IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 747 Experimental Evaluation of a CPT-Based Four-Leg Active Power Compensator for Distributed Generation Claudio Burgos-Mellado, Carlos Hernández-Carimán, Roberto Cárdenas, Senior Member, IEEE, Doris Sáez, Senior Member, IEEE, Mark Sumner, Senior Member, IEEE, Alessandro Costabeber, Member, IEEE, and Helmo K. Morales Paredes, Member, IEEE Abstract— Four-wire microgrids (MGs) and distribution systems are inherently unbalanced with the presence of negative and zero sequence components in voltages and currents. In small autonomous systems, the imbalance, in addition to the harmonic distortion produced by nonlinear loads, can significantly affect the power quality, loadability, and stability of the system. Furthermore, in isolated networks with significant generation from intermittent renewable energy sources, the stiffness of the system is reduced and this could amplify the effects of imbalance on the stability and power quality. To mitigate some of these problems, a novel methodology based on the application of a four-leg active power filter is proposed in this paper. The control of the compensator is based on the conservative power theory augmented by resonant controllers. The behavior of the proposed system is demonstrated using an experimental prototype deployed in a laboratory scale MG. Index Terms— Active power filter (APF), conservative power theory (CPT), harmonic distortion, imbalance, microgrids (MGs), resonant control. I. INTRODUCTION POWER systems are undergoing a paradigm change, moving from centralized distribution to distributed gen- eration including microgrids (MGs) and smart grids. In dis- tributed generation systems, it is expected that a relatively high penetration of electrical energy provided by noncon- ventional renewable energy (NCRE) sources of intermittent nature will be present, usually connected to the MG using power electronic converters that can affect the stiffness of the network. Droop control is one of the methods typically Manuscript received June 30, 2016; revised October 3, 2016; accepted November 10, 2016. Date of publication November 24, 2016; date of current version May 1, 2017. This work was supported in part by Conicyt under Grant FONDECYT 1140775 and Grant FONDEF ID14I10063 and in part by Conicyt-Basal under Project FB0008. Recommended for publication by Associate Editor Xiongfei Wang. C. Burgos-Mellado, C. Hernández-Carimán, R. Cárdenas, and D. Sáez are with the Department of Electrical Engineering, Facultad de Ciencias Físi- cas y Matemáticas, University of Chile, 8370451 Santiago, Chile (e-mail: rcardenas@ing.uchile.cl). M. Sumner and A. Costabeber are with the PEMC Group, Univer- sity of Nottingham, NG72RD, Nottingham, U.K. (e-mail: mark.sumner@ nottingham.ac.uk). Helmo K. Morales Paredes is with São Paulo State University (Unesp), Institute of Science and Technology, Sorocaba, 18087-180 Sorocaba, Brazil (e-mail: hmorales@sorocaba.unesp.br). 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/JESTPE.2016.2633064 used to share active and reactive power between these gen- erating units [1], [2], and this may lead to some variations in the MG fundamental frequency: this must be considered when designing control systems for active power filter (APF) applications. An MG could be implemented as a low-voltage power distribution system operating in grid connected or islanded mode [3]–[5] feeding single-phase linear and nonlinear loads, typically using three-phase four-wire topologies [6], [7]. These inherently unbalanced loads produce negative and zero sequence components in the currents and voltages of the network. According to [8], the ratio of unbalanced to balanced loads will increase in the future with higher penetration of hybrid and electric vehicles, heat pumps, and so on. In this context, some well-known problems related to load imbalance could appear [9]. For instance, negative sequence voltage components produce oscillations in the torque of induction machines and synchronous generators. This in turn may reduce the efficiency and useful life of these machines [8], [10]. Other effects of imbalance are localized heating in machines and power converters, and reduced loadability of conventional synchronous generators (see [10], [11]), which affects the stability of the MGs [11]. The zero sequence current flowing through the neutral wire can produce additional problems such as overloading of the neutral conductor [9], [12] and malfunction of sensitive equipment due to ground voltage fluc- tuations if the current flowing through the neutral wire is large and/or the impedance of the neutral connection has a relatively large magnitude [9], [12]. In addition, the load served by a four-leg MG could be of nonlinear nature [12]–[14], generating distorted load currents that could also diminish the loadability of the power generating sources in the MG. Several solutions have been proposed in the literature to compensate for imbalance and harmonic distortion [15]–[17]. Among them, APFs are considered appropriate topologies with several papers discussing issues such as the design of the APF’s passive components [6], [12], compensation objectives [8], [18], and serial and/or parallel connection of APFs [6]. The performance of the APF is heavily dependent on the control system applied, which is usually based on a power theory, with many applications using the p–q or modified p–q power theories. However, one of the reported disadvan- tages of these methodologies is their sensitivity to distortion in 2168-6777 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 748 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 Fig. 1. Proposed control strategy for a four-leg compensator connected to a distribution network. the signals and the generation of unwanted current components in some operating conditions [19], [20]. The experimental validation of the control systems and hardware topologies proposed in this paper has been partly based on the operating conditions of a real MG implemented in the north of Canada. The values of total harmonic distor- tion (THD), current imbalance, and variations of the load are based on the experimental data measured at this location. From these data (see Table I and Section IV), it is concluded that the zero sequence current components can have a relatively large magnitude when a real case of an isolated MG operating at a remote location is considered. Most of the previous publi- cations related to the use of APFs in distributed generation are focused on three-leg applications without discussing the problems associated with low-voltage distribution systems that are mainly four-wire systems. Therefore, in this paper, the control of a four-leg APF based on the conservative power theory (CPT) is presented. Unlike previous publication where a four-leg converter is controlled using a fixed duty cycle of 50% in the fourth leg (see [21]), in this paper, full utilization of the dc link is achieved using proper modulation algorithms and control systems. In addition, resonant controllers instead of low dynamic controllers, as those reported in [21] and [22], are designed and implemented in this application. Using a CPT-based algorithm is relatively simple to separate the unwanted current into several decoupled components, for instance, calculating which components are produced by unbalanced or nonlinear loads and which are due to power supply distortion (for accountability purposes [23], [24]). This is important considering that a typical MG has several power converters interfacing the intermittent NCRE sources to the MG. Therefore, it would be advantageous to use the residual VA capability of these converters to share the compensation of unwanted currents. This in turn could reduce the rating of the APF. The proposed compensating topology is shown in Fig. 1. On the left-hand side, the Thévenin equivalent combination of the four-leg power supplies, obtained at the point of common coupling (PCC), is shown. The linear/nonlinear load and the compensator are connected at the PCC. If an energy storage system is required, this could be connected to the dc link of TABLE I MG OPERATING CONDITIONS the APF to provide active power to the MG. The contributions of this paper are as follows. 1) In MGs, relatively large variations in the electrical frequency may occur. The sensitivity to grid frequency variations is a known limitation of the CPT [21], [24], and this paper proposes and validates an implementa- tion approach that shows limited impact of frequency variation on the APF performance. This is confirmed by the experimental results presented in this paper where the performance of the CPT-based power compensator algorithm has been experimentally evaluated during transient operation and under grid frequency variations. Unlike [21], [23]–[25], in this paper, the CPT is applied to four-wire systems considering full control of the four legs in the APF, to regulate the positive, negative, and zero sequence voltages synthesized by the power con- verter. This includes operation of the CPT compensator with single-phase nonlinear loads. 2) The current control is realized using seven paralleled- connected self-tuning resonant controllers in each phase. The tracking of the resonant frequency is realized using a tuning algorithm, based on the real-time discretization of controllers implemented using the bilinear transform with frequency prewarping. As discussed in [26], this discretization method has important advantages, in terms of preserving the resonant frequency accuracy, partic- ularly when high-order harmonics have to be com- pensated for. To the best of the authors’ knowledge, self-tuning adaptive algorithms for the bilinear transform with frequency prewarping have not been discussed in the literature where most of the reported applications are based on the conventional bilinear transform [27]. The rest of this paper is organized as follows. In Section II, the CPT is briefly introduced. In Section III, the proposed control systems for the four-leg APF are discussed. The operating conditions for the small MG in northern Canada are briefly described in Section IV. In Section V, the experimental results obtained from a small prototype are presented. Finally, an appraisal of the proposed methodology is summarized in Section VI. II. CONSERVATIVE POWER THEORY The CPT has been proposed as a new power theory to analyze distribution systems and MGs, where single-phase loads, nonlinear loads, and strong harmonic distortion could BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 749 Fig. 2. Calculation of the compensating currents using the CPT. Only currents of phase A are shown. be present [24], [25]. Using the CPT, an orthogonal separation of the unwanted current components can be achieved to allow selective compensation of them. Moreover, the implementation of a CPT-based control algorithm can be realized in the stationary a–b–c frame: it does not require a synchronous rotating reference frame [24]. The CPT has been discussed before (see [24], [28], [29]). However, for completeness, a brief introduction is presented here. To implement the CPT, two instantaneous quantities are defined [24], [28]. The first is the instantaneous power that corresponds to the scalar product p(t) = v ◦ i = [va vb vc] ◦ [ia ib ic]T . (1) The second is the instantaneous reactive energy defined as w(t) = v̂ ◦ i = [v̂a v̂b v̂c] ◦ [ia ib ic]T (2) where v̂ is the vector containing the unbiased integral of the phase voltages. This vector v̂ is calculated as v̂μ = ∫ t 0 vμ(τ )dτ − v̄∫ μ. (3) Note that the index “μ” (μ = a, b, c) represents the variable per phase and the term v̄∫ μ, corresponds to the average component of each phase voltage integral. For the application depicted in Fig. 1, phase voltages are measured with respect to the neutral conductor at the PCC [24]. Considering the mean values of (1) and (2), the active power (P) and reactive energy (W ) are defined as P = 1 T ∫ T 0 v ◦ i dt andW = 1 T ∫ T 0 v̂ ◦ i dt . (4) Based on (1)–(4), the load current can be decomposed in five orthogonal components. These are: 1) balanced active cur- rents (i b aμ); 2) balanced reactive currents (i b rμ); 3) unbalanced active currents (i u aμ); 4) unbalanced reactive currents (i u rμ); and 5) void currents (ivμ) [24], [28]. The balanced active currents are defined as i b aμ = P V2 vμ = Gbvμ (5) such that V = (V 2 a + V 2 b + V 2 c ) 1/2 is the collective RMS value (Euclidean norm) of the voltage, parameter Gb is the equivalent balanced conductance, and P is the active power. The balanced reactive currents are defined as i b rμ = W V̂ 2 v̂μ = Bbv̂μ (6) such that v̂μ is the unbiased voltage integral, V̂ is the col- lective RMS value of the unbiased voltage integral, Bb is the equivalent balanced reactivity, and W is the reactive energy (see [24], [28]). The unbalanced currents are defined as i u μ = i u aμ + i u rμ = (Gμ − Gb)vμ + (Bμ − Bb)v̂μ (7) where the per-phase conductance and per-phase reactivity are defined as Gμ = Pμ V 2 μ vμ and Bμ = Wμ V̂ 2 μ v̂μ. (8) Note that the unbalanced currents (7) exist only if Gμ �= Gb and/or if Bμ �= Bb, i.e., when the load is unbalanced. In single-phase circuit, the currents of (7) disappear. The void currents are the remaining currents that do not transfer active or reactive energy, and are given by ivμ = iμ − i b aμ − i b rμ − i u μ. (9) All the current components (i.e., i b aμ, i b rμ, i u aμ, i u rμ, and ivμ) are orthogonal. The implementation of the CPT used in this paper is shown in Fig. 2. Voltage and current transducers are used to measure the load currents and voltages at the PCC. In this paper, a bandpass filter (BPF) is used to obtain the unbiased integral of the voltages (i.e., to obtain [v̂a v̂b v̂c]). 750 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 Note that this technique is widely used for the estimation of the magnetic flux in electrical machines [30]. The BPF eliminates the dc component of the signals and behaves as an ideal integrator for frequencies above ≈3 Hz (see [30]). Low-pass filters (LPFs) are used to obtain the average value of the power P and the reactive energy W in each phase. The effective voltages and the Euclidian norms required by the CPT algorithm are calculated in the block labeled “RMS Calculator” shown at the top right of Fig. 2. This RMS calculator utilizes a filter with a transfer function equal to that used in the others LPFs shown in Fig. 2. This filter has been designed with a relatively high cut-off frequency to avoid jeopardizing the overall dynamic response. Note that the application of filters is also necessary to implement APFs based on other power theories, for instance, p–q power theory [19], [31]. As shown in the left-hand side of Fig. 2, the outputs of the CPT algorithm are the currents [i b aμ, i u aμ, i b rμ, i u rμ, ivμ]. These currents are used to calculate the references required by the current control. An important remark related with the practical implemen- tation of the CPT algorithm is the impact of grid frequency variations. As discussed above, the calculation of the unbiased integral (3), of the active power and reactive energy (4), and of the Euclidean norms requires BPFs or LPFs. In [21], these filters have been implemented using moving average digital filters, resulting in selective frequency responses but highly sensitive to grid frequency variations. From a practical perspective, moving average filters must be made frequency adaptive using the frequency measured by a phase-locked loop (PLL). This leads to considerable computational burden that might reduce the attractiveness of CPT-based filters. In this paper, a different approach has been considered: rather than implementing highly selective and adaptive filters, fixed filters with lower selectivity have been adopted. Considering that the range of frequency variations is expected to be narrow, the impact on filtering will also be limited. This choice simplifies the structure of the CPT algorithm, with limited impact on the effectiveness of the algorithm, as demonstrated in the experimental results under grid frequency transients. A final comment about the implementation of the CPT is related with the practical need for complete current decompo- sition. If the APF is designed to fully compensate for the load nonidealities, only the balanced active components (5) of the load current must be evaluated, and all the remaining unwanted components can be derived subtracting the active balanced current from the load current. In this case, the computational burden of the CPT algorithm will be much reduced. On the other hand, if the APF has small power rating, or the active filtering is performed using the residual power capability of distributed generators, it might not be possible to compensate for the nonidealities in full, but an external command could be sent to another APF or power converter (with residual VA capability available) to demand for the compensation of a specific set of unwanted components. For the sake of generality, this paper addresses the case where a full current decomposition is implemented, giving maximum flexibility in the selection of the compensation objectives. Fig. 3. Proposed current control system. The capability of separating the unwanted signals into several orthogonal components (which can be compensated for using several power converters) is a very powerful feature of the CPT algorithm described in (1)–(9). III. PROPOSED CONTROL SYSTEM The proposed control system, for one of the phases, is shown in Fig. 3. In each phase, a PI controller and seven resonant controllers have been implemented in a parallel topology. The PI controller is required to compensate for the load dc components produced when nonlinear loads such as diode rectifiers are connected to the MG. The control system has been implemented in a–b–c coordinates. Resonant controllers have been selected for this applica- tion because they can regulate sinusoidal signals with zero steady-state error in a–b–c coordinates. Moreover, they have better dynamic response than that obtained with other control topologies (e.g., repetitive controllers [22]). In each phase, a PI controller and seven resonant controllers, tuned to regulate the fundamental and the second-, third-, fourth-, fifth-, sixth-, and seventh-order harmonics, have been implemented in this paper. These frequencies have been selected considering the harmonic distortion presented in the case-study MG discussed in Section IV. However, in other cases, the elimination of more (or fewer) harmonic frequencies could be desirable by parallel connection of more resonant controllers. Regarding implementation issues, it is well known that dig- ital signal processors (DSPs) have experienced an exponential development in processing power [32]. Therefore, even if the proposed control algorithm, based on 21 self-tuning resonant controllers, seems relatively complex, it is simple to implement using a commercial DSP with a good processing capability and a suitable field-programmable gate array (FPGA) platform. For instance, the authors have implemented high-order resonant control systems using the low-cost Texas Instrument processor, TMS320C6713 DSK augmented with an Altera FPGA board BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 751 Fig. 4. (a) Pole and zero placement of the resonant part of the PR controller [see the right-side term of (10)]. (b) Control system considering the plant and the converter. (see [33]). A detailed analysis of implementation issues is considered outside the scope of this paper. In a parallel topology, each resonant controller can be sep- arately designed assuming that the response of each controller is selective and alters only the frequency response around its resonant peak [34]. This simplifies the design procedure significantly. A. Control System Design The design and digital implementation of proportional reso- nant (PRs) controllers has been broadly discussed in previous publications (see [26], [33]–[35]) and is briefly summarized here. In the s-plane, a PR controller, designed to regulate a current of frequency ω j , can be written as Gcj (s) = k pj + ki j s s2 + 2ζω j s + ω2 j (10) where ζ is the controller damping and kpj and ki j are the controller gains. Note that (10) is equivalent to the transfer function of a PI controller when ω j = 0. The poles and zero of the resonant part of the PR controller [see the right-side term of (10)] are shown in Fig. 4(a). Note that in this graph, ω j is defined as ω j = ωn . Using Fig. 4(a) and the pole–zero placement method is relatively simple to design the term ωc = ζω j in order to achieve a given bandwidth [36]. Assuming that the term ωc in (10) is very small compared with ωn , the peak amplitude (P) of the resonant part of the controller is obtained when s = jωn . From Fig. 4(a), it is also simple to conclude that for s = j (ωn+ωc) and s = j (ωn−ωc), Fig. 5. Bode diagram of the current control system. the gain is reduced in ≈3 dB, corresponding to an amplitude value of P/ √ 2. Therefore, the term ωc could be used to set the bandpass of the resonant frequency and helps to modify the selectivity of the PR controller of (10) (see [36]). In this paper, ωc = 5 rads−1 has been selected and this value allows to achieve good dynamic performance in the current control loop, as demonstrated by the experimental results presented in this paper. The control diagram for design purposes is shown in Fig. 4(b). Assuming that each controller could be separately designed and that the voltage at the PCC is an external perturbation (unaffected by the operation of the APF), the following transfer function can be derived from Fig. 4(b): i f a i∗ a = Gcj (s)Plant(s)e−STs 1 + Gcj (s)Plant(s)e−STs (11) where the term plant is defined as plant(s) = 1/(sL f + R f ) and ifa is the current injected by the active filter in the phase “a” (see Fig. 3). Note that L f and R f are the inductance and the resistance per phase (respectively) of the impedance connecting the APF to the PCC. A delay of one sample in (11) is used to represent the transfer function of the four- leg APF. This delay is a simplified representation of the effects associated with the power converter modulation algorithm. Adding the transfer functions of the controllers depicted in Fig. 3, the transfer function of the whole current control system (phase A) is obtained as v∗ a f (s) [ i∗ a (s) − i f a(s) ] = kpT + 7 ∑ j=0 [ ki j s s2 + 2ζω j s + ω2 j ] (12) where kpT = ∑ k pj is the overall controller gain. Note that (12) includes the PI controller. There are many control design methods reported in the literature for determining the controller gains kpj and ki j [see (10)] [33], [34]. In this paper, linear control tools such as Bode diagrams and root locus reshaping have been applied to design each of the eight parallel controllers shown in Fig. 3. Assuming that the resonant controllers alter only the frequency response around their own resonant frequency, each controller (as shown in Fig. 3) has been designed for a phase margin of at least 50° and a bandwidth of ≈30 rads−1. The Bode diagram of the proposed control system is shown in Fig. 5. In this paper, the z-plane implementation of (10) is realized by applying the bilinear transform with frequency prewarping 752 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 to (12). This discretization method has been selected because it preserves, with relatively good accuracy, the resonant fre- quency and the phase margin of the original design in the “s”-plane [26], [34]. Therefore, the digital version of (12) is obtained by replacing the Laplace operator “s” using s = ω j tan ( ω j Ts 2 ) ( z − 1 z + 1 ) = kT ω j ( z − 1 z + 1 ) (13) where ω j is the j th controller resonant frequency, Ts is the sampling period, and kT ω j is a nonlinear function of the resonant and sampling frequencies. Replacing (13) in (12), the z-plane transfer function of the current control system is obtained as Note that (14), as shown at the bottom of this page, is the transfer function of a self-tuning resonant control system, which can be used to maintain the control system tuned in spite of changes in the fundamental frequency (ωe = ω1). In this paper, the value of ω1 is estimated using a PLL (as shown in Fig. 3) and used to recalculate the values of kT ω j in (13) and (14), updating the controller coefficients. To the best of our knowledge, the implementation of self- tuning resonant controllers, using the bilinear transform with frequency prewarping, has not been reported before. B. Current Components Supplied by the APF As shown in Fig. 2 and from (5)–(9), the CPT algorithm separates the load current into five orthogonal components [i b aμ, i u aμ, i b rμ, i u rμ, ivμ]. It is assumed that the load active balanced current i b aμ is supplied by the power source, and all the other components are supplied by the APF. Therefore, the unwanted current components being compensated for by the APF are obtained as i∗ μ = i u aμ + irμ + ivμ (15) where irμ = i b rμ+i u rμ [see (6) and (7)]. If the dc-link capacitor of Fig. 1 is floating, the four-leg APF has to supply the converter losses from the grid. Therefore, a balanced active current component has to be added to (15). This is obtained as i b aμ_dc = Pdc V2 vμ (16) where Pdc is obtained from a PI controller (as shown in Fig. 3). Using (15) and (16), the current references are obtained as i∗ μ = i u aμ + irμ + ivμ + i b aμ_dc. (17) As shown in Fig. 3, the current references (i∗ a , i∗ b , and i∗ c ) are processed by 24 controllers (eight per phase, see Fig. 3) generating three instantaneous voltages v∗ a f , v ∗ b f , and v∗ c f . These voltages are modulated by the four-leg converter using a sine-weighted pulsewidth modulation algorithm implemented in the DSPACE experimental platform discussed in Section V. In order to achieve full utilization of the dc link, a common voltage component is added to the modulation signals of all the four legs, including the neutral leg. This additional component is derived according to the well-known min–max algorithm using the methodology proposed in [37] and [38]. This algorithm is briefly summarized in the following. The phase to neutral voltages v∗ a f , v∗ b f , and v∗ c f are calcu- lated as v∗ a f = v∗ az − v∗ f z (18) v∗ b f = v∗ bz − v∗ f z (19) v∗ c f = v∗ cz − v∗ f z (20) where the subscripts a, b, c, and f represent the four legs of the APF and the subscript “z” is used to identify a fictitious neutral point that is located at a midpoint in the dc-link capacitors. The additional component v∗ f z of (18)–(20) is derived using the min–max algorithm [37], where the common component added to each modulation signal is v∗ f z = −min ( v∗ a f , v ∗ b f , v ∗ c f ) + max ( v∗ a f , v ∗ b f , v ∗ c f ) 2 . (21) This guarantees maximum line to neutral voltage generation capability and, therefore, maximum utilization of the dc-link voltage, which is favorably compared with simpler solutions where the fourth leg is modulated at 50% duty cycle and the peak line to neutral voltage is constrained to half the dc-link voltage [21]. It can also be shown that the min–max method discussed in [37] and [38] is equivalent to space vector modulation, and as a result, the line to neutral voltage could increase up to 15.4% when compared with the case where a 50% duty cycle is used for the fourth leg. IV. OPERATING CONDITION OF THE CASE-STUDY MICROGRID To validate the performance of the proposed compensator, the operating conditions of an MG located in the north of Canada have been analyzed. The population of this community is about 1000 inhabitants. The MG power sources are three diesel generators (0.4, 0.6, and 1 MW), 3 × 10 kW Bergey wind turbines, a 30-kW Wenvor wind turbine, and a 10-kW solar PV array. Fig. 6 shows the unifiliar diagram of the MG power system. The operating conditions, measured during the summer season, are presented in Table I. For the experimental work, the unbalanced currents shown in Table I were scaled, using per unit analysis, to currents that could be handled by the experimental prototype built at the Power Electronic Lab, University of Chile. It is important to highlight that the values shown in Table I were used to set the minimum operating conditions for the v∗ a f (z) [ i∗ a (z) − i f a(z) ] = k pT + 7 ∑ 0 [ kTω j ki j (z2 − 1) ( 2ζω j kT ω j + k2 T ω j + ω2 j ) z2 + 2 ( ω2 j − k2 T ω j ) z + ( k2 Tω j + ω2 j − 2ζω j kTω j ) ] (14) BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 753 Fig. 6. Unifiliar diagram of the case-study MG. Fig. 7. Frequency variation. proposed APF. However, in order to test the performance of the proposed system considering the worst case situation, in some of the experimental results discussed in the next section, higher values of THDs, than those shown in Table I, were used. The frequency variation of the MG used as the case study in this paper is shown in Fig. 7. However, for the experimental work presented in this paper, the base frequency is set to 50 Hz corresponding to the nominal frequency used in Chile. V. EXPERIMENTAL RESULTS The control systems depicted in Fig. 3 have been imple- mented in the experimental system shown in Fig. 8. In this paper, an Ametek four-wire programmable power supply emu- lates the four-leg power supply shown in Fig. 1. An Ametek three-phase programmable load of 9 kW (left side of Fig. 8) is used to emulate linear/nonlinear load profiles replicating the operation conditions discussed in Section IV (Table I). A four-leg voltage source power converter, based on the Semikron SKM50GB123D IGBT module, was designed and built for this paper. The control system shown in Fig. 2 is embedded in a DSPACE 1103 platform. The computational time of the proposed control system composed of resonant controllers, LPF/BPF, etc., is less than 50 μs. Hall effect transducers are used to measure the voltages and currents required for the implementation of the CPT algorithm shown in Fig. 3. A switching frequency of 5 kHz is utilized in the four-leg power compensator. To analyze the power quality, a Hioki 3196 power analyzer has been used in this paper. Optical fiber links are used to transmit the switching signals So–S7 (see Fig. 3) required to modulate the voltages v∗ az , v∗ bz , v∗ cz , and v∗ f z in the four-leg power converter. A. Control System Performance for Unbalanced Operation The performance of the CPT-based four-leg APF com- pensating a linear unbalanced system is shown in Fig. 9. Fig. 8. Experimental system. An unbalanced four-wire resistive load of 10, 19.6, and 13.5 � has been programmed in the 3ϕ load. With these resistors, scaled values of the load currents shown in Table I (i.e., 333.07, 247.14, and 172.5 A) are produced. The power source is controlled to supply a balanced voltage of 120 V peak, 50 Hz. The dc-link voltage of the four-leg converter is regulated at 400 V. Fig. 9(a) shows the power supply currents. Note that between 0 and 0.25 s, the compensator control system is disabled and the power supply current is heavily unbalanced with a peak current (phase A) of about 12 A. At t = 0.25 s, the control system is enabled and the APF supplies to the PCC the currents shown in Fig. 9(b), eliminating unwanted components from the power supply currents. Fig. 9(c) shows an amplified view of Fig. 9(a). Note that the current waveforms have little distortion and the dynamic performance is good. The APF compensates for the power supply currents with a settling time of about 30–35 ms. The dynamic performance of the CPT-based control algo- rithm has also been analyzed considering a load step in one of the phases. For this experimental test, the results were captured using a data acquisition interface. The experimental results are shown in Fig. 10. In this case, the APF control system is enabled for the whole test duration. Fig. 10(a) shows the step change in phase B, where the phase to neutral resistance is changed from 19.6 to 8 � (t = 40 ms) changing the phase B current from 10 to 15 A (peak). The magnitude of this load-step variation has been selected based on the values of the negative/zero sequence currents presented in Table I. Note that the peak currents in the other phases (A, C, and N) are not modified during this test. Fig. 10(b) shows the power supply currents. After the load step, the APF compensates for the power supply cur- rents in less than one cycle. For this test, fifth-order LPFs 754 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 Fig. 9. Performance of the proposed APF compensating imbalances produced by a linear resistive load. (a) Currents in the power supply (5 A/50 ms/div). (b) Current supplied by the power compensator (5 A/50 ms/div). (c) Amplified view of (a) (5 A/10 ms/div). Fig. 10. Performance of the proposed control system for an unbalanced load step. (a) Load currents. (b) Power supply currents. with a cut-off frequency of 20 Hz have been used in the implementation of the CPT algorithm shown in Fig. 2 Fig. 11. Performance of the proposed control algorithm compensating nonlinear loads. (a) Power supply currents before and after enabling the APF (10 ms/5 A/div). (b) Neutral current corresponding to the test of Fig. 11(a) (20 ms/5 A/div). (c) Currents supplied by the APF to the PCC (10 ms/div-5 A/div). (see the block labeled LPF). The BPF is also implemented using a fifth-order transfer function. As discussed in Section II, this BPF eliminates the dc component and behaves as an ideal integrator for frequencies above ≈3 Hz. B. Control System Performance Considering a Nonlinear Load To evaluate the performance of the proposed control system to reduce the harmonic distortion in the power supply currents, a nonlinear load was implemented using a star-connected four- wire load of 10 � per phase. A rectifier diode was serially connected to the resistor of phase A. In Fig. 11(a), the power supply currents are shown. Initially, the control system is disabled and only the positive semicycle of the phase A current is flowing. In t = 50 ms, the APF is enabled, and after a relatively fast transient, the current in the power supply becomes well balanced and undistorted. Fig. 11(b) depicts the neutral current, showing that before compensation, the power supply current has a strong zero sequence current component that is heavily distorted. Fig. 11(c) shows the steady-state currents supplied by the APF. The currents in phase A and in the neutral wire have large peak values that are injected to the system in BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 755 Fig. 12. Spectral estimation of the power supply currents. (a) Without compensation. (b) With the proposed four-leg APF. order to eliminate unwanted components (imbalances and reactive and void currents) from the power supply. The THD is compensated for using the proposed methodology. Without the compensator [for t < 50 ms in Fig. 11(a)], the THDs for the power supply currents are 44.47%, 0.4%, and 0.4% (phases A, B, and C, respectively). After the control system is enabled, the THD in phase A is reduced to 2.27%. In the other two phases, the THD is little affected by the operation of the APF, maintaining similar values during the whole test. The spectrum of the power supply currents, corresponding to the experimental test depicted in Fig. 11, is shown in Fig. 12. Fig. 12(a) shows the magnitude of the harmonics before the APF control system is enabled. Note that in phase A, where a nonlinear load is connected, there is a strong dc component and even harmonics (mainly second and fourth) produced by the rectifier diode. When the CPT-based control system is enabled, the harmonics are almost eliminated and there is a significant reduction in the distortion of the power supply currents. One of the reported advantages of the CPT [25], [28] is that the load current can be separated into current components that can be compensated for by different power converters located in the MG, e.g., using the residual VA capability of the power converters interfacing PV and wind energy in Fig. 6. Fig. 13(a) shows a distorted and unbalanced load current that has been obtained by modifying the crest factor, in each phase, of the Ametek programmable load. For this load, the current has been separated into the currents defined by (5)–(7). This separation has been realized by the DSPACE platform in real- time operation. Fig. 13(b) shows the balanced active currents [see (5)]. As mentioned before, this current is supplied by the four-leg power source (as shown in Fig. 1). Fig. 13(c) shows the unbalanced active current component [as shown in (7)], which is supplied by the APF. The unbalanced reactive current components are shown in Fig. 13(d); finally, the void current is shown in Fig. 13(e). For this experimental test, the balanced reactive currents have a negligible magnitude and they are not shown in Fig. 13. Finally, in Fig. 14, the compensated power supply currents, corresponding to the load currents of Fig. 13(a), are shown. Fig. 13. Separation of the load current components using the CPT. (a) Load currents. (b) Balanced active current. (c) Unbalanced active currents. (d) Unbalanced reactive currents. (e) Void currents. C. Operation of the Proposed Four-Leg APF Considering Frequency Variations The electrical frequency of an MG can be subjected to relatively large variations, e.g., produced by the application of P– f droop control or due to the effect of intermittent generation from renewable sources (see Fig. 7). For the correct operation of the proposed control system, self-tuning resonant controllers have been implemented in this paper. In the experimental implementation discussed in this paper, tuning of the resonant controller is achieved by the online calculation of the kT ω j values [as shown in (13) and (14)] required by the bilinear transform with frequency prewarping. In addition, a PLL is necessary to estimate the fundamental frequency of the network (as shown in Fig. 3). To test the performance of the self-tuning resonant control system, the programmable power supply used in this paper is controlled using the frequency profile depicted in Fig. 15. Note that this profile is a piecewise linearization of that shown in Fig. 7 with some modifications. For instance, the duration of 756 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 2, JUNE 2017 Fig. 14. Power supply currents corresponding to the experimental test of Fig. 13(a) (10 ms/div-5 A/div). Fig. 15. Frequency profile used in this paper. Fig. 16. Effective (RMS) currents circulating in the programmable power supply. (a) Power supply neutral current before and after enabling the APF. (b) Power supply phase currents considering the active filter enabled. the profile has been reduced to 10 s and the frequency variation is larger (48–52 Hz). Moreover (as mentioned before), the nominal electrical frequency used in this paper is 50 Hz instead of the 60 Hz utilized for the frequency profile shown in Fig. 7. The performance of the self-tuning algorithm has been tested considering operation of the system, feeding a load programmed with the current profile depicted in Fig. 13(a) and subjected, during 10 s, to the frequency variations shown in Fig. 15. Fig. 16 shows the currents in the programmable power supply (captured using the DSPACE data acquisition system). Note that effective currents are shown because of the problems associated with displaying the instantaneous currents for 10 s. Fig. 17. (a) Fifth harmonic produced by the load current of Fig. 13(a). (b) Fifth harmonic component compensated in the power supply dur- ing a relatively fast frequency transient. (c) Amplified view of (b). (d) Seventh harmonic produced by the load current of Fig. 13(a). (e) Seventh harmonic component compensated in the power supply during the same frequency transient. (f) Amplified view of (e). When the power compensator is enabled, the neutral current shown in Fig. 16(a) is reduced to a small value produced by the zero sequence harmonics that are not compensated for by the APF. As shown in Fig. 16(b), in the phases of the programmable power supply, the effective currents are well balanced. However, because effective currents by themselves cannot be used to demonstrate that the self-tuning algorithm is well tuned, an additional test is proposed and realized in this paper. Frequency-adaptive filters have been programmed to process the data captured by the DSPACE platform. The filters are designed to isolate the fifth and seventh harmonics of phase B in the load and power source currents. In Fig. 17(a) and (b), the fifth harmonics of the load and power supply currents are depicted between t = 5 and 6 s BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 757 (see Fig. 15). Note that the frequency is varying between fe = 48 and 51 Hz during that period of time. As shown in Fig. 17(a), the amplitude of the fifth harmonic in the load current is about 7.1% of the peak current. Fig. 17(b) shows the fifth harmonic component in the power supply current. Even with the relatively large frequency variation produced in this time period, the harmonic has been compensated and its amplitude is only 0.075 A, a reduction of 91% with respect to the uncompensated value. An amplified view of the fifth harmonic present in the power supply current is shown in Fig. 17(c). Using the proposed methodology, the performance of the APF to reject the seventh harmonic has also been evaluated. Again the performance of the APF-based self-tuning resonant controllers is excellent, eliminating most of this harmonic from the power supply current as shown in Fig. 17(d)–(f). The amplitude of the seventh harmonic in the load current is about 3.33% of the peak current. However, the amplitude of the seventh harmonic in the power supply current is only 0.05 A, a reduction of 87.5% with respect to the uncompensated value. VI. CONCLUSION A new methodology for the control of a four-leg APF has been presented in this paper. The proposed control system is based on the CPT augmented with a PI and seven self- tuning resonant controllers in each phase. The compensation is achieved by regulating the positive, negative, and zero sequence voltages modulated by a four-leg voltage source converter. The performance of the proposed control system has been tested considering the operating conditions of an MG located in northern Canada. Using per-unit analysis, the current and voltages have been referred to values that could be handled by the prototype implemented at the University of Chile. 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Wheeler, “Analysis and experimental validation of control systems for four-leg matrix converter applications,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 141–153, Jan. 2012. [34] A. G. Yepes, F. D. Freijedo, Ó. López, and J. Doval-Gandoy, “Analysis and design of resonant current controllers for voltage-source converters by means of Nyquist diagrams and sensitivity function,” IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5231–5250, Nov. 2011. [35] A. Rodríguez, C. Girón, M. Rizo, V. Sáez, E. Bueno, and F. J. Rodríguez, “Comparison of current controllers based on repetitive-based control and second order generalized integrators for active power filters,” in Proc. 35th Annu. Conf. IEEE Ind. Electron. (IECON), Porto, Portugal, Nov. 2009, pp. 3223–3228. [36] S. P. Oe, “Power quality improvement of microgrids, Nottingham,” Ph.D. dissertation, Dept. Elect. Electron. Eng., Univ. Nottingham, Not- tingham, U.K., 2014. [37] J.-H. Kim and S.-K. Sul, “A carrier-based PWM method for three- phase four-leg voltage source converters,” IEEE Trans. Power Electron., vol. 19, no. 1, pp. 66–75, Jan. 2004. [38] D. G. Holmes and Thomas A. Lipo, Pulse Width Modulation for Power Converters: Principles and Practice. Hoboken, NJ, USA: Wiley, 2003, p. 744. Claudio Burgos-Mellado was born in Cunco, Chile. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Chile, Santiago, Chile, in 2012 and 2013, respectively. He is currently pursuing the double-award Ph.D. program in electri- cal engineering with the University of Chile and the University of Nottingham, Nottingham, U.K. His current research interests include battery energy storage systems, electrical vehicle tech- nologies, power electronics, microgrids, and power quality. Carlos Hernández-Carimán was born in Panguipulli, Chile. He received the B.Sc. degree in electronic engineering from the University of Concepción, Concepción, Chile, in 2013, and the M.Sc. degree in electrical engineering from the University of Chile, Santiago, Chile, in 2016. His current research interests include four-leg active filter, power electronics, microgrids, and renewable energy systems. Roberto Cárdenas (S’95–M’97–SM’07) was born in Punta Arenas, Chile. He received the B.S. degree from the University of Magallanes, Punta Arenas, in 1988, and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. He was a Lecturer with the University of Magallanes from 1989 to 1991 and from 1996 to 2008. From 1991 to 1996, he was with the Power Electronics Machines and Control Group, University of Nottingham. From 2009 to 2011, he was with the Electrical Engineering Department, University of Santiago, Santiago, Chile. He is currently a Full Professor of Power Electronics and Drives with the Electrical Engineering Department, University of Chile, Santiago, Chile. His current research interests include the control of electrical machines, variable speed drives, and renewable energy systems. Doris Sáez (S’93–M’96–SM’05) was born in Panguipulli, Chile. She received the M.Sc. and Ph.D. degrees in electrical engineering from the Pontificia Universidad Católica de Chile, Santiago, Chile, in 1995 and 2000, respectively. She is currently an Associate Professor with the Electrical Engineering Department, Univer- sity of Chile, Santiago. She has authored or co-authored the books entitled Hybrid Predic- tive Control for Dynamic Transport Problems (Springer-Verlag, 2013) and Optimization of Indus- trial Processes at Supervisory Level: Application to Control of Thermal Power Plants (Springer-Verlag, 2002). Her current research interests include predictive control, fuzzy control design, fuzzy identification, control of power generation plants, and control of transport systems. Dr. Sáez is an Associate Editor of the IEEE TRANSACTIONS ON FUZZY SYSTEMS. Mark Sumner (SM’05) received the B.Eng. degree in electrical and electronic engineering from Leeds University, Leeds, U.K., in 1986, and the Ph.D. degree in induction motor drives from the University of Nottingham, Nottingham, U.K., in 1990. He was with Rolls Royce Ltd, Ansty, U.K. In 1992, he joined as a Research Assistant and later became a Lecturer at the University of Nottingham, where he is currently a Professor of Electrical Energy Systems. His current research interests include the control of power electronic systems including sensorless motor drives, diagnostics and prognostics for drive systems, power electronics for enhanced power quality, and novel power system fault location strategies. BURGOS-MELLADO et al.: EXPERIMENTAL EVALUATION OF A CPT-BASED FOUR-LEG ACTIVE POWER COMPENSATOR 759 Alessandro Costabeber (S’09–M’13) received the B.S. Degree (Hons.) in electronic engineering and the Ph.D. degree in information engineering with a specialization on energy efficient architectures and control techniques for the development of future residential microgrids from the University of Padova, Padova, Italy, in 2008 and 2012, respectively. From 2012 to 2014, he was a Research Fellow with the University of Padova. In 2014, he joined the Power Electronics Machines and Control Group, Department of Electrical and Electronic Engineer- ing, University of Nottingham, Nottingham, U.K., as a Lecturer in Power Elec- tronics. His current research interests include HVDC converters topologies, high-power density converters for aerospace applications, control solutions and stability analysis of ac and dc microgrids, control and modeling of power converters, power electronics, and control for distributed and renewable energy sources. Dr. Costabeber was a recipient of the IEEE Joseph John Suozzi INTELEC Fellowship Award in Power Electronics in 2011. Helmo K. Morales Paredes (S’10–M’11) received the B.S. degree in electrical engineering from the National University of Saint Agustine, Arequipa, Peru, in 2002, and the M.Sc. and Ph.D. degrees from the University of Campinas, Campinas, Brazil, in 2006 and 2011, respectively. In 2009, he joined the Department of Informa- tion Engineering, University of Padova, Padova, Italy, as a Visiting Student. In 2014, he joined the PEMC Group, Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K., as a Visiting Scholar. Since 2011, he has been an Assistant Professor with São Paulo State University (Unesp), Institute of Science and Technology, Sorocaba, Brazil, where he joined the Group of Automation and Integrating Systems. His current research interests include power quality, power theories and power electronics applied to local and/or cooperative control of compensators, accountability, revenue metering, and grid-connected converters for renewable energy systems and microgrids. Dr. Morales Paredes is a member of the Brazilian Power Electronics Society, Brazilian Automatic Society, IEEE Power Electronics Society, and IEEE Industrial Electronics Society. He was a recipient of the Prize Paper Award in the IEEE TRANSACTIONS ON POWER ELECTRONICS in 2011. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.4 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /sRGB /DoThumbnails true /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize true /OPM 0 /ParseDSCComments false /ParseDSCCommentsForDocInfo true /PreserveCopyPage true 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/ZWAdobeF ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 600 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages false /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 600 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 400 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /CHS /CHT /DAN /DEU /ESP /FRA /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN /KOR /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /PTB /SUO /SVE /ENU (Use these settings to create PDFs that match the "Required" settings for PDF Specification 4.0) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice