Advances in Control Technologies for Brushless Doubly-fed Induction Generators
Year: 2022 Language: english Author: Yi Liu Genre: Reference book Publisher: Springer ISBN: 9811904235 Format: PDF Quality: eBook Pages count: 418 Description: This book presents advances in control technologies for efficient operation of the brushless doubly-fed induction generator (BDFIG). For robust and low-cost operation of BDFIGs, it is required to keep high-quality output voltage and eliminate the speed/position encoder under different loads and operation conditions. Some advanced control technologies, from the authors' latest work on these topics, are presented to achieve this goal with simple and accurate texts, illustrations, and tables. The qualified outcomes obtained from this book assure the high-performance operation of BDFIGs and also give the readers a straight insight toward challenges in this research area in the future.
Contents
Fig. 1.1 The topology of the BDFG-based ac power generation system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fig. 1.2 The BDFIG application in wind power generation [12] . . . . . . . . 3 Fig. 1.3 The BDFIG application in ship shaft power generation [10] . . . . 4 Fig. 1.4 The BDFIG application in hydropower generation [12] . . . . . . . . 5 Fig. 1.5 The SFRF-VC method: a Structure of SFRF, b Obtained PW and CW current vectors by the SFRF-VC method proposed in [39] and [40] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Fig. 1.6 Structure of the proposed SSM-DPC strategy for BDFIG: a Schematic diagram of the super-twisting sliding mode control, b Overall DPC strategy with the super-twisting sliding mode control, where F and D are two matrices determined the time-derivative formula of sliding surface [42] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Fig. 1.7 DPC diagram of the open-winding BDFIG [43] . . . . . . . . . . . . . . 11 Fig. 1.8 The block diagram of the duty ratio modulation DTC for BDFIG proposed in [51] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Fig. 1.9 Block diagram of the indirect stator-quantities control system with the reactive power controller for BDFIG [54] . . . . . 13 Fig. 1.10 Summarized control structures presented in [55–57] for the BDFIG under unbalanced grid with PI/PIR controllers, respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Fig. 1.11 Different kinds of LVRT methods for the grid-connected BDFIG systems [61–65] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Fig. 1.12 The block diagram of the crowbarless LVRT control strategy based on flux linkage tracking for BDFIG under symmetrical voltage dips proposed in [66] . . . . . . . . . . . . . 16 Fig. 1.13 The stator-flux-oriented control and the direct voltage control based on CW current PI controller without decoupling [10, 67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 xxixxii List of Figures Fig. 1.14 Simulated and experimental results of the CW current PI controller without decoupling: a At the sub-synchronous speed of 400 rpm, b At the super-synchronous speed of 600 rpm [10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Fig. 1.15 The CW current control loop with cross feedforward compensation proposed in [68] . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Fig. 1.16 Simulated and experimental results of the CW current control loop with cross feedforward compensation: a At the sub-synchronous speed of 600 rpm, b At the super-synchronous speed of 1200 rpm [68] . . . . . . . . . . . . . . 20 Fig. 1.17 The CW current control loop with the decoupling network proposed in [70] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Fig. 1.18 Experimental results of the CW current control loop with the decoupling network, where DN and FF indicate decoupling network and feedforward, respectively: a At the sub-synchronous speed of 350 rpm, b At the super-synchronous speed of 650 rpm [70] . . . . . . . . . . . . . . . 21 Fig. 1.19 Different compensation methods based on MSC for standalone BDFIG under special loads: a Indirect calculation of CW voltage compensation components-Type I, b Indirect calculation of CW voltage compensation components-Type II, c Direct calculation of CW voltage compensation components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Fig. 1.20 Compensation method based on LSC for standalone BDFIG under special loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Fig. 1.21 Compensation method based on the collaborative control of MSC and LSC for standalone BDFIG under special loads . . . 26 Fig. 1.22 Experimental results of the compensation method based on the collaborative control of MSC and LSC with the weight factor reduction from 1 to 0.2: a Weight factor, b CW current, c PW line voltage, d Amplitude of CW current, e LSC current and f Electromagnetic torque [79] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Fig. 1.23 The actual and reference PW voltage vectors in the rotating dq reference frame [80] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Fig. 1.24 The structure of the linearized control loop for tracking the PW voltage phase proposed in [80] . . . . . . . . . . . . . . . . . . . . . 29 Fig. 1.25 Flowchart of the direct calculation approach for the BDFIG rotor position as developed in [84] and [85] . . . . . . . . . . . . . . . . . 30 Fig. 1.26 Structure of the proposed CW-P/Q/X MRAS speed observers for standalone BDFIGs [98–100] . . . . . . . . . . . . . . . . . 32 Fig. 2.1 Typical configuration of the BDFIG system . . . . . . . . . . . . . . . . . 42 Fig. 2.2 The steady-state -type model of BDFIG . . . . . . . . . . . . . . . . . . 46 Fig. 2.3 Equivalent circuit of the simplified inner core model [29] . . . . . . 46 Fig. 2.4 Equivalent circuit of the steady-state T-type model [31] . . . . . . . 47List of Figures xxiii Fig. 2.5 System structure of the standalone BDFIG [39] . . . . . . . . . . . . . . 49 Fig. 2.6 The power flow of the standalone BDFIG system, a under sub-synchronous speed, b under super-synchronous speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Fig. 2.7 Control loop for CW current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Fig. 2.8 Conceptual diagram of the DVC strategy for the standalone BDFIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Fig. 2.9 Performance test under the condition of the step load change from the full load to the no load with the rotor speed of 600 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Fig. 2.10 Experimental test under the condition of the step load change from the no load to 42 kW with the rotor speed of 400 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Fig. 2.11 Test analysis under the condition of speed variation from the super-synchronous to sub-synchronous speed with the load of 42 kW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Fig. 2.12 Experimental analysis under the condition of speed variation from the sub-synchronous to super-synchronous speed with the load of 42 kW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Fig. 3.1 Vector diagram describing the relationship among various reference frames under unbalanced loads . . . . . . . . . . . . . . . . . . . 61 Fig. 3.2 Vector diagram showing the relationship among different frames under nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Fig. 3.3 Vector diagram showing the relationship among different frames under the unbalanced plus nonlinear load . . . . . . . . . . . . . 66 Fig. 3.4 Vector diagram showing the relationship among different frames under single-phase nonlinear loads . . . . . . . . . . . . . . . . . . 69 Fig. 3.5 Conventional DVC control scheme . . . . . . . . . . . . . . . . . . . . . . . . 72 Fig. 3.6 Block diagram of the negative-sequence voltage compensator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Fig. 3.7 Overall control scheme for unbalanced voltage compensation of PW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Fig. 3.8 Block diagram of DSOGI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Fig. 3.9 Simulation results of the PW voltage amplitude with the conventional method at 600 rpm: a balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Fig. 3.10 Simulation results of the PW voltage with the conventional control strategy at 600 rpm: a balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Fig. 3.11 Simulationresults of the amplitude of the negative-sequence PW voltage with the conventional method at 600 rpm: a balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . 80 Fig. 3.12 Simulation results of the CW current with the conventional strategy at 600 rpm: a balanced load, b unbalanced load . . . . . . . 81xxiv List of Figures Fig. 3.13 Simulation results of the PW voltage amplitude with the conventional method at 900 rpm: a balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Fig. 3.14 Simulation results of the PW voltage with the conventional strategy at 900 rpm: a balanced load, b unbalanced load . . . . . . . 83 Fig. 3.15 Simulationresults of the amplitude of the negative-sequence PW voltage with the conventional method at 900 rpm, a balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . 84 Fig. 3.16 Simulation results of the CW current with the conventional strategy at 900 rpm: a balanced load, b unbalanced load . . . . . . . 85 Fig. 3.17 Simulation results of the conventional strategy with balanced and unbalanced loads under the variable rotor speed: a amplitude of the PW voltage, b PW voltage, c CW current, d amplitude of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Fig. 3.18 Simulation results at 600 rpm with the unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d PW current, e harmonic spectrum of the PW current (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Fig. 3.19 Simulation results at 900 rpm with the unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d PW current, e THD of the PW current (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . 91 Fig. 3.20 Simulation results during the proposed strategy startup and under the speed variation with the unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 94 Fig. 3.21 Experimental results at 600 rpm with the three-phase unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d PW current, e harmonic spectrum of the PW current (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Fig. 3.22 Experimental results at 900 rpm with the three-phase unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d harmonic spectrum of the CW current, e PW current, f harmonic spectrum of the PW current (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . 99 Fig. 3.23 Dynamic performance test with the three-phase unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 103List of Figures xxv Fig. 3.24 Experimental results with the single-phase load: a PW voltage, b PW current, c CW current, d amplitude of the negative-sequence PW voltage, e expanded view of (a), f expanded view of (a), g expanded view of (b), h expanded view of (c), i harmonic spectrum of the CW current in (h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Fig. 3.25 Block diagram of the low-order harmonic voltage compensator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Fig. 3.26 Block diagram of MSOGI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Fig. 3.27 Overall control scheme for low-order harmonic voltage compensation of PW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Fig. 3.28 Simulation results of the PW voltage with the conventional strategy at 650 rpm: a linear load, b nonlinear load . . . . . . . . . . . 110 Fig. 3.29 The harmonic spectrum of the PW voltage at 650 rpm in simulation: a linear load, b nonlinear load . . . . . . . . . . . . . . . . 111 Fig. 3.30 Simulation results of the amplitudes of the 5th and 7th harmonic components of the PW voltage with the conventional method at 650 rpm: a linear load, b nonlinear load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Fig. 3.31 Simulation results of the CW current with the conventional method at 650 rpm: a linear load, b nonlinear load . . . . . . . . . . . 113 Fig. 3.32 Simulation results of the PW voltage with the conventional strategy at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . 114 Fig. 3.33 The harmonic spectrum of the PW voltage at 850 rpm in simulation: a linear load, b nonlinear load . . . . . . . . . . . . . . . . 115 Fig. 3.34 Simulation results of the amplitudes of the 5th and 7th harmonics of the PW voltage with conventional method at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . . . . . . . . 116 Fig. 3.35 Simulation results of the CW current with the conventional method at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . 117 Fig. 3.36 Simulation results at 650 rpm under the nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . 118 Fig. 3.37 Simulation results at 850 rpm under the nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . 121 Fig. 3.38 Simulation results under the speed change with the nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124xxvi List of Figures Fig. 3.39 Experimental results at 650 rpm under the three-phase nonlinear load: a PW voltage, b PW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Fig. 3.40 Dynamics performance test of the proposed strategy during startup: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 128 Fig. 3.41 Experimental results under the speed change with the three-phase nonlinear load: a PW voltage, b CW current, c expanded view of the PW voltage at 850 rpm, d expanded view of the PW voltage at 650 rpm, e amplitudes of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 129 Fig. 3.42 Structure of the dual-resonant controller (DRC) . . . . . . . . . . . . . . 137 Fig. 3.43 Overall control scheme for compensating unbalanced and nonlinear loads based on DRC . . . . . . . . . . . . . . . . . . . . . . . . 138 Fig. 3.44 Simulation results at 675 rpm with the single-phase load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Fig. 3.45 Simulation results at 675 rpm with the nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . 141 Fig. 3.46 Dynamic performance test with the combination of the unbalanced and nonlinear loads: a PW voltage, b CW current, c extended view of (a) between 0.2 and 0.4 s, d extended view of (a) between 0.5 and 0.7 s . . . . . . . . . . . . . . . . 144 Fig. 3.47 Simulation results with the speed change under the combination of the unbalanced and nonlinear loads: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d amplitudes of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 145 Fig. 3.48 Experimental results at 675 rpm with the unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Fig. 3.49 Dynamic performance test at 675 rpm with the unbalanced load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 149List of Figures xxvii Fig. 3.50 Experimental results at 675 rpm under the three-phase nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage (the subscripts 1 and 2 indicate the conventional and proposed strategies, respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Fig. 3.51 Dynamic performance test at 675 rpm under the three-phase nonlinear load: a PW voltage, b CW current, c amplitudes of the 5th and 7th harmonics of the PW voltage, d harmonic spectrum of the PW voltage . . . . . . . . . . . . . . . . . . . . . . 153 Fig. 3.52 Effectiveness test for the proposed strategy under the unbalanced plus nonlinear load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d expanded view of (a) between 3.2 and 3.4 s, e expanded view of (a) between 6.1 and 6.3 s, f harmonic spectrum of the PW voltage depicted in (d), g harmonic spectrum of the PW voltage depicted in (e) . . . . . . . . . . . . . . . . . 154 Fig. 3.53 Effectiveness test for the proposed strategy under the single-phase nonlinear load: a PW voltage, b CW current, c amplitude of the negative-sequence PW voltage, d expanded view of (a) between 0 and 0.15 s, e expanded view of (a) between 0.32 and 0.47 s, f harmonic spectrum of the PW voltage depicted in (d), g harmonic spectrum of the PW voltage depicted in (e) . . . . . . . . . . . . . . . . . 157 Fig. 4.1 The CW current vector control loop . . . . . . . . . . . . . . . . . . . . . . . 165 Fig. 4.2 The block diagram of the proposed vector control strategy with CW transient current compensation . . . . . . . . . . . . . . . . . . . 168 Fig. 4.3 Experimental results for the 90-kVA standalone BDFIG feeding a 7.5-kW three-phase induction motor at 600 rpm without the CW transient current compensation: a PW voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 170 Fig. 4.4 Experimental results for the 90-kVA standalone BDFIG feeding a 7.5-kW three-phase induction motor at 600 rpm with the CW transient current compensation: a PW voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 171 Fig. 4.5 Experimental results for the 90-kVA standalone BDFIG feeding a 15-kW three-phase induction motor at 900 rpm without the CW transient current compensation: a PW voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 172 Fig. 4.6 Experimental results for the 90-kVA standalone BDFIG feeding a 15-kW three-phase induction motor at 900 rpm with the CW transient current compensation: a PW voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 173 Fig. 4.7 Compensation strategy based on MSC . . . . . . . . . . . . . . . . . . . . . 174xxviii List of Figures Fig. 4.8 The positive directions of the three-phase currents of PW, load and LSC (i1abc, ilabc and isabc) . . . . . . . . . . . . . . . . . . . . . . . . . 176 Fig. 4.9 Compensation strategy based on LSC . . . . . . . . . . . . . . . . . . . . . . 177 Fig. 4.10 Cooperative compensation strategy based on dual power converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Fig. 4.11 Experimental results of the control strategy without compensation at the sub-synchronous speed of 900 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . 180 Fig. 4.12 Experimental results of the control strategy based on the MSC compensation at the sub-synchronous speed of 900 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . 182 Fig. 4.13 Experimental results of the control strategy based on the LSC compensation at the sub-synchronous speed of 900 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . 184 Fig. 4.14 Experimental results of the control strategy based on the dual-converter cooperative compensation at the sub-synchronous speed of 900 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Fig. 4.15 Experimental results of the control strategy without compensation at the super-synchronous speed of 1100 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . 190 Fig. 4.16 Experimental results of the control strategy based on the MSC compensation at the super-synchronous speed of 1100 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . 192 Fig. 4.17 Experimental results of the control strategy based on the LSC compensation at the super-synchronous speed of 1100 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . 195List of Figures xxix Fig. 4.18 Experimental results of the control strategy based on the dual-converter cooperative compensation at the super-synchronous speed of 1100 rpm: a PW voltage amplitude, b CW d-axis current, c CW q-axis current, d PW line voltage, e CW phase current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Fig. 5.1 The flow chart of the MPCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Fig. 5.2 The overall control scheme of the standalone BDFIG . . . . . . . . . 209 Fig. 5.3 Simulation results at 900 rpm with the load added at 1.5 s: a dq-axis CW currents with the MPCC, b dq-axis CW currents with the PI controller, c Amplitude of the PW phase voltage (the upper figure is under the PI control and the lower one is under the MPCC), d Frequency of the PW voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Fig. 5.4 Simulation results under the speed change from 600 to 900 rpm with the constant load: a dq-axis CW currents with the MPCC, b dq-axis CW currents with the PI controller, c Amplitude of the PW phase voltage (the upper figure is under the PI control and the lower one is under the MPCC), d Frequency of the PW voltage, e Three-phase CW current (the upper figure is under the PI controller and the lower one is under the MPCC) . . . . . . . . . . . . . 213 Fig. 5.5 The value of each term in (5.18) with various operating states: a Value of A2 i2d(k −2), b Value of A1 i1d(k −2), c Value of u2d(k − 2), d Detailed view of u2d(k − 2) between 2.104 and 2.106 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Fig. 5.6 The NPCC strategy for the CW current control: a Whole control system, b Main procedures of the NPCC implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Fig. 5.7 The minimum value of u2d(k − 2) at different rotor speeds: a CW frequency 30 Hz at 1200 rpm, b CW frequency 10 Hz at 600 or 900 rpm, c CW frequency 1 Hz at 735 or 765 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Fig. 5.8 Simulation results under the variable load at the rotor speed of 600 rpm: a PW voltage, b CW current, c Reference and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 224 Fig. 5.9 Simulation results under the variable load at the rotor speed of 900 rpm: a PW voltage, b CW current, c Reference and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 225 Fig. 5.10 Simulation results under the constant load and variable rotor speed: a PW voltage, b CW current, c Reference and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 226xxx List of Figures Fig. 5.11 Simulation results under the CW selfand mutual-inductances change from 100 to 80% at the rotor speed of 600 rpm: a Three-phase CW current with MPCC, b Reference and actual values of dq-axis CW currents with MPCC, c Three-phase CW current with NPCC, d Reference and actual values of dq-axis CW currents with NPCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Fig. 5.12 Simulation results under PW self- and mutual-inductances change from 100 to 80% at the rotor speed of 600 rpm: a Three-phase CW current with MPCC, b Reference and actual values of dq-axis CW currents with MPCC, c Three-phase CW current with NPCC, d Reference and actual values of dq-axis CW currents with NPCC . . . . . . . . . 228 Fig. 5.13 Experimental results under the variable load at the rotor speed of 600 rpm: a PW voltage, b CW current, c Reference and feedback values of the d-axis CW current, d PW current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 Fig. 5.14 Experimental results under the constant load and variable rotor speed: a PW voltage, b CW current, c Reference and feedback values of the d-axis CW current . . . . . . . . . . . . . . . 232 Fig. 5.15 Experimental results under the CW resistance change with MPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 233 Fig. 5.16 Experimental results under the CW resistance change with NPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 234 Fig. 5.17 Experimental results under the CW self-inductance change with MPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 235 Fig. 5.18 Experimental results under the CW self-inductance change wiht NPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 236 Fig. 5.19 Experimental results under the generator overload with MPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW current, d PW voltage . . . . . . . 238 Fig. 5.20 Experimental results under the generator overload with NPCC: a Reference and feedback values of the d-axis CW current, b CW current, c PW current, d PW voltage . . . . . . . 239 Fig. 6.1 Phase-axis relationship of the BDFIG for the sensorless control based on RPO_1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Fig. 6.2 Main block diagram of the sensorless control method based on the RPO_1 for the standalone BDFIG . . . . . . . . . . . . . . 244List of Figures xxxi Fig. 6.3 Simulation results of the sensorless control of the standalone BDFIG based on the RPO_1 under speed variation (started with 900 rpm and then decelerated to 600 rpm) followed by the load change condition (started with 11.6 kW and then reduced to 9.7 kW): a Estimated and actual rotor positions, b three-phase PW voltages, c PW voltage amplitude and frequency, d CW dq-axis currents, e three-phase PW and CW currents . . . . . . . . . . . . . . . . 247 Fig. 6.4 Phase-axis relationship of the BDFIG for the sensorless control based on RPO_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Fig. 6.5 Main block diagram of the sensorless control method based on the RPO_2 for the standalone BDFIG . . . . . . . . . . . . . . 250 Fig. 6.6 Flowchart of the RPO_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Fig. 6.7 Relationship of the phase-axes for the BDFIG with the fictitious frame and the consideration of the estimated-position error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Fig. 6.8 Simulationresults of the sensorless control of the standalone BDFIG based on the RPO_2: a Estimated and actual rotor positions, b PW voltage amplitude and frequency, c CW dq-axis currents, d three-phase PW and CW currents . . . . . . . . . 256 Fig. 6.9 Performance test of the observer under 130% change in the machine inductances (L1,L1r,Lr): a Estimated and actual rotor positions, b PW voltage amplitude and frequency, c CW dq-axis currents, d three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Fig. 6.10 Performance test of the proposed observer under 130% change in PW resistance: a Estimated and actual rotor positions, b PW voltage amplitude and frequency, c CW dq-axis currents, d three-phase PW and CW currents . . . . . . . . . 261 Fig. 6.11 Experimental results of the RPO_2 under the start-up operation: a Estimated and actual rotor positions at start up, b estimated and actual rotor positions at steady state, c rotor position error, d CW q-axis current, e PW phase voltage, f extended view of e, g PW phase current, h extended view of g, i CW phase current, j extended view of i at 600 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Fig. 6.12 Experimental results of the RPO_2 under the load variation (50% reduction): a Estimated and actual rotor positions under load change, b PW phase voltage, c PW phase current, d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266xxxii List of Figures Fig. 6.13 Experimental results of the RPO_2 under the speed change (600–700 rpm): a Estimated and actual rotor positions (at 600 rpm), b estimated and actual rotor positions (at 700 rpm), c rotor position error, d CW q-axis current, e PW phase voltage, f extended view of e, g PW phase current, h extended view of g, i CW phase current, j extended view of i at 700 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Fig. 6.14 Experimental results of the RPO_2 under the BDFIG parameter change (130% uncertainty): a Estimated and actual rotor positions, b PW phase voltage, c PW phase current, d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . 270 Fig. 6.15 Structure of the basic RSO [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Fig. 6.16 The whole control structure of the improved RSO, where PSC denotes the positive-sequence calculator . . . . . . . . . . 277 Fig. 6.17 The characteristics with magnitude–frequency of the presented LPF where the frequency is represented by a normalized scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Fig. 6.18 Experimental results of basic and improved RSOs the under the unbalanced resistive load (25, 100, and 100 in phases a, b, and c): a PW voltage (1 p.u. = 500 V) and CW current (1 p.u. = 50 A), b expanded view of a, c rotor speed estimated by the basic RSO, d speed error using the basic RSO, e rotor speed estimated by the improved RSO, f speed error using the improved RSO . . . . . . . . . . . . . . . . 282 Fig. 6.19 Experimental results of basic and improved RSOs under the nonlinear load (a diode-rectifier with a 25 resistor at the dc side): a PW voltage (1 p.u. = 500 V) and CW current (1 p.u. = 50 A), b expanded view of a, c rotor speed estimated by the basic RSO, d speed error using the basic RSO, e rotor speed estimated by the improved RSO, f speed error using the improved RSO . . . . . . . . . . . . . . . . 283 Fig. 6.20 Experimental results of basic and improved RSOs under both the unbalanced and nonlinear loads: a PW voltage (1 p.u. = 500 V) and CW current (1 p.u. = 50 A), b expanded view of a, c rotor speed estimated by the basic RSO, d speed error using the basic RSO, e rotor speed estimated by the improved RSO, f speed error using the improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Fig. 6.21 The expanded view and the harmonic spectrum of the estimated rotor speed under the unbalanced load: a Expanded view of the rotor speed observed by basic RSO, b harmonic spectrum of the rotor speed observed by basic RSO, c expanded view of the rotor speed observed by improved RSO, d harmonic spectrum of the rotor speed observed by improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285List of Figures xxxiii Fig. 6.22 The expanded view and the harmonic spectrum of the estimated rotor speed under the nonlinear load: a Expanded view of the rotor speed observed by basic RSO, b harmonic spectrum of the rotor speed observed by basic RSO, c expanded view of the rotor speed observed by improved RSO, d harmonic spectrum of the rotor speed observed by improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Fig. 6.23 The expanded view and the harmonic spectrum of the estimated rotor speed under both unbalanced and nonlinear loads: a Expanded view of the rotor speed observed by basic RSO, b harmonic spectrum of the rotor speed observed by basic RSO, c expanded view of the rotor speed observed by improved RSO, d harmonic spectrum of the rotor speed observed by improved RSO . . . . . . . . . . . . . . . 287 Fig. 7.1 Basic MRAS observer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Fig. 7.2 Relationship of the BDFIG phase-axis for the sensorless control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Fig. 7.3 Block diagram of the proposed sensorless control strategy for the adopted BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Fig. 7.4 Main block diagram of the adopted CW power factor MRAS observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Fig. 7.5 Performance test of the proposed sensorless control strategy based on CW power factor MRAS observer: a Actual and estimated rotor positions. b PW three-phase voltage and PW frequency. c PW dq-axis flux. d Three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . 295 Fig. 7.6 The proposed sensorless system based on the CW power factor MRAS observer under load change: a Actual and estimated rotor positions. b PW three-phase voltage and PW frequency. c PW dq-axis flux. d Three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Fig. 7.7 The proposed sensorless system based on the CW power factor MRAS observer under the increased CW resistance (1.3 R2): a Actual and estimated rotor positions. b PW three-phase voltage and PW frequency. c PW dq-axis flux. d Three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . 298 Fig. 7.8 Experimental results of the CW power factor-based rotor position observer under the start-up operation and speed variation: a Actual and estimated rotor positions at 600 rpm. b Actual and estimated rotor positions at 700 rpm. c PW phase voltage. d CW phase current at 600 rpm. e CW phase current at 700 rpm. f PW phase current . . . . . . . . . . . . . . . 300xxxiv List of Figures Fig. 7.9 Experimental results of the CW power factor-based rotor position observer under the load change condition: a Actual and estimated rotor positions. b PW phase voltage. c PW phase current. d CW phase current . . . . . . . . . . . . . . . . . . . 302 Fig. 7.10 Experimental results of the CW power factor-based rotor position observer under the case of BDFIG parameter change (130% uncertainty): a Actual and estimated rotor positions. b PW phase voltage. c PW phase current. d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Fig. 7.11 Structure of the αβ-axis PW flux MRAS observer . . . . . . . . . . . . 305 Fig. 7.12 Structure of the proposed sensorless control method based on the αβ-axis PW flux MRAS observer for the standalone BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 Fig. 7.13 Structure of the dq-axis PW flux MRAS observer . . . . . . . . . . . . 308 Fig. 7.14 Structure of the proposed sensorless control method based dq-axis PW flux MRAS observer for the standalone BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Fig. 7.15 Simulation results under the speed ramp change and the constant load with the αβ-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c PW dq-axis voltage. d PW three-phase currents. e CW three-phase currents. f PW αβ-axis flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Fig. 7.16 Simulation results under the load variation and the constant speed with the αβ-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c Detailed PW three-phase voltages between 0.9 and 1.1 s. d PW dq-axis voltage. e PW three-phase currents. f CW three-phase currents. g PW αβ-axis flux . . . . . . . 314 Fig. 7.17 Simulation results under 130% variation in the PW resistance with the αβ-axis PW flux based MRAS sensorless control: a Actual and estimated rotor speeds. b PW three-phase voltages. c Detailed view of PW three-phase voltages. d dq-axis PW voltage. e PW three-phase currents. f CW three-phase currents. g αβ-axis PW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Fig. 7.18 Simulation results under 150% variation in the whole inductance with the αβ-axis PW flux based MRAS sensorless control: a Actual and estimated rotor speeds. b PW three-phase voltages. c Detailed view of PW three-phase voltages. d dq-axis PW voltage. e PW three-phase currents. f CW three-phase currents. g αβ-axis PW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319List of Figures xxxv Fig. 7.19 Simulation results under the speed ramp change and the constant load with the dq-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c Detailed PW three-phase voltages. d CW three-phase currents. e PW three-phase currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Fig. 7.20 Simulation results under the load variation and the constant speed with the dq-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c Detailed PW three-phase voltages between 0.9 and 1.1 s. d PW three-phase currents. e Detailed PW three-phase currents between 0.9 and 1.1 s. f CW three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . . . . . 322 Fig. 7.21 Simulation results under 130% variation in the PW resistance with the dq-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c Detailed PW three-phase voltages between 0.9 and 1.1 s. d PW three-phase currents. e Detailed PW three-phase currents between 0.9 and 1.1 s. f CW three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . 325 Fig. 7.22 Simulation results under 150% variation in the whole inductance with the dq-axis PW flux based MRAS sensorless control: a Actual and estimated speeds. b PW three-phase voltages. c Detailed PW three-phase voltages between 0.9 and 1.1 s. d PW three-phase currents. e Detailed PW three-phase currents between 0.9 and 1.1 s. f CW three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . 328 Fig. 7.23 Experimental results under variable speed (from 700 to 600 rpm) with the dq-axis PW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Rotor speed error. c PW phase voltage. d Overall CW phase current. e Detailed CW phase current between 2 and 3 s. f Detailed CW phase current between 43 and 44 s . . . . . 330 Fig. 7.24 Experimental results under variable load at the rotor speed of 600 rpm under the dq-axis PW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Rotor speed error. c Overall PW phase voltage. d Detailed PW phase voltage between 3.55 and 3.68 s. e Overall CW phase current. f Detailed CW phase current between 0 and 1.8 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Fig. 7.25 Experimental results under variable speed and variable load with 1.5 L variation under the dq-axis PW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Rotor speed error. c PW phase voltage. d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333xxxvi List of Figures Fig. 7.26 Experimental results under PW resistance variation (1.3 R1) and the speed of 600 rpm with 1.5 L variation under the dq-axis PW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Rotor speed error. c Overall PW phase voltage. d Detailed PW phase voltage between 3.2 and 3.35 s. e Overall CW phase current. f Detailed CW phase voltage between 6 and 8 s . . . . . . . 335 Fig. 7.27 Experimental results under the speed change from 700 to 600 rpm and load change from 50 to 25 under the dq-axis PW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Rotor speed error. c PW phase voltage. d Overall CW phase current. e Detailed CW phase current between 1 and 2 s. f Detailed CW phase current between 49 and 50 s . . . . . . . . . . . . . 336 Fig. 7.28 Structure of the αβ-axis CW flux MRAS observer . . . . . . . . . . . . 337 Fig. 7.29 Structure of the proposed sensorless control method based on the αβ-axis CW flux MRAS observer for the standalone BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Fig. 7.30 Structure of the dq-axis CW flux based MRAS observer . . . . . . . 342 Fig. 7.31 Structure of the proposed sensorless control method based on the dq-axis CW flux MRAS observer for the standalone BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Fig. 7.32 Simulation results under the speed ramp change and the constant load with the αβ-axis CW flux based MRAS sensorless control strategy: a Actual and estimated speeds. b PW three-phase voltage. c dq-axis PW voltage. d CW three-phase current. e PW three-phase current. f αβ-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Fig. 7.33 Simulation results under the load variation and the constant speed with the αβ-axis CW flux based MRAS sensorless control strategy: a Actual and estimated speeds. b PW three-phase voltage. c Detailed PW three-phase voltage between 0.9 and 1.1 s. d dq-axis PW voltage. e CW three-phase current. f PW three-phase current. g αβ-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Fig. 7.34 Simulation results under 130% variation in the PW resistance with the αβ-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c Detailed view of PW three-phase voltage. d dq-axis PW voltage. e CW three-phase current. f PW three-phase current. g αβ-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350List of Figures xxxvii Fig. 7.35 Simulation results under 150% variation in the whole inductance with the αβ-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c Detailed view of PW three-phase voltage. d dq-axis PW voltage. e CW three-phase current. f PW three-phase current. g αβ-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Fig. 7.36 Simulation results under the speed ramp change and the constant load with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c Detailed PW three-phase voltage between 0.5 and 0.56 s. d Detailed PW three-phase voltage between 2 and 2.06 s. e CW three-phase current. f dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . 354 Fig. 7.37 Simulation results under load change at the constant rotor speed with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c Detail view of PW three-phase voltage. d CW three-phase current. e Detail view of CW three-phase current. f PW active power. g dq-axis CW flux . . . . 356 Fig. 7.38 Simulation results under 130% variation in the PW resistance with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c detailed view of PW three-phase voltage. d PW three-phase current. e Detailed view of PW three-phase current. f PW active power. g dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 Fig. 7.39 Simulation results under 150% variation in the whole inductance with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b PW three-phase voltage. c Detailed view of PW three-phase current. d CW three-phase current. e Detailed view of CW three-phase current. f PW active power. g dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Fig. 7.40 Experimental results under the variable speed from 700 to 600 rpm with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c PW phase voltage. d Overall CW phase current. e Detailed CW phase current between 1 and 2 s. f Detailed CW phase current between 16 and 17 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362xxxviii List of Figures Fig. 7.41 Experimental results under variable load at the rotor speed of 600 rpm with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c Overall PW phase voltage. d Detailed PW phase voltage between 4 and 4.45 s. e Overall CW phase current. f Detailed PW phase current between 3.5 and 5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 Fig. 7.42 Experimental results under variable speed, load and inductance with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c PW phase voltage. d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 Fig. 7.43 Experimental results under PW resistance variation at the speed of 700 rpm with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c Overall PW phase voltage. d Detailed PW phase voltage between 3.8 and 4.2 s. e Overall PW phase current. f Detailed PW phase current between 1.5 and 2 s . . . . . . . . . . . . . . . . . . . . . . . . . 367 Fig. 7.44 Experimental results under inductance variation at the speed of 700 rpm with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c Overall PW phase voltage. d Detailed PW phase voltage between 2.8 and 3.5 s. e Overall PW phase current. f Detailed PW phase current between 2.9 and 3.5 s . . . . . . . . . . . . . . . . . . . . . . . . 369 Fig. 7.45 Experimental results under the changed speed, constant load and varied inductance with the dq-axis CW flux based MRAS sensorless control strategy: a Actual and estimated rotor speeds. b Speed percentage error. c PW phase voltage. d Overall CW phase current. e Detailed CW phase current between 0 and 5 s. f Detailed CW phase current between 45 and 50 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Fig. A.1 Structure of the used BDFIG experimental platforms . . . . . . . . . 380 Fig. A.2 Photograph of the 60-kVA BDFIG experimental platform (used as the ship shaft power generation system in a container vessel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Fig. A.3 Photograph of the first 30-kVA BDFIG experimental platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Fig. A.4 Photograph of the second 30-kVA BDFIG experimental platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Fig. A.5 Photograph of the 90-kVA BDFIG experimental platform . . . . . . 383 Table 1.1 Comparison of strengths and weaknesses between DFIG and BDFG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Table 1.2 Classification of SSF-VC methods according to utilized synchronous frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Table 1.3 Classification of SSF-VC methods based on the stator synchronous frame according to applicable machine types . . . . 6 Table 1.4 Classification of SSF-VC methods according to frame orientation styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Table 1.5 Comparison among compensation methods based on MSC, LSC, and dual power converters . . . . . . . . . . . . . . . . . . 27 Table 1.6 Comparison of different sensorless control methods . . . . . . . . . . 33 Table 3.1 Frequencies in the rotor and stator of BDFIG with unbalanced loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Table 3.2 Frequencies in the rotor and stator of BDFIG with nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Table 3.3 Frequencies in the rotor and stator of BDFIG with the unbalanced plus nonlinear load . . . . . . . . . . . . . . . . . . . 66 Table 3.4 Frequencies in the rotor and stator of BDFIG with single-phase nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . 69 Table 3.5 The proportional and integral gains tuned by the Ziegler-Nichols strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Table 4.1 Comparison of the amplitude drop and settling time of the PW voltage with different compensation strategies . . . . . 200 Table 5.1 Values of uα and uβ at various IGBT switch states of MSC . . . . 221 Table 6.1 Control parameters and settling time for the improved RSO . . . 281 Table A.1 Main parameters of the 60-kVA BDFIG . . . . . . . . . . . . . . . . . . . 380 Table A.2 Main parameters of the 30-kVA BDFIG . . . . . . . . . . . . . . . . . . . 381 Table A.3 Main parameters of the 90-kVA BDFIG . . . . . . . . . . . . . . . . . . . 383 Table A.4 Main parameters of the 3-kVA BDFIG . . . . . . . . . . . . . . . . . . . . 384 Table A.5 Main parameters of the 5-kVA BDFIG . . . . . . . . . . . . . . . . . . . . 385
Screenshots
5
Advances in Control Technologies for Brushless Doubly-fed Induction Generators.pdf
Вы не можете начинать темы Вы не можете отвечать на сообщения Вы не можете редактировать свои сообщения Вы не можете удалять свои сообщения Вы не можете голосовать в опросах Вы не можете прикреплять файлы к сообщениям Вы не можете скачивать файлы
Advances in Control Technologies for Brushless Doubly-fed Induction Generators
Language: english
Author: Yi Liu
Genre: Reference book
Publisher: Springer
ISBN: 9811904235
Format: PDF
Quality: eBook
Pages count: 418
Description: This book presents advances in control technologies for efficient operation of the brushless doubly-fed induction generator (BDFIG). For robust and low-cost operation of BDFIGs, it is required to keep high-quality output voltage and eliminate the speed/position encoder under different loads and operation conditions. Some advanced control technologies, from the authors' latest work on these topics, are presented to achieve this goal with simple and accurate texts, illustrations, and tables. The qualified outcomes obtained from this book assure the high-performance operation of BDFIGs and also give the readers a straight insight toward challenges in this research area in the future.
Contents
Fig. 1.1 The topology of the BDFG-based ac power generationsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Fig. 1.2 The BDFIG application in wind power generation [12] . . . . . . . . 3
Fig. 1.3 The BDFIG application in ship shaft power generation [10] . . . . 4
Fig. 1.4 The BDFIG application in hydropower generation [12] . . . . . . . . 5
Fig. 1.5 The SFRF-VC method: a Structure of SFRF, b Obtained
PW and CW current vectors by the SFRF-VC method
proposed in [39] and [40] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Fig. 1.6 Structure of the proposed SSM-DPC strategy for BDFIG:
a Schematic diagram of the super-twisting sliding mode
control, b Overall DPC strategy with the super-twisting
sliding mode control, where F and D are two matrices
determined the time-derivative formula of sliding surface
[42] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Fig. 1.7 DPC diagram of the open-winding BDFIG [43] . . . . . . . . . . . . . . 11
Fig. 1.8 The block diagram of the duty ratio modulation DTC
for BDFIG proposed in [51] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Fig. 1.9 Block diagram of the indirect stator-quantities control
system with the reactive power controller for BDFIG [54] . . . . . 13
Fig. 1.10 Summarized control structures presented in [55–57]
for the BDFIG under unbalanced grid with PI/PIR
controllers, respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Fig. 1.11 Different kinds of LVRT methods for the grid-connected
BDFIG systems [61–65] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Fig. 1.12 The block diagram of the crowbarless LVRT control
strategy based on flux linkage tracking for BDFIG
under symmetrical voltage dips proposed in [66] . . . . . . . . . . . . . 16
Fig. 1.13 The stator-flux-oriented control and the direct
voltage control based on CW current PI controller
without decoupling [10, 67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
xxixxii List of Figures
Fig. 1.14 Simulated and experimental results of the CW current PI
controller without decoupling: a At the sub-synchronous
speed of 400 rpm, b At the super-synchronous speed
of 600 rpm [10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Fig. 1.15 The CW current control loop with cross feedforward
compensation proposed in [68] . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Fig. 1.16 Simulated and experimental results of the CW current
control loop with cross feedforward compensation:
a At the sub-synchronous speed of 600 rpm, b At
the super-synchronous speed of 1200 rpm [68] . . . . . . . . . . . . . . 20
Fig. 1.17 The CW current control loop with the decoupling network
proposed in [70] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Fig. 1.18 Experimental results of the CW current control loop
with the decoupling network, where DN and FF indicate
decoupling network and feedforward, respectively:
a At the sub-synchronous speed of 350 rpm, b At
the super-synchronous speed of 650 rpm [70] . . . . . . . . . . . . . . . 21
Fig. 1.19 Different compensation methods based on MSC
for standalone BDFIG under special loads: a Indirect
calculation of CW voltage compensation components-Type
I, b Indirect calculation of CW voltage compensation
components-Type II, c Direct calculation of CW voltage
compensation components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Fig. 1.20 Compensation method based on LSC for standalone
BDFIG under special loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Fig. 1.21 Compensation method based on the collaborative control
of MSC and LSC for standalone BDFIG under special loads . . . 26
Fig. 1.22 Experimental results of the compensation method
based on the collaborative control of MSC and LSC
with the weight factor reduction from 1 to 0.2: a Weight
factor, b CW current, c PW line voltage, d Amplitude
of CW current, e LSC current and f Electromagnetic
torque [79] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Fig. 1.23 The actual and reference PW voltage vectors in the rotating
dq reference frame [80] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Fig. 1.24 The structure of the linearized control loop for tracking
the PW voltage phase proposed in [80] . . . . . . . . . . . . . . . . . . . . . 29
Fig. 1.25 Flowchart of the direct calculation approach for the BDFIG
rotor position as developed in [84] and [85] . . . . . . . . . . . . . . . . . 30
Fig. 1.26 Structure of the proposed CW-P/Q/X MRAS speed
observers for standalone BDFIGs [98–100] . . . . . . . . . . . . . . . . . 32
Fig. 2.1 Typical configuration of the BDFIG system . . . . . . . . . . . . . . . . . 42
Fig. 2.2 The steady-state -type model of BDFIG . . . . . . . . . . . . . . . . . . 46
Fig. 2.3 Equivalent circuit of the simplified inner core model [29] . . . . . . 46
Fig. 2.4 Equivalent circuit of the steady-state T-type model [31] . . . . . . . 47List of Figures xxiii
Fig. 2.5 System structure of the standalone BDFIG [39] . . . . . . . . . . . . . . 49
Fig. 2.6 The power flow of the standalone BDFIG system, a
under sub-synchronous speed, b under super-synchronous
speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Fig. 2.7 Control loop for CW current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Fig. 2.8 Conceptual diagram of the DVC strategy for the standalone
BDFIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Fig. 2.9 Performance test under the condition of the step load
change from the full load to the no load with the rotor
speed of 600 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Fig. 2.10 Experimental test under the condition of the step load
change from the no load to 42 kW with the rotor speed
of 400 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Fig. 2.11 Test analysis under the condition of speed variation
from the super-synchronous to sub-synchronous speed
with the load of 42 kW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Fig. 2.12 Experimental analysis under the condition of speed
variation from the sub-synchronous to super-synchronous
speed with the load of 42 kW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Fig. 3.1 Vector diagram describing the relationship among various
reference frames under unbalanced loads . . . . . . . . . . . . . . . . . . . 61
Fig. 3.2 Vector diagram showing the relationship among different
frames under nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Fig. 3.3 Vector diagram showing the relationship among different
frames under the unbalanced plus nonlinear load . . . . . . . . . . . . . 66
Fig. 3.4 Vector diagram showing the relationship among different
frames under single-phase nonlinear loads . . . . . . . . . . . . . . . . . . 69
Fig. 3.5 Conventional DVC control scheme . . . . . . . . . . . . . . . . . . . . . . . . 72
Fig. 3.6 Block diagram of the negative-sequence voltage
compensator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Fig. 3.7 Overall control scheme for unbalanced voltage
compensation of PW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Fig. 3.8 Block diagram of DSOGI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Fig. 3.9 Simulation results of the PW voltage amplitude
with the conventional method at 600 rpm: a balanced load,
b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Fig. 3.10 Simulation results of the PW voltage with the conventional
control strategy at 600 rpm: a balanced load, b unbalanced
load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Fig. 3.11 Simulationresults of the amplitude of the negative-sequence
PW voltage with the conventional method at 600 rpm: a
balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . 80
Fig. 3.12 Simulation results of the CW current with the conventional
strategy at 600 rpm: a balanced load, b unbalanced load . . . . . . . 81xxiv List of Figures
Fig. 3.13 Simulation results of the PW voltage amplitude
with the conventional method at 900 rpm: a balanced load,
b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Fig. 3.14 Simulation results of the PW voltage with the conventional
strategy at 900 rpm: a balanced load, b unbalanced load . . . . . . . 83
Fig. 3.15 Simulationresults of the amplitude of the negative-sequence
PW voltage with the conventional method at 900 rpm, a
balanced load, b unbalanced load . . . . . . . . . . . . . . . . . . . . . . . . . 84
Fig. 3.16 Simulation results of the CW current with the conventional
strategy at 900 rpm: a balanced load, b unbalanced load . . . . . . . 85
Fig. 3.17 Simulation results of the conventional strategy
with balanced and unbalanced loads under the variable
rotor speed: a amplitude of the PW voltage, b PW voltage,
c CW current, d amplitude of the negative-sequence PW
voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Fig. 3.18 Simulation results at 600 rpm with the unbalanced
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage, d PW current, e
harmonic spectrum of the PW current (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Fig. 3.19 Simulation results at 900 rpm with the unbalanced
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage, d PW current, e
THD of the PW current (the subscripts 1 and 2 indicate
the conventional and proposed strategies, respectively) . . . . . . . . 91
Fig. 3.20 Simulation results during the proposed strategy startup
and under the speed variation with the unbalanced
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 94
Fig. 3.21 Experimental results at 600 rpm with the three-phase
unbalanced load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage, d PW current, e
harmonic spectrum of the PW current (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Fig. 3.22 Experimental results at 900 rpm with the three-phase
unbalanced load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage, d harmonic
spectrum of the CW current, e PW current, f harmonic
spectrum of the PW current (the subscripts 1 and 2 indicate
the conventional and proposed strategies, respectively) . . . . . . . . 99
Fig. 3.23 Dynamic performance test with the three-phase
unbalanced load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 103List of Figures xxv
Fig. 3.24 Experimental results with the single-phase load: a PW
voltage, b PW current, c CW current, d amplitude
of the negative-sequence PW voltage, e expanded view
of (a), f expanded view of (a), g expanded view of (b),
h expanded view of (c), i harmonic spectrum of the CW
current in (h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Fig. 3.25 Block diagram of the low-order harmonic voltage
compensator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Fig. 3.26 Block diagram of MSOGI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Fig. 3.27 Overall control scheme for low-order harmonic voltage
compensation of PW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Fig. 3.28 Simulation results of the PW voltage with the conventional
strategy at 650 rpm: a linear load, b nonlinear load . . . . . . . . . . . 110
Fig. 3.29 The harmonic spectrum of the PW voltage at 650 rpm
in simulation: a linear load, b nonlinear load . . . . . . . . . . . . . . . . 111
Fig. 3.30 Simulation results of the amplitudes of the 5th
and 7th harmonic components of the PW voltage
with the conventional method at 650 rpm: a linear load, b
nonlinear load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Fig. 3.31 Simulation results of the CW current with the conventional
method at 650 rpm: a linear load, b nonlinear load . . . . . . . . . . . 113
Fig. 3.32 Simulation results of the PW voltage with the conventional
strategy at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . 114
Fig. 3.33 The harmonic spectrum of the PW voltage at 850 rpm
in simulation: a linear load, b nonlinear load . . . . . . . . . . . . . . . . 115
Fig. 3.34 Simulation results of the amplitudes of the 5th and 7th
harmonics of the PW voltage with conventional method
at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . . . . . . . . 116
Fig. 3.35 Simulation results of the CW current with the conventional
method at 850 rpm: a linear load, b nonlinear load . . . . . . . . . . . 117
Fig. 3.36 Simulation results at 650 rpm under the nonlinear load:
a PW voltage, b CW current, c amplitudes of the 5th
and 7th harmonics of the PW voltage, d harmonic
spectrum of the PW voltage (the subscripts 1 and 2 indicate
the conventional and proposed strategies, respectively) . . . . . . . . 118
Fig. 3.37 Simulation results at 850 rpm under the nonlinear load:
a PW voltage, b CW current, c amplitudes of the 5th
and 7th harmonics of the PW voltage, d harmonic
spectrum of the PW voltage (the subscripts 1 and 2 indicate
the conventional and proposed strategies, respectively) . . . . . . . . 121
Fig. 3.38 Simulation results under the speed change
with the nonlinear load: a PW voltage, b CW
current, c amplitudes of the 5th and 7th harmonics
of the PW voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124xxvi List of Figures
Fig. 3.39 Experimental results at 650 rpm under the three-phase
nonlinear load: a PW voltage, b PW current, c amplitudes
of the 5th and 7th harmonics of the PW voltage, d
harmonic spectrum of the PW voltage (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Fig. 3.40 Dynamics performance test of the proposed strategy
during startup: a PW voltage, b CW current, c amplitudes
of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 128
Fig. 3.41 Experimental results under the speed change
with the three-phase nonlinear load: a PW voltage, b CW
current, c expanded view of the PW voltage at 850 rpm, d
expanded view of the PW voltage at 650 rpm, e amplitudes
of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 129
Fig. 3.42 Structure of the dual-resonant controller (DRC) . . . . . . . . . . . . . . 137
Fig. 3.43 Overall control scheme for compensating unbalanced
and nonlinear loads based on DRC . . . . . . . . . . . . . . . . . . . . . . . . 138
Fig. 3.44 Simulation results at 675 rpm with the single-phase
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Fig. 3.45 Simulation results at 675 rpm with the nonlinear load: a
PW voltage, b CW current, c amplitudes of the 5th and 7th
harmonics of the PW voltage, d harmonic spectrum
of the PW voltage (the subscripts 1 and 2 indicate
the conventional and proposed strategies, respectively) . . . . . . . . 141
Fig. 3.46 Dynamic performance test with the combination
of the unbalanced and nonlinear loads: a PW voltage, b
CW current, c extended view of (a) between 0.2 and 0.4 s,
d extended view of (a) between 0.5 and 0.7 s . . . . . . . . . . . . . . . . 144
Fig. 3.47 Simulation results with the speed change
under the combination of the unbalanced and nonlinear
loads: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage, d amplitudes
of the 5th and 7th harmonics of the PW voltage . . . . . . . . . . . . . . 145
Fig. 3.48 Experimental results at 675 rpm with the unbalanced
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Fig. 3.49 Dynamic performance test at 675 rpm with the unbalanced
load: a PW voltage, b CW current, c amplitude
of the negative-sequence PW voltage . . . . . . . . . . . . . . . . . . . . . . 149List of Figures xxvii
Fig. 3.50 Experimental results at 675 rpm under the three-phase
nonlinear load: a PW voltage, b CW current, c amplitudes
of the 5th and 7th harmonics of the PW voltage, d
harmonic spectrum of the PW voltage (the subscripts 1
and 2 indicate the conventional and proposed strategies,
respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig. 3.51 Dynamic performance test at 675 rpm under the three-phase
nonlinear load: a PW voltage, b CW current, c amplitudes
of the 5th and 7th harmonics of the PW voltage, d
harmonic spectrum of the PW voltage . . . . . . . . . . . . . . . . . . . . . . 153
Fig. 3.52 Effectiveness test for the proposed strategy
under the unbalanced plus nonlinear load: a PW voltage,
b CW current, c amplitude of the negative-sequence PW
voltage, d expanded view of (a) between 3.2 and 3.4 s, e
expanded view of (a) between 6.1 and 6.3 s, f harmonic
spectrum of the PW voltage depicted in (d), g harmonic
spectrum of the PW voltage depicted in (e) . . . . . . . . . . . . . . . . . 154
Fig. 3.53 Effectiveness test for the proposed strategy
under the single-phase nonlinear load: a PW voltage, b
CW current, c amplitude of the negative-sequence PW
voltage, d expanded view of (a) between 0 and 0.15 s, e
expanded view of (a) between 0.32 and 0.47 s, f harmonic
spectrum of the PW voltage depicted in (d), g harmonic
spectrum of the PW voltage depicted in (e) . . . . . . . . . . . . . . . . . 157
Fig. 4.1 The CW current vector control loop . . . . . . . . . . . . . . . . . . . . . . . 165
Fig. 4.2 The block diagram of the proposed vector control strategy
with CW transient current compensation . . . . . . . . . . . . . . . . . . . 168
Fig. 4.3 Experimental results for the 90-kVA standalone BDFIG
feeding a 7.5-kW three-phase induction motor at 600 rpm
without the CW transient current compensation: a PW
voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 170
Fig. 4.4 Experimental results for the 90-kVA standalone BDFIG
feeding a 7.5-kW three-phase induction motor at 600
rpm with the CW transient current compensation: a PW
voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 171
Fig. 4.5 Experimental results for the 90-kVA standalone BDFIG
feeding a 15-kW three-phase induction motor at 900 rpm
without the CW transient current compensation: a PW
voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 172
Fig. 4.6 Experimental results for the 90-kVA standalone BDFIG
feeding a 15-kW three-phase induction motor at 900
rpm with the CW transient current compensation: a PW
voltage, b PW current, c CW current . . . . . . . . . . . . . . . . . . . . . . . 173
Fig. 4.7 Compensation strategy based on MSC . . . . . . . . . . . . . . . . . . . . . 174xxviii List of Figures
Fig. 4.8 The positive directions of the three-phase currents of PW,
load and LSC (i1abc, ilabc and isabc) . . . . . . . . . . . . . . . . . . . . . . . . . 176
Fig. 4.9 Compensation strategy based on LSC . . . . . . . . . . . . . . . . . . . . . . 177
Fig. 4.10 Cooperative compensation strategy based on dual power
converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Fig. 4.11 Experimental results of the control strategy
without compensation at the sub-synchronous speed of 900
rpm: a PW voltage amplitude, b CW d-axis current, c CW
q-axis current, d PW line voltage, e CW phase current, f
Load phase current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . 180
Fig. 4.12 Experimental results of the control strategy based
on the MSC compensation at the sub-synchronous speed
of 900 rpm: a PW voltage amplitude, b CW d-axis current,
c CW q-axis current, d PW line voltage, e CW phase
current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . 182
Fig. 4.13 Experimental results of the control strategy based
on the LSC compensation at the sub-synchronous speed
of 900 rpm: a PW voltage amplitude, b CW d-axis current,
c CW q-axis current, d PW line voltage, e CW phase
current, f Load phase current, g dc bus voltage . . . . . . . . . . . . . . 184
Fig. 4.14 Experimental results of the control strategy based
on the dual-converter cooperative compensation
at the sub-synchronous speed of 900 rpm: a PW voltage
amplitude, b CW d-axis current, c CW q-axis current,
d PW line voltage, e CW phase current, f Load phase
current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Fig. 4.15 Experimental results of the control strategy
without compensation at the super-synchronous speed
of 1100 rpm: a PW voltage amplitude, b CW d-axis
current, c CW q-axis current, d PW line voltage, e CW
phase current, f Load phase current, g dc bus voltage . . . . . . . . . 190
Fig. 4.16 Experimental results of the control strategy based
on the MSC compensation at the super-synchronous speed
of 1100 rpm: a PW voltage amplitude, b CW d-axis
current, c CW q-axis current, d PW line voltage, e CW
phase current, f Load phase current, g dc bus voltage . . . . . . . . . 192
Fig. 4.17 Experimental results of the control strategy based
on the LSC compensation at the super-synchronous speed
of 1100 rpm: a PW voltage amplitude, b CW d-axis
current, c CW q-axis current, d PW line voltage, e CW
phase current, f Load phase current, g dc bus voltage . . . . . . . . . 195List of Figures xxix
Fig. 4.18 Experimental results of the control strategy based
on the dual-converter cooperative compensation
at the super-synchronous speed of 1100 rpm: a PW voltage
amplitude, b CW d-axis current, c CW q-axis current,
d PW line voltage, e CW phase current, f Load phase
current, g dc bus voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Fig. 5.1 The flow chart of the MPCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Fig. 5.2 The overall control scheme of the standalone BDFIG . . . . . . . . . 209
Fig. 5.3 Simulation results at 900 rpm with the load added at 1.5
s: a dq-axis CW currents with the MPCC, b dq-axis CW
currents with the PI controller, c Amplitude of the PW
phase voltage (the upper figure is under the PI control
and the lower one is under the MPCC), d Frequency
of the PW voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Fig. 5.4 Simulation results under the speed change from 600
to 900 rpm with the constant load: a dq-axis CW currents
with the MPCC, b dq-axis CW currents with the PI
controller, c Amplitude of the PW phase voltage (the upper
figure is under the PI control and the lower one is
under the MPCC), d Frequency of the PW voltage, e
Three-phase CW current (the upper figure is under the PI
controller and the lower one is under the MPCC) . . . . . . . . . . . . . 213
Fig. 5.5 The value of each term in (5.18) with various operating
states: a Value of A2 i2d(k −2), b Value of A1 i1d(k −2),
c Value of u2d(k − 2), d Detailed view of u2d(k − 2)
between 2.104 and 2.106 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Fig. 5.6 The NPCC strategy for the CW current control: a
Whole control system, b Main procedures of the NPCC
implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Fig. 5.7 The minimum value of u2d(k − 2) at different rotor
speeds: a CW frequency 30 Hz at 1200 rpm, b CW
frequency 10 Hz at 600 or 900 rpm, c CW frequency 1 Hz
at 735 or 765 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Fig. 5.8 Simulation results under the variable load at the rotor speed
of 600 rpm: a PW voltage, b CW current, c Reference
and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 224
Fig. 5.9 Simulation results under the variable load at the rotor speed
of 900 rpm: a PW voltage, b CW current, c Reference
and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 225
Fig. 5.10 Simulation results under the constant load and variable
rotor speed: a PW voltage, b CW current, c Reference
and actual values of dq-axis CW currents . . . . . . . . . . . . . . . . . . . 226xxx List of Figures
Fig. 5.11 Simulation results under the CW selfand mutual-inductances change from 100 to 80%
at the rotor speed of 600 rpm: a Three-phase CW current
with MPCC, b Reference and actual values of dq-axis
CW currents with MPCC, c Three-phase CW current
with NPCC, d Reference and actual values of dq-axis CW
currents with NPCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Fig. 5.12 Simulation results under PW self- and mutual-inductances
change from 100 to 80% at the rotor speed of 600 rpm:
a Three-phase CW current with MPCC, b Reference
and actual values of dq-axis CW currents with MPCC,
c Three-phase CW current with NPCC, d Reference
and actual values of dq-axis CW currents with NPCC . . . . . . . . . 228
Fig. 5.13 Experimental results under the variable load at the rotor
speed of 600 rpm: a PW voltage, b CW current, c
Reference and feedback values of the d-axis CW current,
d PW current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
Fig. 5.14 Experimental results under the constant load and variable
rotor speed: a PW voltage, b CW current, c Reference
and feedback values of the d-axis CW current . . . . . . . . . . . . . . . 232
Fig. 5.15 Experimental results under the CW resistance change
with MPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 233
Fig. 5.16 Experimental results under the CW resistance change
with NPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 234
Fig. 5.17 Experimental results under the CW self-inductance change
with MPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 235
Fig. 5.18 Experimental results under the CW self-inductance change
wiht NPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW voltage . . . . . . . . . . . . . . . . . . . 236
Fig. 5.19 Experimental results under the generator overload
with MPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW current, d PW voltage . . . . . . . 238
Fig. 5.20 Experimental results under the generator overload
with NPCC: a Reference and feedback values of the d-axis
CW current, b CW current, c PW current, d PW voltage . . . . . . . 239
Fig. 6.1 Phase-axis relationship of the BDFIG for the sensorless
control based on RPO_1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Fig. 6.2 Main block diagram of the sensorless control method
based on the RPO_1 for the standalone BDFIG . . . . . . . . . . . . . . 244List of Figures xxxi
Fig. 6.3 Simulation results of the sensorless control
of the standalone BDFIG based on the RPO_1 under speed
variation (started with 900 rpm and then decelerated
to 600 rpm) followed by the load change condition (started
with 11.6 kW and then reduced to 9.7 kW): a Estimated
and actual rotor positions, b three-phase PW voltages,
c PW voltage amplitude and frequency, d CW dq-axis
currents, e three-phase PW and CW currents . . . . . . . . . . . . . . . . 247
Fig. 6.4 Phase-axis relationship of the BDFIG for the sensorless
control based on RPO_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Fig. 6.5 Main block diagram of the sensorless control method
based on the RPO_2 for the standalone BDFIG . . . . . . . . . . . . . . 250
Fig. 6.6 Flowchart of the RPO_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Fig. 6.7 Relationship of the phase-axes for the BDFIG
with the fictitious frame and the consideration
of the estimated-position error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Fig. 6.8 Simulationresults of the sensorless control of the standalone
BDFIG based on the RPO_2: a Estimated and actual rotor
positions, b PW voltage amplitude and frequency, c CW
dq-axis currents, d three-phase PW and CW currents . . . . . . . . . 256
Fig. 6.9 Performance test of the observer under 130% change
in the machine inductances (L1,L1r,Lr): a Estimated
and actual rotor positions, b PW voltage amplitude
and frequency, c CW dq-axis currents, d three-phase PW
and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Fig. 6.10 Performance test of the proposed observer under 130%
change in PW resistance: a Estimated and actual rotor
positions, b PW voltage amplitude and frequency, c CW
dq-axis currents, d three-phase PW and CW currents . . . . . . . . . 261
Fig. 6.11 Experimental results of the RPO_2
under the start-up operation: a Estimated and actual rotor
positions at start up, b estimated and actual rotor positions
at steady state, c rotor position error, d CW q-axis current,
e PW phase voltage, f extended view of e, g PW phase
current, h extended view of g, i CW phase current, j
extended view of i at 600 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Fig. 6.12 Experimental results of the RPO_2 under the load variation
(50% reduction): a Estimated and actual rotor positions
under load change, b PW phase voltage, c PW phase
current, d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266xxxii List of Figures
Fig. 6.13 Experimental results of the RPO_2 under the speed change
(600–700 rpm): a Estimated and actual rotor positions
(at 600 rpm), b estimated and actual rotor positions (at 700
rpm), c rotor position error, d CW q-axis current, e PW
phase voltage, f extended view of e, g PW phase current,
h extended view of g, i CW phase current, j extended view
of i at 700 rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Fig. 6.14 Experimental results of the RPO_2 under the BDFIG
parameter change (130% uncertainty): a Estimated
and actual rotor positions, b PW phase voltage, c PW
phase current, d CW phase current . . . . . . . . . . . . . . . . . . . . . . . . 270
Fig. 6.15 Structure of the basic RSO [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Fig. 6.16 The whole control structure of the improved RSO,
where PSC denotes the positive-sequence calculator . . . . . . . . . . 277
Fig. 6.17 The characteristics with magnitude–frequency
of the presented LPF where the frequency is represented
by a normalized scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Fig. 6.18 Experimental results of basic and improved RSOs
the under the unbalanced resistive load (25, 100, and 100
in phases a, b, and c): a PW voltage (1 p.u. = 500 V)
and CW current (1 p.u. = 50 A), b expanded view of a, c
rotor speed estimated by the basic RSO, d speed error using
the basic RSO, e rotor speed estimated by the improved
RSO, f speed error using the improved RSO . . . . . . . . . . . . . . . . 282
Fig. 6.19 Experimental results of basic and improved RSOs
under the nonlinear load (a diode-rectifier with a 25
resistor at the dc side): a PW voltage (1 p.u. = 500 V)
and CW current (1 p.u. = 50 A), b expanded view of a, c
rotor speed estimated by the basic RSO, d speed error using
the basic RSO, e rotor speed estimated by the improved
RSO, f speed error using the improved RSO . . . . . . . . . . . . . . . . 283
Fig. 6.20 Experimental results of basic and improved RSOs
under both the unbalanced and nonlinear loads: a PW
voltage (1 p.u. = 500 V) and CW current (1 p.u. = 50 A),
b expanded view of a, c rotor speed estimated by the basic
RSO, d speed error using the basic RSO, e rotor speed
estimated by the improved RSO, f speed error using
the improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Fig. 6.21 The expanded view and the harmonic spectrum
of the estimated rotor speed under the unbalanced load:
a Expanded view of the rotor speed observed by basic
RSO, b harmonic spectrum of the rotor speed observed
by basic RSO, c expanded view of the rotor speed observed
by improved RSO, d harmonic spectrum of the rotor speed
observed by improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285List of Figures xxxiii
Fig. 6.22 The expanded view and the harmonic spectrum
of the estimated rotor speed under the nonlinear load:
a Expanded view of the rotor speed observed by basic
RSO, b harmonic spectrum of the rotor speed observed
by basic RSO, c expanded view of the rotor speed observed
by improved RSO, d harmonic spectrum of the rotor speed
observed by improved RSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Fig. 6.23 The expanded view and the harmonic spectrum
of the estimated rotor speed under both unbalanced
and nonlinear loads: a Expanded view of the rotor speed
observed by basic RSO, b harmonic spectrum of the rotor
speed observed by basic RSO, c expanded view of the rotor
speed observed by improved RSO, d harmonic spectrum
of the rotor speed observed by improved RSO . . . . . . . . . . . . . . . 287
Fig. 7.1 Basic MRAS observer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Fig. 7.2 Relationship of the BDFIG phase-axis for the sensorless
control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Fig. 7.3 Block diagram of the proposed sensorless control strategy
for the adopted BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Fig. 7.4 Main block diagram of the adopted CW power factor
MRAS observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Fig. 7.5 Performance test of the proposed sensorless control
strategy based on CW power factor MRAS observer: a
Actual and estimated rotor positions. b PW three-phase
voltage and PW frequency. c PW dq-axis flux. d
Three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . 295
Fig. 7.6 The proposed sensorless system based on the CW power
factor MRAS observer under load change: a Actual
and estimated rotor positions. b PW three-phase voltage
and PW frequency. c PW dq-axis flux. d Three-phase PW
and CW currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Fig. 7.7 The proposed sensorless system based on the CW power
factor MRAS observer under the increased CW resistance
(1.3 R2): a Actual and estimated rotor positions. b PW
three-phase voltage and PW frequency. c PW dq-axis flux.
d Three-phase PW and CW currents . . . . . . . . . . . . . . . . . . . . . . . 298
Fig. 7.8 Experimental results of the CW power factor-based rotor
position observer under the start-up operation and speed
variation: a Actual and estimated rotor positions at 600
rpm. b Actual and estimated rotor positions at 700 rpm. c
PW phase voltage. d CW phase current at 600 rpm. e CW
phase current at 700 rpm. f PW phase current . . . . . . . . . . . . . . . 300xxxiv List of Figures
Fig. 7.9 Experimental results of the CW power factor-based rotor
position observer under the load change condition: a
Actual and estimated rotor positions. b PW phase voltage.
c PW phase current. d CW phase current . . . . . . . . . . . . . . . . . . . 302
Fig. 7.10 Experimental results of the CW power factor-based rotor
position observer under the case of BDFIG parameter
change (130% uncertainty): a Actual and estimated rotor
positions. b PW phase voltage. c PW phase current. d CW
phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Fig. 7.11 Structure of the αβ-axis PW flux MRAS observer . . . . . . . . . . . . 305
Fig. 7.12 Structure of the proposed sensorless control method based
on the αβ-axis PW flux MRAS observer for the standalone
BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Fig. 7.13 Structure of the dq-axis PW flux MRAS observer . . . . . . . . . . . . 308
Fig. 7.14 Structure of the proposed sensorless control method
based dq-axis PW flux MRAS observer for the standalone
BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Fig. 7.15 Simulation results under the speed ramp change
and the constant load with the αβ-axis PW flux based
MRAS sensorless control: a Actual and estimated speeds.
b PW three-phase voltages. c PW dq-axis voltage. d PW
three-phase currents. e CW three-phase currents. f PW
αβ-axis flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Fig. 7.16 Simulation results under the load variation and the constant
speed with the αβ-axis PW flux based MRAS sensorless
control: a Actual and estimated speeds. b PW three-phase
voltages. c Detailed PW three-phase voltages between 0.9
and 1.1 s. d PW dq-axis voltage. e PW three-phase
currents. f CW three-phase currents. g PW αβ-axis flux . . . . . . . 314
Fig. 7.17 Simulation results under 130% variation in the PW
resistance with the αβ-axis PW flux based MRAS
sensorless control: a Actual and estimated rotor speeds.
b PW three-phase voltages. c Detailed view of PW
three-phase voltages. d dq-axis PW voltage. e PW
three-phase currents. f CW three-phase currents. g αβ-axis
PW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Fig. 7.18 Simulation results under 150% variation in the whole
inductance with the αβ-axis PW flux based MRAS
sensorless control: a Actual and estimated rotor speeds.
b PW three-phase voltages. c Detailed view of PW
three-phase voltages. d dq-axis PW voltage. e PW
three-phase currents. f CW three-phase currents. g αβ-axis
PW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319List of Figures xxxv
Fig. 7.19 Simulation results under the speed ramp change
and the constant load with the dq-axis PW flux based
MRAS sensorless control: a Actual and estimated speeds.
b PW three-phase voltages. c Detailed PW three-phase
voltages. d CW three-phase currents. e PW three-phase
currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Fig. 7.20 Simulation results under the load variation and the constant
speed with the dq-axis PW flux based MRAS sensorless
control: a Actual and estimated speeds. b PW three-phase
voltages. c Detailed PW three-phase voltages between 0.9
and 1.1 s. d PW three-phase currents. e Detailed PW
three-phase currents between 0.9 and 1.1 s. f CW
three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . . . . . 322
Fig. 7.21 Simulation results under 130% variation in the PW
resistance with the dq-axis PW flux based MRAS
sensorless control: a Actual and estimated speeds. b PW
three-phase voltages. c Detailed PW three-phase voltages
between 0.9 and 1.1 s. d PW three-phase currents. e
Detailed PW three-phase currents between 0.9 and 1.1 s. f
CW three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . 325
Fig. 7.22 Simulation results under 150% variation in the whole
inductance with the dq-axis PW flux based MRAS
sensorless control: a Actual and estimated speeds. b PW
three-phase voltages. c Detailed PW three-phase voltages
between 0.9 and 1.1 s. d PW three-phase currents. e
Detailed PW three-phase currents between 0.9 and 1.1 s. f
CW three-phase currents. g dq-axis PW flux . . . . . . . . . . . . . . . . 328
Fig. 7.23 Experimental results under variable speed (from 700 to 600
rpm) with the dq-axis PW flux based MRAS sensorless
control strategy: a Actual and estimated rotor speeds. b
Rotor speed error. c PW phase voltage. d Overall CW
phase current. e Detailed CW phase current between 2
and 3 s. f Detailed CW phase current between 43 and 44 s . . . . . 330
Fig. 7.24 Experimental results under variable load at the rotor speed
of 600 rpm under the dq-axis PW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b Rotor speed error. c Overall PW phase voltage.
d Detailed PW phase voltage between 3.55 and 3.68 s. e
Overall CW phase current. f Detailed CW phase current
between 0 and 1.8 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
Fig. 7.25 Experimental results under variable speed and variable
load with 1.5 L variation under the dq-axis PW flux based
MRAS sensorless control strategy: a Actual and estimated
rotor speeds. b Rotor speed error. c PW phase voltage. d
CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333xxxvi List of Figures
Fig. 7.26 Experimental results under PW resistance variation
(1.3 R1) and the speed of 600 rpm with 1.5 L variation
under the dq-axis PW flux based MRAS sensorless control
strategy: a Actual and estimated rotor speeds. b Rotor
speed error. c Overall PW phase voltage. d Detailed PW
phase voltage between 3.2 and 3.35 s. e Overall CW phase
current. f Detailed CW phase voltage between 6 and 8 s . . . . . . . 335
Fig. 7.27 Experimental results under the speed change from 700
to 600 rpm and load change from 50 to 25
under the dq-axis PW flux based MRAS sensorless control
strategy: a Actual and estimated rotor speeds. b Rotor
speed error. c PW phase voltage. d Overall CW phase
current. e Detailed CW phase current between 1 and 2 s. f
Detailed CW phase current between 49 and 50 s . . . . . . . . . . . . . 336
Fig. 7.28 Structure of the αβ-axis CW flux MRAS observer . . . . . . . . . . . . 337
Fig. 7.29 Structure of the proposed sensorless control method based
on the αβ-axis CW flux MRAS observer for the standalone
BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Fig. 7.30 Structure of the dq-axis CW flux based MRAS observer . . . . . . . 342
Fig. 7.31 Structure of the proposed sensorless control method based
on the dq-axis CW flux MRAS observer for the standalone
BDFIG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Fig. 7.32 Simulation results under the speed ramp change
and the constant load with the αβ-axis CW flux based
MRAS sensorless control strategy: a Actual and estimated
speeds. b PW three-phase voltage. c dq-axis PW voltage.
d CW three-phase current. e PW three-phase current. f
αβ-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
Fig. 7.33 Simulation results under the load variation and the constant
speed with the αβ-axis CW flux based MRAS sensorless
control strategy: a Actual and estimated speeds. b PW
three-phase voltage. c Detailed PW three-phase voltage
between 0.9 and 1.1 s. d dq-axis PW voltage. e CW
three-phase current. f PW three-phase current. g αβ-axis
CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Fig. 7.34 Simulation results under 130% variation in the PW
resistance with the αβ-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b PW three-phase voltage. c Detailed view
of PW three-phase voltage. d dq-axis PW voltage. e CW
three-phase current. f PW three-phase current. g αβ-axis
CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350List of Figures xxxvii
Fig. 7.35 Simulation results under 150% variation in the whole
inductance with the αβ-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b PW three-phase voltage. c Detailed view
of PW three-phase voltage. d dq-axis PW voltage. e CW
three-phase current. f PW three-phase current. g αβ-axis
CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Fig. 7.36 Simulation results under the speed ramp change
and the constant load with the dq-axis CW flux based
MRAS sensorless control strategy: a Actual and estimated
rotor speeds. b PW three-phase voltage. c Detailed PW
three-phase voltage between 0.5 and 0.56 s. d Detailed
PW three-phase voltage between 2 and 2.06 s. e CW
three-phase current. f dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . 354
Fig. 7.37 Simulation results under load change at the constant rotor
speed with the dq-axis CW flux based MRAS sensorless
control strategy: a Actual and estimated rotor speeds. b
PW three-phase voltage. c Detail view of PW three-phase
voltage. d CW three-phase current. e Detail view of CW
three-phase current. f PW active power. g dq-axis CW flux . . . . 356
Fig. 7.38 Simulation results under 130% variation in the PW
resistance with the dq-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b PW three-phase voltage. c detailed view of PW
three-phase voltage. d PW three-phase current. e Detailed
view of PW three-phase current. f PW active power. g
dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
Fig. 7.39 Simulation results under 150% variation in the whole
inductance with the dq-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b PW three-phase voltage. c Detailed view of PW
three-phase current. d CW three-phase current. e Detailed
view of CW three-phase current. f PW active power. g
dq-axis CW flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Fig. 7.40 Experimental results under the variable speed from 700
to 600 rpm with the dq-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b Speed percentage error. c PW phase voltage.
d Overall CW phase current. e Detailed CW phase
current between 1 and 2 s. f Detailed CW phase current
between 16 and 17 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362xxxviii List of Figures
Fig. 7.41 Experimental results under variable load at the rotor
speed of 600 rpm with the dq-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b Speed percentage error. c Overall PW phase
voltage. d Detailed PW phase voltage between 4 and 4.45
s. e Overall CW phase current. f Detailed PW phase
current between 3.5 and 5 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
Fig. 7.42 Experimental results under variable speed, load
and inductance with the dq-axis CW flux based MRAS
sensorless control strategy: a Actual and estimated rotor
speeds. b Speed percentage error. c PW phase voltage. d
CW phase current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Fig. 7.43 Experimental results under PW resistance variation
at the speed of 700 rpm with the dq-axis CW flux based
MRAS sensorless control strategy: a Actual and estimated
rotor speeds. b Speed percentage error. c Overall PW
phase voltage. d Detailed PW phase voltage between 3.8
and 4.2 s. e Overall PW phase current. f Detailed PW
phase current between 1.5 and 2 s . . . . . . . . . . . . . . . . . . . . . . . . . 367
Fig. 7.44 Experimental results under inductance variation
at the speed of 700 rpm with the dq-axis CW flux based
MRAS sensorless control strategy: a Actual and estimated
rotor speeds. b Speed percentage error. c Overall PW
phase voltage. d Detailed PW phase voltage between 2.8
and 3.5 s. e Overall PW phase current. f Detailed PW
phase current between 2.9 and 3.5 s . . . . . . . . . . . . . . . . . . . . . . . . 369
Fig. 7.45 Experimental results under the changed speed, constant
load and varied inductance with the dq-axis CW flux based
MRAS sensorless control strategy: a Actual and estimated
rotor speeds. b Speed percentage error. c PW phase
voltage. d Overall CW phase current. e Detailed CW phase
current between 0 and 5 s. f Detailed CW phase current
between 45 and 50 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Fig. A.1 Structure of the used BDFIG experimental platforms . . . . . . . . . 380
Fig. A.2 Photograph of the 60-kVA BDFIG experimental platform
(used as the ship shaft power generation system in a
container vessel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Fig. A.3 Photograph of the first 30-kVA BDFIG experimental
platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Fig. A.4 Photograph of the second 30-kVA BDFIG experimental
platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Fig. A.5 Photograph of the 90-kVA BDFIG experimental platform . . . . . . 383
Table 1.1 Comparison of strengths and weaknesses between DFIG
and BDFG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Table 1.2 Classification of SSF-VC methods according to utilized
synchronous frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Table 1.3 Classification of SSF-VC methods based on the stator
synchronous frame according to applicable machine types . . . . 6
Table 1.4 Classification of SSF-VC methods according to frame
orientation styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Table 1.5 Comparison among compensation methods based
on MSC, LSC, and dual power converters . . . . . . . . . . . . . . . . . . 27
Table 1.6 Comparison of different sensorless control methods . . . . . . . . . . 33
Table 3.1 Frequencies in the rotor and stator of BDFIG
with unbalanced loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Table 3.2 Frequencies in the rotor and stator of BDFIG
with nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Table 3.3 Frequencies in the rotor and stator of BDFIG
with the unbalanced plus nonlinear load . . . . . . . . . . . . . . . . . . . 66
Table 3.4 Frequencies in the rotor and stator of BDFIG
with single-phase nonlinear loads . . . . . . . . . . . . . . . . . . . . . . . . . 69
Table 3.5 The proportional and integral gains tuned
by the Ziegler-Nichols strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Table 4.1 Comparison of the amplitude drop and settling time
of the PW voltage with different compensation strategies . . . . . 200
Table 5.1 Values of uα and uβ at various IGBT switch states of MSC . . . . 221
Table 6.1 Control parameters and settling time for the improved RSO . . . 281
Table A.1 Main parameters of the 60-kVA BDFIG . . . . . . . . . . . . . . . . . . . 380
Table A.2 Main parameters of the 30-kVA BDFIG . . . . . . . . . . . . . . . . . . . 381
Table A.3 Main parameters of the 90-kVA BDFIG . . . . . . . . . . . . . . . . . . . 383
Table A.4 Main parameters of the 3-kVA BDFIG . . . . . . . . . . . . . . . . . . . . 384
Table A.5 Main parameters of the 5-kVA BDFIG . . . . . . . . . . . . . . . . . . . . 385
Screenshots
Advances in Control Technologies for Brushless Doubly-fed Induction Generators.pdf
Скачать [19 KB]
Поделиться