Performance investigation of artificial intelligence based controller for three phase four leg shunt active filter

Abstract

In this paper, the choice of power quality compensator is a DSTATCOM which constitutes a three phase four leg voltage source converter (VSC) with a DC capacitor. The control strategy proposed for the DSTATCOM is a neural network based one cycle control (OCC). This control strategy involves neural network block, digital circuits and linear elements, which eliminates the sensors required for sensing the load current and coupling inductor current in addition to the multiplier employed in the conventional method. The calculation of harmonic and reactive currents for the reference current generation is also eliminated, thus minimizing the complexity in the control strategy. The control strategy mitigates harmonic/reactive currents, ensures balanced and sinusoidal source current from the supply mains that are nearly in phase with the supply voltage, compensates neutral current, and maintains voltage across the capacitor under unbalanced source and load conditions. The performance of the DSTATCOM with the proposed artificial neural network (ANN) controllers is validated and investigated through simulations using Matlab software. The simulation results prove the efficacy of the proposed neural network based control strategy under varying source and load conditions.

Graphical abstract

Keywords

neural network / DSTATCOM / neutral current mitigation / total harmonic distortion (THD) / three phase four wire distribution system / unbalanced and/or distorted source

1 Introduction

The proliferation application of various 1- \phi/3- \phi nonlinear loads like uninterruptible power supply (UPS), switched mode power supply (SMPS), solid state drives, etc., results in several power quality problems such as burden of reactive power, distorted current and voltage waveforms which have high harmonic content. Most of the commercial, residential, official and IT industry buildings are unbalanced nonlinear/linear loads connected to the three phase four wire (3P4W) distribution system. These loads are the cause for the enormous flow of neutral current having both fundamental and harmonic currents that create overload on neutral conductor. Unbalanced nonlinear/linear loads connected to the 3P4W distribution system make the utility side to have a lower power factor, decreased energy efficiency, low power handling capacity, and create vulnerable disturbances to the appliances connected to the distribution system [1−4]. The viable solution to eliminating the power quality problems is passive and active filters. The research and development in the area of power electronics prove that active power filters are superior to passive filters due to the evident advantages like less response time, compact size, better performances, etc [5].

In the distribution system, customer power devices (CPDs) are employed for the mitigation of power quality problems. The problems related to the source voltage are solved and suppressed by the series connection of CPD with the load which is coined as a dynamic voltage restorer (DVR) and the problems related to the current are inhibited by the shunt connection of the DSTATCOM which is a CPD across the load. The power quality issues related to both voltage and current are solved by the unified power quality conditioner (UPQC) which is the combination of both the DVR and DSTATCOM [6,7]. The compensation of neutral current along with the mitigation of power quality issues related to source current in a 3P4W distribution system is achieved by the implementation of any of the topologies of DSTATCOM like a 4 leg VSC, a 3 single phase VSC with a capacitor, a 3 leg VSC with a split capacitors, or a 3 leg VSC with any of the transformer connections like T-connection [8,9], Zig-Zag [9], Hexagonal and star-delta transformers [9,10]. The 3 leg VSC with a transformer can mitigate the neutral current to a large extent, but the performance depends upon its impedance, transformer position and the conditions of source voltage. Most of the researchers prefer the 4 leg VSC topology as a better choice for the compensation of neutral current compared to other configurations, in spite of its complex control and cost [5,8−26].

The performance of the DSTATCOM relies on the selection of suitable control strategy with good accuracy, less filter response time with minimal number of calculation steps [27]. To fulfill these requirements, many control strategies are developed and proposed by various researchers, such as the instantaneous reactive power theory (IRP) [28], the space vector pulse width modulation (SVPWM), the power balance theory [14], the synchronous reference frame theory (SRF) [12], etc. The conventional control approaches entail sensors and multipliers to sense the load current and source voltages for the extraction of harmonic and reactive component utilized for the calculation and generation of reference current. To make the controller perform with high accuracy and better speed of response, high speed processor and high performance data converters are essential for the calculation of reference current, but this configuration suffers from evident disadvantages like low stability, more complexity and high cost [8,20,28]. The control strategy without reference current calculation for 3 \phi active power filter (APF) was first reported in literature which is one cycle control (OCC) [29−33].

The conventional controllers such as proportional-integral (PI), proportional-integral-derivative (PID), etc., need precise linear mathematical models which are hard to derive and perform unsatisfactorily during variation in parameters under nonlinear load conditions. In recent years, the major effort of the researchers is made to replace these conventional controllers with a new unconventional control strategy. The recently developed unconventional control approaches, especially neural network controllers, offer the best solution for many complicated power quality problems in the industrial and manufacturing sector. The developed control algorithm can learn, remember and make decisions. The apparent advantages like fast dynamic response, better steady-state and transient stability, robustness, improved tracking and adaptive ability, accuracy and precision under parameter variation make the neural network controller superior to other controllers. The input layer, hidden layer and output layer are the various layers which constitute the feed forward back propagation artificial neural network (ANN). The feed forward back propagation provides a better solution for complex nonlinear problems [34−36]. The performance of the DSTATCOM depends upon the controller used for harmonic current extraction and reference current generation. In the proposed control strategy, the conventional PI controllers are replaced by ANN controller for the control of DSTATCOM. A separate coding is developed for training the ANN controller off-line.

A neural network based OCC algorithm for 3P4W DSTATCOM is proposed in this paper to accomplish the function of power quality compensator. The topology implemented for the DSTATCOM is an IGBT based 4-limb VSC with a DC capacitor where the fourth limb is used to mitigate excessive neutral current with separate neural network control strategy. The proposed neural network based control strategy makes the system robust and simple by the elimination of reference current calculation, voltage sensors and multipliers. The proposed control strategy drives the control variables to meet the requirement in each switching cycle with apparent advantages of high accuracy and faster response by employing a neural network block, an integrator with reset, digital and linear components. Separate ANN controllers are proposed to mitigate the neutral current under unbalanced load and source conditions and to maintain voltage across the capacitor under all varying conditions of source and load. The controller makes the source to supply only the active component of fundamental load current under all possible utility voltage source conditions for the 3P4W distribution system. The features of the ANN based control strategy of the DSTATCOM are balanced and sinusoidal source current from the supply mains that are nearly in phase with the supply voltage, even under unbalanced linear and nonlinear load conditions; reduction in the %THD of source current in the 3P4W distribution system thus making the source current sinusoidal even under varying source and load conditions; compensation of reactive power; regulation of DC bus capacitor voltage under varying load and source conditions; recompense of neutral current under unbalanced load conditions; requirement of sensors for sensing only the source current, while not sensing load current and compensation current, thus requiring less number of sensors when compared to conventional systems; discarding the requirement of high speed processor, data converters and multipliers due to the elimination of reference current calculation; and reduction in the switching losses as the frequency of switching circuit is constant.

2 System configuration of DSTATCOM

Figure 1 depicts the power circuit diagram of a DSTATCOM with a three phase three leg IGBT based VSC and a single phase inverter with a DC capacitor performing as energy buffer, connected to the 3P4W distribution network. Star connection of 3 \phi voltage source with a neutral point realizes the 3P4W supply system. Z_sa, Z_sb and Z_sc represent the impedances of the three phase lines while Z_sn represents the impedance of the neutral conductor. L_c and R_c stand for the coupling inductor and resistor of the DSTATCOM. The capacitor C_dc maintains the DC source voltage V_dc which is feasible, since the DSTATCOM processes only the powers of harmonics and reactive component. In the schematic diagram, the 3P4W DSTATCOM, ripple filter and different types of loads are shunted at the PCC [20,28]. The DSTATCOM fired by appropriate switching signals generates compensating currents and injects the currents into the distribution system. Therefore, the DSTATCOM makes the source to supply only the active part of load current, ensuring the reduction in the %THD of source current, compensating the reactive part of the load current, ensuring the balanced and sinusoidal source current from the supply mains even under unbalance in the three phase load currents, performing voltage regulation during varying load and source conditions [8,20]. The mitigation of neutral current under unbalanced load conditions is accomplished by the fourth limb of the DSTATCOM. The switching transients and ripples present in the PCC are filtered out by the series connection of capacitor C_f and resistor R_f.

3 Proposed control strategy of DSTATCOM

The proposed control strategy generates switching signals for the DSTATCOM by employing a neural network block, an integrator with reset, and digital and linear components. A separate neural network controller is also implemented for the single phase APF to mitigate the neutral current under unbalanced load conditions. The proposed control strategy is preferred for industrial applications due to constant switching frequency and absence of reference current calculation even when the supply voltage is distorted and/or unbalanced with unbalanced linear/nonlinear loads. Two different ANN controllers are proposed in this algorithm to extract the power loss in the inverter and interfacing inductor, thereby keeping up the DC bus capacitor voltage to its reference value by compensating the power loss; and to generate switching signals for single phase APF for mitigation of neutral current under unbalanced load conditions.

In the proposed neural network based control strategy, the control circuit for the DSTATCOM is designed as two independent parts, that is, ANN based control strategy for three leg VSC APF and ANN based reference current generation for neutral current mitigation, for better flexibility of operation.

3.1 ANN based control strategy for three leg VSC APF

As the three leg VSC APF depicted in Fig. 1 requires bidirectional flow of energy between the DC capacitor and source side, it operates in four quadrant with continuous current mode (CCM). Equation (1) gives the steady-state relationship between AC source voltage V _Sand output DC voltage V _dc.

(1) \mathit{K}(\mathit{d}){\mathit{V}}_{\mathrm{dc}}={\mathit{V}}_s,

where {\mathit{V}}_s=\left[\begin{array}{l}{V}_{sa}\\ V_{sb}\\ V_{sc}\end{array}\right] is the AC source voltage vector and d=\left[\begin{array}{l}{d}_{an}\\ d_{bn}\\ d_{cn}\end{array}\right] is the duty ratio vector.

K(d) is expressed as

K(d)=A+Bd

where A and B are linear matrices.

The main aim of the control strategy is to attain unity power factor (UPF) in all the three phases, which can be expressed as

(2) V_s=R_C{I}_s,

where R _C is the connoted resistance that represents the active power of the load and I _S is the source current vector represented as \left[\begin{array}{l}{I}_{sa}\\ I_{sb}\\ I_{sc}\end{array}\right].

Equating Eqs. (1) and (2) gives

(3) R_{\mathrm{s}}{I}_{\mathrm{s}}=K(d)V_{\mathrm{f}},

where R _s is the resistance of current sensor and V _f is defined as

(4) V_f=R_s{\displaystyle \frac{V_{\mathrm{dc}}}{R_C}}.

The signal V _f is obtained from the neural network block, which gives the information of the power loss in the inverter and interfacing inductor, thereby maintaining the DC bus capacitor voltage to its reference value by compensating the power loss. To achieve UPF operation, the switching of the APF must satisfy Eq. (3) and it implies that APF operates on unified constant frequency integration control (UCI).

Figure 2 shows the block diagram of the ANN based OCC for three leg VSC APF. The control circuit consists of three blocks:

1) OCC core: it comprises of an integrator with reset, three adders, two flip-flops and comparators.

2) Vector operation logic: the vector operation logic performs the following functions:

a) The selection circuit for vector region divides the line cycle into six regions in variation with zero crossing point of phase voltage V _a.

b) Selection of the vector current I _p and I _n from the three phase source current with the help of multiplex circuit.

3) Feedback loop: the feedback loop includes a neural network block which extracts the power loss in the inverter and interfacing inductor, thereby keeping up the DC bus capacitor voltage to its reference value by compensating the power loss and feed as input to OCC. The error signal obtained by comparing V _dc and V _ref is fed as the input to the neural network block to derive the modulating signal V _f. The OCC core incorporates the V _f signal along with I _p and I _n vector currents in order to derive the switching drive signals Q _p and Q _n from the flip-flops output. The switch is ON when the Q _p or Q _n is 1 and OFF when it is 0.

With reference to Fig. 2 and the OCC principle in Refs. [29−33], a generalized equation is derived for the entire region (0°−360°) which is represented as

(5) V_f\left[\begin{array}{l}\mathrm{1}-d_p\\ \mathrm{1}-d_n\end{array}\right]=R_s\left[\begin{array}{ll}\mathrm{2}& \mathrm{1}\\ \mathrm{1}& \mathrm{2}\end{array}\right]\left[\begin{array}{l}{i}_p\\ i_n\end{array}\right],d_t=\mathrm{1},

where d _p, d _n, and d _t are duty ratios of switches, i _p and i _n are phase currents of any two phases.

Using Eq. (5), various controlling parameters for the entire region (0°−360°) are calculated and tabulated in Table 1. It shows that the proposed neural network based OCC strategy changes its parameters for every 60°.

3.2 ANN based reference current generation for neutral current mitigation

Figure 3 depicts the block diagram of the ANN based control strategy for neutral current mitigation. The 3- \phi load currents are sensed and summed up using a summer. The reference value i_sn* which is zero is compared with the summed up value i_sn. The difference between the compared values is fed as an input to the ANN controller which generates the reference current signal for the single phase APF. The output of the ANN controller is fed as an input to the hysteresis current controller which generates the gate pulses for the single phase APF.

4 Building of neural network block

The primary requirements for better performance of the DSTATCOM are that the dynamic response of the controller should be high; the reference signal should be processed at a faster rate; and the signals should be sensed with high accuracy.

The performance of the conventional controller is not satisfactory under nonlinear load condition with variation in parameters. But the ANN controller fulfills the above mentioned requirements by maintaining the system stability.

ANN is rapidly flourishing in the discipline of power electronics. This consists of elements that operate in parallel. A neural network when fed with input produces output of a desired target. The neuron model and its contribution are the parameters that produce a particular output for specific input. The generated output is compared to the target to produce a feedback that adjusts the neural network. This adjustment made in neural network now produces an output closer to the target and the process is repeated to attain the target.

For better performance of the DSTATCOM, the feed forward multi-layered back propagation neural network has been designed and trained. About 5000 sets of data of the conventional PI controller and DC link current for n and (n−1) periods have been fetched from the conventional controller Matlab simulation and stored in the workspace. For NN training the stored data are retrieved from the workspace. To train a network, input vectors and related target vectors are habituated until the input vector associates with the specific output vector. The ANN feed forward network topology is shown in Fig. 4.

In this paper, the following neural coding is implemented for normalization, training and generation of neural network block.

[pn,ps]\mathrm{=mapminmax}(p);

[tn,ts]\mathrm{=mapminmax}(t);

\mathrm{net=newff}(pn,tn,50,\{\prime tansig\prime ,\prime tansig\prime ,\prime purelin\prime \},\prime trainlm\prime );

\mathrm{net=init}(\mathrm{net});

\mathrm{net}\mathrm{.trainParam}.show=70;

\mathrm{net}\mathrm{.trainParam}\mathrm{.lr=}.07;

\mathrm{net}\mathrm{.trainParam}.mc\; =0.95;

\mathrm{net}\mathrm{.trainParam}.epochs=900;

\mathrm{net}\mathrm{.trainParam}.goals=1e-6;

[net,tr]\mathrm{=train}(net,pn,tn);

\mathrm{a=sim}(net,pn);

\mathrm{gensim}(net,-1);

[m,b,r]\mathrm{=postreg}(a,t)\mathrm{.}

The first two codes in the program are used to normalize the input data (p) and the target data (t). The neural network (net) is generated with the normalized input and target data by newff using transfer functions and the training algorithm. Various parameters such as epochs, goals, learning rate are specified by coding while generating the neural network. Later the training and simulation of the created neural network is conducted. Depending on the results obtained from training and simulation, the changes in the number of samples of input and target data, and the changes in parameters could be made repeatedly to obtain the desired results. The neural network block is then generated after simulation using gensim. Thus the required trained neural block is obtained using the above coding.

5 Simulation results and discussion

The performance of the propounded neural network control for the DSTATCOM, THD reduction, balancing of load, reactive power compensation and mitigation of neutral current is analyzed for varying load and source conditions using the Matlab/Simulink software. The simulations are also conducted using the conventional OCC controller for all the varying source and load conditions. The performance of the DSTATCOM with the conventional OCC controller is compared with that of the neural network control strategy in Tables 2, 3, 4 and 5. Appendix A lists the details of system parameters. The performance of the propounded DSTATCOM with the ANN control strategy is validated for the following load conditions.

1) Nonlinear load [three 1- \phi bridge rectifiers with RL load] + linear unbalanced load;

2) Nonlinear load [three 1- \phi bridge rectifiers with RL load] + nonlinear load [three 1- \phi bridge rectifiers with RC load];

3) Nonlinear load [three 1- \phi bridge rectifiers with RL load] + nonlinear load [3- \phi controlled bridge rectifier fired at α=15° with RL load];

4) Linear unbalanced load+ nonlinear load [three 1- \phi bridge rectifiers with RL load] + nonlinear load [three 1- \phi bridge rectifiers with RC load];

5) Linear unbalanced load+ nonlinear load [three 1- \phi bridge rectifiers with RC load] + nonlinear load [3- \phi phase controlled bridge rectifier fired at α=15° with RL load];

6) Linear unbalanced load;

7) Nonlinear load [three 1- \phi bridge rectifiers with RL load (i.e., R and L are in series)];

8) Nonlinear load [three 1- \phi bridge rectifiers with RC load (i.e., R and C are in parallel)];

9) Nonlinear load [3- \phi controlled bridge rectifier fired at α=15° with RL load].

The DSTATCOM with the neural network control strategy is simulated for the above nine varying load conditions with the following four different utility conditions of source voltage:

CaseA : ideal voltage source condition.

CaseB : unbalanced sinusoidal voltage source condition.

CaseC : balanced [no unbalance in magnitude and phase] and distorted voltage source condition.

CaseD : unbalanced and distorted voltage source condition.

The details of various source voltage conditions are tabulated in Table 6.

The performance of the DSTATCOM with the neural network control strategy is analyzed and tabulated for all the nine types of loads with the four cases of voltage source condition in Tables 2, 3, 4 and 5. Due to limitation in the number of pages, the waveforms are shown only for load condition 5 with all the four cases of voltage source conditions.

Load condition 5: linear unbalanced load+ nonlinear load [three 1- \phi bridge rectifiers with RC load] + nonlinear load [3- \phi phase controlled bridge rectifier fired at α=15° with RL load].

5.1 Case A: performance of DSTATCOM under ideal voltage source condition

The dynamic performance of the DSTATCOM for the above mentioned source condition is depicted in Fig. 5. The propounded neural network control algorithm reduces the THD of the compensated source current to 0.37%, 0.48%, and 0.49% for phases a, b, and c whereas the load current THD are 12.87%, 8.35%, and 6.83%, respectively. The THD of the compensated supply current is within 5% which is the benchmark value of IEEE-519 recommendation. The neural network based single phase APF reduces the source neutral current from 20.93 A to 0.2792 A which is nearly zero.

5.2 Case B: performance under unbalanced sinusoidal voltage source condition

In many practical applications, the possibility of occurrence of unbalanced source voltage is frequent, which may cause a zero-sequence voltage in the distribution system. To study the effect of unbalance on the DSTATCOM, a magnitude unbalance of 15% sag is made to occur in phases a, b, and c for the time period between t = 0.25 s and 0.35 s and phase unbalance of 20°, −120°, and 120° for the entire time period.

The dynamic performance of the DSTATCOM for the above mentioned source condition is demonstrated in Fig. 6. The propounded neural network control algorithm reduces the THD of the compensated source current to 2.27%, 2.35%, and 2.23% for phases a, b, and c whereas the load current THD are 9.34%, 15.42%, and 7.89%, respectively. The THD of the compensated source current is within 5% which is the benchmark value of IEEE-519 recommendation. The neural network based single phase APF reduces the source neutral current from 21.12 A to 0.276 A which is nearly zero.

5.3 Case C: performance under balanced and distorted voltage source condition

The frequency of occurrence of distorted source voltage condition is likely to be frequent in many practical applications, which may cause a zero-sequence voltage in the distribution system. To study the impact of distorted source voltage condition on the DSTATCOM, 15% of the 3rd and the 5th harmonic are injected into the source for a time period of 0.35 s to 0.5 s.

The dynamic performance of the DSTATCOM for the above mentioned source condition is illustrated in Fig. 7. The propounded neural network control algorithm reduces the THD of the compensated source current to 2.24%, 2.21%, and 2.35% for phases a, b, and c whereas the load current THD are 12.96%, 8.92%, and 6.94%, respectively. The THD of the compensated source current is within 5% which is the benchmark value of IEEE-519 recommendation. The neural network based single phase APF reduces the source neutral current from 20.93 A to 0.2792 A which is nearly zero.

5.4 Case D: performance under unbalanced sinusoidal voltage source condition and distorted voltage source condition

When the source voltage is distorted and also unbalanced, the magnitude of zero sequence voltage is very high and the impact on the load is also critical. To study the impact of distorted and unbalanced voltage source conditions in the DSTATCOM, a magnitude unbalance of 10% sag is made to occur in phases a, b, and c for the time period between 0.25 s to 0.35 s and phase unbalance of 20°, −120°, and 120° for the entire time period along with 15% of the 3rd and the 5th harmonic is injected into the source for a time period of 0.35 s to 0.5 s.

The dynamic performance of the DSTATCOM for the above mentioned source condition is displayed in Fig. 8. The propounded neural network control algorithm reduces the THD of the compensated source current to 2.44%, 2.48%, 2.50% for phases a, b, and c whereas the load current THD are 9.21%, 15.54%, and 7.80%, respectively. The THD of the compensated source current is within 5% which is the benchmark value of IEEE-519 recommendation. The neural network based single phase APF reduces the source neutral current from 21.39 A to 0.276 A which is nearly zero.

The dynamic performance of the neural network based proposed system is validated using the following inferences made from the simulation results.

1) Under all changing conditions of load and source, the source currents are sinusoidal, balanced and nearly in phase with the supply voltage. The %THD of the compensated source current is well below 5% which is the bench mark value of IEEE-519 standard, whereas the %THD of the uncompensated source current is high.

2) When the 1- \phi APF is switched ON, the neutral current of the source is nearly zero which ensures proper neutral current compensation.

3) It is also inferred from the waveform that the DC bus voltage of the DSTATCOM is retained at the reference value under varying load and source conditions.

4) Compensated source current THD is well below 5% even for unbalanced and distorted source voltage condition which makes the load more critical. Harmonic mitigation is achieved effectively in spite of the high harmonic content of the supply voltage.

Based on the performance comparison of the DSTATCOM with the proposed controller and the conventional OCC controller for varying source and load conditions in Tables 2, 3, 4 and 5, it is inferred that the %THD of the source current with the proposed controller is lesser than that of the conventional OCC controller for all varying source and load conditions in most of the cases; the single phase APF with the proposed neural network controller mitigates the source neutral current nearly to zero; and the voltage across the DC bus capacitor is well regulated at 680V using the proposed controller compared to the conventional OCC controller.

6 Conclusions

A neural network based control strategy is proposed and has been implemented for the DSTATCOM in a 3P4W distribution system. The performance of the proposed control strategy is evaluated for all possible source conditions with varying nine types of nonlinear and linear loads. The propounded DSTATCOM performance has been investigated and validated through simulation employing Matlab/Simulink software. The simulation results and tabulation proves the efficacy of the control strategy over the conventional OCC under varying load and source conditions. The dynamic performance of the neural network based DSTATCOM is validated and highlighted using the following inference made from the simulation results.

1) Compensation of harmonic content.

2) Under all changing conditions of load and source, the supply currents are sinusoidal, balanced and nearly in phase with supply voltage.

3) Reactive power compensation.

4) Compensation of neutral current under unbalanced linear and nonlinear loads.

5) Maintenance of DC capacitor voltage to its reference value under all operating conditions. In addition, the proposed control scheme reduces the THD of the source current is well below 5% which is the benchmark value of IEEE-519 standard.

6) The performance of the DSTATCOM with the proposed controller is found to be superior to the conventional OCC controller for all varying source and load conditions.

References

[1] Acha E, Agelids V G, Anaya-Lara O, Miller T J E. Power Electronic Control in Electric Systems (Newness Power Engineering Series). Oxford: Newnes, 2002

[2] Arrillaga J, Watson N R. Power System Harmonics. 2nd ed.New York: John Wiley & Sons Ltd, 2003

[3] Ghosh A, Ledwich G. Power Quality Enhancement Using Custom Power Devices. London: Kluwer Academic Publishers, 2002

[4] Moreno-Munoz A. Power Quality: Mitigation Technologies in a Distributed Environment. London: Springer-Verlag, 2007

[5] IEEE Industry Applications Society. 519−1992—IEEE recommended practices and requirements for harmonics control in electric power systems. IEEE Std. 2014-11-10

[6] Jayachandran J, Preethi N M, Malathi S. Application of fuzzy logic in PWM technique and DC link voltage control for a UPQC system. International Review on Modelling and Simulations, 2013, 6(4): 1198–1204

[7] Jayachandran J, Preetha S A, Malathi S. Power quality improvement in three phase system using neural network controller based unified power quality conditioner. International Review on Modelling and Simulations, 2013, 6(4): 1190–1197

[8] Sreenivasarao D, Agarwal P, Das B. A T-connected transformer based hybrid D-STATCOM for three-phase, four wire systems. International Journal of Electrical Power & Energy Systems, 2013, 44(1): 964–970

[9] Sreenivasarao D, Agarwal P, Das B. Neutral current compensation in three-phase, four-wire systems: a review. Electric Power Systems Research, 2012, 86: 170–180

[10] Jayaprakash P, Singh B, Kothari D P. Three-phase 4-wire DSTATCOM based on H-bridge VSC with a star/hexagon transformer for power quality improvement. In: Proceedings of IEEE Region 10 and the Third International Conference on Industrial and Information Systems. Kharagpur, India, 2008, 1–6

[11] Quinn C A, Mohan N. Active filtering of harmonic currents in three-phase, four-wire systems with three-phase and single-phase nonlinear loads. In: Proceedings of IEEE APEC, 1992, 829–835

[12] Benhabib M C, Saadate S. New control approach for four-wire active power filter based on the use of synchronous reference frame. Electric Power Systems Research, 2005, 73(3): 353–362

[13] Haddad K, Thomas T, Joos G, Jaafari A. Dynamic performance of three phase four wire active filters. In: Proceedings of Conference of the Twelfth Annual Power Electronics Conference and Exposition (APEC). Atlanta, USA, 1997, 206–212

[14] Singh B, Chandra A, Al-Haddad K, Anuradha , Kothari D P. Reactive power compensation and load balancing in electric power distribution systems. International Journal of Electrical Power & Energy Systems, 1998, 20(6): 375–381

[15] Salmeron P, Montano J C, Vazquez J R, Prieto J, Valles A. Compensation in nonsinusoidal, unbalanced three-phase four-wire systems with active power line conditioner. IEEE Transactions on Power Delivery, 2004, 19(4): 1968–1974

[16] Montero M I M, Cadaval E R, Gonzalez F B. Comparison of control strategies for shunt active power filters in three-phase four-wire systems. IEEE Transactions on Power Electronics, 2007, 22(1): 229–236

[17] Ucar M, Ozdemir E. Control of a 3-phase 4-leg active power filter under non-ideal mains voltage. Electric Power Systems Research, 2008, 78(1): 58–73

[18] Singh B, Solanki J. A comparison of control algorithms for DSTATCOM. IEEE Transactions on Industrial Electronics, 2009, 56(7): 2738–2745

[19] Zaveri T, Bhalja B, Zaveri N. Comparison of control strategies for DSTATCOM in three-phase, four-wire distribution system for power quality improvement under various source voltage and load conditions. International Journal of Electrical Power & Energy Systems, 2012, 43(1): 582–594

[20] Singh B, Jayaprakash P, Kothari D P. New control approach for capacitor supported DSTATCOM in three-phase four wire distribution system under non-ideal supply voltage conditions based on synchronous reference frame theory. International Journal of Electrical Power & Energy Systems, 2011, 33(5): 1109–1117

[21] Zaveri T, Bhalja B R, Zaveri N. Load compensation using DSTATCOM in three-phase,three-wire distribution system under various source voltage and delta connected load conditions. International Journal of Electrical Power & Energy Systems, 2012, 41(1): 34–43

[22] Quinn C A, Mohan N, Mehta H. A four-wire, current-controlled converter provides harmonic neutralization in three-phase, four-wire systems. In: Proceedings of Conference of the Eighth Annual Applied Power Electronics Conference and Exposition. 1993, 841–846

[23] Enjeti P N, Shireen W, Packebush P, Pitel I J. Analysis and design of a new active power filter to cancel neutral current harmonics in three-phase four-wire electric distribution systems. IEEE Transactions on Industry Applications, 1994, 30(6): 1565–1572

[24] Singh B, Jayaprakash P, Kumar S, Kothari D P. Implementation of neural-network controlled three-leg VSC and a transformer as three-phase four-wire DSTATCOM. IEEE Transactions on Industry Applications, 2011, 47(4): 1892–1901

[25] Jou H L, Wu K D, Wu J C, Li C H, Huang M S. Novel power converter topology for three-phase four-wire hybrid power filter. IET Power Electronics, 2008, 1(1): 164–173

[26] Enjeti P, Shireen W, Packebush P, Pitel I. Analysis and design of a new active power filter to cancel neutral current harmonics in three-phase four-wire electric distribution systems. IEEE Transactions on Industry Applications, 1994, 30(6): 1565–1572

[27] Bhuvaneswari G, Nair M G. Design, simulation, and analog circuit implementation of a three-phase shunt active filter using the Icos φ algorithm. IEEE Transactions on Power Delivery, 2008, 23(2): 1222–1235

[28] Akagi H, Watanabe E H, Aredes M. Instantaneous Power Theory and Applications to Power Conditioning. New Jersey: John Wiley & Sons, 2007

[29] Smedley K, Cuk S. One-Cycle Control of Switching Converters. In: Proceedings of the 22nd Annual IEEE Power Electronics Specialist Conference. Cambridge, USA, 1991, 888–896

[30] Qiao C, Jin T, Smedley K. Unified constant-frequency integration control of three-phase active power filter with vector operation. IEEE Power Electronics Specialists Conference. Vancouver, British Columbia, Canada, 2001, 1608–1614

[31] Jin T, Qiao C, Smedley K. Operation of unified constant- frequency integration controlled three-phase active power filter in unbalanced system. In: Proceedings of the 27th Annual Conference of the IEEE Industrial Electronics Society. Denver. CO, USA, 2001, 1539–1545

[32] Smedley K, Qiao C. Unified constant-frequency integration control of three-phase recitifiers, inverters and active power filters for unity power factor. U.S. Patent 6 297 980. 2001

[33] Qiao C, Jin T, Ma Smedley K. One-cycle control of three phase active power filter with vector operation. IEEE Transactions on Industrial Electronics, 2004, 51(2): 455–463

[34] Arya S R, Singh B. Neural network based conductance estimation control algorithm for shunt compensation. IEEE Transactions on Industrial Electronics, 2014, 10(1): 569–577

[35] Singh B, Arya S R. Back propagation control algorithm for power quality improvement using DSTATCOM. IEEE Transactions on Industrial Electronics, 2014, 61(3): 1204–1212

[36] Kinhal V G, Agarwal P, Gupta H O. Performance investigation of neural-network based unified power-quality conditioner. IEEE Transactions on Industrial Electronics, 2011, 26(1): 431–437

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