Electric Power Systems Research 90 (2012) 1–10 Contents lists available at SciVerse ScienceDirect Electric Power Systems Research jou rn al h om epage: www.elsevier.com/locate/epsr A generalized compensation theory for active filters based on mathematical optimization in ABC frame Alejandro Garces a,b,∗ , Marta Molinas a , Pedro Rodriguez c a Norwegian University of Science and Technology, Campus Gløshaugen, Trondheim, Norway b Universidad Tecnológica de Pereira, La Julita, Pereira, Colombia c Polytechnic University of Catalunya, Terrassa 08222, Spain a r t i c l e i n f o Article history: Received 24 July 2011 Received in revised form 13 February 2012 Accepted 12 March 2012 Available online 14 April 2012 Keywords: Reactive power compensation ABC theory Optimization Non-linear programming Lagrange multipliers Active filters a b s t r a c t This paper presents a generalization of the ABC compensation theory based on mathematical optimiza- tion which integrates the neutral losses into the optimization model. The classical ABC theory is shown to be a particular case of the presented generalized compensation approach. The main contribution of this paper is the generalization of the ABC theory considering conflictive objectives which include among them the minimization of the network losses. The work presented here takes into account not only con- ventional balanced and pure sinusoidal voltage source but also unbalances and harmonic distortions on the voltage. Four different compensation objectives are studied: invariant instantaneous power, con- stant power, unity power factor, and pure sinusoidal current. Through these four cases, the flexibility and simplicity of implementation of this approach is demonstrated. In addition, the proposed compensation strategy optimizes the line currents and therefore minimizes the network losses. The main contributions A simulation study which considers the switching effect, the control of the DC link and the size of the shunt compensator is presented. Experimental tests are carried out to verify the theory. © 2012 Elsevier B.V. All rights reserved. 1. Introduction It is becoming a stringent need to take into account the pres- ence of non linear loads in modern power systems [1]. One of the most fascinating discussion in this new context is the power def- initions and the physical interpretation of the power terms [2–4]. Flexible operation of active filters will play a key role in the opti- mal operation of those modern power systems by improving the performance of the network and by reducing the negative effects of the non-linear and inductive loads [5]. Several compensation strategies have been proposed for reactive power compensation and active filtering. One of the most important is the pq theory due to its successful and wide spread implementation [6]. Recent developments in power electronics permit more efficient converters that can be used as active filters [7–12]. On the other hand, new control methodologies are also active topics in the field [13,14]. However, one of the most important topics is perhaps the compensation strategy that is going to be used by the active filter. Herrera and Salmerón, have presented a complete review of the ∗ corresponding author at: NTNU – O.S Bragstads plass 2E. 4th floor, Trondheim, Norway. Tel.: +47 73594285. E-mail addresses: alejandrogarces@gmail.com (A. Garces), marta.molinas@elkraft.ntnu.no (M. Molinas), Pedro.Rodriguez@upc.edu (P. Rodriguez). different power theories and compensation strategies in [15–18]. These compensation strategies may be classified in different ways. In this paper, a classification according to the reference frame is proposed: pq-dq based strategies ABC based strategies The pq strategy uses the Clark transformation to define reactive power and all variables in ˛, ˇ stationary frame [19]. A more spe- cialized compensation strategy is the dq which is based on the same principles as the pq but in a rotational reference frame [16]. Many other modifications have been proposed for pq theory, for example in [20] a pqr power theory applicable to four wired systems was presented where the main basis remains the same [19]. On the other hand, the ABC theory, also known as vectorial the- ory due to the formulation presented by Peng and Lai [21], is defined in the three-phase reference frame, simplifying the analysis and the implementation. Czarnecki [22,23] and Williems [24], working in ABC frame, have made important contributions on the physical interpretation of the different components of the power. Despite of the advantages of the ABC frame, theories based on the Clark or Park transformations are the most widely implemented in reactive power compensation due to their robust functionality. However, these theories do not foresee a framework that allows integration 0378-7796/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2012.03.011