Fuzzy-PI-Based Direct-Output-Voltage Control

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009 2401 Fuzzy-PI-Based Direct-Output-Voltage Control Strategy for the STATCOM Used in Utility Distribution Systems An Luo, Member, IEEE, Ci Tang, Zhikang Shuai, Student Member, IEEE, Jie Tang, Xian Yong Xu, and Dong Chen Abstract—In this paper, the control strategy for the static synchronous compensator (STATCOM) used in utility distribu- tion systems is investigated, and a novel fuzzy-PI-based direct- output-voltage (DOV) control strategy is presented. Based on power balancing principle and feedforward decoupling control, this novel DOV control strategy cannot only reduce the active and reactive current control loops of a conventional double-loop control strategy but also achieve the decoupling control to regulate dc-link voltage and maintain the voltages at the point of common coupling (PCC). In order to effectively improve the immunity capability of this novel DOV control strategy to the uncertainties in system parameters, two fuzzy PI controllers are separately em- ployed to maintain the voltages at the PCC and to simultaneously regulate dc-link voltage. The validity and effectiveness of this novel control strategy for the STATCOM used in utility distribution systems have been verified by simulation results, and a scaled physical prototype rated at ±300 kVAr is also developed to test the STATCOM system. Index Terms—Converters, decoupling of systems, fuzzy control, static VAR compensators. I. INTRODUCTION R ECENTLY, with the growth of nonlinear loads in indus-trial manufactures, the electric power quality has become more and more important. As one of the most common issues about the electric power quality, voltage fluctuations influence domestic lighting and sensitive apparatus in transmission and distribution systems [1]. As a key component for the implementation of a flexible ac transmission system, the main function of a static syn- chronous compensator (STATCOM) is to regulate the voltages at the point of common coupling (PCC) in transmission and Manuscript received November 27, 2008; revised February 23, 2009 and March 12, 2009. First published April 28, 2009; current version published July 1, 2009. This work was supported in part by the National Natural Science Foundation of China (60774043), in part by the National High Technology Research and Development of China (2008AA05Z211), and in part by the National Basic Research Program of China (973 Program) (2009CB219706). A. Luo, Z. Shuai, X. Y. Xu, and D. Chen are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: an_luo@126.com; zhikangshuai@hotmail.com). C. Tang is with the College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China (e-mail: tangci2679@126.com). J. Tang is with the Department of Electrical Engineering, Shaoyang Univer- sity, Changsha 422000, China. Digital Object Identifier 10.1109/TIE.2009.2021172 distribution systems. It achieves such an objective by drawing controllable reactive currents from power systems. In contrast with other traditional static reactive power generators, such as the static VAR compensator using thyristor-controlled reac- tors, the STATCOM also has an intrinsic ability to exchange active power with power systems. To effectively improve the STATCOM performance, previous researchers mainly focus on its topology and control strategy. In large-capacity applications, multipulse inverters, such as 24- and 48-pulse inverters, are widely used to achieve lower harmonic distortions [2], [3]. Electromagnetic interfaces con- stituted by complex phase-shifting transformers, however, are required to connect multipulse inverters and power systems. Therefore, many inherent benefits of multilevel inverters have led to an increasing interest in the STATCOM applications. At present, there are four multilevel configurations: diode- clamped (neutral point clamed) [4], [5], flying capacitor [6], cascade H-bridge [7]–[10], and hybrid multilevel inverters [11], [12]. Two technical challenges in the application of multi- level inverters, nevertheless, are the unbalanced voltages across dc-link capacitors and lots of sensors to measure every dc- link voltage [13]. In recent years, significant progresses have been made in power semiconductor technologies, which re- sults in an emergence of the 4.5-kV insulated-gate bipolar transistor. This development of power devices helps to apply the STATCOM with a two-level inverter in utility distribution systems. In the aspect of control strategy, Schauder and Mehta [14] have proposed a typical double-loop control strategy: The outer loop forms the desired active and reactive current commands to maintain the voltages at the PCC and to compensate the STATCOM losses, and the inner loop realizes to control inverter currents with zero steady-state errors. However, this control strategy not only needs four PI controllers in its control system so that the tuning of PI parameters should be done empirically or by trial and error, but also has a coupling relationship between the active current and the reactive current, and thus, it is hard to maintain the voltages at the PCC with small effects on the dc-link voltage. To obtain decoupling control, nonlinear control strategies are widely used by linearized models via the feedbacks near steady-state operating points [15]–[18]. However, it is not easy to tune controller parameters because these approaches still need four PI controllers. Based on power balancing principle, Chen and Hsu [19] have given a 0278-0046/$25.00 © 2009 IEEE 2402 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009 Fig. 1. Schematic representation for a two-level STATCOM connected to the PCC of a utility distribution system. direct-output-voltage (DOV) control strategy for the STATCOM to reduce its active and reactive current control loops. However, this control strategy does not implement the decoupling control, and its control performance may not be satisfactory due to the uncertainties in system parameters. In this paper, a novel fuzzy-PI-based DOV control strategy for the STATCOM used in utility distribution systems is pro- posed. Configuration and dynamic model of the STATCOM are briefly introduced in Section II. The conventional double- loop and an improved DOV control strategy are deduced in Section III. Design methodology of the new fuzzy-PI-based controller is then described in Section IV. Both simulation and experimental results are provided to validate the new design considerations. II. SYSTEM CONFIGURATION AND STATCOM DYNAMIC MODEL A. System Configuration Fig. 1 shows the STATCOM configuration applied to the PCC of a utility distribution system which is represented by a three-phase voltage source behind series resistance (Rn) and inductance (Ln) in each phase. The STATCOM system in parallel with a three-phase RL local load consists of a dc-link capacitor, a two-level inverter, and series resistances (Rs) as well as inductances (Ls) in three lines connecting to the PCC. In this circuit, Ls accounts for the leakage inductance of an actual coupling transformer, Rs represents conduction losses of the inverter and the coupling transformer, and Rc denotes the sum of switching losses in the inverter and power losses in the capacitor. B. STATCOM Dynamic Model In this section, a mathematical model for the STATCOM sys- tem in Fig. 1 is developed to deduce the conventional double- loop control strategy and an improved DOV control strategy. In terms of Fig. 1, the following dynamic equations can be obtained: ⎧⎪⎪⎨ ⎪⎪⎩ Ls dias dt = −Rsias + vas − val Ls dibs dt = −Rsibs + vbs − vbl Ls dics dt = −Rsics + vcs − vcl. (1) By using the abc−dq transformation with its d-axis aligned to the voltage vector of the PCC, full equations in (1) can be described in the synchronously rotating reference frame as follows: { Ls dids dt = −Rsids + ωLsiqs + vds − vdl Ls diqs dt = −Rsiqs − ωLsids + vqs − vql (2) where ids and iqs represent the d- and q-axis currents, which correspond to three-phase STATCOM output currents (ias, ibs, and ics); ω is the synchronously rotating angle speed of the voltage vector of the PCC; vds and vqs account for the d- and q-axis voltages, which correspond to three-phase STATCOM output voltages (vas, vbs, and vcs); and vdl and vql denote the d- and q-axis voltages, which correspond to three-phase load voltages (val, vbl, and vcl), namely, the voltages at the PCC (vPCCa, vPCCb, and vPCCc). III. CONVENTIONAL DOUBLE-LOOP AND IMPROVED DOV CONTROL STRATEGY A. Conventional Double-Loop Control Strategy and Its Characteristics According to the definitions of instantaneous active and reactive power, the instantaneous power of load terminal is given as { pl = 32 (vdlids + vqliqs) ql = 32 (vdliqs − vqlids) (3) where a constant 3/2 is chosen so that the definition coincides with the classical phasor definition under a balanced steady- state condition [14]. Considering that the d-axis is always coincident with the voltage vector of the PCC and the q-axis is in quadrature with it, the following equation can be obtained: vql = 0. (4) Therefore, (2) and (3) can be separately simplified as{ Ls dids dt = −Rsids + ωLsiqs + vds − vdl Ls diqs dt = −Rsiqs − ωLsids + vqs (5) { pl = 32vdlids ql = 32vdliqs. (6) Apparently, we can achieve to control the active power by controlling the d-axis current (ids) and to regulate the voltages LUO et al.: FUZZY-PI-BASED DIRECT-OUTPUT-VOLTAGE CONTROL STRATEGY FOR THE STATCOM 2403 Fig. 2. Schematic configuration of the double-loop control strategy. at the PCC (namely to control the reactive power) by controlling the q-axis current (iqs). Based on the aforementioned analysis results and formulas (5) as well as (6), the conventional double-loop control strategy can be obtained, which is shown in Fig. 2 (resistances in (5) are neglected for simplicity [14]). From Fig. 2, some characteristics of the double-loop control strategy can be concluded in the following. 1) The d- and q-axis currents (i.e., ids and iqs) are coupled with each other; thus, it is difficult to independently maintain the voltages at the PCC with small impacts on the dc-link voltage. That is to say, the STATCOM system cannot quickly compensate the required reactive power. 2) There are four PI controllers in the STATCOM control system; therefore, the tuning of PI parameters should be achieved empirically or by trial and error. B. DOV Control Strategy and Its Characteristics Similar to the analysis method mentioned earlier, the instantaneous output power of the STATCOM system can be obtained as { ps = 32 (vdsids + vqsiqs) qs = 32 (vdsiqs − vqsids). (7) The instantaneous power consumed by the connecting resistance Rs and the connecting inductance Ls can be expressed as [19]{ pRL = 32Rs ( i2ds + i 2 qs ) qRL = 32ωLs ( i2ds + i 2 qs ) . (8) According to power balancing principle, the instantaneous output power of the STATCOM (i.e., ps + jqs) is the sum of the instantaneous power consumed by Rs as well as Ls (i.e., pRL + jqRL) and that of the load terminal (i.e., pl + jql){ ps = pRL + pl qs = qRL + ql. (9) Substituting (6)–(8) into (9) yields{ vds = Rsids − ωLsiqs + vdl vqs = Rsiqs + ωLsids. (10) From (10), it is obvious that the output voltages of the STATCOM (i.e., vds and vqs) can be directly obtained from the output currents of the STATCOM (i.e., ids and iqs) together with Rs, Ls, and vdl. That is to say, the transformation from Fig. 3. Schematic configuration of the DOV control strategy. ids and iqs to vds and vqs can be realized by (10). If we take the currents ids and iqs as commands, then the voltages vds and vqs become the output commands of the STATCOM. With the aforementioned analysis results, a block diagram of the DOV control strategy can be shown in Fig. 3, in which two limiters are included in the PI controllers to avoid overload operations. From Fig. 3, there exists a coupling relationship between regulating dc-link voltage and maintaining the voltages at the PCC via i∗ds and i∗qs. A feedforward decoupling control is hence proposed to resolve this problem, as shown in Fig. 4. The feedforward decoupler, including D1 and D2, works to can- cel the interaction effects, and then, the double-input double- output system can be decoupled into two individual single-input single-output systems. In order to achieve a decoupling control, the following equation should hold: 1 D1D2 − 1 [ Rs −ωLs ωLs Rs ] [−1 D2 D1 −1 ] = [ Rs 0 0 Rs ] (11) where the transfer matrix in the right-hand side is a diagonal decoupled system from [d1 d2] to [v∗ds v∗qs]. The decoupler is therefore derived as { D1 = ωLsRs D2 = −ωLsRs . (12) IV. FUZZY-PI-BASED CONTROLLER DESIGN As is known to everyone, the traditional PI controller is widely used in industrial applications for its simplicity and reliability. However, in practice, a traditional PI controller with constant parameters may not be robust enough due to the variations of design parameters. To improve the static and dynamic performances of the STATCOM with this improved DOV control strategy, two fuzzy PI controllers have been adopted to separately regulate the dc-link voltage and maintain the voltages at the PCC, as shown in Fig. 5. A fuzzy adjustor is used to adjust the parameters of propor- tional gain KP and integral gain KI based on the error e and the change of error Δe{ KP = K∗P + ΔKP KI = K∗I + ΔKI (13) where K∗P and K∗I are the reference values of fuzzy-PI-based controllers. In this paper, K∗P and K∗I are calculated offline based on the Ziegler–Nichols method [20]. The error e and the change of error Δe are used as numerical variables from the real system. To convert these numerical variables into linguistic variables, the following seven fuzzy 2404 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009 Fig. 4. Schematic configuration of the DOV control strategy with a feedforward decoupler. Fig. 5. Schematic configuration of the improved DOV controller based on fuzzy PI. Fig. 6. Membership functions of fuzzy variables. sets are chosen: negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), and positive big (PB). To ensure the sensitivity and robustness of controllers, the membership function is shown in Fig. 6. The controller core is the fuzzy control rules which are mainly obtained from intuitive feeling and experience. The design process of fuzzy control rules involves defining the rules that relate the input variables to the output model properties [21]–[23]. For designing the control rule bases to tune ΔKP and ΔKI , the following important factors have been taken into account. 1) For large value of |e|, a large ΔKP is required, and vice versa. 2) For e∗Δe > 0, a large ΔKP is required, and vice versa. 3) For the large values of |e| and |Δe|, ΔKI is set to zero, which can avoid control saturation. 4) For small value of |e|, ΔKI is effective, and ΔKI is larger when |e| is smaller, which is better to decrease steady-state error. Therefore, the tuning rules of ΔKP and ΔKI can be ob- tained as Tables I and II. TABLE I ADJUSTING RULES OF ΔKP PARAMETER TABLE II ADJUSTING RULES OF ΔKI PARAMETER The inference method employs the MAX–MIN method. The imprecise fuzzy control action generated from the inference must be transformed to a precise control action in application. LUO et al.: FUZZY-PI-BASED DIRECT-OUTPUT-VOLTAGE CONTROL STRATEGY FOR THE STATCOM 2405 Fig. 7. Response curves of vPCC and vdc with the three control strategies. The center gravity method is used to defuzzify fuzzy variables into their physical domains ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ KP = K∗P + n∑ j=1 μj(e,Δe)ΔKPj n∑ j=1 μj(e,Δe) KI = K∗I + n∑ j=1 μj(e,Δe)ΔKIj n∑ j=1 μj(e,Δe) (14) where μ denotes a membership function of fuzzy sets. V. SIMULATION RESULTS To verify the validity and effectiveness of this fuzzy-PI- based DOV control strategy for the STATCOM system, several simulation investigations are carried out by MATLAB/Simulink to compare the performances among the typical double-loop control strategy [14], the improved DOV control strategy, Fig. 8. Response curves of vPCC and vdc with the three control strategies after changing Rs and Ls. and the novel control strategy in this paper. All the param- eters used in simulations are shown in Tables III–V in Appendix I. Case 1: In this case, the production of a voltage drop at the PCC is realized by switching a reactive power (inductive) load at t = 0.2 s, while a swell at the PCC is obtained by disconnect- ing the given load at t = 0.4 s. Fig. 7 shows the response curves of vPCC and vdc with the three control strategies. From Fig. 7, it is obvious that there are less overshoot and shorter settling time in the response curves of vPCC and vdc with the fuzzy-PI- based DOV control strategy than those with the typical double- loop and improved DOV control strategy; a further merit of this novel control strategy is its full decoupling capability to regulate the dc-link voltage and maintain the voltages at the PCC. That is to say, the fuzzy-PI-based control strategy not only has more perfect dynamic performance but also achieves to quickly maintain the voltages at the PCC with very small influence on the dc-link voltage. Case 2: To verify the immunity ability of this novel control strategy to system uncertainties, the variation of design parame- ters is simulated by changing the parameters of the STATCOM system. Fig. 8 shows the response curves of vPCC and vdc 2406 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 7, JULY 2009 Fig. 9. Experimental setup and snapshots of the scaled physical prototype. (a) Photograph of the STATCOM system. (b) Photograph of the digital control subsystem based on DSP. (c) Photograph of the dc-link voltage and the two-level inverter. (d) Photograph of the LC filter. (e) Photograph of the coupling transformer. (f) Photograph of the variable-capacity reactive power (inductive) load. with the three control strategies after changing the connecting resistance from Rs = 0.5 Ω to Rs = 0.05 Ω and the connecting inductance from Ls = 1 mH to Ls = 0.01 mH. From Fig. 8, we can observe that the response curves of vPCC and vdc with the typical double-loop and improved DOV con- troller are all oscillating after changing the STATCOM system parameters. On the other hand, the fuzzy-PI-based controller enhances the immunity ability of the improved DOV control strategy to the uncertainties in the STATCOM system and thus unfolds its robustness. VI. EXPERIMENTAL RESULTS For the further verification of the STATCOM system with this novel control strategy, several experiments are also accom- plished in the laboratory by a scaled physical prototype rated at ±300 kVAr. Fig. 9 shows the snapshots of this scaled physical prototype which mainly consists of three modules: a fixed- capacity active power load rated at 600 kW, a variable-capacity reactive power (inductive) load with its maximum rating of 120 kVAr, and the STATCOM system constituted by coupling transformer, LC filter for eliminating switch ripples, two-level LUO et al.: FUZZY-PI-BASED DIRECT-OUTPUT-VOLTAGE CONTROL STRATEGY FOR THE STATCOM 2407 inverter, dc-link capacitor, and digital control subsystem based on DSP. All the parameters used in experiments are illustrated in Appendix II. Case 1: In this case, several experimental results obtained by Tektronix oscilloscopes with the same scales are presented to effectively compare the performances among the typical double-loop control strategy [14], the improved DOV control strategy, and the control strategy introduced by us. The pro- duction of a voltage drop at the PCC is realized by switch- ing the variable-capacity reactive pow