Archiv

Archiv ffir Elektrotechnik 71 (1988) 369--380

fllr Elektrotechnik

9 Springer-Verlag 1988

Modelling the operation of voltage control equipment in the reliability evaluation of power distribution systems E. N. Dialynas, Athens

Contents: The reliability assessment of power distribution systems requires the development of modelling and evaluating techniques that reflect the operational behaviour of these systems and evaluate their effect on the consumers. One operating procedure is to transfer load from one substation to others in the event of a failure causing total or partial loss of supply at the load-point being analysed. The aim of this paper is to extend the existing techniques modelling the conceptual ideas of transferable load procedures by describing the models that more efficiently and accurately simulate the capacity limitations of the distribution system feeders and the operation of voltage control equipment. These models recognise the system voltage drop restrictions and the operation of the on-load transformer tap changing facilities, voltage regulators and compensation equipment. The increased information that can be gained from these improved techniques are illustrated by the analysis of a 150/20 kV system based on a real Hellenic transmission and distribution system.

Modelldarstellung fiber das Verhalten yon Ger~iten zur [Jberpriifung der Spannung bei der Zuverllissigkeitsberechnung yon Systemen der Energieverteilung

~bersieht: Die Zuverliissigkeitsanalyse yon Systemen der Energieverteilung setzt die Entwicklung yon Modellen und Berechnungsverfahren voraus, welche die Wirkung des Betriebsverhaltens dieser Systeme und die Berechnung ihrer Wirkung anf den Verbraucher zum Ausdruck bringen. Ein Verfahren, das bei Gesamt- oder teilweisen Verlusten der Sammelschienen angewendet werden kann, wird durch Umschaltung der Belastung vom einen zu anderen Umspannwerken verwirklicht. Diese Arbeit ist eine Studie fiber die Verbesserung yon Modellen bei Umschalten der Belastung. Dadurch wird eine Verbesserung bzw. genauere Ausnutzung des Spannungsfiberwachungsgerites bewirkt. Durch diese Modelle werden die Spannungsgrenzwerte des Systems und die Transformatoren durch Spannungswechsel der Kompensationsgeriite nnd Regelgerite unter Belastung fiberwacht. Die gewonnenen Erkenntnisse dieses verbesserten Verfahrens wurden an einem realen grieehischen 150/20 kV ~bel"tragungs- und Verteilungssystems dargestellt.

1

Introduction

In recent years the development and application of probabilistic modelling and evaluating techniques for power system reliability evaluation have improved considerably and have been the subject of many papers [1]. The emphasis has generally been directed towards the system generation and transmission sections due to the possible total collapse of the system that can be caused by certain failure states in these areas. The ability to assess emergency conditions together with the evaluation of load-point reliability indices have added considerable impetus to reliability evaluation. More recently, reliability evaluation of distribution systems has been considered to a greater extent [2]. :Further considerations are still required, however, particularly since they have the greatest average effect on loss of supply to the consumers [3]. The aim of further developments must be to develop modelling and computational techniques that more truly reflect the operational behaviour of these systems and their effect on the consumers. These techniques must evaluate a suitable set of indices that quantify the reliability performance of system load-points and enchanee the decision making process associated with reinforcement schemes [4]. Computational modelling techniques have already been published [5--7] that evaluate five reliability indices for each load-point of interest (Interruption Frequency /, Interruption Duration d, Interruption Probability U, Load Disconnected per Interruption L, Energy not Supplied per year E) using both total and partial loss of continuity criteria. One operating proeedure in distribution systems is the use of generation whieh is on stand-by and ready to run during certain periods of day. This additional generation is only used in outage conditions to supply the load which can not be supplied through bulk supply points from the generation plants that are run continuously. Reli-

370

Archiv ffir Elektrotechnik 71 (1988) --

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ability models and techniques have been developed [8] that simulate the local generation operation and evaluate its impact on the reliability indices of system load-points. Another operating procedure is to transfer load from one substation to others by disconnecting feeders at their normal source end and closing one or more normally open points. This can be done in the event of either total or partial loss of continuity at the source substation. Modelling and evaluating techniques have been published [5] to translate the conceptual ideas of transferable load procedures into practical analysis. The purpose of this paper is to extend the existing techniques b y describing the models that more efficiently and accurately simulate the operational behaviour of distribution systems and in particular the operation of voltage control equipment and evaluate

their impact on the load-point indices. These models recognise the capacity limitations of the distribution system feeders, the voltage drop restrictions and the operation of the on-load transformer tap changing facilities, voltage regulators and compensation equipment. The increased and more meaningful information of load-point reliability indices that can be gained from these improved techniques is illustrated by the analysis of a 150/20 kV system based on a real Hellenic transmission and distribution system.

2

Features of transferable load

procedures

The hypothetical 150/20 kV system shown in Fig. 1 is based on a real Hellenic transmission and distribution system. It illustrates the complexity of likely

E. N. Dialynas: Modelling the operation of voltage control equipment features in a system and serves as a useful example to demonstrate the developed modelling and evaluation techniques. Both the 150 kV network (superior voltage) and the 20 kV network (inferior voltage) are shown, the main features being: a) a 20 kV feeder can be defined as a series of lines and cables, one end of which is connected to the source substation via a circuit breaker and the other to a normally open point of isolation (switch). Each feeder has a number of load-points distributed along its length. b) the 20 kV feeders can be either interconnected feeders (feeders A, B, C, D, E of substation L31), which are connected through normally open switches to other feeders, or pot-ended feeders (feeder F of substation L31) with no such interconnections. The interconnected feeders can be either connected to one normally open point (normal interconnected feeders, feeders A, B, C, D of substation L31) or to more than one normally open points (teed interconnected feeders, feederE of substation L31). c) loads m a y be transferred from one substation to another b y disconnecting feeders at their normal source end and closing one or more normally open points. This is done only in the event of a failure causing total or partial loss of supply at the source substation and it is not normal practice to parallel sources. d) several alternative and sequential switching actions m a y exist to transfer the load of any given feeder. e) external source points m a y exist to differentiate from the ordinary system sources and ean supply a prespecified amount of load at a n y time it is asked, such as source busbar ES1 supplying the feeder D of substation L31. The duration of the switching procedure on a normally open switch includes the time spent from the instant the failure event occurs till the time the whole procedure is completed. This time depends on the time required for isolating the necessary feeders from the faulted substation, the importance which is placed on restoring the feeder load which is to be transferred through the normally open switch, the location of the switch and the time t a k e n for the engineers to arrive. Since the normally open isolation point is used to transfer the load of at least two feeders from one side of the switch to the other, it is believed t h a t it is more reMistie to indicate two switching times for every open switch to give the times required to transfer load through this point according to the two possible directions of power flow. Computational modelling techniques have been published [5] for identifying all the possible operating procedures which can transfer the load of each system substation to adjacent busbars. If a series of transfer

371

actions causes a feeder to be supplied by more than one route from the same alternative substation, then the transfer actions can, if necessary, be completed sequentially in order to restore the load (compatible actions). If however the transfer actions cause a feeder to be supplied from several substations, then only selective transfers can be made since operationally the paralleling of substations is undesirable. These switching strategies can be illustrated by considering feeder B fed normally from substation L32 in Fig. 1. Three transfer actions are possible to cope with loss of supply at substation L32. (i) Close switch $8 and transfer the load to substation L30 (ii) Close switch $9 and transfer the load to substation L30 (iii) Close switches $9 and $10 and transfer the load to substation L34 (this would require creation of a temporary open point at the teed nearest to substation L30 to prevent paralleling of substations L30 and L34). The options available in this case are therefore (iii) 01% (i) OR (ii) OR [(i) AND (ii)].

3 Modelling the operational behaviour of distribution systems 3.1

General

The t e r m "transferable load" refers to the amount of load t h a t can be transferred away from a system substation to adjacent substations or external source points when an outage prevents the substation from carrying the load t h a t it would normally be required to supply. I n the case of total loss of continuity failure events all the source breakers operate and all feeders are disconnected while in the case of partial loss of continuity failure events, only selective number of feeders are disconnected so t h a t the load of the remaining ones can be supplied. The amount of feeder load t h a t can be recovered during a transferable load action m a y be less than its m a x i m u m demand due to limitations caused b y a) the capacity of the feeder itself b) the capacity of the feeder or feeders through which is being transferred c) the capacity of the source point to which it will be connected d) the voltage limits of the feeder load-points. The first two restrictions depend only on the capacity and loading profiles of the system feeders involved in the transferable action while the other two restric-

372

Archly ffir Elektrotechnik 71 (1988)

tions vary according to the severity of the failure event under consideration and the operational characteristics of system substations at the time the transferable action is completed. The main objective of the computational techniques described in this paper is the more efficient and accurate simulation of system operational behaviour under emergency conditions and the evaluation of the load-points re]lability indices. These simulation techniques recognise the capacity limitations of the system feeders and supply points, the voltage drop restrictions and the operation of the on-load transformer tap-changing facilities, voltage regulators and compensation equipment.

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The feeders in a distribution system consist of a series of lines and cables. The loading and capacity profiles of the feeders are necessary for the analysis of the corresponding transferable load actions because they define the distribution of load along the feeders and the feeders' capacity. The described modelling techniques assume t h a t the loading profile of each system feeder can be either uniform or discrete by specifying the load and distance of up to five discrete points (Figs. 2 and 3). Similarly the capacity profile of a feeder is described by indicating the capacity and the length of up to three rated feeder sections (Fig. 4). 100i ~ o

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If the feeder is treated as a single component only one loading capacity profile is required. However, in the case that a feeder is represented by a number of components one loading and capacity profile must be produced for every part of the feeder identified as a feeder component. If the number of five discrete points for the loading profile or the number of three different sections for the capacity profile can not represent accurately the characteristics of a particular feeder component, two or more feeder components connected in series can be introduced and one loading and capacity profile must be prepared for each of them. The loading and capacity profiles are specified as seen from the substation which normally supplies the feeder load. However, when a transferable action is performed, the loading profile of the corresponding feeder reverses since, in this case, it is seen from the opposite direction (Figs. 2 and 3) while the capacity profile remains the same (Fig. 4). The feeder loading profiles must be also modified to consider the load of the other feeders supplied through them and represent the actual load flowing through them. Figure 5 shows the loading profiles of the feeder in Fig. 3, seen from the two opposite ends. This feeder has a m a x i m u m demand of 4 MVA and supplies feeders with a total load of 6 MVA. The feeder-components which are involved or supplied b y a transfer action are divided into two groups. The first group contains the feeder-components which are normally supplied by the source

E. N. Dialynas: Modelling the operation of voltage control equipment point before the transfer action and the feeder-components which are not involved in the transfer action although their load is supplied through it. Their loading profile is seen fl'om the same end before and after the transfer action is completed and therefore should not be modified. The second group contains all the remaining feeder-components in the transfer action and their loading profile is seen, after the action is completed, from the opposite end. The following algorithm has been developed to evaluate the amount of load that may be transferred from the substation in consideration to adjacent busbars performing a transfer switching procedure and considering only the capacity restrictions of the involved feeder-components : (i) Deduce the order list of feeder-components being supplied and evaluate the load to be transferred

LT (ii) Consider the first feeder-component in the list (a) Modify its loading profile to consider the extra supplied load. (b) Consider its capacity profile and for each capacity rated section evaluate the load flowing through it. If the load is greater than the capacity of the section : consider the feeder component furthest from the source point and its corresponding loading profile (seen from the 0~ or 100% end as appropriate) --drop enough load so that the load flowing through the section is less than or equal to its capacity -- update the loading profile so that it does not include the dropped load and subtract it from

--

Lr -- in the case that the load of this feeder-compo.nent is not enough delete this component from the list and repeat the same procedure. (iii) Repeat step (ii) for each feeder-component included in the updated list. If the component belongs to the second group of feeder-components, firstly modify its loading profile so that it is seen from its remote end. Although a switching procedure in the "inferior" voltage level of a distribution system can transfer load from one substation to another, it is not certain that the substation, to which it is transferred, is capable of supplying the full amount of the transferred load. This may be caused by the limited capacity of the circuits in the "superior" voltage system and in particular when the failure event being analysed also affects other system busbars. The capacity limi-

373

tations of the external source points are analysed by applying the above described algorithm and considering each external source point as equivalent to a feeder component. This component has zero loading data and a capacity profile with only one rated section having capacity equal to the capacity of the source. Another algorithm has been incorporated in the developed computational techniques for simulating the potential failure events of the load-point-being analysed and selecting which of the possible and alternative transfer actions are to be performed [5]. This algorithm simulates the capacity limitations of the system ordinary sources and evaluates the amount of load which can be supplied after each transfer action is completed. The used load flow routine is based on a fast-decoupled load flow program Which has been modified very effectively to incorporate sparsity techniques and a diaeoptieal representation of the simulated outages. These modifications permit a very quick outage simulation with the minimum computer memory requirements.

3.3 On-load trans/ormer tap changing/acilitie8 The basic function of a distribution system is to distribute electric power to consumers at voltage levels which must be within the limits imposed by the national and international standards. When voltage dips occur, corrective measures shall be undertaken within a reasonable time to improve voltages to meet the imposed system requirements. These measures, known as voltage control, include the operation of voltage control equipment, such as the on-load tap changing facilities of the substation power transformers and the feeder voltage regulators, and the use of capacitors banks installed at different locations along the feeder length. These voltage control procedures constitute a significant operational practice during the transferable load actions because higher voltage drops are usually measured due to the fact that the network length has increased significantly and more load is flowing through the system feeders compared with what is flowing during normal operation. In distribution systems the substation transformers are usually equipped with a mechanism for changing the ratio of transformation by increasing or decreasing the number of active turns in one winding with respect to another winding. In normal conditions this ratio remains constant (off-nominal tap setting) while in outage conditions it changes either manually or automatically by selecting the appropriate tap setting until the voltage of the transformer secondary is within the permissible limits. This operation may be conducted without interfering with the load (on-load).

374 In practice the number of tap settings is not infinite (upper and lower tap settings) and the tap adjustment is made in discrete steps. The following computational procedure has been incorporated in the fast decoupled load flow algorithm of the computational techniques [5] evaluating the load supplied to each system load-point under outage conditions so that the voltage of the busbars having on-load tap changing facilities is maintained constant in each performed load flow solution: a) After each iteration and the evaluation of busbar voltages, the tap settings of all system transformers having on-load tap changing facilities are updated so that the voltages of their secondary are as close as they can be to their prespecified values. The conventional adjustment feedback error for a continuous in-phase off-nominal tapping t~ in p.u. controlling the voltage V~ of busbar k at iteration ] to its specified voltage V~p is t~ew = = ~t old + ( v~ - v F ) This new tapping is set equal to the appropriate limit if it lies outside the permissible limits. b) After convergence has been obtained the tap settings are set to the nearest discrete values. c) The iteration procedure starts again but now the tap settings are assumed to be fixed and no change is allowed. This step is not executed when the tap settings of a transformer are assumed to be continuous. The application of the above computational procedure results in a greater execution time for an outage simulation because a greater number of iterations is executed in each load flow solution. A change of the transformer tap settings creates also a different value of the equivalent transformer impedance and the system matrices should be refaetorised in each load flow iteration. In order to prevent significant increase in computing time it is assumed that these changes have negligible impact on the evaluation of system matrices but they are taken into account in the mismatch equations. The operation of on-load transformer tap changing facilities results in different values of the busbar voltages and the power losses along the system branches. It is therefore evident that in outage conditions the values of the load supplied to the load-points of interest will also be changed which may have a significant impact on the partial loss of continuity reliability indices. In order to illustrate this fact, the double 150/20kV transformer system shown in Fig. 6 is analysed. Both transformers are identical with an equivalent resistance of 0.086 p.u., an equivalent reactance of 0.953 p.u. and a rating of 24 MVA. It is also assumed that the tap changing range for both transformers is --20% to -~-20% while the preferable

Archiv ffir Elektrotechnik 71 (1988) 1

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voltage of busbars 2 and 3 is 0.99 p.u. if the voltage of the system source is assumed to be 1.0 p.u. The following four different tapping arrangements have been examined applying the computational algorithm described in reference [5] and the above mentioned modifications: Case I no on-load tap changing facilities, tap setting 0% Case 2 no on-load tap changing facilities, tap setting - - 4 % Case 3 on load tap changing facilities, tap setting 0% Case 4 on load tap changing facilities, tap setting - - 4 %

off-nominal off-nominal off-nominal off-nominal

The load supplied to load-poirlt 2, after an outage on branch 2 has occurred, has been evaluated to be 7.51 MW, 7.76 MW, 8.10 MW, 8.10 MW for the four cases respectively. The similar results of cases 3 and 4 indicate that the values of the initial off-nominal tap settings have no effect on the final results because the developed algorithm evaluates the optimal tap settings irrespective of the initial conditions. However the results of cases 1 and 2 are worse than that of cases 3 and 4 and this fact indicates the usefulness of transformer tap changing facilities in the system operation. Furthermore, the simulation of transformer tap changing facilities provides a more accurate representation of system operation under outage conditions. Cases 3 and 4 took only 5% more computer time to be execured compared with cases 1 and 2, this increase being very small for a more realistic simulation of distribution system operation.

3.4

Voltage drop restrictions

The one-line diagram of a distribution feeder (before or after a particular transferable load action) can be constructed by defining the nodes and the branches of the equivalent network. The "nodes" of the network are the points of load connections, the points of change in the line characteristics and the teed connections while the feeder segments between two nodes are

E. N. Dialynas: Modelling the operation of voltage control equipment defined as "branches". For simplicity reasons, it is assumed that the voltage regulating equipment and the capacitor banks can be only installed at points of load connections. For each transferable load action to be performed, the topology of the equivalent radial distribution network is constructed considering the topology of the feeders involved in the action, the loading and capacity profiles of the feeder components and the existing voltage control equipment (regulators, capacitors). These loading profiles are the updated profiles of load supplied by the action under consideration and are obtained applying the algorithms modelling the feeder capacity restrictions and substation capacity limitations (section 3.3 of the paper). If a component feeder has a uniform distribution loading profile, an equivalent discrete representation can be used for voltage drop calculations assuming that a load Si = S . IJl is connected at the middle point of each capacity rated section i of the feeder, where S, l are the total load and length of the feeder component respectively and li is the length of Section i. The nodes of the equivalent distribution network are numbered sequentially with the only limitation that a node further from the source point takes a number higher than a node nearer to it. This means that because of the network's radiality the power flow is always directed from nodes with lower to nodes with higher numbers. The branches of the network have the same numbers with their receiving ends. This convention allows the storage of network information to a single array whose dimension is equal to the number of branches n (n X 1). The source point takes the number zero and it is not considered in the voltage drop calculations because its voltage is calculated from the "superior" voltage system applying the modified load flow routine described previously. If transformer tap changing facilities are available in the system to control the voltage of the system substations, the routine can also evaluate the actual voltage of the system substations by selecting the appropriate tap settings. This computational procedure may increase the voltage of the substation being the source of the transferable load action under consideration to compensate for the feeder voltage drop. The branch current flows can be easily calculated from matrix eq. (1) which is a simple application of the basic network analysis [I] ---- [A]. [J]

(1)

where J, I are the vectors of the load and branch currents respectively with dimension (n X 1). The elements Aij of the incidence square matrix A (n X n) describe the network topology and can be either zero or one only when the node j is fed via the branch i.

375

The network complex impedance Z (n • n) is equal to [Z] = [A] T [Zb] [A]

(2)

where Zb is a diagonal (n • n) matrix, the elements of which are the complex impedances of the corresponding network branches. The voltage Vk of node k (/c = 1, 2 . . . . , n) can be evaluated from the following equation V~ = Vo -- z~V~ = Vo -- ~ Z~yJj

(3)

j-1

where V0 is the voltage of the source substation. This equation can be easily modified to include the effects of installed capacitor banks and voltage regulators. If Jc represents the vector (n X 1) of the capacitor infeeding currents at the corresponding nodes, Eq. (3) can be modified to the following one Vk = Vo -- ~ Z~j(J1 + Jcj) 1=1

(4)

Furthermore, if a voltage regulator is connected at node m, the eq. (4) is modified to the following one Vo -- ~ Z~j(Jj + Jcj) Vk=

for ]c < m

n

V o - - ~ Z k j ( J j + J c 1 ) 4- V,,. R V for/c>_m j--1 100 -

-

(5) where R V is the percentage upper limit of voltage regulation. This equation can be applied sequentially for all the voltage regulators connected at the nodes of the equivalent network. However, in practical distribution systems the maximum number of voltage regulators connected to each feeder is one and this equipment is regulated to operate in only one direction of power flow (power flow during normal operating conditions). Therefore, the equivalent network after a transferable load action will contain one voltage regulator, at the maximum, because the regulator, which is connected to the feeder whose load is transferred, is short-circuited. It should be noted that the above analysis considers the current loads independent from the voltage changes in the "inferior" voltage system and evaluates them as having the same per unit values with the corresponding inputted power loads. However, the error introduced by this assumption is negligible because, in practice, the voltage changes are less than 5% of the nominal values while the precision with which the magnitude of load can be estimated is significantly lower. The following computational algorithm has been developed to evaluate the load which can be trans-

376 ferred during a particular transferable load action by considering all the necessary voltage control procedures which can be taken to ensure that the feeder load is supplied at satisfactory voltage levels: (i) Construct the topology of the equivalent radial network (incidence matrix A) and the vector o f load currents by considering the loading and capacity profiles of the feeder-components contained in the action. (ii) Evaluate the network complex impedance Z applying eq. (2) and deduce the vector of infeeding capacity currents Jc and the connection point m of the voltage regulator (if any) from system data. (iii) Evaluate the voltage at each node of the equivalent network applying eq. (5). (iv) Consider the last node in the list and compare the voltage of all nodes with the prespecified lower voltage limit of system load-points. If one at least node voltage is less than the limit: a) drop the load at the node being considered and omit the node from the network list of nodes b) if it is operationally appropriate disconnect the capacitor and/or voltage regulator which is connected to the node (if any) c) if the node is a fictitious node of a feeder component with uniform distribution profile drop its load in 10 steps d) update the vectors of load J and capacitor Jc currents respectively and the position of the voltage regulator so that they do no include the disconnected load and equipment. These steps are not executed if the last node belongs to the main line of the equivalent network and the voltage of one or more nodes belonging to the laterals of the network is less than the prespeeified voltage limit. (v) Repeat steps (iii) and (iv) until the voltages of all the nodes in the system are greater or equal to the prespecified lower voltage limit. Evaluate the load to be transferred by summating the loads in vector J for all the nodes belonging to the feeder being transferred. The first two steps of the above algorithm are executed once for each load-point being analysed while the other three steps are executed for each simula ted failure event. The voltage V0 of the source substation used in step (iii) of the algorithm is obtained applying the load flow routine under the respective system topology, loading and generation conditions. If transformer tap changing facilities exist in the source substation, the algorithm described in the previous section of the paper is used and the substation specified voltage is the preferred voltage under either

Archiv fiir Elektrotechnik 71 (1988) n o r m a l or emergency conditions. The upper voltage limit sustained by the inferior voltage system loadpoints may be used as the voltage under emergency conditions which results in less load disconnected due to the system capacity restrictions. After completing the simulation of all the available transfer actions and evaluating the load supplied by each of them, the incompatible actions which are selected to be performed are the ones which achieve the greatest reduction in energy not supplied to the load-point being analysed. The five reliability indices

Input the system data - system topology, busbar loadings, branch data component r e l i a b i l i t y data, transfer switching data, external sources 1 capacity data, loading and capacity profiles of the inferior voltage feeders, data of voltage control equipment l

=V Choose a load-point of interest I

T Deduce all possible load transfers and their compatibility, identify I priority order of switching and associated switching times

]

For each transferable load action, consider the capacity restrictions of the involved feeders and update their loading profiles

T Identify all

failure

events l I

I Consider a failure event and simulate the outage 1 I

Partial Loss of Continuity

/ ~

I

Total Loss of

:

= Continuity I I

Identify the feeders to be disconnected and the possible transferable load actions, identify the new priority order of switching and I associated switching times

I Disconnect all the feeders

L

J

] NO.t / / ~ YES

Transformer tap changing facilities

~

Identify the preferred voltage of substation ~econdaries (normal or emergency conditions)

For each possible transferable load action, identify its source point and evaluate the load supplied by i t considering the source and network capacity limitations

v Construct the topology of the equivalent radial network and evaluate the amount of load to be transferred.considering the voltage droprestrictions

V Specify the transfer actions to be performed, the priority order of switching and the associated tranpfarred load. Evaluate the r e l i a b i l i t y indices of the fail~re event being considered .mYES . ~

Any other failure events O

I Evaluate the r e l i a b i l i t y indices of the

L

YES < ? >

load-point

being considered

Any other load-points ?

N

Fig. 7. Flowchart showing tile compubwtional modelling techniques

E. N. DiMynas: Modelling the operation of voltage control equipment

377

of each l o a d - p o i n t of i n t e r e s t are e v a l u a t e d a p p l y i n g t h e d e v e l o p e d r e l i a b i l i t y models s i m u l a t i n g t h e o p e r a t i o n of t r a n s f e r switchings [5].

and was t e s t e d on a C Y B E R 171 c o m p u t e r a nd a P R I M E 2250 m i n i - c o m p u t e r . A c o m p l e t e f l o w c h a r t of these t e c h n i q u e s is sh o w n in Fig. 7.

3.5 Flowchart o/the computational techniques

4

Th e c o m p u t a t i o n a l t e c h n i q u e s described in this p a p e r h a v e been i m p l e m e n t e d efficiently into a comp u t e r p r o g r a m which was w r i t t e n in F O R T R A N 77

To illustrate t h e increased an d more m e a n i n g f u l results t h a t can be a c h i e v e d f r o m t h e use of t h e p r e v i o u s l y described c o m p u t a t i o n a l techniques, t h e 1 5 0 / 2 0 k V

Analysis of a typical system

Table 1. Branch data (Per Unit Base 100 MVA)

Branch (S.E.-R.E.)

Resistance

Reactance

Susceptance

Rating

or Line Type No.

in p.u.

in p.u.

in p.u.

in MVA

Type 1 100 km Type 2 100 km Type 3 100 km Type 4 100 km Type 5 100 km 18--19 26--32, 22--29, 28--34 23--30, 24--31, 26--32 22--29, 27--33

0.081 0.043 0.043 0.032 0.060 0.0 0.144 0.027 0.027

0.198 0.187 0.174 0.056 0.064 0.0 0.864 1.624 1.624

0.058 0.062 0.066 1.837 1.271 0.0 0.0 0.0 0.0

138.0 202.0 202.0 133.0 88.0 450.0 25.0 12.5 12.5

Table 2. Busbar loading and generation data Busbar No.

1

17

18

19

3

5

2

4

7

8

47.0 35.7 62.0 22.1

29.1 18.0

22.1 13.7

28.4 20.0 1 7 . 6 10,0

225.5 275.4 0.0 63.7 7 2 . 1 28.2

0.0 23.4

il

14

15

20

Load in MW in Mvar

0.0 0.0

0.0 0.0

145.4 21.2

56.9 7.2

2.9 1.8

Generation in MW in Mvar Busbar No.

9

10

12

13

21

Load in MW in Mvar

14.2 8.8

Busbar No.

29

318.6 5.7

21.8 13.5

30

31

5.9 3.7

6.6 4.1

0.75 0.84 1.03 0.84 1.21 1.23

7.7 4.8

19.4 12.0

3.8 2.4

32

33

34

10.9 6.8

11.2 6.9

6.2 3.8

0 . 8 1 1.36 1.05 3.14 1.43 1 . 6 1 1.55 1 . 7 8 1 . 6 1 2.29 0.15 0.72

3.24 2.04 3.07 1.87 0.98

0.68 1.19 0.77 0.94 1.53 1.09

30.6 19.0

7.5 4.6

Load in MW in Mvar Demand of feeder code in MW

13.3 8.2 A B C D E F

1.74 2.76 2.15 3.68 1.94 1.03

Busbar No.

ES1

ES2

ES3

ES4

ES5

ES6

ES7

ES8

Capacity in I~IVA

2.0

1.0

1.5

1.0

1.5

1.9

3.6

2.5

6.8 4.2

14.5 9.0

378

Archiv ffir Elektrotechnik 71 (1988)

Table 3. Component reliability~dgta Index

->

Permanent Failures Independent

Temporary Failures

Maintenance

Common Mode

Component

Frequency / in 1/100 a

Time r in h

Frequency /cm in 1/100 a

Time rcm in h

Frequency /' in 1/100 a

Time r' in h

Frequency /m in 1/100 a

Time rm in h

line 1 km transformer cable 1 km 150 kV breaker 20 kV breaker isolator busbar 1 km

0.18 13.14 0.85 7.75 10.41 1.33 2.23

33.0 89.0 96.0 21.0 28.0 50.0 19.0

0.12 --

28.0 --

0.06 4.72

0.3 1.5

0.2 0.5

i h/km 19.0

0.5 0.5 0.5 0.5

11.0 17.0 3.0 4.0

Table 4. Transfer switching data Normally Open Switch

Busbar*

Time in h

Busbar*

Time in h

Normally Open Switch

Busbar*

Time in h

Busbar*

Time in h

S1 $2 $3 $4 $5 $6 $7 $8 $9 S10 Sll

ES1 L31 L31 L31 L31 L32 L32 L32 L32 L30 L32

5.2 3.1 4.0 0.7 1.0 0.5 1.5 2.1 2.7 1.8 3.1

-L30 L30 L32 L33 L33 L29 L30 L30 L34 L34

-4.2 3.7 0.8 0.5 1.5 0.5 1.8 2.9 3.5 4.8

S12 S13 S14 $15 $16 $17 $18 $19 $20 $21 $22

L32 L33 ES5 L29 ES4 ES3 ES8 ES6 ES7 ES2 L31

2.4 2.2 3.3 4.1 0.7 1.2 4.3 3.4 2.1 1.9 1.7

L29 L29 -L34 ------L33

3.1 5.1 -2.6 ------1.9

* to which load is transferred

t r a n s m i s s i o n a n d d i s t r i b u t i o n system shown in Fig. 1 was analysed. This s y s t e m consists of 34 busbars, 6 150/20 kV substations, 52 150 kV branches, 29 20 kV branches a n d 288 components. There are 8 e x t e r n a l sources, 22 n o r m a l l y open switches, 43 feeder comp o n e n t s , 15 capacitors a n d 2 voltage regulators. The b r a n c h a n d b u s b a r loading a n d g e n e r a t i o n d a t a are given i n Tables 1 a n d 2 respectively while the reliability a n d m a i n t e n a n c e indices of the system c o m p o n e n t s can be extracted from Table 3 t a k i n g i n t o a c c o u n t the l e n g t h of lines a n d cables shown i n Fig. 1. The i n t e r r u p t i o n frequencies (/, /cm, /', /m) are g i v e n i n failures per one h u n d r e d years. All system t r a n s f o r m e r s have t a p c h a n g i n g facilities, r a n g i n g from --15~o to + 1 5 % in 24 discrete steps. The switching t i m e of all system c o m p o n e n t s is assumed to be 0.5 hours a n d the stuck b r e a k e r p r o b a b i l i t y 0.001. Also, the source a n d the n o load p o i n t s are assumed to be 100~ reliable. The s y s t e m t r a n s f e r switching d a t a are shown in T a b l e 4. F i n a l l y , the r a t i n g s of all system capacitors

is 450 k v a r except those m a r k e d with a n asterisk in Fig. 1 which are 300 kvar, while the two system regulators have a n 8~ u p p e r limit of voltage regulation. The five reliability indices of all the 20 kV loadpoints have b e e n e v a l u a t e d a s s u m i n g t h a t the lower voltage l i m i t of feeder l o a d - p o i n t s is 0.95 p.u. a n d the preferred voltage of s u b s t a t i o n secondaries u n d e r n o r m a l conditions is 0.98 (specified voltage). These results are presented i n Table 5. I n order to illustrate t h e i m p a c t of s y s t e m p a r a m e t e r s a n d voltage control e q u i p m e n t on the reliability performance of distrib u t i o n system load-points, the system i n Fig. 1 was studied for the following eight cases: Case1 system as i n Fig. 1 Case 2 no voltage drop restrictions are considered Case 3 no voltage regulators exist Case 4 no capacitor b a n k s exist Case 5 no voltage regulators a n d capacitor b a n k s exist Case 6 as i n case 5 b u t the lower voltage limit of

E. N. Dialynas: Modelling the operation of voltage control equipment

379

Table 5. Reliability indices of system load-points Index -~ Loadpoint No.

[ in 1/a

d in h

U in h/a

L in MW

E in iKWh/a

29 30 31 32 33 34

1.108 1.030 0.815 1.290 1.057 0.516

1.137 1.238 1.443 3.780 11.153 31.790

1.260 1.275 1.176 4.876 11.785 16.377

5.094 2.996 2.699 1.879 1.653 2.278

6.417 3.820 3.173 9.162 19.479 37.313

r

Table 6. l~eliability indices of load-point L32 Case

Index ] d U L E

in in in in in

1/a h h/a MW MWh/a

1

2

3

4

5

6

7

8

1.290 3.780 4.876 1.879 9.162

1.290 3.780 4.876 1.071 5.223

1.290 3.780 4.876 2.070 10.092

1.290 3.780 4.876 2.335 11.385

1.290 3.780 4.876 2.498 12.179

1.290 3.780 4.876 1.918 9.354

1.290 3.780 4.876 1.071 5.223

1.307 4.616 6.032 2.477 14.943

feeder-load points is assumed to be 0.92 p.u. (instead of 0.95 p.u. assumed in case 1) Case 7 as in case 5 but the upper voltage limit of feeder-load points is 1.05 and it is assumed to be the specified voltage of source substations during the transfer actions (emergency voltage) Case 8 as in case 5 b u t all system transformers have no tap-changing facilities The five reliability indices of load-point L32 were evaluated for each of the above eight cases and the obtained results are presented in Table 6. These results clearly indicate t h a t the restoration capability of distribution systems and the associated reliability performance of the system load-points is significantly affected by the existing voltage control equipment and the imposed consumer supply requirements. The /, d and U indices of cases 1--7 are identical because the voltage drop restrictions and the operation of capacitor and voltage regulators affect only the transferable load capability of the system and therefore the indices L and E. However, the operation of transformer t a p changing facilities also changes the load supplied b y the superior voltage system and therefore all the load-point indices are affected (case 8). Furthermore, the modelling of voltage drop restrictions has added significant degree of precision to the evaluation of the Energy not Supplied index E as it can be seen comparing the result of case 2 (5.223 MWh/a) with the corresponding ones of all the other cases (increase by 133.2% in case 5). I t is therefore evident t h a t the

described in the paper modelling techniques provide a more accurate simulation of distribution system operational behaviour and efficiently evaluate the impact of the voltage control equipment on the system reliability performance. This means t h a t voltage control equipment can be considered as alternative reinforcement schemes to improve the reliability of a load-point. Finally, more detailed sensitivity studies can be also executed to identify the effect of each system parameter individually. 5

Conclusions

Measurement of the improvement in system reliability due to reinforcement or operational changes is the prime objective of a n y reliability study. This can then be associated with the cost of such changes and hence the benefits (or disbenefits) which accrue can be determined. I n order to achieve this the reliability assessment must essentially be both realistic and practical. The models and evaluating techniques described in this paper meet these criteria because they extend the existing techniques by simulating more efficiently and accurately the operational behaviour of power distribution systems and evaluating its impact on the reliability performance of system loadpoints. The developed techniques recognise the capacity limitations of distribution system feeders, the voltage drop restrictions and the operation of voltage control equipment. Finally, using these improved

380 techniques a system p l a n n e r is able to i n c l u d e a n u m b e r of new r e i n f o r c e m e n t options i n his reliability assessment which is n o t possible using previously published models.

References 1. IEEE SubCommittee Report: Bibliography on the application of probability methods in power system reliability evaluation. IEEE Trans. Power Appar. Syst. PAS-97 (1978) 2235--2242 2. Allan, R. N. ; Billinton, R. ; Lee, S. :H. : Bibliography on the application of probability methods in power system reliability evaluation. IEEE Trans. Power Appar. Syst. PAS-103 (1984) 275--282 3. Dixon, G. F. L.; Hammersley, H. : Reliability and its cost in distribution systems. IEE Conf. on Reliability of Power Supply Systems, 1977, IEE Conf. Publ. 148, pp. 81--84 4. Allan, R. N. ; Homer, I. R. ; Dialynas, E. N. : Reliability indices and reliability worth in distribution systems. EPRI Workshop on Power System Reliability Research Needs and Priorities, Asilomar, California, March 1978, EPRI Pub. WS 77-60, pp. 6.21--6.28

Archiv ffir Elektroteehnik 71 (1988) 5. Allan, R. :N. ; Dialynas, E. N. ; :Homer, I. R. : Modelling and evaluating the reliability of distribution systems. IEEE Trans. Power Appar. Syst. PAS-98 (1979) 2181-2189 6. Billinton, R.; Allan, R. N.: Reliability evaluation of power systems. London: Pitman Books Ltd., 1984 7. Allan, R. N.; Dialynas, E. N.; Homer, I. R.: Modelling common mode failures in the reliability evaluation of power system netowrks. IEEE Winter Power Meeting, New York, 1979, Paper A 79040-7 8. Dialynas, E. N. ; Allan~ R. N. : Local generating facilities in the reliability evaluation of power distribution systems. IEEE Trans. Power Syst. PWRS-1 (1986) 62--67

Received January 14, 1988

E. N. Dialynas National Technical University Department of Electrical Engineering 42, 28th October Street Athens, 10682 Greece