Application of Generalized Instantaneous Reactive/ Non-active Power Theories in the Control of Shunt Active Power Line Conditioners: Practical Evaluation under Nonideal Voltage and Unbalanced Load Mihaela Popescu, Alexandra Pătraşcu, and Mircea Dobriceanu University of Craiova, Faculty of Electrical Engineering, Decebal Bd. 107, 200440 Craiova, Romania {mpopescu,apatrascu,mdobriceanu}@em.ucv.ro Abstract. This paper is focused on the practical evaluation of two generalized theories of powers in phase coordinate system, namely generalized instantaneous reactive power and generalized instantaneous non-active power, by their implementation in the real time control of a three-phase three-wire shunt active power line conditioner through a dSPACE-based platform. Based on each theory concepts, specific blocks for reference current generation to achieve the global compensation were conceived first. Then, experimental tests were conducted to prove the ability of the active filtering system to compensate a nonlinear distorted and unbalanced load under nonideal voltage conditions. The good dynamics behaviour of the compensating system is illustrated too. Keywords: Active power line conditioner, Generalized instantaneous nonactive power theory, Generalized instantaneous reactive power theory, Nonlinear load. 1 Introduction For quite a long time, the compensation of the nonlinear and distorted load in electric power systems is an important topic in the field of power quality improvement due to the increasingly use of such loads. Clearly, recent advances in power electronics devices and control make the socalled shunt active power line conditioners (APLCs) or active power filters (APFs) the more flexible and efficient solution to eliminate the current harmonic distortion and to compensate both the reactive power and load unbalance. In order to obtain unity power factor or perfect harmonic cancellation after compensation irrespective of the supply voltage waveform, many methods of reference compensating current generation have been adopted until now. Most of them are time domain based and provide either the current to be compensated or the desired supply current after compensation. While the most common approaches involve the transformation from phase coordinate system to stationary or rotating two-phase system in order to apply the p-q V.M. Mladenov and P.C. Ivanov (Eds.): NDES 2014, CCIS 438, pp. 125–133, 2014. © Springer International Publishing Switzerland 2014 126 M. Popescu, A. Pătraşcu, and M. Dobriceanu theory of the instantaneous reactive power concepts [1], [2] or the id-iq method [3], [4], there are different approaches whose implementation does not require any reference frame transformation. This last set refers to the theories such as FryzeBuchholz-Depenbrock (FBD) [5], the generalized instantaneous reactive power [6] and generalized instantaneous non-active power [7]. The attention in this paper is directed to the two above mentioned generalized theories and their practical implementation for total compensation in a shunt compensator through a dSPACE based control system operating together with Matlab/Simulink software. After a brief description of the compensating system, the reference current generation algorithms and the associated developed Simulink blocks are presented. Section 4 refers to the experimental setup and the results achieved under nonideal voltage and unbalanced load, in order to prove the high performance of the developed APLC system. At the end, some conclusions are pointed out. 2 APLC System Structure A shunt APLC including its control system has been developed for experimental testing. As depicted in Fig. 1, the voltage source inverter is connected to the point of common coupling (PCC) by an inductive filter. Power source u Rectifier load is PCC AC controller load iL LC uDC iF Acquisition u iL system iF APL C Nonlinear load uDCref DC iFlos voltage control Compensating iFref current calculation Current control IGBTs’ gating Control system Fig. 1. Single-phase block diagram of shunt APLC system Based on the sensed load currents and supply voltages, the compensating current calculation block generates the reference currents (iFref) by the real time implementation of the adopted algorithm. To keep the DC-voltage at its prescribed value in order to cover the power system losses, the additional compensating current iFloss, which is an active current, is generated by the DC-voltage control block. The ability of the current controller to ensure the accurate tracking of the resulting reference current gives the compensation system efficiency. Application of Generalized Instantaneous Reactive/ Non-active Power Theories 3 127 Reference Current Generation The compensation goal taken into consideration in the reference current generation is to eliminate the load generated harmonics, the load unbalance, as well as the reactive power. Depending on the current decomposition method, the reference compensating current supplied to the current controller (iFref) can be provided either directly from the expression of load current decomposition, or by subtracting the load current (iL) from the desired (reference) supply current (isref), as follows in the vectorial writing: i Fref = i sref − i L , (1) where the vector of the line currents is defined as: i = [i a (t ) ib (t ) ic (t )]T . 3.1 (2) Generalized Instantaneous Reactive Power Theory-Based Approach The foundation of the generalized instantaneous reactive power (GIRP) theory for three-phase power systems, which was introduced by Peng and Lai in 1996, is the decomposition of the current vector into the instantaneous active component (ip) and the instantaneous reactive component (iq) [6]. When used to decompose the load current vector (iL), the associated expression is: i L = i Lp + i Lq . (3) Following the GIRP’s theory concepts, the active and reactive current vectors are expressed by using the instantaneous active power (pL) and the instantaneous reactive power vector (qL), whose definitions make use of the dot product ( · ) and cross product ( x ) of voltage and current vectors, i.e. i Lp = p L (u ⋅ u ) ⋅ u ; pL = u ⋅ i L ; i Lq = (q L × u ) (u ⋅ u ) ; qL = u × iL . (4) (5) The vector u in (4) and (5) corresponds to the three-phase supply voltages system, u = [u a (t ) u b (t ) u c (t )]T . (6) After making evident the average (PL) and oscillatory (pL~) components of pL, expression (3) of the load current can be written as follows: i L = PL (u ⋅ u ) ⋅ u − [− p L ~ (u ⋅ u ) ⋅ u − (q L × u ) (u ⋅ u )] . (7) Thus, for total compensation, the reference current vector to be extracted from PCC is: 128 M. Popescu, A. Pătraşcu, and M. Dobriceanu i Fref = − ( p L − PL ) (u ⋅ u ) ⋅ u − (q L × u ) (u ⋅ u ) . (8) The associated block diagram shown in Fig. 2 was created in Matlab/Simulink and further used for the experimental implementation on a dSPACE-based platform. Fig. 2. Block diagram for total compensation strategy based on the GIRP theory concepts As the quantity in the denominator of the active current given in (4) is not constant when the voltage waveform is distorted, it is expected that the supply current waveform will be more different compared to the voltage waveform as the voltage distortion is higher. 3.2 Generalized Instantaneous Non-active Power Theory-Based Approach The proposal of a generalized decomposition of the load current vector in poly-phase circuits into the instantaneous active component (iLp) and the so-called instantaneous non-active component (iLq) belongs to Peng and Tolbert [7]. From the very beginning, the applicability in shunt compensation was envisaged. Neglecting the compensator power losses, the active power at the supply side (P) during an averaging interval TC is equal to the load active power (PL). As only the active current expression is actually defined and the remaining current is the non-active component, the calculation of the reference compensating current is performed by imposing the desired supply current, as required by (1). The flexibility in implementing the generalized instantaneous non-active power (GINAP) theory for shunt compensation of the load current comes from the general expression of the supply active current, 1 i sref = P U P2 ⋅ u p = TC u(τ ) ⋅ i L (τ )dτ t −TC t 1 T C u p (τ ) ⋅ u p (τ )dτ ⋅ u p , t −TC t (9) where the imposed reference voltages in vector up give the resulting waveforms of the supply line currents. Thus, when unity power factor (UPF) is the compensation goal, up must be the voltage vector itself. But, in order to obtain sinusoidal supply currents and unity displacement power factor, up must contain the fundamental components of u. In the associated Simulink block diagram shown in Fig. 3, the unity power factor strategy is implemented and the equivalent conductance is highlighted. Application of Generalized Instantaneous Reactive/ Non-active Power Theories 129 Moreover, by imposing a proper averaging interval TC in (9) in relation to the fundamental period of the supply voltage (T), both periodic and non-periodic currents can be compensated [8], [9]. Fig. 3. Block diagram for UPF compensation strategy based on the GINAP theory concepts 4 Experimental Setup and Results The experimental tests were conducted on a three-phase 15 kVA laboratory prototype consisting of an IGBT-based voltage source inverter with a DC-link capacitor of 1100 µF and an inductive filter of 4.4 mH on the AC side. Based on dSPACE DS1103 PPC controller board with comprehensive I/O, the real-time control system was implemented via Matlab/Simulink environment. The conceived Simulink model of the control system illustrates the analog to digital conversion, the generation of the prescribed currents, the DC-voltage and current control, the digital to analog conversion and the output signals transfer to the digital I/O channels (Fig. 4). The start-up process and the required protections are also taken into consideration. Fig. 4. Compiled Simulink model for the real time control through dSPACE platform The voltage controller of PI type was designed in accordance with the principle of Modulus Optimum criterion [10], [11]. The DC-voltage prescribed value is 700 V. 130 M. Popescu, A. Pătraşcu, and M. Dobriceanu By adopting a sampling time of 20 μs and a hysteresis band of 0.4 A for the current controller, the IGBTs’ switching frequency was kept below their capability. One of the nonlinear loads is an AC voltage controller manufactured by Nokian Capacitors Ltd. and especially aimed for testing, which allows producing an unbalanced current. It is connected in parallel with a controlled thyristor-bridge rectifier and acts together as the three-phase nonlinear unbalanced load to be compensated. A reactive power exists too. The three-phase nonideal system of supply voltages has an low average harmonic distortion of 2.4 % and an unbalance factor of about 1.4% (Fig. 5 and Fig. 6). Fig. 5. The acquired waveforms in the Control Desk panel in the case of GIRP theory implementation Fig. 6. The acquired waveforms in the Control Desk panel in the case of GINAP theory implementation for TC = T =20 ms Table 1 summarizes the results of the experimental tests conducted for both GIRP and GINAP based methods of reference current generation. As subharmonic and interharmonic components exist in the current drawn by the line-commutated loads, three values of the averaging interval were taken into consideration (i.e. TC = T/2, TC = T and TC = 2T) for the GINAP based method. Application of Generalized Instantaneous Reactive/ Non-active Power Theories 131 To quantify the compensation performance, besides the total harmonic distortion factor (THD) on each phase and its average value (THDe), the three-phase rms value of the line currents (Ie), the unbalance factor (UF) according to IEC definition,. the global power factor (PF) and the displacement power factor (DPF) were calculated. As it can be seen in Table 1 and results displayed in the conceived Control Desk panel (Fig. 5 and Fig. 6), the compensating system is able to significantly improve the power quality at the supply side in all experimental tests. The good dynamics behaviour of the filtering system is shown in Fig. 7. The APLC is charged for UPF compensation through the reference current calculation according to GINAP theory for TC = 20 μs. The steady state regime is rapidly established in both situations of partial coupling of the load and suddenly coupling of the filter. Table 1. Summary of the compensation performance ILa (A) GIRP 19.3 GINAP - T/2 19.4 GINAP - T 18.8 GINAP - 2T 19.4 GIRP GINAP - T/2 GINAP - T GINAP - 2T ILb (A) 17.5 17.7 17.2 17.6 ILc (A) 14.3 14.4 14.2 14.6 ILe (A) 17.1 17.3 16.8 17.3 Load side PL THDLa THDLb THDLc THDLe (W) (%) (%) (%) (%) 8659.0 33.52 31.22 24.37 29.70 8789.1 33.68 30.91 24.63 29.74 8506.9 33.41 31.08 24.35 29.61 8779.3 33.04 30.57 24.67 29.43 Supply side after compensation PS THDSa THDSb THDSc THDSe ISa ISb ISc Ise (A) (A) (A) (A) (W) (%) (%) (%) (%) 14.0 14.3 13.9 14.3 14.1 13.8 13.5 14.1 14.4 14.6 14.3 14.7 14.2 14.2 13.9 14.4 9165.4 9281.1 8998.1 9267.3 4.92 5.29 4.69 5.13 5.69 6.21 6.53 6.38 5.58 5.44 5.16 5.56 5.40 5.65 5.46 5.69 (a) PFL 0.7775 0.7768 0.7769 0.7827 DPFL UFL (%) 0.8140 15.60 0.8131 15.61 0.8135 15.35 0.8185 15.08 PFS DPFS UFS (%) 0.9965 0.9967 0.9971 0.9971 0.9990 0.9987 0.9989 0.9989 1.83 2.93 2.95 2.90 (b) Fig. 7. Experimental phase voltage and supply for GINAP theory implementation when TC = T =20 ms: (a) APLC compensates the AC controller current and the rectifier is suddenly connected; (b) APLC is suddenly connected to compensate the global load. As the existing power supply in the laboratory provides a low degree of distortion in the voltage waveform, there is little difference between the results related to GIRP 132 M. Popescu, A. Pătraşcu, and M. Dobriceanu theory, which was conceived for sinusoidal voltage conditions, and those related to GINAP theory applied for UPF strategy under distorted voltage conditions. The implementation of the two strategies gets the supply currents to be almost sinusoidal and balanced, with a power factor over 0.996. The filtering efficiency, in terms of ratio of average harmonic distortion factors at the load and supply sides, the highest value of 5.5 corresponds to GIRP theory, whereas the lowest value (about 5.17) corresponds to GINAP theory in case of TC = 2T. The unbalance level of the supply current is of about 5 times lower by implementing the GINAP theory are even over 8 times lower through GIRP theory implementation (Table 1). Though a small degree of disturbance is identified in the electric power system, the choice of an averaging interval other then the fundamental cycle does not improve the compensation quality. 5 Conclusions The GIRP and GINAP theories, both of them associated with the phase coordinate system, provide the necessary foundation to develop appropriate strategies for the reference supply current generation in three-phase shunt active line conditioners, so that the total compensation goal is achieved. 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