Evaluation of a Trapezoidal Predictive Controller for a Four-Wire Active Power Filter for Utility Equipment of Metro Railway, Power-Land Substations

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2016, Article ID 2712976, 11 pages http://dx.doi.org/10.1155/2016/2712976 Research Article Evaluation of a Trapezoidal Predictive Controller for a Four-Wire Active Power Filter for Utility Equipment of Metro Railway, Power-Land Substations Sergio Salas-Duarte,1 Ismael Araujo-Vargas,1 Jazmin Ramirez-Hernandez,1 and Marco Rivera2 1 Escuela Superior de Ingenierı́a Mecanica y Eléctrica, Unidad Culhuacan, Instituto Politécnico Nacional, Avenida Santa Ana No. 1000, Col San Francisco Culhuacan, 04430 México, DF, Mexico 2 Universidad de Talca, 2 Norte 685, Talca, Chile Correspondence should be addressed to Ismael Araujo-Vargas; Received 14 August 2015; Accepted 20 December 2015 Academic Editor: Shengbo Eben Li Copyright © 2016 Sergio Salas-Duarte et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The realization of an improved predictive current controller based on a trapezoidal model is described, and the impact of this technique is assessed on the performance of a 2 kW, 21.6 kHz, four-wire, Active Power Filter for utility equipment of Metro Railway, Power-Land Substations. The operation of the trapezoidal predictive current controller is contrasted with that of a typical predictive control technique, based on a single Euler approximation, which has demonstrated generation of high-quality line currents, each using a 400 V DC link to improve the power quality of an unbalanced nonlinear load of Metro Railway. The results show that the supply current waveforms become virtually sinusoidal waves, reducing the current ripple by 50% and improving its power factor from 0.8 to 0.989 when the active filter is operated with a 1.6 kW load. The principle of operation of the trapezoidal predictive controller is analysed together with a description of its practical development, showing experimental results obtained with a 2 kW prototype. 1. Introduction The use of Active Power Filters (APFs) in the electrical grid is critical for on-land transportation applications, such as Metropolitan Railway Substations, which reduce the flowing of current harmonics caused by the increased utilization of nonlinear loads, whilst improving the power quality of the supply. APFs are an attractive solution to comply with the national and international power quality standards at every level of the network infrastructure, [1–3], since highperformance switching devices appear available in the market to develop power converters [4]. In addition, the development of fast and versatile microprocessors has facilitated the implementation of nonlinear control techniques, and thereby, APFs are becoming accurate power processors that reshape clean sinusoidal supply currents [5–9]. Four-wire shunt APFs are a commonplace strategy that exhibit attractive characteristics to inject currents and reshape the line currents drawn by unbalanced nonlinear loads, whilst providing a path to cancel the neutral current by using either an additional switching limb or a split DC link [10, 11]. These circuits typically incur in the use of a power theory to calculate the reference currents [12], such that the filter may operate as a current amplifier that injects compensating currents to the grid, causing a complex transistor switching scheme since the generated filter currents must track the references. Predictive control is an attractive method for controlling current waveforms in three-phase converters [6, 7, 13–20], since a piecewise linear model of the converter is used together with a cost function to determine an appropriate converter switching. 2 Mathematical Problems in Engineering N 󳨀 󳨀→ 󳨀s𝛼𝛽0 󳨀󳨀󳨀→ iL𝛼𝛽0 󳨀󳨀→ i𝛼𝛽0 󳨀 󳨀→ 󳨀s𝛼𝛽0 󳨀󳨀→ i𝛼𝛽0 q𝛼 q𝛽 P-Q theory q0 󳨀 󳨀→ 󳨀󳨀󳨀→ 󳨀s𝛼𝛽0 iL𝛼𝛽0 󳨀 󳨀→ 󳨀s𝛼𝛽0 i𝛼 Inverse P-Q theory pT ̃T p DC ∑ reject + − ploss HE (s) Eref − 400 V + ∑ ∗ i𝛽 ∗ i0 ∗ Predictive current controller → 󳨀 s PLL and clark transform → 󳨀 iL Clark transform vge1 vge2 ∗ vge2 vge6 ∗ D6 v SC Q3 D4 Q1 v RC C1 E E1 vdiff Q6 D1 vge6 E D2 Q2 v TC D3 .. . IGBT drivers 󳨀󳨀󳨀→ iLoad Lf D5 Q5 ∑ + −i 0bal Hbal (s) → 󳨀 iL Clark transform vge1 ∗ .. . → 󳨀 is N C2 Q4 E2 + ∑ ∑ Unbalanced nonlinear load Active power filter + − + Figure 1: Four-wire shunt active filter and its corresponding control block diagram. This paper presents the realization and experimental verification of a trapezoidal predictive current controller for a four-wire shunt APF that improves the power quality of unbalanced AC loads in contrast to the typical predictive Euler control strategy. The trapezoidal strategy relies its operation on a discrete trapezoidal linear approximation that more accurately determines the switching of the active filter for the one-step ahead current sample, such that three significant advantages are potentially exhibited: first, the trapezoidal predictive controller slightly increments the processing time without affecting the switching of the power converter; second, in contrast to the typical Euler approximation used in other works [6, 7, 13–20], the trapezoidal method generates lower AC current ripple; and third, the convergence time and load operating performance are wider than those obtained using the typical predictive control strategy, which improves the reference current tracking and, therefore, the power quality. Experimental results obtained with a 2 kVA prototype are presented, demonstrating that the trapezoidal predictive control may accurately compensate the currents drawn by an unbalanced nonlinear load under static and dynamic conditions. neutral node 𝑁 to provide a path to mitigate a common mode current: a typical three-phase, current-feed active converter, formed by transistors 𝑄1 to 𝑄6 and diodes 𝐷1 –𝐷6 , and three line filter inductors 𝐿 𝑓 used to generate the filter current → 󳨀 𝑇 vector, 𝑖𝐿 = [𝑖𝐿𝑅 𝑖𝐿𝑆 𝑖𝐿𝑇 ] , by the difference between the 𝑇 󳨀 supply and converter voltage vectors → V𝑠 = [V𝑅𝑁 V𝑆𝑁 V𝑇𝑁] 𝑇 and 󳨀 V→ 𝐶 = [V𝑅𝐶𝑁 V𝑆𝐶𝑁 V𝑇𝐶𝑁 ] , thereby obtaining virtual → 󳨀 𝑇 sinusoidal supply currents 𝑖𝑠 = [𝑖𝑆𝑅 𝑖𝑆𝑆 𝑖𝑆𝑇 ] . 2.2. Principle of Operation of the Active Filter. The principle of operation of the APF of Figure 1 may be described using the control block diagram presented at the left-hand side of Figure 1. An instantaneous active and reactive power theory, P-Q theory block in Figure 1 [12], is used to obtain an effective calculation of the reference currents that the APF may inject to the supply to instantaneously mitigate the reactive and distorted power components, drawn by the nonlinear load, and balance the active power per phase. The P-Q theory uses the Clarke transformation of the supply voltage and load current as shown in 2. Four-Wire Shunt Active Filter 2.1. Circuit Description. The four-wire shunt APF is connected (...truncated)