Reactive Power Limits in Distributed Generators from Generic Capability Curves Gustavo Valverde, Member, IEEE and Juan J. Orozco Electrical Power Engineering Research Laboratory School of Electrical Engineering, University of Costa Rica 11501-2060 UCR, San Jos´ e, Costa Rica gvalverde@eie.ucr.ac.cr, jorozco@cndcr.com Abstract—This paper presents a generic trapezoid-type capa- bility curve for any distributed generation technology. This curve is used to estimate the machine reactive power limits in terms of the actual active power and terminal voltage. The proposed simplification was tested on synchronous machines, doubly fed induction generators and full power converter interfaced genera- tors. This methodology can be implemented in Volt/VAR control schemes when the estimation of DG capability is required. Index Terms—Voltage control, distributed generation, distri- bution network, reactive power capability, synchronous machine, doubly fed induction machine, full power converters, solar arrays. I. I NTRODUCTION Distributed generators (DG) can absorb or inject reactive power for voltage regulation and operation optimization of the grid [1]. Examples of these opportunities are reported in [2], [3] and [4]. Although many control schemes have assumed fixed DG power limits, reactive limits vary depending on the actual generator active power P and terminal voltage V [5]. Fig. 1 presents the typical reactive power capacity of a DG as a function of active power production and terminal voltage. Note that reactive capacity increases as P reduces. If the DG reactive capacity is fixed at Q lim , the generator capacity will be underused for low P values. Hence, updated reactive power limits could be used to take full advantage of DG capabilities. Actual reactive power limits can be calculated from gen- erator parameters and their respective limiting factors [6]. Unfortunately, these calculations usually require too much information from (most privately owned) DGs, making it difficult to be used by centralized control schemes and on-line applications. Thus, there is a need for estimating the reactive power limits from limited information of DGs. The estimation should be computationally efficient for on- line applications while keeping a reliable level of accuracy. A simplistic model could lead to violation of DG actual limits or impose over restrictions on generators power outputs. This paper proposes a simplified method to calculate reac- tive power limits of distributed generators based on parame- terized generic capability curves. These curves are made of eight points extracted from the actual capability curves for two different terminal voltages. Interpolation is later used to calculate the generator reactive power limits. The remaining of this paper is organized as follows: The main limiting factors of different DG technology is summa- Active Power Reactive Power Fixed Q lim P max unused V 2 V 1 Figure 1. Fixed and actual reactive power limits rized in Section II. The proposed methodology to estimate DG reactive power limits is introduced in Section III. Results and conclusions are presented in Sections IV and V, respectively. II. CAPABILITY CURVE The capability curve defines the machine permissible oper- ating region for a given terminal voltage V [6]. This region is generally bounded by equipment limitations expressed by maximum voltage or current limits. The following sub-sections summarize some of these limits in different DG technologies. The reader should recall that these limits (and approximations in Section III) are often true, but other factors not mentioned here may lead to more or less conservative estimates of the actual capabilities. To be sure, vendors should be asked to provide information regarding DG capability at different operating conditions. A. Synchronous Machines Synchronous generators can be found in distribution net- works driven by small hydro and thermal turbines. The main limiting factors are listed below: - Armature Current Limitation: This limit is defined by the allowable armature winding heating, expressed in terms of a maximum armature current I max a . This limit corresponds to a circle centered at the origin of the Q-P plane with radius VI max a .