تجزیه و تحلیل عملکرد زمان واقعی و مقایسه طرح های مختلف برای کنترل ازدحام ذرات فیلترهای توان اکتیو شانت مبتنی بر بهینه سازی

Selection of proper reference compensation current extraction scheme plays the most crucial role in the performance of an active power filter (APF). This paper mainly describes three different control schemes used in APFs namely, Conventional instantaneous active and reactive power (p–q), Modified p–q, and Instantaneous active and reactive current component (id–iq) schemes. Our objective here is to bring down the total harmonic distortion (THD) of source current sufficiently below 5% at the point of common-coupling (PCC), in order to satisfy the IEEE 519-1992 Standard recommendations on harmonic limits. Comparative evaluation of the three control schemes shows that, id–iq method is the best control scheme to be implemented on shunt APFs, irrespective of the supply voltage conditions, even under sudden load fluctuations. Results have been validated using MATLAB/Simulink simulations followed by real-time performance verification in Opal-RT Lab simulator. Here, the APF is comprised of a voltage source inverter (VSI) based on pulse-width modulation (PWM) technique. Hence, undesirable power loss takes place inside VSI due to the presence of inductors and frequent switching of IGBTs. This is effectively minimized with inverter DC-link voltage regulation using a PI controller, whose gains are optimized using particle swarm optimization (PSO).

Active filters have grabbed huge attention as proficient devices in compensating the current harmonics and reactive power produced by non-linear loads. It can suppress different order harmonic components of non-linear loads simultaneously, by confining the harmonics at load terminals and hindering its penetration into AC lines [1], [2], [3], [4] and [5]. It automatically adapts to changes in network and load fluctuations [6]. Few most important advantages of APF are: (i) intelligent filter, (ii) can be used globally or locally, (iii) extremely efficient even when the harmonic content varies randomly, and (iv) more than one device can be installed on the same supply. The shunt APF has many configurations, amongst which the standard inverter type configuration is most widely used and discussed as given in [3] and the references there-in. APFs are generally developed with PWM converters of either current-source inverter (CSI) or voltage-source inverter (VSI) type [3], [6], [7] and [8]. The CSI structure as shown in Fig. 1a presents good reliability [3] and [6], but has important losses and requires higher values of parallel capacitor filters at the AC terminals to remove unwanted current harmonics. A diode is used in series with the self-commutating IGBT for reverse voltage blocking. On the other hand, VSI structure shown in Fig. 1b is more convenient as it is lighter, cheaper, and expandable to multilevel and multistep versions, for improved performance at high power ratings with lower switching frequencies [3] and [7]. It has to be connected to the AC mains through coupling reactors. An electrolytic capacitor keeps the DC-link voltage constant and ripple-free [6]. Therefore, here we have preferred to use the VSI configuration. Full-size image (8 K) Fig. 1a. CSI configuration. Figure options Full-size image (9 K) Fig. 1b. VSI configuration. Figure options Two types of VSI configurations are possible for three-phase four-wire power systems, (i) three-leg six-switch structure, where neutral conductor is connected to midpoint of DC-link capacitor as depicted in Fig. 2a, and (ii) four-leg eight-switch structure, where an additional fourth leg is provided exclusively for neutral current compensation as shown in Fig. 2b. The latter is preferred, as many researchers have appointed this configuration as the most proficient alternative for shunt APFs [9], [10], [11], [12] and [13]. The three-leg configuration suffers from several shortcomings such as: (i) control circuit is somewhat complex, (ii) voltages of the two capacitors of split-capacitor need to be properly balanced, and (iii) large DC-link capacitors are required. Despite of the fact, this topology is seldom preferred owing to less number of switching devices and lower switching losses compared to the eight-switch topology. The higher order harmonics generated in eight-switch configuration due to frequent switching of semiconductor devices can be eliminated by the use of RC high-pass filter as shown in Fig. 2b. Switching losses occurring in VSI can be minimized using DC-link voltage regulator, which is basically consisted of a PI controller. For optimal harmonics mitigation, particle swarm optimization (PSO) has been employed to find out the gains of PI controller. Section 2 describes the entire DC-link voltage regulation action elaborately. Full-size image (10 K) Fig. 2a. Three-leg VSI-PWM based APF. Figure options Full-size image (10 K) Fig. 2b. Four-leg VSI-PWM based APF. Figure options The control schemes for APF constitute a crucial part in harmonic compensation, as any inaccuracy leads to inexact compensation. Various schemes such as Instantaneous active and reactive power (p–q), Instantaneous active and reactive current component (id–iq), Perfect harmonic cancellation (PHC), Generalized integral, Adaptive filter, Delay-less filtering based on Artificial Neural Network (ANN), Adaptive Linear Neuron (ADALINE), Wavelet Transform, Fast Fourier Transform (FFT) and Recursive Discrete Fourier Transform (RDFT) have been proposed since the development of APFs [13], [14], [15] and [16]. Time-domain methods are preferred here because of fast response to changes in power system, easy implementation with less memory requirements, and less computational burden unlike frequency-domain methods, where the number of calculations increases with an increase in the highest order of harmonic to be eliminated, resulting in longer response time. The ANN and ADALINE methods are also associated with few shortcomings. Number of ADALINE required to tune is equal to the number of harmonics considered in load current, thus slowing down the convergence. Generation of the input vector, X = [cos ωt, sin ωt, …, cos n ωt, sin n ωt]T is difficult and involves a tedious process. Moreover, the error being minimized by gradient-based method has likelihood of converging to local minima [16]. The p–q scheme proposed by Akagi in 1984 is recognized as a viable solution to the problems created by non-linear loads, and is most widely used [17] and [18]. This offers a very precise reference compensation current template and allows obtaining a clear difference between instantaneous active and reactive powers. However, it is criticized as a disappointment under non-ideal supply conditions [9], [19], [20] and [21]. Therefore, an enhancement to this scheme was proposed in the year 2005 and was validated to be better than Conventional p–q scheme for both three-phase three-wire and four-wire systems [9] and [19]. Few other papers have been reported that state, id–iq scheme to be more efficient than p–q scheme [20] and [21]. The present discussion is focused on the competency of id–iq and Modified p–q schemes, in contrast to Conventional p–q scheme for load compensation in three-phase four-wire distribution systems. This paper is aimed at both summarizing the aforementioned APF control schemes and comparing their relative performances. The balanced sinusoidal, balanced non-sinusoidal and unbalanced sinusoidal mains supplies are taken into consideration in conjunction with typical non-linear balanced/unbalanced loading and sudden load change scenarios, so as to achieve compensated source currents which are as realistic as possible. The actual filter currents are compared with their references, and errors are processed in Hysteresis controller to generate PWM signals for VSI. The VSI in turn generates required compensation currents to be injected into the AC lines at PCC. Fig. 3 depicts the system configuration of shunt APF. Full-size image (31 K) Fig. 3. Line diagram representation for system configuration of shunt APF. Figure options Testing and validation of power conditioning devices has become very essential in the design and engineering process. Here, MATLAB simulation results are validated with real-time performance analysis in RT-Lab Simulator developed by Opal-RT technologies [22]. It is one of the most promising real-time simulation tools for analyzing the system build models by running them on fixed-step solvers for automatic code generation. RT-Lab is a very fast, flexible, scalable, industrial grade and real-time platform for simulation, control testing and related applications. Other advantages include: (i) computation time within each time step is almost independent of system size, (ii) overruns cannot occur once the model is running, (iii) simulation time step can be very small i.e. in the order of 250 ns, (iv) in the design of real prototype, it may be prone to many troubles related to integration of different modules at a time and (v) off-line non-real-time simulation may become tediously long for any moderately complex system. Section 2 describes the regulation of DC-link capacitor voltage using a PSO-based PI controller. The Conventional p–q, Modified p–q and id–iq control schemes have been thoroughly discussed in the next section. The MATLAB and Opal RT-Lab simulation results for comparative evaluation of the three control schemes under ideal, distorted and unbalanced supplies along with sudden load fluctuation conditions are presented in Sections 4 and 5 respectively. The conclusion is summarized in Section 6.

A comparison between the Conventional p–q, Modified p–q and id–iq control schemes for three-phase four-wire eight-switch VSI-based APF is realized. The reference compensation currents for the four-wires are extracted and Hysteresis PWM is carried out to generate switching signals for VSI. DC-link voltage has been regulated successfully using a PSO-based PI controller, minimizing the undesirable power loss responsible for degradation of APF performance, thereby providing optimal load compensation. MATLAB/Simulink results showing response of the control schemes under transient and steady-state conditions are presented. All the control schemes discussed here are effective in harmonic compensation under ideal supply and satisfy the IEEE-519 Standards on harmonic limits. Under distorted supply, though Modified p–q scheme lowers down the THD to values smaller than Conventional p–q, it fails to bring down the THD below 5%, which can be seen from Table 3. In contrast, id–iq scheme yields the lowest values of source current THDs. Even under unbalanced supply, id–iq scheme gives the best values of THDs, whereas the other two schemes fail to compensate for current harmonics adequately. The excessive neutral current has been compensated by all the control schemes under all kinds of supplies. The unbalance in source current is fully compensated by all the control schemes only under ideal and distorted supply conditions. Only id–iq scheme is able to compensate the unbalance in source current under unbalanced supply. This proves that, id–iq scheme is the best control scheme to be employed in shunt APF compared to the other two mentioned control schemes. Real-time simulation results obtained from Opal-RT Lab further validate the MATLAB simulation results.