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5376 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 A Noniterative Optimized Algorithm for Shunt Active Power Filter Under Distorted and Unbalanced Supply Voltages Parag Kanjiya, Vinod Khadkikar, Member, IEEE, and Hatem H. Zeineldin, Member, IEEE Abstract—In this paper, a single-step noniterative optimized algorithm for a three-phase four-wire shunt active power filter under distorted and unbalanced supply conditions is proposed. The main objective of the proposed algorithm is to optimally determine the conductance factors to maximize the supply-side power factor subject to predefined source current total harmonic distortion (THD) limits and average power balance constraint. Unlike previous methods, the proposed algorithm is simple and fast as it does not incorporate complex iterative optimization techniques (such as Newton–Raphson and sequential quadratic programming), hence making it more effective under dynamic load conditions. Moreover, separate limits on odd and even THDs have been considered. A mathematical expression for determining the optimal conductance factors is derived using the Lagrangian formulation. The effectiveness of the proposed single-step noniterative optimized algorithm is evaluated through comparison with an iterative optimization-based control algorithm and then validated using a real-time hardware-in-the-loop experimental system. The real-time experimental results demonstrate that the proposed method is capable of providing load compensation under steady-state and dynamic load conditions, thus making it more effective for practical applications. Index Terms—Active power filter (APF), harmonic compensation, optimized control, power quality, unity power factor (UPF). I. I NTRODUCTION T HE INCREASING demand of power-electronics-based nonlinear loads has raised several power quality problems. The uneven distribution of dynamically changing single-phase loads gives rise to the additional problems of excessive neutral current and current unbalance (UB) [1]. The combined effects of the above on today’s power distribution systems result in increased voltage and current distortions, unbalanced supply voltages, excessive neutral currents, poor power factor, increased losses, and reduced overall efficiency. Manuscript received May 31, 2012; revised August 2, 2012 and October 19, 2012; accepted November 29, 2012. Date of publication December 19, 2012; date of current version June 21, 2013. This work was supported by the Masdar Institute of Science and Technology under MISRG Internal Grant 10PAAA2. P. Kanjiya and V. Khadkikar are with the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates (e-mail: pkanjiya@ masdar.ac.ae; [email protected]). H. H. Zeineldin is with the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates, and also with Cairo University, Giza, Egypt (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2012.2235394 Active power filters (APFs) are widely used to overcome such power quality problems [2]–[5]. There are two main APF control strategies for load compensation when the supply voltages are unbalanced and distorted [6]–[13]: 1) harmonicfree (HF) source currents and 2) unity-power-factor (UPF) source currents. The HF strategy results in sinusoidal source currents [6], while the UPF strategy can achieve minimum rootmean-square (rms) source current magnitudes. Additionally, the UPF strategy can provide effective damping to avoid any resonance [7], [8]. Both HF and UPF control strategies under sinusoidal and balanced supply condition will lead to identical performance. However, when the supply voltages are distorted and unbalanced, HF and UPF operations cannot be achieved simultaneously. For this reason, previous literature in the area of shunt APFs under distorted and unbalanced supply condition use either the HF or the UPF control strategy [6]–[13]. Recently, several approaches have been proposed to combine the advantages of both control strategies using nonlinear optimization techniques [15]–[20]. Papers on optimization-based shunt APF control under distorted and unbalanced voltages can be classified into two main categories. In the first category, the distorted and unbalanced supply voltages of each phase are processed through a set of filters (such as bandpass). The filter gains are optimized considering both voltage total harmonic distortion (THD) and voltage UB limit constraints to achieve the desired compensated voltages. These compensated voltages are then multiplied with constant conductance factors to obtain the desired source currents. In [15], the compensated voltages are obtained in the α−β−0 reference frame, whereas in [16]–[18], the compensated voltages are generated in the a−b−c stationary reference frame to avoid the complex transformation from one frame to the other. As stated in [16]–[18], due to computational delay, the studied approach is not suitable for loads that operate dynamically. In the second category, to reduce the complexity and dimensionality of the optimization problem, the authors in [19] and [20] formulated the optimization problem considering the conductance factors as variables. The conductance factors for each harmonic order are optimally determined. These conductance factors are then multiplied with a balanced set of supply voltages to obtain the desired source currents. In [19], the supply voltages are considered as distorted and balanced. In [20], to enhance the performance of the system under unbalanced and distorted voltages, the balanced set of voltages is 0278-0046/$31.00 © 2012 IEEE KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER extracted using instantaneous symmetrical components along with complex Fourier transform. One of the main disadvantages of all the aforementioned optimization-based approaches is the use of iterative techniques for solving the optimization problem. The use of an iterative technique can result in a computational delay, which can constrain the applicability of these control approaches under dynamic load conditions. As a result, the methods proposed in [15]–[20] focused on steady-state load compensation only. In [21], Pogaku and Green have considered only one conductance factor to compute the reference current for a distributed generator inverter controller in a microgrid application to provide adjustable damping at harmonic frequencies to mitigate voltage distortion. To overcome the aforementioned challenges, a single-step noniterative optimized control algorithm for shunt APFs under distorted and unbalanced supply conditions is proposed in this paper. The algorithm is based on direct calculation of conductance factors without incorporating any iterative optimization technique. It is shown that there is no need to compute the conductance factors for each harmonic order separately. Three conductance factors (for the fundamental, odd, and even harmonics) are sufficient to achieve the desired performance. Since the algorithm is based on direct calculation of the conductance factors (only three) without incorporating any iterative technique, it can effectively work under steady-state as well as dynamic load conditions. The Lagrangian formulation is utilized to develop the proposed single-step noniterative approach. Moreover, to extract a balanced set of voltages from unbalanced and distorted supply voltages, a novel and simple balanced voltage extractor based on synchronous reference frame (SRF) theory is proposed. The performance of the proposed single-step algorithm is evaluated through comparison with the Newton–Raphson (NR)-based optimization-based control algorithm (OCA). A real-time hardware-in-the-loop (HIL) test bed system is developed using an OPAL-RT simulator and a digital signal processor (DSP) DS1103 from dSPACE to validate the performance of the proposed algorithm for practical applications. The real-time experimental results show the compensation effectiveness of the proposed algorithm, particularly under a dynamic load condition. II. E XTRACTION OF BALANCED S ET OF VOLTAGES F ROM D ISTORTED AND U NBALANCED S UPPLY VOLTAGES U SING SRF T HEORY One of the main objectives of the four-leg shunt APF is to achieve balanced source currents by compensating unbalanced load currents. In order to generate the balanced reference source currents to control the shunt APF under distorted and unbalanced supply conditions, a balanced set of voltages needs to be extracted. In [27], a voltage detector approach is given, where the sum of all harmonic components is extracted (by subtracting fundamental positive-sequence voltages from measured voltages) to control the shunt APF for damping the voltage harmonic propagation in distribution systems. The extracted voltages by this method contain unbalanced harmonics as it does not 5377 extract the individual balanced harmonics and cannot be used here directly. To optimally compensate the load currents under unbalanced and distorted supply conditions using a shunt APF, the individual balanced harmonic components were extracted in [20]. An instantaneous symmetrical component theory combined with complex Fourier transform is utilized to extract the balanced set of voltages in [20]. This approach is complex, and the use of a fixed-frequency moving-average technique to carry out integration into the Fourier transform may affect the extraction under the following: 1) supply frequency variations [22] and 2) the presence of interharmonics into the supply voltages. A new approach to extract the balanced set of voltages utilizing SRF theory is proposed in this paper and discussed in the following. Let the three distorted and unbalanced supply voltages at the point of common coupling be represented as follows: vsx (t) = h √ 2 Vxn sin(nωt + θxn ), x = a, b, c (1) n=1 where subscript s denotes the supply, subscript x denotes the phase of the system, n denotes the harmonic order, h denotes the maximum harmonic order (the choice of h will depend on the maximum harmonic order to be expected in the supply voltages, and it is selected by the user), V denotes the rms value of the voltage, and θ denotes the phase angle. For the nth-order harmonic, the voltages given in (1) can be converted into the SRF using Park’s transformation as ⎡ ⎤T ⎡ ⎤ sin n(ωt) cos n(ωt) vsa (t) 2⎣ vdn sin n(ωt − 120) cos n(ωt − 120) ⎦ ⎣ vsb (t) ⎦ = vqn 3 sin n(ωt + 120) cos n(ωt + 120) vsc (t) (2) where ω is the fundamental angular frequency of the supply voltages which can be obtained using the phase-locked loop. vdn and vqn are the direct- and quadrature-axis voltage components of the nth-order harmonic voltage. With this approach, there is no need to extract the positive-, negative-, and zerosequence components separately. The components vdn and vqn can be represented as v̄dn + ṽdn vdn = (3) vqn v̄qn + ṽqn where v̄dn and v̄qn are the dc components corresponding to the balanced part of the nth-order harmonic voltage present in the supply voltages while ṽdn and ṽqn are the ac components corresponding to the unbalanced part of the nth harmonics. The zerosequence component does not contain any information about the balanced part of the voltages; hence, it is not considered in (2). The dc direct- and quadrature-axis components v̄dn and v̄qn can be obtained after processing vdn and vqn through low-pass filters (LPFs). The use of LPFs over fixed-frequency movingaverage filters into the proposed SRF-theory-based extractor gives robustness to the extraction against supply frequency variations and the presence of interharmonics. The balanced set of supply voltages in the stationary reference frame for the 5378 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 nth harmonic is then obtained using inverse Park transform as follows: ⎤ ⎡ ⎤ ⎡ sin n(ωt) cos n(ωt) vsan (t) v̄ ⎣ vsbn (t) ⎦ = ⎣ sin n(ωt − 120) cos n(ωt − 120) ⎦ dn . v̄qn (t) sin n(ωt + 120) cos n(ωt + 120) vscn (4) The above procedure is carried out for n = 1, 2, . . . , h. Finally, the three-phase balanced set of voltages can be expressed as follows: (t) = vsx h vsxn (t), x = a, b, c. (5) n=1 Since all the quantities on the right-hand side of (5) are balanced, vsx represents the balanced set of supply voltages derived from the distorted and unbalanced supply voltages. III. P ROPOSED S INGLE -S TEP N ONITERATIVE O PTIMIZED A LGORITHM To achieve UPF operation, under distorted and unbalanced supply conditions, the following conditions should be satisfied: 1) The source currents should have the same harmonic content as the supply voltages, and 2) all the phase currents should be in phase with their respective phase voltages. This suggests that, in the case of UPF operation, the source current THD should equate to the source voltage THD value while maintaining inphase relationship with respect to the individual phase voltage. Therefore, the source current THD and UB factor may not be within the acceptable limit. By controlling the harmonic ratios and balancing the average power equally among the three phases, the source current THD and UB factor can be maintained within the specified limits. For the source current to meet all the aforementioned constraints while maximizing the power factor, the APF control algorithm is formulated as an optimization problem where the main variable is the conductance factor Gn for each individual harmonic order. Using (5), the desired source currents can be expressed as follows: + i∗sx (t) = G1 vsx1 h Gn vsxn , x = a, b, c (6) n=2 where ∗ denotes the reference or desired quantity. G1 and Gn are the conductance factors for the fundamental and nth-order harmonic components. The values of these conductance factors can be controlled to maximize the power factor while satisfying the average power balance and THD constraints. Since the same conductance factor value will be applied to each phase to achieve balanced source currents, the optimization problem can be solved and formulated considering one phase. The next sections will highlight the proposed problem formulation for determining the optimal conductance factors. A. Objective Function There are various objectives that can be applied to the shunt APF problem which include minimization of the source current THD, minimization of the APF kilovoltampere rating, or maximization of the source power factor [16], [18]. The most practical objective is to maximize the source power factor, which consequently reduces the cost of electricity consumption under power-factor-based tariff (the most commonly used electricity tariff plan for industrial users). Therefore, the objective chosen here is to maximize the power factor which can be achieved by minimizing the square of the apparent power calculated using the extracted balanced set of voltages and the desired source current of any phase [19], [20]. Since both the extracted voltages and the desired source currents are balanced, the threephase rms quantities are equal and thus can be represented as follows: = Vsbn = Vscn = Vsn Vsan , for n = 1, 2, 3, . . . , h ∗ ∗ ∗ ∗ Isan = Isbn = Iscn = Isn (7) where the rms value of the balanced nth-order harmonic voltage of any phase can be computed as follows: 2 + v̄ 2 v̄dn qn . (8) = Vsn 2 Using (7), the objective function f , which is the square of the apparent power of any phase, is given by f= h n=1 2 Vsn h 2 G2n Vsn . (9) n=1 B. Equality Constraint For the desired source currents to be balanced, the three source currents should supply the demanded average total power equally. Therefore, the equality constraint for any phase can be written as PLavg + PLoss 2 − Gn Vsn =0 3 n=1 h (10) where PLavg is the demanded average load power, which is computed using instantaneous three-phase source voltages and load currents. This instantaneous power PL (t) is then processed by an LPF to obtain PLavg . PLoss is the average power required to overcome the losses in the shunt APF and thus to maintain the dc-link voltage. C. Inequality Constraints The approaches discussed in [19] and [20] consider one THD limit on the source current THD (THDi ). As per IEEE Standard 519, the limit on the current distortion for individual even harmonics is 25% of the limit for odd harmonics. To address this, different THD limits for the current distortion due to odd and even harmonics are considered in this paper. The upper bounds on the source current harmonic distortion due to odd and even harmonics are denoted as THDi,max _o and KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER THDi,max _e , respectively. The inequality constraints on current distortion due to odd and even harmonics are given by THD2i_o ≤ THD2i,max _o (11) ≤ THD2i,max _e (12) THD2i_e where THDi_o = THDi_e = h 2 2 o=3,5,... Go Vso G1 Vs1 h 2 2 e=2,4,... Ge Vse G1 Vs1 (13) (14) The source-side power factor is maximum (UPF) when both the source voltage and current THDs are equal (UPF operation). Let THDspec_o and THDspec_e be the user-defined (prespecified) THD limits on the source current harmonic distortion due to odd and even harmonics, respectively. For the cases where the source voltage THDs due to odd and even harmonics (THDv_o and THDv_e ) are greater than THDspec_o and THDspec_e , respectively, the source current THDs should be equal to the prespecified THD values to achieve maximum power factor. On the other hand, for the cases where THDv_o and THDv_e are less than THDspec_o and THDspec_e , respectively, the source current THDs should be equal to the supply voltage THDs to maximize the source-side power factor. This can be mathematically represented as follows: THDi,max _o = THDspec_o , if THDspec_o < THDv_o = THDv_o , otherwise THDi,max _e = THDspec_e , = THDv_e , (15) if THDspec_e < THDv_e . otherwise (16) For optimality, the source current THDs will always reach their upper limits as per (15) and (16), and thus, the inequality constraints given in (11) and (12) can be reformulated as equality constraints as follows: h G2o Vso − THD2i,max _o G21 Vs1 =0 2 2 (17) o=3,5,... h G2e Vse − THD2i,max _e G21 Vs1 = 0. 2 of the problem, and thus, a simple single-step noniterative solution is achievable. D. Proposed Single-Step Noniterative Solution The optimization problem presented in the previous sections is a constrained nonlinear optimization problem where the main variables are the conductance factors. Using the Lagrangian function, the problem can be transformed into an unconstrained optimization problem as follows [25]: L= . 2 h 2 h G2n Vsn 2 n=1 + λ1 PLavg + PLoss 2 − Gn Vsn 3 n=1 h h + λ2 2 G2o Vso − 2 THD2i,max _o G21 Vs1 − 2 THD2i,max _e G21 Vs1 o=3,5,... h + λ3 2 G2e Vse . (19) e=2,4,... By applying the Karush–Kuhn–Tucker optimality conditions to (19) [25], the following set of equations can be derived: h ∂L 2 2 2 2 = 2G1 Vs1 Vsn − λ1 Vs1 − 2G1 λ2 Vs1 THD2i,max _o ∂G1 n=1 − 2G1 λ3 Vs1 THD2i,max _e = 0 2 (20) h ∂L 2 2 2 2 = 2Go Vso Vsn − λ1 Vso − 2Go λ2 Vso = 0, ∂Go n=1 o = 3, 5, . . . , h (21) h ∂L 2 2 2 2 = 2Ge Vse Vsn − λ1 Vse − 2Ge λ3 Vse = 0, ∂Ge n=1 e = 2, 4, . . . , h (22) ∂L PLavg + PLoss 2 − = Gn Vsn =0 ∂λ1 3 n=1 h (18) In the following section, it will be proven that, by converting the inequality constraints given in (11) and (12) into equality constraints as per (17) and (18) [by selecting THDi,max _o/e according to the conditions given in (15) and (16)], the closedform solution of the optimum conductance factors is possible without incorporating any iterative optimization technique. The identification of the optimum source current THDs to achieve the maximum power factor significantly reduces the complexity Vsn n=1 ∂L = ∂λ2 e=2,4,... 5379 ∂L = ∂λ3 h (23) G2o Vso − THD2i,max _o G21 Vs1 =0 (24) G2e Vse − THD2i,max _e G21 Vs1 = 0. (25) 2 2 o=3,5,... h 2 2 e=2,4,... From (21) and (22), it can be deduced that the conductance factors for all odd harmonics as well as for all even harmonics will be equal and can be represented as follows: G3 = G5 = · · · = GH _o (26) G2 = G4 = · · · = GH _e . (27) 5380 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 By substituting (26) and (27) into (23)–(25), the following equations can be derived: PLavg+PLoss 2 −Vs1 G1+GH _o THD2v_o+GH _e THD2v_e =0 3 (28) THD2v_o G2H _o − THD2i,max _o G21=0 (29) THD2v_e G2H _e − THD2i,max _e G21=0 (30) where THDv_o = THDv_e = h o=3,5,... Vs1 2 Vso h e=2,4,... Vs1 2 Vse (31) . (32) From (29) and (30), GH _o and GH _e can be represented in terms of G1 as follows: GH _o = THDi,max _o G1 THDv_o (33) GH _e = THDi,max _e G1 . THDv_e (34) Furthermore, by substituting (33) and (34) into (28), an expression for G1 can be derived as follows: G1 = PLavg +PLoss . 2 3Vs1 (1+THDi,max _o THDv_o +THDi,max _e THDv_e ) (35) Equations (33)–(35) present closed-form mathematical formulas for determining the optimal values for the conductance factors. By substituting the values of G1 , GH _o , and GH _e from (33)–(35) into (6), the reference source currents can be rewritten as i∗sx (t) = G1 vsx1 + GH _o h vsxo o=3,5,... + GH _e h vsxe , x = a, b, c. (36) e=2,4,... Equation (36) suggests that the proposed algorithm may have superior performance compared to the algorithms given in [19] and [20] due to the direct calculation of the conductance factors G1 , GH _o , and GH _e using (33)–(35). The distinguishing features of the proposed single-step optimized approach can be summarized as follows. 1) The proposed approach involves only three conductance factors (one for the fundamental harmonic and two other for odd and even harmonics) as opposed to the h conductance factors in [19] and [20]. This will reduce the complexity of the problem. 2) The different conductance factors for the odd and even harmonics facilitate the selection of separate THD limits on odd and even harmonics. Fig. 1. Flowchart to determine the conductance factors G1 , GH _o , and G H _e . 3) Mathematical formulas that can calculate the optimal conductance factors directly and thus avoid the use of iterative techniques are derived. The direct calculation of G1 , GH _o , and GH _e can greatly reduce the computation time and thus achieve faster response time when compared to other methods [19], [20]. 4) As opposed to the previous approaches in [15]–[20], since the proposed method does not involve an iterative approach, it can be more effective for dynamic load variations. The flowchart of the proposed single-step noniterative solution procedure is shown in Fig. 1. The algorithm will start by measuring the source voltage and extracting the rms value of each balanced harmonic component. This will be used to determine THDv_o and THDv_e . As mentioned previously in (15) and (16), THDv_o and THDv_e will be compared with THDspec_o and THDspec_e , respectively, to determine THDi,max _o and THDi,max _e . For the cases where THDspec_o is less than THDv_o , THDi,max _o will be set equal to THDspec_o . Otherwise, the value of THDi,max _o will be set equal to THDv_o . Similarly, THDi,max _e will be selected by comparing THDspec_e with THDv_e . Using the derived formulas in (33)–(35), the optimal conductance factors are determined. The flowchart is an integral part of the overall control block of the APF which is discussed in the next section. The noniterative solution of the optimization problem with constraints on different power quality factors, such as distortion factor (DF) and K-factor (KF), is also discussed briefly in Appendix III. KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER 5381 (36). The reference source neutral current is set equal to zero. These reference source currents are compared with the actual measured currents using the hysteresis current controller which determine the switching signals for the VSI. V. S IMULATION R ESULTS To verify the performance of the proposed single-step noniterative optimized control algorithm, a detailed simulation study is carried out under the MATLAB/SIMULINK environment. The simulated test system data are given in Appendix I. The performance of the proposed single-step noniterative optimized control algorithm is validated and compared with that of an iterative OCA given in [20]. The simulation studies for both steadystate and dynamic conditions are performed and discussed in the following. Fig. 2. Four-leg VSI-based shunt APF system configuration. A. Case 1: Unbalanced Supply Voltages Distorted With Odd Harmonics Only—Steady-State Load Condition IV. OVERALL C ONTROL B LOCK OF S HUNT APF Fig. 2 represents the system under study which consists of an equivalent grid behind an impedance, combined single- and three-phase loads, and the shunt APF. The four-leg voltagesource inverter (VSI) topology is utilized to realize a threephase four-wire (3P4W) APF system. The overall control block diagram of the proposed single-step noniterative optimized control algorithm to control the shunt APF under distorted and unbalanced supply conditions is shown in Fig. 3. The inputs to the block of single-step calculation of G1 , GH _o , and GH _e are the specified source current THD limits (THDspec_o and THDspec_e ), the demanded average total power (PLavg + PLoss ), and the rms values of the balanced , n = 1, 2, . . . , h). The demanded set of harmonic voltages (Vsn instantaneous load power is calculated as PL (t) = vsa iLa + vsb iLb + vsc iLc . (37) The instantaneous power PL (t) is then processed by an LPF to obtain the average power PLavg . To maintain the dclink capacitor voltage constant at a prespecified value, a small amount of active power should be drawn from the grid. To accomplish this, a discrete proportional–integral (PI) controller is used, which can be given as follows: PLoss (k) = Ploss (k − 1) + Kp {e(k) − e(k − 1)} + Ki e(k) (38) where f ∗ e(k) = vdc − vdc (k) (39) f (k) is the measured instantaneous voltage across where vdc ∗ is the the dc-link capacitor processed through the LPF, vdc reference dc-link voltage, and k is the sample number. Kp and Ki are the proportional and integral gains, respectively, of the PI controller. The rms values of the balanced set of harmonic voltages are calculated as in (8) using the extracted balanced set of harmonic voltages in the SRF. After calculating the conductance factors G1 , GH _o , and GH _e as shown in Fig. 1, the three-phase reference source currents are calculated as in In order to test the proposed approach under distorted and unbalanced supply voltage conditions, the unbalanced threephase supply voltages are expressed in Table I. Fig. 4 shows the simulated results with the proposed singlestep optimized algorithm under steady-state load condition. The profiles of the distorted–unbalanced supply voltages and the nonlinear distorted–unbalanced load currents are given in Fig. 4(a) and (b). Table II gives the rms and THD values of each phase voltage and load current with the source voltage and load current UB factors. The values of the power factor and the source current UB, with APF compensation, using the proposed control algorithm and OCA are also presented in Table II. The UB factor is calculated as follows: UB = avg(rms a, b, c) − min(rms a, b, c) × 100. avg(rms a, b, c) (40) The extracted balanced set of voltages using the d−q transformation method is depicted in Fig. 4(e). The performance of the proposed optimized control algorithm is evaluated for the following three conditions: 1) HF (0% THD) operation; 2) UPF operation; and 3) a specified-THD-limit operation. Fig. 4(f) gives the compensated source currents when the APF is controlled under HF condition using the proposed optimized control. For this case, the THD limits THDspec_o and THDspec_e are set equal to 0%. The source currents after the compensation are balanced and sinusoidal. As noticed from Table II, the THD of the source currents with HF mode of operation is around 1.7%. The power factors in the HF mode measured with respect to the unbalanced supply voltages are 0.955 lagging (phase a), 0.905 lagging (phase b), and 0.884 lagging (phase c), while the power factor of all phases measured with respect to the extracted balanced set of voltages is 0.969 lagging. To test the controller performance, the odd and even THD limits were specified as 100%. As discussed in the previous sections and shown in the flowchart (refer to Fig. 1), the proposed algorithm compares the specified THD limits THDspec_o and THDspec_e of 100% with the balanced set of source voltage 5382 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 Fig. 3. Overall control block diagram for the proposed noniterative optimized control of the four-leg VSI-based shunt APF. TABLE I D ISTORTED AND U NBALANCED S UPPLY VOLTAGES (C ASE 1) THDs THDv_o and THDv_e which, in this case, are 24% and 0%, respectively. The specified THD limits of 100% are greater than the balanced set of supply voltage THDs, and therefore, the control algorithm operates in the UPF mode to achieve the maximum possible power factor operation. Fig. 4(g) illustrates the compensated source currents when the APF system operates in the UPF operation. The UPF with respect to the balanced set of voltages is achieved in this mode of operation with the source current THD close to 24% (equal to the value of the balanced set of supply voltage THDs). The power factors of each phase measured with respect to the unbalanced supply voltages are given in Table II. Finally, the performance of the proposed single-step optimized control algorithm is evaluated considering constraints on source current THD levels while maximizing the power factor. The THD limits of the source currents are specified as 5%. Fig. 4(h) depicts the simulation results under the optimized mode of operation. From Table II, the source current THD is achieved around 5.6% with the source-side power factors, measured with respect to the unbalanced supply voltages, as 0.967 lagging (phase a), 0.912 lagging (phase b), and 0.900 lagging (phase c). The power factor of all the phases is measured to be 0.983 lagging with respect to the extracted balanced set of voltages. Note that the slight increase in the actual source current THD values (greater than specified 5%) is due to the switching operation of the VSI. It can be viewed from the previously discussed three modes that the compensated source current profile in the optimized mode is in between HF and UPF operations. In all the afore- Fig. 4. Simulation results under unbalanced supply voltages distorted with odd harmonics using the proposed single-step optimized control algorithm. (a) Supply voltages. (b) Load currents. (c) Load neutral current. (d) DC-link voltage. (e) Extracted balanced set of voltages. (f) Source currents (HF mode). (g) Source currents (UPF mode). (h) Source currents (optimized mode). mentioned operating modes, the fourth leg of the shunt APF effectively compensates the load neutral current [Fig. 4(c)] and thus reduces the source-side neutral current to zero [shown with cyan color in Fig. 4(f)–(h)]. KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER 5383 TABLE II P ERFORMANCE I NDICES W ITH THE P ROPOSED O PTIMIZED A PPROACH AND THE OCA A PPROACH (S TEADY-S TATE C ONDITION ; C ASE 1) Fig. 5 gives the simulated results for the system under consideration, under three operating modes (HF, UPF, and optimized), with an iterative OCA method. The performance indices of the OCA method are also provided in Table II. As viewed from Figs. 4 and 5 and Table II, the performance of the proposed single-step optimized algorithm is identical to that of the OCA method since the supply voltages are distorted with only odd harmonics and the THD limit in the case of OCA was set the same as THDspec_o . The proposed optimized method, however, requires minimum computational burden compared to the OCA method since the model relies on only three control variables (G1 , GH _o , and GH _e ) and the direct computation of the variables without any iterative technique. Table III gives the comparison between NR-based OCA and the proposed singlestep optimized control method. The steady-state per-unit values used to determine the conductance factors using both methods are given in Appendix II. The CPU used for this study has a Core i5 processor with 4-GB RAM. For the NR method, the optimization problem with seven conductance factors is formulated and solved using MATLAB optimization toolbox [19], [20]. The optimum value is found to be 0.088 which was reached in 0.11 s or 5.5 cycles (average) utilizing eight iterations (average) compared to 10 μs or almost instantaneous (Inst.) for the proposed single-step method. For both cases, 0.11 s and 10 μs represent the times required to compute the conductance factors which do not include the time required for the extraction of the balanced set of voltages. This demonstrates that the proposed optimized algorithm computes the conductance factors almost instantaneously. The extremely low computational time makes the proposed method capable of compensating dynamically changing loads. The results by the NR method, with maximum numbers of iterations set equal to four and two iterations, are shown in Table III. It can be noticed that, despite the reduction in the computational time, the solution is not optimum. Moreover, it is worthy to note that the execution time and the number of iterations taken by the NR method to find the optimum value are highly dependent on the initial guess of the control variables and, in some cases, might not guarantee the global optimal solution. The NR method was run 50 times with random initial guesses Fig. 5. Simulation results under unbalanced supply voltages distorted with odd harmonics using OCA. (a) Supply voltages. (b) Load currents. (c) Load neutral current. (d) DC-link voltage. (e) Extracted balanced set of voltages. (f) Source currents (HF mode). (g) Source currents (UPF mode). (h) Source currents (optimized mode). for all control variables, and it was found that the maximum number of iterations taken was 11 with an execution time of 7.5 cycles, while the minimum number of iterations recorded was three with an execution time of 2.5 cycles. The average number of iterations and the average execution time found for 50 runs of the NR method were eight and 5.5 cycles, respectively. It is important to note that the sampling time of the controller for the shunt APF with the NR method should be higher than the maximum optimization execution time. 5384 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 TABLE III OVERALL C OMPARISON B ETWEEN THE I TERATIVE NR A PPROACH AND THE P ROPOSED N ONITERATIVE S INGLE -S TEP O PTIMIZED A PPROACH Fig. 7. Simulation results for dynamic load condition under unbalanced supply voltages distorted with odd harmonics using an iterative optimization method. (a) Source currents (optimized mode). (b) DC-link voltage. TABLE IV P ERFORMANCE I NDICES W ITH THE P ROPOSED O PTIMIZED A PPROACH AND THE OCA A PPROACH (A FTER L OAD C HANGE ) Fig. 6. Simulation results for dynamic load condition under unbalanced supply voltages distorted with odd harmonics using the proposed algorithm. (a) Supply voltages. (b) Load currents. (c) Source currents (optimized mode). (d) DC-link voltage. B. Case 2: Unbalanced Supply Voltages Distorted With Odd Harmonics Only—Dynamic Load Condition The performance of the proposed control algorithm, considering the distorted and unbalanced supply voltages given in Table I, during a sudden load change condition is illustrated in Fig. 6. To create the dynamic condition, at time t = 0.2 s, the load is changed from L1 to L1+L2 (Appendix I) and again brought back to L1 at time t = 0.3 s. The change in the load current profile can be viewed from Fig. 6(b). The compensated source current profile is shown in Fig. 6(c). As noticed, the APF system with the proposed single-step optimized approach achieves the new steady-state condition within one cycle and without affecting the APF compensation capability during both load increase and decrease. Furthermore, the dc-link controller, as shown in Fig. 6(d), effectively regulates the dc-bus voltage at the set reference value. Under the same dynamic condition, the performance of the iterative OCA method is given in Fig. 7. As observed from Fig. 7(a), the compensated source currents are not balanced. In addition, the dc-link voltage, shown in Fig. 7(b), settles at a new operating point, lower than the set reference value. This is mainly because of the ten-cycle computational delay (maximum execution time of 7.5 cycles plus 2.5-cycle safety margin) in calculating the new conductance factors. Therefore, for a duration of ten cycles, the OCA-based controller tries to compensate the source currents based on the previously computed conductance factors, and thus, the source currents become more distorted and unbalanced. Table IV presents the compensated current THDs, power factors, rms values, and UB factors under the new operating condition using the proposed optimized algorithm and OCA. Thus, this dynamic condition demonstrates the true capability and enhanced performance of the proposed single-step optimized algorithm over other optimization-based approaches. C. Case 3: Unbalanced Supply Voltages Distorted With Both Odd and Even Harmonics—Steady-State Load Condition The superiority of the proposed algorithm over OCA in terms of computation time was highlighted in the previous two cases. In order to show the advantage of having different THD limits on odd and even harmonics, the performance of the proposed algorithm is evaluated and compared with that of OCA under unbalanced supply voltages distorted with both even and odd harmonics (Table V). KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER TABLE V D ISTORTED AND U NBALANCED S UPPLY VOLTAGES (C ASE 3) 5385 its are imposed on odd and even harmonics with the proposed method, the measured second and fourth harmonics in the source currents are 0.95% and 0.88%, respectively (below the limit). The measured odd harmonics (fifth and seventh) in the source currents are within the individual odd harmonic limit as per IEEE Standard 519 with both algorithms. The KF of the source current is slightly higher with the proposed algorithm due to higher amount of higher order harmonics (fifth and seventh) compared to OCA. It is worthy to note that considering different THD limits on odd and even harmonics is one step toward the optimized control of the shunt APF taking into account individual harmonic constraints. As seen from the results, the proposed approach improves upon existing methods. Future work would be to implement a noniterative approach that considers directly constraints on individual harmonics. VI. R EAL -T IME HIL I MPLEMENTATION Fig. 8. Simulation results under unbalanced supply voltages distorted with both odd and even harmonics using the proposed optimized control algorithm and OCA. (a) Supply voltages. (b) Load currents. (c) Source currents (proposed algorithm). (d) Source currents (OCA). The source current THD limit in the case of OCA is set equal to 5%, while the THD limits (THDspec_o and THDspec_e ) in the case of the proposed algorithm are set equal to 4.85% and 1.21%, respectively. THDspec_o is set equal to four times THDspec_e to comply with IEEE Standard 519. The aforementioned limits for the proposed algorithm are calculated using the following to maintain an overall THD limit (THDspec_all ) of 5%: THD2spec_all = THD2spec_o + THD2spec_e . (41) The profiles of the supply voltages and load currents are given in Fig. 8(a) and (b). The compensated source currents using the proposed algorithm are shown in Fig. 8(c), while Fig. 8(d) depicts the source currents using OCA. Note that there is a slight difference in the shape of the source current waveforms with the proposed algorithm and OCA due to different odd and even harmonic levels in the source currents. The different performance indices with the proposed algorithm and OCA are provided in Table VI. The performances of the shunt APF with both algorithms are almost identical in terms of rms value, power factor, and THD of the source currents; the main differences lie in the individual harmonic distortion (IHD), the filter’s kilovoltampere rating, and the KF as shown in Table VI. The average IHDs of the three-phase source currents for both algorithms are shown shaded in Table VI. IEEE Standard 519 recommends that the individual even and odd harmonics in the source current should be less than 1% and 4%, respectively, for a system with short-circuit ratio less than 20. The second and fourth harmonics in the source currents are measured to be 2.88% and 2.62%, respectively, with OCA (shown bold) which are above the individual even harmonic limit as per IEEE Standard 519. On the other hand, since individual lim- A real-time HIL system is built to validate the feasibility of the proposed single-step optimized approach for practical applications. Fig. 9 illustrates the developed laboratory experimental setup. The real-time HIL system is composed of an OPAL-RT digital simulator and a rapid prototyping DSP board from dSPACE, DS1103. The OPAL-RT is a real-time simulation platform based on two Intel Xeon QuadCore 2.40-GHz processors (total of eight cores or CPUs) working under the RTLAB software environment. OPAL-RT is equipped with analog inputs/outputs (16 each) and digital inputs/outputs (32 each). The DS1103 has 20 analog-to-digital converter (ADC) ports, eight digital-to-analog converter (DAC) ports, and 32 digital inputs/outputs. As shown in Fig. 9, the OPAL-RT represents the power system where all the power circuit components, such as the 3P4W unbalanced–distorted source, the unbalanced load, and the shunt APF, are implemented. The DS1103, on the other hand, represents the digital controller for the shunt APF. In an actual practical system, the OPAL-RT will be replaced by the actual power source, load, and inverter, whereas the digital controller will remain the same. The necessary seven signals (three supply voltages, three load currents, and the dcbus voltage) are measured and taken out of OPAL-RT through its DAC ports. These real-time signals are available in the MATLAB/SIMULINK platform on the host computer through the ADC ports of DS1103 and are utilized to generate the reference source currents based on the proposed control algorithm (indirect control). For the neutral current compensation, the source neutral current is directly considered as zero. These generated reference source currents (total of four, namely, three phase currents and one neutral current) are taken out of the DSP through DAC ports. The actual source current signals (total of four, namely, three phase currents and one neutral current) are also taken out from the OPAL-RT. An external analog hysteresis current control board is developed to perform pulsewidth modulation. The actual and reference source current signals are then compared, and the eight necessary switching pulses for the shunt inverter are generated. Finally, these eight switching/gate pulses are transferred to OPAL-RT using digital input–output (I/O) ports and utilized to control the shunt APF inverter in real time. It should be noted that all the signals are 5386 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 TABLE VI P ERFORMANCE I NDICES FOR THE P ROPOSED O PTIMIZED A PPROACH AND THE OCA A PPROACH (S TEADY-S TATE C ONDITION ; C ASE 3) Fig. 9. Laboratory real-time HIL system representation. normalized on a 5-V scale (5 V = 1 p.u.; the base values in Appendix I). The maximum limits on the I/O signals for OPALRT are ±16 and ±10 V for dSPACE. The sampling times for both OPAL-RT and DS1103 systems were 20 μs each. The performance of the shunt APF real-time HIL system is evaluated for both steady-state and dynamic conditions. Fig. 10 gives the real-time test system results. The source voltage and load current profiles in steady state are given in Fig. 10(a) and (b), respectively. It is worthy to note that identical system parameters and load conditions are considered (the same as discussed in Section V-A and B). The real-time experimental results with the proposed optimized algorithm for three different modes of operation are given in Fig. 10(c)–(e). As noticed from Fig. 10(c) for the case of HF operation, the source currents are achieved as balanced and sinusoidal. The actual THD values of the source currents are noticed as 3.9%. The harmonics are mostly due to the sampling time of the OPAL-RT and the switching operation of the inverter. Fig. 10(d) gives the source currents when the optimized algorithm is operated to achieve maximum power factor at 5% THD limit. In this case, the THD of the source currents is measured to be 5.94%. The harmonic spectrum of the phase-a supply voltage, load current, and source current up to the seventh harmonic during 5%-THD-limit operation is given in Table VII. The source current profiles when the THD limits are defined as 100% are illustrated in Fig. 10(e). In this case, the proposed algorithm determines the maximum THD limits by comparing them with a balanced set of source voltages (THDv_o = 24% and THDv_e = 0%). The compensated source currents have a THD of 24.47%. Note that the source currents are identical to the extracted distorted–balanced set of supply voltage profiles shown in Fig. 4(e). The dynamic performance of the proposed noniterative optimized control algorithm is shown in Fig. 10(f)–(i). Initially, the load on the system is a three-phase diode bridge rectifier with a resistor. Suddenly, an unbalanced load is connected to the system. The load current profile due to this dynamic load change is shown in Fig. 10(f). Prior to the load change, the controller is working under HF mode. As seen from Fig. 10(g), the shunt APF system, together with the proposed algorithm, maintains the desired performance. Additionally, as noticed from the three-phase source currents in Fig. 10(h) and (i), the dynamic performance can be achieved in different modes of operation. The load neutral current compensation during dynamic load change is depicted in Fig. 11. It can be seen that the source neutral current is achieved equal to zero by injecting a compensating neutral current opposite to the load neutral current through the fourth leg of the shunt APF. This study thus validates that the proposed optimized control algorithm can perform well under dynamic conditions. VII. C ONCLUSION A single-step noniterative optimized control algorithm has been proposed for a 3P4W shunt APF to achieve an optimum performance between power factor and THD. The proposed optimized approach is simple to implement and does not require complex iterative optimization techniques to determine the conductance factors. It is shown mathematically that only three conductance factors (one for the fundamental harmonic and two other for odd and even harmonics) are sufficient to determine the desired reference source currents. The proposed algorithm determines the conductance factors in 10 μs. Because of the smaller computational time, the proposed algorithm KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER 5387 Fig. 10. Real-time experimental results (scale: X-axis = 10 ms/div and Y -axis = 1 p.u./div for all the quantities except for Vdc where Y -axis = 0.2 p.u./div). (a) Source voltages (vsa , vsb , and vsc ). (b) Load currents (iLa , iLb , iLc , and iLn ). (c) Source currents (HF mode). (d) Source currents (optimized mode). (e) Source currents (UPF mode). (f) Load currents (load change). (g) Phase-a performance (HF-mode load change). (h) Source currents (HF-mode load change). (i) Source currents (optimized-mode load change). TABLE VII H ARMONIC S PECTRUM OF D IFFERENT Q UANTITIES D URING 5%-THD-L IMIT O PERATION performs satisfactorily under dynamically changing load conditions (other optimization-based approaches are limited to steady-state conditions). The performance of the proposed algorithm is validated by a real-time HIL experimental prototype. The satisfactory real-time experimental results for steady-state as well as dynamic conditions demonstrate the feasibility of the proposed algorithm for practical implementation. Fig. 11. Real-time experimental results: Neutral current compensation (scale: X-axis = 10 ms/div and Y -axis = 1 p.u./div). A PPENDIX II A PPENDIX I The system data for simulation as well as experimental study are shown in Table VIII. The steady-state per-unit values used to determine the conductance factors are as follows: THDspecified = 0.05, PLavg = = 0.6566, Vs5 = 0.1389, Vs7 = 0.1, and Vs2 = 0.8645, Vs1 Vs3 = Vs4 = Vs6 = 0. 5388 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 12, DECEMBER 2013 TABLE VIII S YSTEM DATA FOR S IMULATION AS W ELL AS E XPERIMENTAL S TUDY TABLE IX P ERFORMANCE I NDICES ACHIEVED FOR THE O PTIMIZATION P ROBLEM W ITH DF C ONSTRAINT when DFv is less than DFspec , the source current DF should equate to DFspec to achieve maximum possible power factor satisfying the DF constraint. The appropriate value of DFmin can be selected by comparing DFv with DFspec . With this selected value of DFmin , the inequality constraint in (44) can be reformulated as equality constraint and expressed as G21 V1 2 A PPENDIX III O PTIMIZATION P ROBLEM F ORMULATION AND I TS S OLUTION W ITH A LTERNATE P OWER Q UALITY C ONSTRAINTS From (45), GH can be represented in terms of G1 as follows: A. Constraint on Source Current DF The DF describes how the harmonic distortion of the source current affects the effective source power factor. The current DF (DFi ) is defined as the ratio of the fundamental rms current to the total rms current I1rms . Irms (42) The lower the DF, the higher the current distortion; therefore, the lower bound on the source current DF is considered and given as DF ≥ DFmin . (43) As discussed before, to achieve maximum power factor, the conductance factors for all the harmonics should be equal, and here, it is denoted as GH . Using the fundamental conductance factor G1 and the harmonic conductance factor GH , the constraint on the source current DF can be rewritten as G21 V12 G21 V12 ≥ DF2min . + G2H hn=2 Vn2 (45) n=2 In the previous discussion, the optimization problem aiming at maximizing the power factor subject to the power balance and THD constraints was introduced. However, there are various power quality constraints other than THD such as DF and KF that are of technical interest in certain conditions. This section provides a brief discussion on how to formulate and solve an optimization problem to compute optimal conductance factors considering DF and KF. DFi = h 2 1 − DF2min − DF2min G2H Vn = 0. (44) The maximum source-side power factor can be achieved when both the source voltage and current DFs are equal. Let DFspec be the lower bound on the DF specified by the user. To achieve the maximum possible power factor under the condition where the source voltage DF (DFv ) is higher than DFspec , the source current DF should equate to DFv . On the other hand, GH = XDF G1 THDv (46) where XDF = 1 − DF2min . DFmin (47) Using G1 and GH , the power balance constraint given in (10) can be rewritten as PLavg + PLoss 2 − Vs1 G1 + GH THD2v = 0. 3 (48) By substituting (46) into (48), an expression to compute G1 can be derived as follows: G1 = PLavg + PLoss . 2 3Vs1 (1 + XDF THDv ) (49) Equations (46) and (49) present closed-form mathematical expressions to compute the optimal conductance factors which maximize the source-side power factor satisfying the power balance and DF constraints. Using the steady-state per-unit values provided in Appendix II, the optimization problem with DF constraint is solved using (46) and (49). The results achieved with different values of DFspec are tabulated in Table IX. First, DFspec is specified equal to 0%. As discussed earlier, the proposed algorithm compares DFspec with DFv to determine DFmin . As seen from Table IX, the specified DF limit of 0% is less than DFv , and therefore, the control algorithm chose DFmin equal to DFv . With this value of DFmin , the optimum conductance factors which ensure the source current DF (DFi ) within the limit (equal to DFv ) are computed and provided in Table IX. The conductance factors and DFi corresponding to DFspec equal to 98% are also provided in Table IX. Note that DFspec is higher than DFv in this case; therefore, the control algorithm chose DFmin equal to DFspec , and the source current DF (DFi ) is achieved equal to DFspec . KANJIYA et al.: NONITERATIVE OPTIMIZED ALGORITHM FOR SHUNT ACTIVE POWER FILTER TABLE X P ERFORMANCE I NDICES ACHIEVED FOR THE O PTIMIZATION P ROBLEM W ITH KF C ONSTRAINT [4] [5] B. Constraint on Source Current KF Another important power quality factor is the KF, particularly when a nonlinear load is supplied through a transformer. The KF is a weighting of the harmonic currents according to their effects on transformer heating, as derived from ANSI/IEEE C57.110. The KF for current is defined as follows: 2 h 2 In n n=1 I1 (50) KFi = 2 . h n=1 In I1 [6] [7] [8] [9] [10] To limit the transformer heating, the upper bound on KF is given by KFi ≤ KFmax . (51) Let KFspec be the user-defined maximum limit on KF. By comparing KFspec with the source voltage KF (KFv ) and following a similar procedure discussed in the previous section, the inequality constraint in (51) can be converted into equality constraint as follows: h h 2 2 2 2 2 2 2 2 2 n Vn − KFmax G1 V1 +GH Vn = 0. G1 V1 + GH n=2 n=2 (52) From (52), GH can be represented in terms of G1 as follows: GH = XKF G1 where XKF = V1 [11] [12] [13] [14] [15] (53) [16] h KFmax − 1 2 2 n=2 n Vn − KFmax h n=2 Vn2 . (54) The expression for G1 can be derived by substituting GH from (53) into the power balance constraint in (48) PLavg + PLoss . 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Akagi, E. H. Watanabe, and M. Aredes, Instantaneous Power Theory and Applications to Power Conditioning. Hoboken, NJ: Wiley, 2007. Parag Kanjiya received the B.E. degree from Birla Vishvakarma Mahavidyalaya Engineering College, Gujarat Technological University (formerly known as Sardar Patel University), Vallabh Vidhyanagar, India, in 2009 and the M.Tech. degree from the Indian Institute of Technology Delhi (IITD), New Delhi, India, in 2011. Since October 2011, he has been a Research Engineer with the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. His research interests include applications of power electronics in distribution systems, power quality enhancement, HVdc, flexible ac transmission systems, and power system optimization. Mr. Kanjiya was the recipient of the K.S. Prakasa Rao Memorial Award for achieving the highest cumulative grade point average at IITD in August 2011. Vinod Khadkikar (S’06–M’09) received the B.E. degree in electrical engineering from the Government College of Engineering, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India, in 2000, the M.Tech. degree in electrical engineering from the Indian Institute of Technology Delhi, New Delhi, India, in 2002, and the Ph.D. degree in electrical engineering from the École de Technologie Supérieure, Montréal, QC, Canada, in 2008. From December 2008 to March 2010, he was a Postdoctoral Fellow with the University of Western Ontario, London, ON, Canada. Since April 2010, he has been an Assistant Professor with the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. From April 2010 to December 2010, he was a Visiting Faculty member with the Massachusetts Institute of Technology, Cambridge. His research interests include applications of power electronics in distribution systems and renewable energy resources, grid interconnection issues, power quality enhancement, active power filters, and electric vehicles. Hatem H. Zeineldin (M’06) received the B.Sc. and M.Sc. degrees in electrical engineering from Cairo University, Giza, Egypt, in 1999 and 2002, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2006. He worked for Smith and Andersen Electrical Engineering Inc., where he was involved with projects involving distribution system design, protection, and distributed generation. He then was a Visiting Professor at the Massachusetts Institute of Technology, Cambridge. He is currently an Associate Professor with the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates, and a Faculty Member with Cairo University. His research interests include power system protection, distributed generation, and deregulation.