Bjelogrlic, M., Calovic, M. S., Ristanovic, P., Babic, B. S.,

APPLICATION OF NEWTON'S OPTIMAL POWER FLOW IN VOLTAGEREACTIVE POWER CONTROL

Milan Bjelogrlie Milan S. CaloviC Bor i vo je Electric Power Board of Serbia Dept. of Electrical Engineering Electric Power

Belgrade, Yugoslavia University of Belgrade Be 1 grade, Belgrade, Yugoslavia

Petar RistanoviC, member IEEE Institute Nikola Tesla Belgrade, Yugoslavia

Abstract. This paper considers an application of Newton's optimal power flow to the solution of the secondary voltage/reactive power control in transmission networks. An efficient computer program based on the latest achievements in the sparse matrix/vector techniques has been developed for this purpose. It is characterized by good robustness, accuracy and speed.A combined objective function appropriate for various system load levels with suitable constraints, for treatment of the power system security and economy is also proposed.

For the real-time voltage/reactive power control, a suboptimal power flow procedure has been derived by using the reduced set of control variables. This procedure is based on the sensitivity theory applied to the determination of zones for the secondary voltage/ reactive power control and corresponding reduced set of regulating sources, whose reactive outputs represent control variables in the optimal power flow program. As a result, the optimal power flow program output becomes a schedule to be used by operators in the process of the real-time voltage/reactive power control in both normal and emergency operating states.

Keywords: optimal power flow, voltage control, reactive power generation dispatch, reactive security.

1. INTRODUCTION

The control of voltages, reactive generations/con- sumptions and line flows represents one of the most important activities in the operation of modern power systems. This control is known as the "voltage/reactive power" or "voltage/VAR" control. The main objective of this control can be generally regarded as an attempt to achieve an overall improvement of the system security, service quality and economy.

System security requires adequate voltage levels and reactive reserves in order to prevent voltage stability crises and to maintain the system integrity when critical contingencies occur. The service quality and economy require appropriate voltage control at all system nodes and consumer terminals within tolerable limits, in order to insure adequate reactive line flows which result in minimal active transmission losses.

Two principal aspects of the voltage/VAR control problem are related to the power system planning and operation. The former includes the planning of system reactive demands and control facilities as well as the installation of the reactive power control resources, while the latter encompasses the operation of the exis- ting voltage/VAR resources and control devices. In this paper we consider the second aspect of the problem, namely the voltage/VAR scheduling and dispatch.

The complexity of the voltage/VAR extended and basic real-time, requires

S. BabiC Board of Serbia Yugoslavia

control in the both the space

and time decomposition of the overall voltage/VAR control problem. The space decomposition follows the natural multi-level hierarchy of a power system and the predominantly local nature of the voltage/VAR control problem, while the time decomposition performs the time separation of various control mode responses attributed to the particular system hierarchy levels. There is a good three-level matching of the natural hierarchy of the voltage/VAR control in a power system from both the time-scale and space decomposition point of view, as illustrated in the following table: Control action Primary Secondary Tertiary Characteristic mode Fast Slow Very slow Attributed to Resource Part of the Entire

unit network network

Three hierarchical levels of the time-decomposition are aimed at coordinating the control of the local, subsystem and overall system disturbances, having different response times. The primary control compensates for small and fast local voltage and reactive power disturbances, and is performed through automatic voltage regulators (AVRs) of the primary control resources. The secondary control is the slow control superimposed on the spontaneous primary action of AVRs of synchronous machines and ULTC transformers. It acts through the modification of input reference values on AVRs in order to achieve a satisfactory coordination of regional voltage/VAR controls. The very slow tertiary control deals with the coordination of decentralized secondary controllers, made for the whole power system. It should be pointed out that the secondary and tertiary controls can be carried out as a unique central control, opposed to the local primary control. Such an approach has been suggested in this paper.

From the practical standpoint the voltage/VAR control at the second and third level can be performed according to three basic approaches [11 as follows:

- decentralized control - centralized control - hierarchical control The hierarchical control [1,21 is best suited to

insure the necessary coordination requirements of the local and/or regional voltage/VAR control regulators. In that respect, two important questions arise:

1. Reference-input values determination on local AVRs, according to the requirements of security and economy of the system operation.

2. Realization of an automatic voltage/VAR control maintaining these desired references.

This paper deals with the first of the above mentioned problems. The second one is considered in detail in [1,21.

The concept of modern computer-based energy manage- ment systems (EMS), with supervisory control and data acquisition (SCADA) and state estimation (SE) functions, enable the application of up to date software systems aimed at the support of the real-time voltage/ /VAR control, being assisted by new mathematical algorithms and practical optimization procedures that sat- isfy requirements of the real-time voltage/VAR control functions [3-81.

CH2747-4/89/0000-0105$1 .OOO 1989 IEEE

One of the basic problems in practical applications of optimization procedures in real-time power systems control is that they give a great number of simultane- ously required changes of control variables at different locations, most of them being very small. For system operators in the large power systems it is almost impossible to perform all these controls in a satisfactory short time period. This fact implies the reduction of the set of simultaneous controls to those having the dominant influence on the solution of the problem, which leads to suboptimal solutions [91. The local character of the voltageNAR control problem sug- gests that, for the purpose of the secondary control, a large power system has to be decomposed into smaller regions, called "zones".A limited number of control resources, having the dominant influence on voltageNAR conditions, is included into secondary control inside each of the control zones. This results in a double benefit:

a)

b)

The decentralized voltageNAR optimization on the level of each zone decreases the required computa- tion time, by reducing the number of control variables within each zone to the resources included only into the secondary control. The outputs of voltageNAR optimization simulations become practically usable schedules to be applied by the system operators in the real-time environ- ment.

This paper is meant to contribute to the aforemen- tioned ideas.It presents a new voltage/VAR control concept, supported by an efficient software package based on Newton's OPF. A model and algorithm of the proposed method, with the description of the software package are presented in this paper. Certain simulation test results on the example of the Yugoslav transmission network are also included. Good performances of the method and hopeful prospects for its further practical implementation are shown.

2. THE CONCEPT OF THE SECONDARY VOLTAGEnAR CONTROL

The complexity of the voltageNAR control problem, originating in the overall system security and economy requirements and a local character of the majority vol- tageNAR disturbances, imply the hierarchical, multi- -level approach to its solution. A two-level hierarchy is proposed here. The first is a local level of AVRs on voltageNAR control resources, and the second one is the centralized zone level. The second-level control represents the superimposed action on AVRs of zone primary control resources aimed at coordinating modifications of their reference inputs. as well as at ob- taining the decisions concerning the status of on-off local reactive compensating devices. The local character of the great part of voltage/VAR disturbances enables their elimination by coordinating actions of regulating facilities in the part of the system where they appeared. Depending on the relative amount of the disturbance, the size of the zone that will participate in disturbance compensation can be flexibly defined. Also, periodic checks of security and economy requirements on system level should be performed in normal operating states. Following these ideas the hierarchical concept of system voltage/VAR control proposed in this paper is based on the:

1. assumption of the availability of SCADA and SE f unct ions.

2. division of the entire power system into control zones with their own secondary voltage/VAR resources and facilities.

3. possibility of an adaptive and flexible zone sizing depending on the severity of the actual disturbance .

4. application of the Newton's OPF for the determination of reference input values on local AVRs within a zone, under both normal and emergency

operating states. 5. participation in the secondary voltageNAR con-

trol of the regulating facilities with pre- vailing influence on the voltageNAR conditions in a particular zone. The remaining voltagehe- active control resources participate in the primary control only. Their control parameters are adjusted on the basis of off-line analyses, made in the operational planning stage. In case of large deviations of the actual regimes in com- parison to the scheduled ones, it is possible to include these resources into the secondary control, according to a priority sequence, by re- adjusting reference inputs on their AVRs.

6. periodical operation of the control algorithm in the normal operating stages, with a cycle-time of 15 minutes, or on operator request in case of disturbances.

The determination of the control zones is based on the w e g a t i o n of strongly coupled nodes into homoge- neous groups in regard to the voltage/VAR performance. Each zone should have a certain number of units, capa- ble of participating in the secondary voltageNAR control.For the definition of control zones, heuristic approaches [21 and algorithms based on the application of the sensitivity theory [lO,lll are applied. The application of the structural analysis approach is also possible [121.

In order to determine the control zones the algorithm proposed in Reference [lo1 is used. It uses the sensitivity matrix for determining the zone pilot nodes. The elements of this matrix are the sensitivity coefficients of node voltages for changes in VARs in- jected at load nodes, assuming the availability of the primary voltage/VAR control only. Control resources are defined by using the sensitivity matrix of the pilot- -node voltage to reactive outputs of control resources, belonging to the zone characterized by this pilot node. If the sensitivity coefficient of a particular source node is greater than a previously specified value, this source should be included into the set of zonal regulating resources; otherwise not. The final selection Of zonal regulating units participating in the secondary control is made heuristically. in respect of the particular characteristics of the considered zone (network configuration, rated capacities of control resources. type of regulating devices etc). It should be pointed out that the concept proposed in this paper incor- porates only synchronous generators and condensers into the secondary voltage/VAR control.

As the size of a zone depends on the specified thresholds of coupling coefficient of any node to the pilot node,it is possible to define several zone bound- .aries by changing these thresholds. This procedure gives several levels of size for each zone and the set of corresponding reactive regulating resources, the final step being when the zone encompasses the entire system transmission network. The heuristic judgment of the designer plays an important role in this process. The software package supporting this concept, requires that data be available for all network nodes, branches. reactive resources and regulating devices, with the basic size and the enlarged zone boundaries, provided from off-line analyses.

A computer program has been developed to support the specified concept of real-time secondary vo1tageNAR control. It is described in the next section.

2.1. DESCRIPTION OF THE OPTIMAL REACTIVE POWER FLOW

The optimal reactive power flow problem can be ex- pressed mathematically as general nonlinear programming problem, with scalar nonlinear nonseparable objective function and nonlinear equality and inequality constraints. It can be stated in the following way:

Minimize scalar nonseparable objective function

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f (x, U) ( 1 ) subject to equality and inequality constraints

(2) ( 3 )

where x and U represent the state and control vector, respectively; g(x,u) and h(x,u) are vector functions of vector arguments.

In the problem of optimal voltage/VAR control, it is assumed that all active generations and phase angles of phase-shifting transformers are constant and known in advance. The set of constraints (2). (3) is defined with following relations: - active and reactive node-balance equations

- upper and lower limits on system variables

Q:, 5 Q,, 5 Q,", , 1 = 1, ..., NC

S v1 S , 1 = 1, ..,, N

(6)

(7)

where Po, Q,,, PLl, Q,, are active and reactive node i

generations and loads, respectively, VI, 6i are node i voltage magnitude and phase angle, respect ive 1 y, t is the relative value of the ULTC transformer

ratio in the branch j, N is the total number of nodes, NC is the number of generators, NT is the number of ULTC transformers, 6 , V and t are vectors of corresponding variables 6

J

i' vl, t,, PGs, is the active generation of slack-node,

QCs is a vector of the reactive injections of nodes

participating in secondary control, index m represents the lower and index U the upper limit of the corresponding variable. The selection of an appropriate objective function

in the optimal voltage/VAR cmtrol is of a great practical importance. This objective function in periods of high loads must insure the highest security level possible avoiding, at the same time, the violation of the economic criterion, stated as the minimization of active transmission losses. References [13,14] show that the practical criterion ensuring a satisfactory level of the system security is a uniform distribution of the reactive reserves to the generators operating in the secondary control. It can be achieved by using the objective function of the type

(9)

where Snl represents the rated apparent capacity of the generator "i" included into the secondary voltage/VAR control and NS the set of generators participating in secondary control.

The use of this objective function in the OPF solution results in a decrease of reactive outputs of the generators participating in the secondary control. The consequence is a global reduction of voltage levels in the entire transmission network, provoking the decrease of line reactive generations, shunt capacitor bank outputs and reactive loads on all nodes where the voltages are not maintained by ULTC transformers. Except for the reduction of bus reactive loads, all other effects have a negative impact on the system voltage profile. As the

problem is nonlinear and mainly depends on the network topology, the size of loads and their types and locations, it is difficult to predict in advance which of these effects will be dominant. On the other hand, if the objective function is the minimization of active transmission losses, the OPF results in high voltages in the network. Also, reactive overloads appear at all generators electrically close to load centers. From the security point of view, the first effect is favorable, while the second one is not.

It is desirable to combine the positive effects of both objective functions mentioned above. This is possible by using the combined objective function of the type

f(x,u) = a P + B (Q~~IQ,"~ - = 1 2 lENS

cs 1 (10)

where a and f3 are weighting coefficients and FS is the average reactive load of units participating in the secondary voltage/VAR control, defined as

= C Q,, / C Q,"l ( 1 1 )

Q,, is the reactive output of generator "i" participa-

ting in the secondary control, and Q:l is its maximal

lENS lENS

available reactive generation. It is obvious that by the appropriate selection of weighting coefficients a and 6 , it is possible to give the priority to economy (minimum active transmission losses) or security (uniform distribution of reactive reserves [141). For low- load periods, the choice u=l, 8-0 reduces the criterion (10) to the minimization of active transmission losses exhibiting satisfactory results.

2.2. WDELING OF CONTROL RESOURCES AND DEVICES

Specific models are used for the representation of important features of control resources and regulating devices in OPF calculations. These encompass:

- Reactive resources participating only in the pri- - ULTC transformers, - Fixed capacitor banks with on-off control achieved

- Performance charts of synchronous generators, - Static load characteristics.

mary voltage/VAR control,

by mechanical circuit breakers,

All the available synchronous machines participate in the primary voltage control. Smaller generators connected to the medium voltage (MV) networks (110 kV and below) are electrically close to the load centers and exert little influence on voltage/reactive conditions in the high voltage (HV) transmission network. These generators are modeled as PV nodes, i.e. as constant voltage buses. Their voltages are defined in off-line analyses in the operational planning stage. The compensation according to the reactive component of the terminal current is introduced in order to maintain the voltages in the neighboring nodes without changing the reference values of those AVRs participating exclusive- ly in the primary control. This compensates for the voltage drop in the unit-generator step-up transformer, i.e. the increase of reactive loads in the system results in an increase of the regulated bus terminal voltage, in spite of a constant reference at the input of its Am. All this pertains to overexcitation operation. On the other hand, in underexcitation regimes, the compensation should be canceled in order to avoid machine overloading and violation of system stability. The effect of reactive current compensation is modeled in such a m y that the reactance of the corresponding unit-generator step-up transformers is decreased by the amount of compensation [IS], specified in off-line calculations during the system operation planning stage.

ULTC transformers with their A m belong to the class of discrete type, slow-acting regulating facilities [16] . Their control actions are much slower than

107

actions of the AVRs of synchronous generators and condensers. Here,three types of ULTC transformers are dis- t i ngui shed :

- Interconnective ultra high voltage/high voltage/ /medium voltage (UHV/HV/MV) ULTC transformers, used for control of the reactive flow exchanges between transmission networks of different rated voltages .

- ULTC step-down load transformers, used for con- nection of the MV subtransmission and MV distribution networks.Their role is to maintain the distribution MV-bus voltages on the desired (reference) values.

- Unit-generator step-up ULTC transformers, used for coupling of generators to the UHV or HV networks. Their role is to secure the best possible use of generator reactive power capability. The UHV/HV/MV transformers are included neither

into the primary, nor into the secondary voltage/VAR control and their turn-ratios are specified in off-line analyses, for a set of possible operating states. It is possible to introduce these transformers into the set of control facilities. This might become necessary in case of sudden and large changes in network topology. The ULTC load transformers used for coupling of the MV subtransmission and distribution networks take part in primary control only. They are used to maintain the distribution bus voltages, specified in off-line analyses, constant. Turn ratios of the ULTC transformers are modeled as dependent continuous variables with upper and lower tap-changer position limits. After the OPF converges to the final solution, each ULTC transformer turn-ratio should be rounded to the nearest discrete tap position. The unit generator step-up ULTC transformers are modeled as constant off-nominal turn- -ratio units.

Shunt capacitor banks are usually located near the load centers, on the MV subtransmission or distribution buses. They have a great influence on the amount of active transmission losses in HV and UHV networks. Ce- neral policy tends to use their reactive capabilities in the high load regimes at maximum, prior to generator reactive loadings. This practice results in the decrease of the active transmission losses, due to the reduced reactive line flows. The secondary voltage/VAR control should encompass only larger capacitor banks connected to higher subtransmission network voltages. Such capacitor banks are modeled as generators, with zero active outputs. The actual reactive generation of a shunt capacitor bank is also adequately constrained in OPF calculations.

The modeling of performance charts of synchronous machines is of great importance for the simulation of the real voltageNAF? regimes in power systems. The

non-linear dependence Q:l = f (PGl, Vel) is approximated in this paper with the third-order polynomial of the form

Q:l = iak1fl k=O

(12 )

where the dependence of QE1 on VGl is neglected. Finally, the static load characteristics QLl=f(F,Vl)

are modeled as (13)

where the value for k depends on the type of load. The load dependence on the system frequency is not a subject of the voltageNAR control, so it is not taken in- to consideration in this paper.

When specifying a particular network zone, the rest of the interconnected power system, with inter-system tie-lines, is modeled as a set of PQ nodes. The active injections and voltages on these nodes are taken to be the actual tie-line exchanges and voltages obtained by the state estimator, with narrow limits of permissible

changes.

3. THE SOLUTION ALGORITHM AND PRACTICAL 1WLEHJNI"TTION

The solution of the optimal reactive power flow problem in the proposed secondary voltage/VAR control concept, is based on the Newton's OPF, which is described in References [3-61. Only the main features of this OPF algorithm when applied to the solution of the voltage/VAR control problem will be underlined below.

Basic control variables here are the reactive outputs of control resources (generators, synchronous condensers, capacitor banks) participating in the secondary control, terminal voltages of reactive resources participating in the primary control only and bus voltages maintained with ULTC transformers.

For the minimization of the objective function (9) or (10) subject to the equality constraints (4) and (51, the extended Lagrange function is defined as

(14) L(y,h) = f(y) - XTg(y) where

Y = [PGsl Q:s xTIT , x = ItT aT VTIT , h = [AT P q hTlT By applying Newton's method for the solution of the

nonlinear system of equations, obtained from the necessary optimality conditions (the gradient of the La- grange function (14) at optimum is equal to zero, i.e. VL(y,AI = 01, the well known relation that defines the iterative procedure for the solution for variables y and A yields

( 1 6 )

Relations (15 ) and (16) can be written in a more com- pact form

where

A is diagonal NS*NS dimensional matrix of second or-

der derivatives of Lagrange function a2Wa2QGs M is 2N*NS dimensional matrix, whose non-zero ele-

ments are defined as

H(x,A) is 2N*2N dimensional matrix of second derivatives of Lagrange function, the elements of which are hll = a2waxT h 1J = a2waxlax,

J(x) is Jacobian matrix of nonlinear system of equations ( 4 ) and ( 5 ) , the elements of which are

jt1 = - a2uahlaX1 jlJ = - a%ah,ax, k = 0,1,2,. . . is an iteration index.

By grouping the variables al, V1, hpl i hql, the 4x4 block structures of the part of matrix V, that cor- respond to submatrices H and J are formed. This matrix has the property of super-sparsity.By applying the modern sparse matrix and vector techniques, an efficient

108

procedure for the solution of system (25) is derived. The programming code has ben developed using the The functional equality and inequality constraints latest achievements in sparse matrix/vector techniques

on generation of reactive resources not included into [18,19,201. In each primary iteration, where the trial Secondary control. as well as the ineaualitv con- iterations are made, in the first trial iteration the

of 1.

2.

3. 4.

5. 6.

7.

8.

straints-on state A d control variables are- enforced by penalty functions as described in References [3-61. Re- active outputs of resources included into secondary control are modeled as explicit control variables. Bus voltages maintained by ULTC transformers,or by reactive resources not included into secondary voltage/VAR control can change in narrow limits. This is also true for terminal points of tie-lines with neighboring zones and external systems.

The solution algorithm used in this paper consists ' the following steps: , . Initialization k = 0, z = z" ' .

Calculation of the gradient VL'k' and the elements of matrix dk'. Choice of the set of active constraints. Test of Kuhn-Tucker optimality conditions

vL'k' < E

test of the sign of variables A,

feasibility test If Kuhn-Tucker conditions are satisfied the calculation is finished; otherwise go to Step 5.

Factorization of matrix U('). Solution of system of linear equations W(k)Az(k) = - VL(k). Determination of satisfactory set of binding constraints, by using trial iterations. Calculation of the vector of unknown variables in the current iteration (k+l) = z(k) + Az(k),

Setting of k=k+l and the continuation of the procedure from Step 2.

The determination of a satisfactory set of active constraints, by trial iterations is made in the following manner: 1. Verification of the validity of the test solution

obtained as a result of primary iteration and detection of candidates for changes in the set of active constraints.

2. For candidates from Step 1, the need for eventual changes in the set of active constraints is tested. If there are no changes, the trial iterations should be left, otherwise go to Step 3.

3. The verification whether all candidates for changes in the set of active constraints are taken into con-

necessary modifications of factors in the matrix dk) are performed using the FCPMR method 1191. The following trial iterations use the factor updating method [181. The sequence of elimination is defined according to the algorithm described in Reference [20]. All the elements of the matrix of the linear system of equations are memorized in ordered lists, according to the sequence of the elimination. This enables fast calculation, with minimum memory requirements.

The strategy of the constraints enforcement on variables of different nature is based on Judgments expres- sed in References [3-51. The algorithm also encompasses the procedure for the detection of infeasible solutions and for the identification of corresponding infeasible constraints, as described in Reference [SI.

The secondary voltage/VAR control should operate in the following cases:

1. Outage of any network element within the zone. 2. Excessive unscheduled reactive exchanges with

3. Unacceptable high/low values of voltages on

4. Operator request. 5. Unconditionally, every 15 minutes [81.

neighboring zones and systems.

certain buses in the zone.

When the voltage disturbance is detected, it should first be eliminated by the local control resources within the zone where the disturbance happened. In case of an infeasible or unsatisfactory solution, the zone is extended to the first corresponding higher level and a new solution is attempted with the increased number of control resources and regulating devices of a newly defined zone. This procedure is continued if necessary, until the level when the zone reaches the size of the entire power system. The total number of zones and levels and sequences of the extensions depends on specific system characteristics.

The proposed concept of secondary voltage/VAR control is based on the steady state optimization of voltage/VAR conditions. General two-level hierarchy of the overall voltage/VAR control is possible, owing to the fact that time responses of primary and secondary controls are different. Therefore, they can be separated in time and studied independently. This assumption is not quite correct when the voltage regulators of ULTC transformers are considered. By nature they belong to primary control, but their time responses overlap with secondary control. Hence, in future research of the problem they should be probably considered as part of the secondary control system.

4. TESTRESULTS sideration. If the answer is yes, the sequence index is set to 1.0 and the procedure goes to Step 4. If not, the normalized sequence indices for candidates for entering and leaving the set of active constraints according to the selected criterion (the value of the deviation from the limit, or the amount of the variation in last trial iteration) should be calculated.

4. For candidates with sequence indices above the threshold value specified in advance (between 0 and 11, the values of the gradient and factors of the matrix U'" should be adjusted.

5. Calculation of a new trial solution and the continuation of the procedure from Step 2.

The criterion for leaving the trial iteration is

1. There are no new candidates for the inclusion

2. The number of trial iterations overpasses the

one of the following:

into the set of binding constraints.

value set in advance.

The proposed concept of secondary voltage/VAR control is verified by computer simulation of Yugoslav 400 kV and 220 kV transmission network, including 110 kV network of the eastern region of the country. Analyses are performed for various load levels and network topo- logies. Here, the simulation results for 1987 peak load condition are presented. In this regime the network en- compassed 209 nodes and 310 branches, with 34 plants and 13 ULTC transformers in operation. Within this transmission network, the control zone of eastern part of Yugoslavian power system, encompassing the above mentioned 110 kV network, was specified, with 144 nodes, 17 generators and 13 ULTC transformers. For the separation of this zone the threshold of sensitivity coefficients defined as Th = S /S B 0.1 was used

PP Pi (where S = AV /AQ and S = AVp/AQLI, V being the pilot node voltage and Q,, are reactive loads on W no-

PP P LP Pi

des). In this zone 9 out of 17 available generators are

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included in secondary voltage/VAR control. The reactive current compensation on AVRs of generators participating in primary control only was set in a way that voltage droops on the HV side of unit generator step-up transformers were of the order of 2-5 %. All the ULTC distribution transformers were assigned to maintain the desired secondary (distribution) bus voltages by changing their turn-ratios.On all the load buses, where the voltages are not maintained at constant values, reactive loads were modeled with static characteristics of the form Q, = = QLo(V/Vo)2.7. Simulation results are shown in Tables I and 11.

1 2 3 4 5 6 7 8 9 10 11

13 14 15 16 17

i 12

R2 R3 R4 FE R6

V(kV) QP V(kV) QP V(kV) Qr V(kV) Qr V(kV) Qr

420.0 .71 420.0 .90 417.4 .75 420.0 .76 418.4 .74 420.0 .99 416.1 .53 418.8 .66 419.1 .57 418.8 .65 420.0 .14 417.0 .47 420.0 .65 420.0 .49 420.0 .64 234.7 1.0 233.1 .96 232.7 .72 234.6 .93 232.8 .71 235.9 .83 234.0 .77 234.0 .72 235.7 .76 234.1 .70 237.2 .89 236.0 1.0 235.3 .69 237.0 .92 235.1 .68 237.2 .07 238.7 .26 242.0 .58 239.8 .26 242.0 .57 414.5 .87 405.8 .68 406.5 .69 410.0 .71 409.3 .76 226.0 1.0 217.3 .79 217.9 .78 221.8 .89 220.4 .83 114.5 .99 111.6 .59 113.9 .74 114.5 1.0 114.5 1.0 116.1 .73 114.7 .67 115.9 .72 116.1 .74 116.1 .77

114.8 .95 111.4 .55 113.3 .76 114.8 1.0 114.8 1.0 114.9 .46 112.5 .62 115.0 .72 114.9 .47 114.9 .53 115.6 .59 114.6 .65 116.3 .72 115.6 .63 115.6 .70 117.1 .32 119.1 .61 119.9 .62 117.1 .32 117.1 .35 419.2 .OO 420.0 .46 420.0 .42 419.2 .22 419.2 .29

117.0 .54 116.6 .64 117.6 .70 117.0 .55 117.0 .62

1 156.7 1191.7 3011.6 2069.8 9.40 18.11 10.45

R1 R2 R3 R4 FE R6

PL QL GL QGZ AV1 AV2 AV3

158.8 1210.5 2987.9 2146.8

19.43 12.26

163.8 1233.1 2922.4 1838.4 10.24 21.62 16.98

Column and row headings in Table I have the following meanings: R1 - Standard procedure for the load-flow calculation, R2 - Optimal power flow with all available control

resources in the whole power system. The optimization criterion is the minimization of active transmission losses,

R3 - Optimal power flow, with reactive generator outputs taken as explicit control variables in the considered zone (17 generators at total). The optimization criterion is given by expression ( 9 ) .

R4 - The same as in column R3, with optimization criterion ( 1 0 ) and a = 1, j3 = 0.25.

FE - The same as in column R3. with only 9 reactive resources within the zone included into the set of control variables.

R6 - The same as in column R4, with reactive resources as in column FE.

PL - Active transmission losses in the whole power system (MW).

QL - Reactive transmission losses i n the whole power system ( M V A r ) .

GL - Reactive line capacitance generation in the whole power system (MVh-1.

QGZ - Total reactive generation of generators participating in the secondary control (MVAr).

AV1 - Average voltage deviation fl-V in the zone, for 110 kV nodes (kV).

AV2 - Average voltage deviation v”-V in the zone, for 220 kV nodes (kV).

AV3 - Average voltage deviation v”-V in the zone, for 400 kV nodes (kV).

Table I1 exhibits voltages and relative reactive loads Qp = QG/Q: for particular generators within the zone.

for simulations whose results are given in Table I. In all simulation tests with the proposed objective

function the program converged in 9 to 12 iterations. The average time length of one primary iteration, without trial iterations for the complete network of 209 nodes and 310 branches was 0.9 s on the computer DEC VAX 11/785. The average time length of the whole OPF calculations for the entire network, depending on the number of iterations was between 12 and 18 s. In all simulations the convergence criteria were

pl,< 0.1 PIW; IAQ~,< 0.1 MVA~; JBYBYJ,< 0.02.

including the verification of Kuhn-Tucker necessary

162.4 1236.8 2976.4 2078.6 10.76 21.13 13.90

optimality conditions. Results given in Tables I and 11 show that with a relatively small increase of active Table I1 Voltages and reactive loads for zone gener-

ators obtained in tests described in Table I.

160.8 158.3 1224.4 1203.9 2978.8 3007.4 2147.9 2071.7 9.95 9.88 20.69 18.97 13.04 12.24

___

1 417.4 .73 2 418.8 .67 3 420.0 .66 4 232.5 .69 5 233.8 .69 6 235.0 .68 7 242.0 .60 8 407.8 .74 9 218.8 .79

10 114.5 1.0 11 116.1 .76 12 117.0 .65 13 114.8 1.0 14 114.9 -58 15 115.6 .72 16 117.1 .34 17 419.2 .36 PL 159.8 MW

transmission losses (160.8 MW instead of 156.7 MW), the proposed objective function insures practically uniform reactive distribution on all 17 generators of the zone. Moreover, even better results are obtained with 9 generators under secondary control, where uniform distribution of reactive generation is achieved with only 2 MU increase of active transmission losses, compared to the optimal regime (158.8 MW instead of 156.7 MW). It is also shown that the proposed objective function, with practically the same amount of active transmission losses guarantees much more uniform distribution of reactive source generations, than the objective function proposed in Reference [141. Table I11 Influence of the weighting factors values on

416.2 .71 414.9 .68 418.7 .68 417.1 .67 420.0 .67 418.4 .67 232.3 .68 231.7 .67 233.5 .68 233.0 .68 235.0 .68 234.0 .66 242.0 .61 242.0 .65 406.2 .72 406.0 .71 217.3 .75 217.3 .77

114.5 .99 114.5 .98 116.1 .75 116.1 .75 117.0 .68 117.0 .77 114.8 1.0 114.8 1.0 114.9 .62 114.9 .71 115.6 .75 115.6 .77 117.1 .39 117.1 .34 419.2 .44 419.2 .45 160.6 MW 162.0 MU

the OPF results.

415.2 .69 417.6 .67 418.9 .67 231.9 .68 233.1 .68 234.3 .67 242.0 .64 406.0 .71 217.3 .77 114.5 .93 116.1 .75 117.0 .74 114.8 1.0 114.9 .75 115.6 .77 117.1 .33 419.2 .45 161.7 MW

a = l a = l a = O a = O I j3 = 0.5 I j3 = 1 I j3 = 0.5 1 j3 = 2 1 BOL=’OtOl 420.0 .79 418.3 .72 419.5 .63 232.8 .89 234.0 .71 234.1 .54 239.2 .32 412.5 .84 224.8 1.0 114.5 1.0 116.1 .78 117.0 .61 114.8 .88 114.9 .54 115.6 .61 117.1 .38 419.2 .OO 157.6 MW

I I I I

Selection of weighting factors a and j3 was performed experimentally through numerous simulations. For the peak load conditions we obtained the best results with values a = 1, B = 0.25. The effects of weighting factors on the active power losses and reactive power dispatch have been fully investigated. Briefly, it could be said that requests for active transmission losses minimization and uniform reactive reserve dis-

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tribution are mutually opposed. The table I11 shows the effects of some combinations of weighting factors values on the OPF results.

5. CONCLUSION

In this paper,a hierarchical scheme of system voltage/VAR real-time control is developed. The base of the proposed scheme is the modern concept of secondary voltage/VAR control, the application of sensitivity theory and Newton's optimal power flow. The location and role of all control resources and regulating devices, participating in system's voltage/VAR control is defined. An efficient computer program for the optimal power flow has been developed based on Newton's method, with appropriate mathematical models and constraints on all resources and regulating devices influencing the system voltage/VAR conditions. For secondary voltage/ /VAR control needs, an appropriate objective function is proposed, encompassing effectively the security and economy of power system operation.

Test results obtained by the simulation of the Yugoslav transmission network and one secondary control zone within this network show promissing prospects for the application of the proposed concept in the real- -time power system voltage/VAR control.It is shown that the suboptimal solution based on the reduced set of control variables insignificantly deteriorates the economic performance index (minimum active transmission losses), while completely respecting the security criterion (uniform distribution of reactive generation reserves). The speed of execution of the proposed program enables the realization of shorter start-intervals of the secondary voltage/VAR control, than the 15 minutes proposed in the paper. Test results obtained for the set of steady-state and emergency operating states have shown that Newton's OPF developed in the paper insures the uniqueness of the solution, which is practically independent of the initial guess.Also, it is shown that it is possible to treat a large power system as a set of independent zones when solving the real-time voltage/VAR control problem. Such an approach significantly decreases the calculation time without reducing the quality of control.

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REFERENCES V.Arcidiacono,"Automatic Voltage and Reactive Power Control in Transmission Systems", CIGRE-IFAC, Flor- ence 1983, Paper 38-83. J. P. Paul, J. Y. Leost, J. M. Tesseron, "Reglage second- aire de la tension sur le resau electrique a tres haute tension francaise: bilan du systeme actuel et perspectives d' evolution( Reglage Coordonne 1 'I, E. D. F. Bulletin, Serie B, Dec. 1986. D. I. Sun, B,Ashley, B. Brewer, A. Hughes, U. F. Tinney, "Optimal Power Flow by Newton Approach",IEEE Trans- actions on PAS, Vol. PAS-103, Oct. 1984. U. F. Tinney, D. I. Sun, "Optimal Power Flow: Research and Code Development",EPRI Research Project 1724-1. Final Report EL-4849, Feb. 1987. D. I. Sun, T. Hu, G. Lin, C. Chen, "Experiencies with Im- plementing Optimal Power Flow for Reactive Sched- uling in the Taiwan Power System",IEEE PES Sumner Meeting, San Francisco, CA, Paper 87 SM 505-1, July 1987. U. F.Tinney, J.M.Bright,K.D.Demaree, B. A.Hughes, "Some Deficiencies in Optimal Power Flow", IEEE PICA Conf. Proc., Montreal, Canada, May 1987. R. C. Burchett, H. H. Happ, D. R. Vierath, "Quadratically Convergent Optimal Power Flow",IEEE Transactions on

M.A.El-Kady, B.D.Bel1, V.F.Carvalho, R.C.Burchett, H. H. Happ, D. R. Vierath, "Assessment of Real-Time Op- timal Voltage Control", IEEE Transactions on PWRS,

R. Eichler, G. Schellstede, "Optimal Power Flow Func- tions: Application and Modelling Aspects", IFAC Symposium, Brussels, Belgium, Sep. 1988.

PAS, Vol. PAS-103, Oct. 1984.

Vol. PWRS-1, May 1986.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

V.Arcidiacono, S.Corsi, A.Garzillo, M. Mocenigo, "Studies on Area Voltage and Reactive Power Control at ENEL", CIGRE Symposium, Dortmund, 1977, Report

J. Zaborsky, H. Huang, S . Y. Lin, "Control of Reactive Power and Voltage in Emergencies", Automatica, Vol. 21, No. 3, 1985. P.Lagonotte, J.C.Sabonnadiere, J.Y.Leost, J.P. Paul, "Structural Analysis of the Electrical System: Ap- plication to Secondary Voltage Control in France", IEEE PES Sunmer Meeting, Portland, OR, Paper 88 SM 670-2, July 1988. L. Franchi, M. Innorta, P. Marannino, E. Mariani, C.Sa- bel 1 i, D. Sapora, "Optimal Short-Term Reactive Sched- uling for a Large Power Systems", Proceedings 7th PSCC, Lausanne, 1981. L. Franchi, M. Innorta, P. Maxannino, C. Sabell i, "Eval- uation of Economy and/or Security Oriented Objec- tive Functions for Reactive Power Scheduling in Large Scale Systems", IEEE Transactions on PAS,

A.Capasso, P.Marannino, E.Mariani, C.Sabelli, "Co- ordination of Voltage Compound and Reference Values in the AVRs of Generators of a Production and Tran- smission Network", IFAC Symposium, Pretoria, 1980. M. S. CaloviC, "Modeling and Analysis of ULTC Trans- formers in Voltage and VAR Control Applications", University of Illinois, Report # PAP-TR-83-3,1983. A. D. Papalexopoulos, C. F. Imparato, F. F. Wu, "Large Scale Optimal Power F1ow:Effects of Initialization, Decoupling and Discretization", IEEE PES S-r Meeting, Portland, OR, Paper SM 734-6, July 1988. S. M. Chan, V. Brandwajn, "Partial Matrix Refactori- zation", IEEE Transactions on PWRS, Vol. PWRS-1, Feb. 1986. P. RistanoviC, M. BjelogrliC, B. S . BabiC, "Improve- ments in Sparse Matrix/Vector Technique Applica- tions for On-Line Load Flow Calculation", IEEE PES Winter Meeting, New York, NY, Paper UM 203-2, Feb. 1988. A. Gomez, L.G. Franquelo, "An Efficient Ordering Al- gorithm to Improve Sparse Vector Methods", IEEE PES Winter Meeting, New York, NY, Paper 88 WM 165-3, Feb. 1988.

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Milan BjelogrliC was born in Gacko, Hercegovina, on june 27, 1948. He received the B.S. and M.S. degree in electrical engineering in 1971 and 1983, respectively, both from Belgrade University. From 1971 to 1982 he was working for the Electric Power Board of Yugoslavia. Since 1982 he has been working for the Electric Power Board of Serbia. His current research interests include power systems operation planning and real-time control. Milan S. bloviC got his B.S., M.S. and Ph.D. degrees from University of Belgrade in 1957, 1966 and 1973, respectively. He is currently professor at the Univer- sity of Belgrade, Dept. of Electrical Engineering, in Bel grade, Yugoslavia. B.S.BabiC was born in Bileca, Hercegovina, in 1941. He received B.S. and M.S. degree in electrical engineering in 1966 and 1980, respectively, both from Belgrade Uni- versity. From 1966 to 1980 he has been working in the Electrical Engineering Institute Nikola Tesla in Elec- tric Power Systems Analysis Division. From 1980 to 1987 he has been working as a head of Electronic Data Processing Sector, Jugohemija, Belgrade. Today he works as a head of Studie and Research Department, Electric Power Board of Serbia, Belgrade. His current research interests include real-time preventive control of electric power systems and optimal power flow analysis. Petar RistanoviC was born in Belgrade, Yugoslavia, on august 1 , 1958. He received the B.S. degree in electrical engineering from Belgrade University in 1983. Since 1984 he has been working in the Electrical Engineering Institute Nikola Tesla, Belgrade, Automatic and Control Division. His current research interests include real- -time security analysis,optimal power flow analysis and expert systems for real-time optimal voltage control.

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Documents

Bjelogrlic, M., Calovic, M. S., Ristanovic, P., Babic, B. S.,