Modified Dynamic Programming Method for Reactive Power Compensating Device Allocation Goran Majstrovic, Davor Bajs, Matislav Majstrovic, Senior Member, IEEE Abstract – The main topic of this paper refers to reactive power compensating device allocation. By means of modified dynamic programming method, as proposed in this paper, optimal rated power and location of a compensating device are obtained in order to simultaneously satisfy voltage limit constraints, minimize active power loss and avoid voltage collapse in transmission network. In other words, it is necessary to unify all three criteria and find single optimal solution. Software package OPTLOK is developed on the basis of proposed method. At the end, an example given for the realistic transmission network of Croatia is exercised. Croatia, as well as some other South East Europe countries is expected to face serious reactive power compensation problem after the UCTE reconnection that happened recently. Index Terms - reactive power compensation, voltage profile, voltage collapse, active power loss I. INTRODUCTION The main task of each System Operator (SO) is to ensure demanded level of supply quality to its customers. In other words, frequency and voltage profile should be within pre-specified limits at all system nodes with demanded system reliability level. All these criteria should be fulfilled with minimal expenses. Transmission system planning process should include an overview on reactive power compensation problem. Generally, reactive power compensation can be divided into primary, secondary and tertiary regulation. Primary regulation includes performance of high-speed regulating systems such as 1) automatic voltage regulator of synchronous generator excitation systems, 2) on-load tap changing transformers, 3) reactive power compensating devices. Primary regulating devices are usually used for control of smaller variations. Consequently, it is necessary to coordinate reactive power flows from a single hierarchical centre. Secondary regulation aims to change primary regulator input values from a single coordinating centre to reach satisfactory voltage profile in certain part of transmission system. Finally, tertiary regulation assumes coordination of regional secondary regulators. Each SO should have clear rules on primary, secondary and tertiary regulation, especially in deregulated environment where this kind of regulation should be a part of ancillary services market. __________________________________ Goran Majstrovic is with the Energy Institute Hrvoje Pozar, Zagreb, Croatia (e-mail: gmajstro@eihp.hr ; web: www.eihp.hr/~gmajstro ) Davor Bajs is with the Energy Institute Hrvoje Pozar, Zagreb, Croatia (e-mail: dbajs@eihp.hr ; web: www.eihp.hr/~dbajs ) Matislav Majstrovic is with the Energy Institute Hrvoje Pozar, Zagreb and Faculty of Electrical Engineering, University of Split, Croatia (e-mail: matislav@fesb.hr , web: www.eihp.hr/~mmajstro ) Transmission network operation and control can be significantly improved by correct reactive power regulation. Compensating device connection to the power grid influences voltage profile and reactive power flows in the network. Active power loss is also changed. So, reactive power compensation can be analyzed at least from two standpoints: voltage profiles and active power loss. If voltage collapse criterion is added, this problem becomes very complex. Objective function is to find the least cost solution of compensating device connection to transmission grid in order to satisfy voltage profile, minimize active power loss and avoid voltage collapse. Mathematical model presented in this paper comprises all three criteria with regard to operational limits and provides compensating device size and location. II. MATHEMATICAL BACKGROUND At the beginning, it is important to point out that this method assumes optimal engagement of all existing reactive power sources (generators, compensating devices), whereas transformer tap-changer positions are optimized with respect to voltage level in the network. It is assumed that the problem could not be solved by using the existing equipment. Many methods for reactive power compensating device allocation have been developed so far. Existing methods can be divided in several groups as follows: 1) dynamic programming method [1], 2) linear programming method [2], [3], [4], 3) non-linear programming method [5], 4) discrete programming method [6], [7]. The method presented in this paper can be defined as modified dynamic programming method. In classical dynamic programming method [2] after each compensating device switching it is necessary a) to find a new network node with maximal voltage sensitivity coefficient, b) to locate compensating device at that specific node and c) to repeat the procedure till the optimal solution is reached. On the contrary to other methods [2]-[6], programming method proposed in this paper neglects a dynamic component of voltage sensitivity. It calculates the coefficients for many possible system conditions, outages and different system configurations. In that way, average voltage sensitivity coefficients are calculated and single optimal compensating device allocation is obtained for all system states. Also, in the case of more than one candidate for final solution, fuzzy logic approach is used. The main principle used in