IEEE Transactions on Power Systems, Vol. 11, No. 3, August 1996 1473 zy Application of an Optimisation Method for Determining the Reactive Margin from Voltage Collapse in Reactive Power Planning C.J. PARKER Pacific Power, Sydney, Australia Abstract- Reactive power planning requires the computation of the reactive power margin from the point of voltage collapse in the steady-state in order to zyxwvutsrq quantify the adequacy of the level of installed reactive power plant. This reactive margin is the difference between the maximum reactive load distributed across selected zyxwvut system nodes and the reactive load at the planned system operating point. The margin can zyxwvutsrqponm be estimated by applying an optimisatia method using the total reactive load as the objective, with the load flow equations as equality constraints. whilst including system limits such as generator reactive capability limits as inequality constraints. This paper describes a full AC formulation of the optimisation problem. It is solved using an interior point implementation of the Newton method developed for the Optimal Power Flow. This avoids potential difficulties in identifying the binding inequality constraints. I. INTRODUCTION The main factors influencing the adequacy of the level of reactive power support include the network loading level, the load-voltage behaviour, the action of on-load tap changing transformers, generator excitation control and the action of over-excitation limiters, The contribution of these factors to reactive power conditions and voltage collapse events have been thoroughly described throughout the literature [1,2]. The response of system voltage to a disturbanceand system behaviour during a voltage collapse situation zyxwvuts can be regarded as dynamic power system phenomena. However as far as reactive planning is concerned a steady-state approach has been shown generally adequate for providing an indication of the margin from voltage collapse and for determining the Mvar rating of any necessary reactive support plant [1,3]. In reactive planning on the New South Wales (NSW) main grid steady-state analysis is used to determine the margin from voltage collapse and thereby to establish the broad rating for any new reactive sources. Dynamic analysis is separately used to examine the performance and to design the controls 95 SM 586-8 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the 1995 IEEE/PES Summer Meeting, July 23-27, 1995, Portland, OR. Manuscript submitted December 12, 1994; made available for printing April 28, 1995. I.F. MORRISON, D. SUTANTO Department of Electric Power Engineering. University of New South Wales, Sydney, Australia. for system reactive support. Within this context this paper deals with the planning application of an optimisation method for direct determination of the voltage collapse point and the reactive margin of the operating point in the steady-state. 11. OF’TIMISATION METHODS FOR DETERMINING THE REACTIVE MARGIN One class of methods for determining the reactive margin tracks the system state as loads are increased. One example is the QE characteristic, generated by successive load flows. Another example is the optimisation-based methods where the collapse point is determined by maximising the loads in an area of the system, subject to power system constraints. The methods of [4] and [51 find the voltage collapse point by directly solving a set of equations representing the fmt- order stationary conditions of the optimisation problem. These methods are closely allied to that presented in this paper. The interior point algorithm used here provides distinct advantages for constraint enforcement. In addition the full range of voltage and reactive constraints and the limits to tap changer operation, necessary for reactive planning, are included. zy An Interior Point method associated zyxw with a sequential quadratic programing approach to an Optimal Power Flow (OPF) is presented in zyxwvu [6]. Published details of the algorithm are scant but the approach appears similar to that here. 111. SAMPLE POWER SYSTEM The NSW power system, operated by Pacific Power, has a winter peak demand of about l0,OOO zyxw MW and a summer peak demand approaching 9,OOO MW. The main grid, shown in Fig. 1, is supported by a 132 kV transmission system. The voltages at the 500/330 kV busbars of the power stations are controlled by automatic excitation control of the generator and manual control of the on-load tap changer of each step-up transformer. The main load centres are located in the Newcastle, Sydney and Dapto areas and the 330 kV voltage levels in these areas are controlled by switching shunt reactors and capacitors under supervisory control aided by automatic excitation control of syncons (in the Sydney area). About 3200 Mvar of capacitors are installed at the 132 kV level. Reactors total about 1300 Mvar. Transformersbelow the 330 kV level usually have on-load tap changing facilities. Generator A m ’ s are equipped with both load drop compensation (LDC) and an overexcitation 0885-8950/96/$05.00 zyxwvu 0 1995 IEEE