.0912 0.0127 7 -9 6 10 0.0168 1.0882 0.0296 8 -8 7 26 0.0415 0.1264 0.0003 8 32 0.0007 0.0051 0.0000 8 33 0.0007 0.0051 0.0000 9 30 0.0065 0.0330 0.0001 9 31 0.0056 0.0288 0.0001 9 10 0.0089 0.0637 0.0002 9 10 0.0090 0.0636 0.0002 9 13 0.0146 0.0442 0.0001 11 14 0.1820 1.1074 0.0185 9 -9 11 30 0.0027 0.0072 0.0000 12 15 0.2626 1.0883 0.02285 6 -7 12 17 0.0220 0.0633 0.0001 12 26 0.0281 0.0814 0.0002 12 31 0.0075 0.0418 0.0001 13 16 0.0148 0.4423 1 0.0167 9 -9 13 18 0.0089 0.0270 0.0001 17 19 0.1737 1.0883 0.0228 6 -7 17 20 0.1100 1.1170 0.0186 9 -9 17 32 0.0046 0.0239 0.0001 17 33 0.0046 0.0239 0.0001 18 21 0.4168 1.0883 0.0228 6 -7 18 22 0.0078 0.0227 0.0001 19 23 0.0074 0.0199 0.0001 22 24 0.0081 0.2730 1.1074 0.0185 9 -9 22 26 0.0159 0.04290 0.0001 23 25 0.4516 1.0455 0.0175 8 -8 26 27 0.0967 1.1170 0.0187 9 -9 27 28 0.0183 0.0337 0.0001 28 29 0.5917 1.1000 0.0275 4 -4 30 32 0.0010 0.0047 0.0000 31 33 0.0018 0.0088 0.0000

Table D.1Test system model data; the bus numbers refer to Figure 3.2.

27

E Modeling of the Three Winding Transformer in Tomelilla Per unit equivalent circuit The per-unit equivalent circuit of the three-winding transformer in Tomelilla is shown in Figure E.1.

��� ���

���

�

/

+ 0

Figure E.1 The per-unit equivalent circuit of the three-winding transformer in Tomelilla: H indicates the high-voltage side, M indicates the medium-voltage side and L indicates the low-voltage side. XH0, XM0 and XL0 are impedances.

The short-circuit voltages, indicated in the data-sheet, are obtained by performing three tests: Test A: The voltage on the high-voltage side of the transformer, required to obtain

rated current on the medium-voltage side, is measured line-to-line, with the medium-voltage side shorted and the low-voltage side open.

Test B: The voltage on the high-voltage side of the transformer, required to obtain

rated current on the low-voltage side, is measured line-to-line, with the medium-voltage side open and the low-voltage side shorted.

Test C: The voltage on the medium-voltage side of the transformer, required to

obtain rated current on the low-voltage side, is measured line-to-line, with the high-voltage side open and the low-voltage side shorted.

Rated current is calculated as:

VS

Irated

rated

rated ⋅=

3

,3φ

28

The rated current is then transformed to the side of the transformer on which the short-circuit voltage is applied. Thus, the impedances of the per unit equivalent circuit are obtained by solving the equation system below:

⋅

⋅

=+

⋅

=+

⋅

=+

−−

−−

−−

C)(Test

B)(Test

A)(Test

VV

IVV

VXX

IVV

VXX

IVV

VXX

rated,M

ratedH,

2

rated,Lrated,M

rated,L

nl,cs,M0L0M

rated,Lrated,H

rated,L

nl,cs,H0L0H

rated,Mrated,H

rated,M

nl,cs,H0M0H

Note that the last factor on the right side of the equation for Test C is necessary to make the sums of the impedances on the left sides of the equations refer to the same side H of the three winding transformer. Desired Model Figure E.2 illustrates the desired structure of the model of the three-winding transformer in Tomelilla. This structure is simplified in order to obtain the structure of the model used in the simulations. The structure of the desired model comprises one 130/50 kV ideal TCUL transformer and one 130/20 kV ideal TCUL transformer with the tap changers controlled in parallel with respect to the 20 kV voltage.

29

���

+

0 /

��� ���

Figure E.2 Desired structure of the model of the three-winding transformer in Tomelilla: H is the high-voltage (130 kV) side, M is the medium-voltage (50 kV) side and L is the low-voltage (20 kV) side. XH0, XM0 and XL0 are the impedances of the per unit equivalent circuit. The two tap changers are controlled in parallel with respect to the voltage on the low voltage side.

Simplified Model Used in the Simulations Figure E.3 illustrates the structure of the simplified model of the three-winding transformer in Tomelilla. The structure of the simplified model comprises two 130/50 kV transformers, which are connected in parallel.

+

0

��� ���

�� ��+

0

Figure E.3 Structure of the simplified model of the three-winding transformer in Tomelilla: H is the high-voltage (130 kV) side and M is the medium-voltage (50 kV) side. XH0, XM0 and XL0 are the impedances of the per unit equivalent circuit. a) The two transformers in Figure E.2 are connected in parallel. b) The structure of the simplified model used in the simulations.

30

F Load Model Parameters and Profiles

Load profile FVK SLA TLA �s 0.426 0.724 1.28 �t 1.94 1.73 1.92

Tp [s] 172 214 173

s 3.44 4.51 1.32

t 5.45 5.11 2.92 Tq [s] 200 54.3 83.5

Table F.1 Parameter values used for each of the three load profiles

Bus Nbr 8 9 11 14 15 16 20 21 23 24 Load

Profile FVK SLA SLA SLA TLA TLA SLA TLA FVK TLA

Bus Nbr 25 26 27 29 Load

Profile FVK TLA TLA TLA

Table F.2 Load profiles used for each of the loads in the test system model. Bus Nbr refers to the bus numbering in Figure 3.2.

31

G Fuzzy Rule Base

1) tapSEEdown =

[high(V130_TLA) and high(V130_TBG) and high(V130_SEE)]

or

[veryhigh (V130_SEE)]

2) tapSEEup =

[low(V130_TLA) and low(V130_TBG) and low(V130_SEE)]

or

[verylow (V130_SEE)]

3) tapAIEdown =

[high(V130_TLA) and high(V130_TBG) and high(V130_AIE) and not tapSEEdown]

or

[veryhigh (V130_AIE)]

4) tapAIEup =

[low(V130_TLA) and low(V130_TBG) and low(V130_AIE) and not tapSEEup]

or

[verylow (V130_AIE)]

5) onetapTLAdown =

[1 if (pre(connectedcapTLA) = 0 and connectedcapTLA =1) else 0] This rule ensures that the tap changer in Tomelilla makes a downward tap operation simultaneously with a connection of the shunt capacitor in Tomelilla.

6) onetapTLAup =

[1 if (pre(connectedcapTLA) = 1 and connectedcapTLA =0) else 0]

32

This rule ensures that the tap changer in Tomelilla makes an upward tap operation simultaneously with a disconnection of the shunt capacitor in Tomelilla.

7) tapTLAdown =

[high(V50_TLA) and not(tapSEEdown or tapAIEdown or onetapTLAdown or

onetapTLAup)]

or

[veryhigh(V50_TLA) and not(onetapTLAdown or onetapTLAup)]

8) tapTLAup =

[low(V50_TLA) and not(tapSEEup or tapAIEup or onetapTLAdown or netapTLAup)]

or

[verylow(V50_TLA) and not(onetapTLAdown or onetapTLAup)] 9) tapTBGdown =

[high(V50_TBG) and not (tapSEEdown or tapAIEdown)]

or

[veryhigh(V50_TBG)]

10) tapTBGup =

[low(V50_TBG) and not (tapSEEup or tapAIEup)]

or

[verylow(V50_TBG)]

11) tapJSDdown =

[high(V20_JSD) and not (tapSEEdown or tapAIEdown or tapTLAdown)]

or

[veryhigh(V20_JSD)]

33

12) tapJSDup =

[low(V20_JSD) and not (tapSEEup or tapAIEup or tapTLAup)]

or

[verylow(V20_JSD)]

13) tapFVKdown =

[high(V20_FVK) and not (tapSEEdown or tapAIEdown)]

or

[veryhigh(V20_FVK)] 14) tapFVKup =

[low(V20_FVK) and not (tapSEEup or tapAIEup)]

or

[verylow(V20_FVK)]

34

H References [Jantzen, 1991] Jantzen, J. (1991). Fuzzy Control. Technical University of Denmark, Publ. No. 9109. [Karlsson, 1992] Karlsson, D. (1992). Voltage Stability Simulations using Detailed Models Based on Field Measurements. PhD thesis, Electrical and Computer Engineering, Chalmers Institute of Technology, Göteborg, Sweden. Tech. Report no. 230. [Karlsson and Hill, 1994] Karlsson, D. and Hill, D. J. (1994). Modelling and identification of nonlinear dynamic loads in power systems. IEEE Transactions on Power Systems, 9(1):157-163. [Larsson, 1997] Larsson, M. (1997). Coordinated Tap Changer Control – Theory and Practice. Licenciate thesis, Dept. of Industrial Electrical Engineering and Automation, Lund Institute of Technology, ISBN 91-88934-07-1. [Larsson, 1998] Larsson, M. (1998). Reserapport EES-UETP Kurs – Reactive Power Management and Voltage Control. Internal Report, Dept. of Industrial Electrical Engineering and Automation, Lund Institute of Technology (in Swedish). [Wahlqvist, 2000] Wahlqvist, L.-Å. (2000). Spänningsmätning i Horsaryd vid provdrift av SwePol-link. Internal Report ND-0006-023, SYDKRAFT AB, Malmö, Sweden (in Swedish).