Voltage reactive security analysis in power systems with automatic secondary voltage control

D.S. Popovic M.S. Calovic V.A. Levi

Indexing t e r m : Critical contingencies, Iteration screening, Power sysrem voltage control

Abstract: The complete methodology for the steady-state voltage/reactive security analysis of power systerns with automatic secondary voltage control is proposed. Both the decentralised and the co-ordinated control concepts are incorpor- ated in a comprehensive procedure, consisting of three principal steps: contingency selection, con- tingency analysis and corrective control. The con- tingency selection stage is based on the extended load flow model and a new voltage/reactive per- formance index. The contingency analysis is per- formed next, by using either the extended load flow model (for decentralised control), or the optimum power flow model (for co-ordinated control). Finally, a simplified linear programming model for corrective resetting of pilot-bus set- point voltages is proposed with the aim to increase voltage security margins. The complete methodology was verified on the eastern part of high-voltage power system of former Yugoslavia.

Introduction

In recent years, ever increasing attention has been given to automation of the overall system voltage/reactive control through the introduction of various multilevel hierarchical control concepts. The development of the three-level voltage control system, recently realised in France and Italy [l, 23, is particularly important since its second level is a fully automatic secondary voltage control (SVC) concept superimposed onto the first level: the primary voltage control. Until now, the SVC system has gone through two development stages: the first is the decentralised secondary voltage control (DSVC) applied in systems consisting of several mutually independent, compact zones [:1]. It is a decoupled control of pilot-bus voltages in individual control zones with the aid of common output signals from secondary voltage regula- tors. The second development stage is the co-ordinated secondary voltage control (CSVC), introduced when a meshed system becomes an indivisible entity [l, 31. This general multivariable control concept is based on the

0 IEE, 1994 Paper 9744C (PI]), first received 14th October 1992 and in revised form 21st May 1993 The authors are at the University of Novi Sad School of Engineering Sciences, 21000 Novi Sad, Yugoslavia

IEE Proc.-Gener. Transm. Disrrib., Vol. 141, No. 3, May 1994

common regulation of all pilot-bus voltages, which is affected by controlling unit reactive generations and by respecting the voltage limits at a reduced set of network buses.

The methods and procedures for the steady-state voltage/reactive security analysis consist of two individ- ual stages : contingency selection, and contingency analysis. In the contingency selection stage, a fast screen- ing method is applied to select the most dangerous con- tingencies, or to rank them according to their severities. In the contingency analysis, detailed AC power studies are applied only to the set of selected potentially critical cases. Today there are three different approaches dealing with the contingency selection problem: direct ranking [4], ranking by 1P-1Q iteration screening [SI, and fast screening by using a local (bounded) solution [ 6 ] . All these contingency selection and analysis methods are based on the standard load flow model, since they take into account only the effects of the primary voltage control. No attempt was ever made to incorporate the SVC in these algorithms, since no general SVC concept was established.

This paper extends the models and procedures for the voltage/reactive security analysis to power systems with automatic SVC. The research was motivated by the desire to explore potential advantages of automatic SVC over the primary control concept alone, and to develop appropriate mathematical tools suitable either for the analysis of security problems in a study mode, or as a software support in real-time applications. The main topic of this paper is the consideration of voltage/reactive security problems within the frame of CSVC, but it also includes the generalisation of recently published results dealing with DSVC [7].

The complete methodology is divided into three sequential stages: contingency selection, contingency analysis, and corrective control. The contingency selec- tion is the 1P-1Q screening algorithm applied to the pro- posed extended load flow model, where common output signals from secondary voltage regulators are introduced as unknown variables. Moreover, it is shown that selec- tion and ranking of contingencies can be done only by using the newly proposed voltage/reactive PI defined through these variables. The detailed contingency analysis of systems with DSVC is performed with the aid of the extended load Row model, while the corresponding analysis of systems with CSVC uses the optimum power flow model with a suitably chosen voltage/reactive security objective function. After a set of critical contin- gencies is determined, corrective control measures, aimed

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for the voltage/reactive security enhancement, should be implemented. One of principal measures is the corrective resetting of pilot-bus set-point voltages, which can be evaluated by using the proposed linear programming model. Finally, the verification of the developed method- ology is done on the power system of the eastern part of former Yugoslavia, through the comparative simulation of the primary control, DSVC and CSVC actions.

2

2. I Decentralised control The essential principle of DSVC is the division of the network into distinct, nonoverlapping compact zones and the decoupled, decentralised control in each of them. The SVC is performed by controlling the voltage in one par- ticular point of the zone, referred to as a pilot-bus. It is realised by forming the common output signal from the secondary voltage regulator, whose input is the pilot-bus voltage deviation

Review of pilot-bus secondary voltage control concepts

1 = 1 , 2, ..., L (1)

N,( t ) = common output signal from secondary voltage regulator in zone 1

Pl, 7, = integral and proportional secondary regulator gains, respectively

V f E F , Vf = set-point and rated values, respectively of pilot-bus voltage in zone 1

V(T), V;(t) = actual and average (of three consecutive measurements) pilot-bus voltages, respectively, in zone I

L =total number of control zones in the system.

The common output signal N,(t) acts through the refer- ence inputs of automatic voltage regulators on all selec- ted generating units within zone 1 in such a way that all generators operate with the same portion of the maximum reactive power that they can produce. The reactive outputs of these units change according to the formula

Q, = Q: + N , A Q ~ " i E acl 1 = 1,2, .. ., L (2)

QP = base-state reactive injection of all regulating units connected to bus i

N , = steady-state value of common output signal NXt + CO), from now on called uniform reac- tive generation level (URGL)

AQP"" = reactive regulating range of all units con- nected to bus i

a,, = set of bus indices with regulating units in zone 1.

The uniform reactive loading of all generators in a zone enables the elimination of large reactive circulations between individual units within a zone, and prevents the excessive reactive loading of units which are close to the location of a disturbance. Consequently, this feature of SVC provides the uniform reactive margins on regulating

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generators and higher level of system security. In case of a voltage/reactive disturbance, all regulating units within a zone participate in its compensation, and the relation between voltage changes and the reactive generations is much more linear than in case of the primary voltage control. Thus, voltage deviations of all nodes within a zone are directly proportional to the corresponding URGL. This idea will be exploited in the following Section for the specification of a new voltage/reactive P I .

2.2 Co-ordinated control When a transmission network becomes too meshed, causing difficulties to define appropriate noninteracting zones for decoupled voltage control, DSVC may not provide the satisfactory voltage profile in certain network portions. These problems were the incentive for the implementation of the CSVC concept [l], which remains on the regional level (the region is formed of several strongly coupled zones). The basic operation principle of CSVC is the multivariable control of several pilot-bus voltages, by using all regulating units within a region. In addition, voltages at a limited number of network buses, called critical buses, are monitored by this control system [3]. The control of pilot-bus voltages is performed within the time interval of two minutes in a stepwise manner: the quadratic security function subject to a set of linear constraints is cyclically minimised (every 10 s). In mathe- matical terms, this control law [3] is

T min z = 1 [ ~ ~ V R E F - y ) - 1 c:: AVk i t OlPYQ k t q

+ r . 1 [ V d q R E F - Qi/QT"") - 1 c?k AV*]' I E Z G k e z o

ai, Qi + C f k A 6 + bi, Ay < ci, [ k s o c 1 i E aG j = 1, 2, 3, 4 (3c)

1AK.l < A V ? i E a, (34 a p y p , aG, ac = sets of indices of pilot buses, gener-

ator buses (aG = U:=, aGI) and criti- cal buses, respectively

S i , v i = regulator gains that allow the deter- mination of closed-loop time con- stants

V f E F , h, A V = set-point voltage, actual voltage and voltage deviation at bus i, respect- ively (superscript max denotes corres- ponding limit value)

Cr', C f k , Crt = (i, k)th elements of sensitivity matrices linking pilot-bus voltage deviations, reactive injection devi- ations, and voltage deviations at critical buses, respectively, with the changes of generator terminal volt- ages P I

r, h = weighting factors Q i , Q Y = actual and limit reactive generations,

respectively, at bus i

I E E Proc.-Cener. Transm. Distrib., Vol. 141, No. 3, May 1994

ai, j , hi. j , ci, = parameters defining the linear form of ith generator operating domain (there are typically four such limits)

qREF = reference value of relative reactive generations within a region, defined by the expression

The constraints in expr. 3 b d of the optimisation model encompass the following operation limits: voltage limits at all monitored critical nodes, linearised operating domains of all regulating units and limits imposed on the variation of generator terminal voltages in one control step, respectively. The only unknown variables in the model of expr. 3 are voltage deviations A V , i s a,, since the quantities v , i E (apvn U a, U ac) and Q i , i E a, are the measurements from the previous instant in the control sequence.

In the objective function (eqn. 3a), the favourisation of the minimum voltage deviations of pilot-buses over the minimum deviation of relative reactive generations from the uniform distribution, or the minimum deviation of control variables, is achieved by the proper choice of weighting factors r and h. In that respect, a power system with CSVC can be found in one of three operating states:

(SI) Pilot-bus voltages are maintained on their set- point values, with no violation of voltage constraints at critical buses. Reactive generations are distributed around the uniform level within a region.

(S2) There are minimum deviations of some pilot-bus voltages with respect to their set-point values, and no violations of voltage constraints at critical buses.

(S3) Critical bus voltages cannot be maintained within specified limits.

State SI is the desired steady state, since there is no devi- ation from the optimum voltage profile defined by the system tertiary control, and suitable reactive margins are provided. State S2 is still secure, but it deviates from the optimum voltage profile. Finally, state S3 is the insecure state, because the violation of voltage constraints at criti- cal buses cannot be compensated by CSVC.

It should be noted that the correlation between S1 states and steady states formed after the DSVC action exists. Namely, all secure DSVC states where the pilot- bus voltages are returned to their set-point voltages with no violation of voltage constraints at critical buses and with the strict uniform distribution of reactive gener- ations within zones, are the subset of S1 states. This idea will be used in the following Section to apply the pro- posed PI for the reduction of the set of potentially critical contingencies that need to be further analysed (CSVC concept).

3 Survey of mathematical models

3.1 Extended load flow model The DSVC described in the previous Section is essen- tially the remote voltage control by regulating gener- ators. Mathematical modelling of this control in the load-flow calculations is based on the error-feedback adjustments of control variables outside the [E] matrix during the fast-clecoupled load-flow (FDLF) solution procedure [8]. It is performed by calculating appropriate sensitivities between pilot-bus and regulating unit volt- ages, and by solving the second, auxiliary iteration.

I E E Proc.-Gener. Trunsm. Distrib., Vol. 141, No. 3, M a y I994

However, since several generators participate in the SVC of the pilot-bus voltage in each of control zones, the vector of incremental reactive mismatches is not very sparse and the fast forward substitution (FFS) cannot be applied efficiently. Moreover, the corresponding sensi- tivity coefficients should be computed each time a new topological contingency is dealt with.

The extended load flow model was developed to over- come the shortcomings mentioned [7]. The unknown URGLs are introduced into the load flow model as state variables, enabling the direct assessment of the SVC action after the first FDLF iteration. To do this, the set of bus types is extended (Table l), so that beside the

Table 1 : Classification of bus types and attributed variables

Typeof nodes (OV) (PO) ( P V ) ( W O ) (P)

Known variables 8, V P, O P. V P, V, 0 P Unknown variables P. 0 8. V 8, 0 8, N 8, v

standard types of buses, two additional bus types are included: (PVQ) bus, being a pilot-bus, and distributed ( P ) buses that constitute a group of generator buses par- ticipating in the SVC. The extended load flow model is then derived from the standard model by taking into account the reactive power balances at all distributed ( P ) buses (eqn. 2), and by substituting the prespecified volt- ages at all (PYQ) buses with the corresponding URGLs (N,, 1 = 1, 2, ..., L). The solution of this model is obtained with the aid of the FDLF method. Then, the numerical symmetry of the [E] matrix is violated, while the incidence symmetry is retained. In the developed computer code, ordering and symbolic factorisation are uniform for both [E '] and [B"] matrices.

3.2 Optimum power flow model with voltagelreactive security objective function

As mentioned in the previous Section, the CSVC action is accomplished by the sequential application of the linear- ised optimisation model of expr. 3. In this paper, the voltage/reactive analysis of CSVC is performed by means of the nonlinear optimisation model to obtain the final steady-state. Within the frame of mathematical pro- gramming the whole problem can be stated as follows

E (Vi - VPEF)' + r 1 (Qi/QYx - qREF)' min z = i E LIPYQ i = q

gq(x, U) = 0 i = 1, 2, . .., n

g:(x, U) = 0 i = 1, 2, . .., n (56)

(54

QY'" < Qi < Qp" i E a, (54 VY'" < < V y i E (a, U a,) ( 5 4

where gq(x, U), g;(x , U) is the pair of active and reactive injection equations at bus i. In this model, the equality constraints (eqns. 56 and 5c) define the active and react- ive load-flow balances at all system buses, while the inequalities (expr. 5d and 5e) encompass reactive gener- ation limits of regulating units, and voltage limits at gen- eration and critical buses. It is assumed that all active

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generations (except at slack bus) are known in advance, so that the state variables ( x ) are the voltage phasor angles (ei, i = 1, 2, . .., n) and magnitudes (vi, i = 1, 2, . . . , n, i uC) and reactive outputs of regulating units ( Q i , i E uG), while the only control variables (U) are the ter- minal voltages of regulating units ( q , i E aG). The problem (expr. 5 ) is solved by forming the extended Lag- range function

U x , U, j., P) = z - I: $(x, U) - LTgV, U) - pC'fb(x, U) (6)

where I,, A,, p are vectors of Lagrange multipliers, and f , ( x , U) is the vector of the active constraints (expr. 5d and 5e). The necessary optimality conditions require that the gradient of the extended Lagrange function (eqn. 6) should be equal to zero (VL(x , U, I, p) = 0). In this way, the system of nonlinear equations is obtained and it is solved by the second-order Newton's iteration method. The recently developed computer code [9] is suitably modified to encompass specific features of the expr. 5 model.

3.3 New voltagelreactive performance index When all regulating units in one zone generate the same relative reactive output, the voltage/reactive PI can be defined in the following way

PI,, = wYil - VlimI/V]im + w , I N , - 1 I (7) i e a v l s o N l

U , = set of all buses with violated voltage con- straints

w v i , w, = weighting factors h , V;'" = actual voltage and voltage limit, respect-

U; = set of indices of all zones, where the absol- ively, at bus i

ute value of URGLs 2 1

It can be easily shown that in the case of properly chosen weighting factors, the PI,, (eqn. 7) and the standard P I p , [ 5 ] are the same [7]. However, since the direct correlation between voltage changes and the URGLs exists, the selection of potentially critical contingencies can be performed by using these levels only. Thus, it is possible to define a new, simplified voltagelreactive PI based on the weighting average of the deviations of the URGLs with respect to certain threshold values, below which no violation of voltage constraints exist

Ulim - , -set of indices of all zones, where absolute values of URGLs are 2 threshold value

NYm = threshold value of URGL bellow which all bus voltage changes are within specified toler- ances.

The proposed PI , is used to rank potentially critical con- tingencies in systems with DSVC, and to select them in the case of the CSVC concept (all steady states where PI, # 0). There are two explanations for the develop- ment of eqn. 8. First, the influence of the voltage term is much smaller than the reactive power term, since the pilot-bus voltages are returned to their set-point values, so that the former term can be neglected [7]. Second, it is a common practice to form the composite PI,, and to translate voltage deviations into the Q-space. However, since the voltage deviations are proportional to URGLs, the influence of the voltage term in eqn. 7 on the relative

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position of contingencies in the ranking list is negligible, enabling the application of eqn. 8.

3.4 Linear programming model for resetting pilot-bus set points

When the set of critical contingencies is determined, it is worthwhile to investigate whether some of them can be transferred into noncritical ones, by the corrective readjustments of pilot-bus set-point voltages. This problem can be formulated as a linear programming model, where the optimisation criterion represents the minimisation of pilot-bus set-point voltage deviations, subject to constraints imposed on bus voltages and react- ive generations. In any zone I (I = 1, 2, . . . , L), the follow- ing simplified optimisation model can be defined for each critical contingency

min (max) z, = AV

subject to

B;' AV - k, A N , = AQJV;

V P < A & + V ; < V F

IAN, + N,"I < 1 (9)

AV = voltage deviation of pilot-bus in zone I B;' = susceptance matrix of zone I reflecting the

contingency under consideration A V , Vy = vectors of bus voltage deviations and cor-

responding base-state values in zone I (including pilot bus), respectively, (superscripts min and max denote limit values)

k , = vector of distribution coefficients describ- ing allocation of URGL to all regulating units in zone I

A N , , N : = deviation and corresponding base-state value, respectively, of URGL in zone I

AQ, = vector of reactive mismatches in zone I

When the contingency analysis is over, the available solu- tion results of the DSVC show that the elimination of voltage problems is one-way directed. This is performed either by raising the pilot-bus set-point voltage to cancel low voltages at demand buses, or by lowering the pilot- bus set-point voltage to eliminate high voltages at gener- ator buses. The simultaneous adjustment of set points in both directions in the same zone is not possible. Since the direction of violated voltage constraints is the result of the contingency analysis, the minimisation procedure (expr. 9) is used in the first case, and the maximisation formulation in the second.

To solve the optimisation problem (expr. 9), the dual simplex algorithm with bounded variables should be applied. Now, only one nonbasic variable exists indicat- ing that the optimum solution is achieved in a single dual simplex iteration. If the optimum solution is primary feasible, voltage problems in the analysed zone I are eliminated.

4 Overall procedure for voltage/reactive security analysis

The voltage/reactive security analysis of power systems with the automatic SVC is carried out in three stages:

IEE Proc.-Gem. Transm. Distrib., Vol. 141, No. 3, May 1994

contingency selection, contingency analysis, and correc- tive control. The overall algorithm of this procedure, encompassing both the systems with DSVC and CSVC,

terion [SI. When the local (bounded) solution is calcu- lated, the voltage subnetwork is extended to all complete zones (called affected zones) that are reached by the

part B

and ranking by

by using extended

assessment of threshold values N,L'M

port A innovation of base-state data

contingency selection by using (1P-10)

based on PIN critical contingencies

by using extended reduced set of potentiolly critical contingencies with the

I j 4

monitoring of the DSVC based on PIN

ranking list 7 / I p::m contingenclks

corrective resetting of pilot-bus set-paint voltages

additional corrective

nesessory

contingencles secure exist 7 control

Fig. 1 Flowchart of proposed methodologyfor voltage/reactive security analysis

is drawn in Fig. 1. Part A of this flowchart is run at regular time intervals, while part B is initiated when char- acteristic base states are reached, as well as when inap- propriate URGL threshold values N:'" are present. Part B of the algorithm is aimed to determine the threshold values of the URGLs. These values can be also efficiently used for voltage monitoring, thus showing another favourable feature of DSVC in the real-time operation. Following lines give a brief description of each of these analysis stages.

4.1 Contingency selection Contingency selection is the IP-lQ method applied to the extended load flow model and is the same for both SVC concepts under consideration. The principal steps of the (IP-1Q) method are

(i) Solve the first half iteration (1P) of the FDLF by using the midcompensation technique

(ii) Calculate reactive power mismatches at the buses of interest

(iii) Solve the second half iteration (1Q) of the FDLF.

Two possibilities are considered in step 2: either to analyse the whole system [SI, or to define the voltage subnetwork by using the incremental reactive loss cri-

voltage subnetwork. This is the consequence of the dis- tributed SVC action over entire zones, and in this case the forward substitution (FS) is applied to the voltage subnetwork, while the backward substitution (BS) is used for the calculations of affected zones. Taking into account these possibilities, four different contingency selection algorithms are defined (Table 2). Algorithms A1 and A3 are used in part B, while algorithms A2 and A4 are applied in part A of the overall procedure illustrated in Fig. 1.

4.2 Contingency analysis In the case of DSVC, the ordered contingencies are analysed by the extended load flow model and this step ends when the stopping criterion is reached [SI. In this stage, the validity of P I , (eqn. 8) can be tested. Namely, if the stopping criterion is not reached before the end of the ranking list, the threshold values of the URGLs are too high, indicating that there exist potentially critical contin- gencies that are not on the ranking list. In that case, part B of the overall procedure (Fig. 1) should be initiated, with the new set of base-state input data. Then, the selec- tion and ranking of contingencies are done by using the 1P-IQ method and PI,, (eqn. 7). The threshold value of the URGL in zone I is determined as the maximum value

Table 2: Comparison of contingency selection algorithms

Algorithm Forward substitution Backward substitution PI

right-hand side terms svmbol unknown variables symbol

A1 AQ, entire network FS AV,, N, entire network BS PI," A2 AQ, entire network FS N , entire network FBS PIN A3 AO, voltage subnetwork FFS AV,, N , affected zones FBS PIN" A4 AO, voltage subnetwork FFS N , affected zones FFBS PI,

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Table 3: Smcification of d o t - b u s e s and reaulatina units

I Zone of secondary Pilot-bus w , Regulating Regulating voltage control (voltage level) buses range [MVAr]

oer unit total

1 Cina Gora S S Ribarevine 4 HP Piva *20 i 8 0 (400 kV) TP Plievlia +20

HP Peruiica i 2 0 HP Trebinje *20

Obrenovac A TPNTA2 *50 (400 kV) TPNTA3 +50

TP NT B f 50

2 Srbija 1 ss 4 T P N T A l *50 *ZOO

3 Kosovo TS Kosovo B 2 TP Kosovo A *75 +150

4 Srbija 2 TS Beograd8 2 TP Drmno + l o 0 i 2 0 0

5 Srbija 3 SS B.BaSta 3 HP Bistrica +50 +150

(400 kV) TP Kosovo B +75

(400 kV) HP Djerdap + l o 0

(220 kV) HP B.Ba3ta +50 HP B.BaSta *50

(400 kV) TP Novi Sad *40 TP Zrenjanin *40

(400 kV) HPVrutok +40

6 Vojvodina TS NSad 3 3 SC Srbobran *40 *120

7 Makedonia TS Dubrovo 2 TP Bitola *40 *80

TP: thermal power plant, HP: hydropower plant, SC: synchronous con- denser, SS: switching station, TS: transformer station.

among all contingency dependent N , values, where vio- lation of voltage constraints does not exist. These quant- ities can be further multiplied by an experience-based safety factor, and they are transferred to part A of the overall procedure. 4.3 Corrective control of pilot-bus voltages

The optimum power flow model (eqn. 5 ) is applied in contingency analysis in the case of CSVC. Only the

reduced set of critical contingencies is examined by this model.

The corrective resetting of pilot-bus set-point voltages with the aid of the simplified model (eqn. 9) gives the

Table 4: Rankina lists and CorresDondina PI values

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Ranking lists PI," PI " PIN" PIN

P1 P2 AP AD AC A1 A2 A3 A4 P1 P2 AP AD AC A1 A3 A2 A4

1 1 11 1 1 1 1 1 1 6.22 6.11 0.63 0.78 0.15 6.20 6.15 6.06 6.04 2 2 3 2 12 3 3 3 3 6.01 6.05 1.23 0.60 0.00 5.89 5.80 5.89 5.80 3 4 1 4 3 2 2 2 2 5.98 5.90 1.50 0.51 0.08 5.92 5.94 5.92 5.94 4 3 18 6 2 4 4 5 4 5.91 5.92 0.31 0.42 0.10 5.83 5.63 5.83 5.63 5 5 19 3 13 5 8 4 5 5.75 5.60 0.30 0.59 0.00 5.70 5.64 5.46 5.43 6 7 4 5 14 6 5 7 7 5.43 5.35 1.12 0.49 0.00 5.60 5.54 5.60 5.54 7 6 2 7 5 7 6 6 6 5.28 5.37 1.30 0.40 0.05 5.47 5.61 5.47 5.61 8 8 7 9 8 8 8 8 8 5.11 5.14 0.90 0.29 0.02 5.10 5.13 5.10 5.13 9 9 8 10 15 10 9 9 9 4.50 4.71 0.87 0.28 0.00 4.35 4.38 4.35 4.38

10 11 5 8 6 9 10 10 10 4.19 4.20 1.11 0.37 0.04 4.40 4.29 4.32 4.21 11 10 13 13 9 11 11 11 11 3.95 4.28 0.50 0.21 0.02 4.01 3.80 4.01 3.80 12 12 9 11 16 12 12 12 12 3.56 3.58 0.80 0.23 0.00 3.65 3.60 3.65 3.60 13 14 6 14 17 13 14 14 14 3.11 3.05 0.99 0.20 0.00 3.17 3.05 3.17 3.05 14 13 10 15 18 14 13 13 13 3.03 3.20 0.69 0.19 0.00 3.15 3.06 3.15 3.06 15 15 21 16 4 15 15 15 15 2.58 2.69 0.20 0.17 0.06 2.50 2.35 2.50 2.35 16 16 16 12 10 16 17 16 17 2.02 1.98 0.36 0.22 0.02 2.13 2.05 2.06 1.99 17 17 12 17 7 17 16 17 16 2.00 1.95 0.56 0.14 0.03 2.11 2.04 2.11 2.04 18 18 22 19 19 18 18 19 19 1.55 1.25 0.19 0.08 0.00 1.41 1.20 1.41 1.20 19 19 17 18 20 19 19 18 18 1.39 1.15 0.32 0.10 0.00 1 4 0 1.32 1.40 1.32 20 20 15 20 11 20 20 20 20 0.80 0.90 0.40 0.06 0.01 0.78 0.95 0.78 0.95 21 21 14 21 21 21 21 21 21 0.65 0.58 0.45 0.03 0.00 0.64 0.63 0.64 0.63 22 22 23 22 22 22 22 22 22 0.37 0.21 0.20 0.02 0.00 0.30 0.26 0.30 0.26 23 23 24 23 23 23 23 23 23 0.20 0.19 0.00 0.00 0.00 0.22 0.20 0.22 0.20 24 24 20 24 24 24 24 24 24 0.12 0.11 0.24 0.00 0.00 0.11 0.11 0.11 0.11

P1 : (1 P-lQ-lAQ) algorithm applied to whole network, where SVC is modelled by error-feedback approach [E] producing the second, auxiliary iteration (1AQ) P2: same procedure as previous, but applied to voltage subnetwork AP: full AC solution based on FDLF and standard load flow model encompassing priman/ voltage control AD: full AC solution obtained with the aid of FDLF and extended load flow model that represents DSVC AC: full AC solution calculated by using optimum power flow model (expr. 5) to take into account csvc Al. A2, A3, A4: algorithms defined in Table 2.

IEE Proc.-Gener. Transm. Distrib., Vol. 141, No. 3, M a y 1994

Table 5: Mean normalised CPU times per considered con- tingency

Analysed network (442 buses) Normalised CPU times

P1 P2 A1 A2 A3 A4

Midcompensation [B’J and [ B ” ] 22 22 23 23 23 23 (P-8) half iteration (1 P ) 68 68 70 70 70 70 Voltage subnetwork definition no 36 no no 36 36 First (0-V) half iteration (IQ) 253 42 252 169 40 30 Second (Q-V) half iteration (1ACl) 253 31 no no no no Total screening time 596 199 345 262 169 159

answer in which direction the system with DSVC is to be moved to pass to the the secure base state. In the case of CSVC, this procedure represents the approximate redefinition of the pilot-bus set-point voltages and enables the possible cancellation of voltage problems.

5 Test results

The verification of the proposed voltage/reactive security assessment procedure was done through an analysis of voltage contingencies within the high-voltage power system of eastern part of former Yugoslavia, consisting of 442 buses, 450 lines and 62 transformers. Since no auto- matic SVC exists in this network, it was simulated by dividing the system into seven control zones. Table 3 gives the specification of pilot-buses and associated gen- erating resources.

The voltage/reactive security assessment of all single contingencies was made through the comparative analysis of six different contingency selection algorithms, and three full AC solutions. The principal results of these procedures are exhibited in Table 4.

The ranking lists and PI values of 24 potentially criti- cal contingencies are presented in Table 4. When the extended load flow model is used (algorithms Al-A4), the differences in ranking orders with respect to P1 and P2 solutions are almost negligible. The PI,, and PI, values are very close to each other, irrespective of whether the entire network or the voltage subnetwork is considered. Finally, by finding full AC solutions it was verified that all other single contingencies not listed in Table 4 were not critical.

The column AP and the corresponding PI, values are included in Table 4 to compare the capabilities of the primary voltage control against automatic SVCs. By inspecting the AP and AD columns, it is generally con- cluded that DSVC produces slightly better steady states. The only exceptions are noticed in the case of heavy topological disturbances, where the circulation of large amounts of reactive power between neighbouring zones, with DSVC in operation, can appear (contingencies I , 4 and 5). It is obvious from Table 4 that the most import- ant difference in ranking orders appears between the AD and AC solutions. In power systems with the DSVC the correspondence between the full AC solution (AD) and A-algorithm ranking orders is very good, since the voltage limit violations are well copied into appropriate reactive generation overloads. Contrary, the capabilities of CSVC to handle voltage contingencies are significantly better, thus giving the different ranking order (AC) and usually smaller PI, values. Both the topological dis- turbances and reactive power mismatches are very efi- ciently compensated by the CSVC action.

Mean normalised CPU times obtained by the six ranking algorithms are presented in Table 5. The A3

IEE Proc.-Gener. Tramm. Disfrih., Vol. 141, N o . 3, May 1994

algorithm, where all variables of the affected zones are solved, represents the compromise solution of the fore- going procedures. Finally, the A4 algorithm turns out to be the most promising contingency selection procedure, since it is possible to reduce the time requirement by 50% in the Q-V half iteration (with respect to the P2 algorithm).

6 Conclusion

The principal goal of this paper was the development of a general methodology for the voltage/reactive security analysis of power systems with the automatic secondary voltage control. Both the decentralised and the co- ordinated control concepts are encompassed in a com- prehensive methodology, consisting of three principal stages, namely contingency selection, contingency analysis and corrective control. To perform the contin- gency selection stage, the extended load-flow model and the new voltage/reactive performance index, based on the introduction of secondary voltage regulator outputs as unknown variables, were developed. In the contingency analysis stage, the extended load-flow model was used in the case of the decentralised control, and the optimum power flow model with the voltage/reactive security objective function, in the case of the co-ordinated control. The results of contingency analyses of systems with these two types of secondary control were compared with the capabilities of the systems with primary voltage control only. It was generally concluded that systems with the secondary voltage control exhibit better steady-state per- formance, particularly those employing the coordinated control. Finally, a simplified linear programming optim- isation model for corrective resetting of pilot-bus set- point voltages was proposed with the aim to increase voltage security margins. The successful verification of the proposed methodology showed that it represents a good prospective tool for the solution of voltage/reactive security problems. In this way, the gap is narrowed between the presently used methodologies for the analysis of the primary voltage control, and the practical needs of power systems applying the secondary voltage control.

7 References

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