11 DEMO TITLES Grid-Imposed Frequency VSC System Case I: Voltage-Mode Control Case II: Current-Mode Control Case III: AFE Feeds a Grid-Imposed Frequency VSC System Author: Tshibain Tshibungu Simsmart Technologies Inc. Brossard, Quebec Canada Software used: Simsmart Engineering Suite V6 (ES V6) A-PDF Merger DEMO : Purchase from www.A-PDF.com to remove the watermark 2 2 1. OBJECTIVE AND DESCRIPTION The following document will help the user in designing step by step controllers of a Grid- Imposed Frequency VSC System using voltage or current mode control. A complete model of AFE feeds a Grid-Imposed Frequency VSC System using current control mode will be simulated. Three test cases are done in order to test and validate theories using the power electronics components from the Engineering suite V6 Electrical library. 1.1. Grid –Imposed Frequency VSC System: Control in dq-frame Two main methods exist for controlling the active power and reactive power in the VSC system. The first mode is known as voltage-mode control and the second is known as current- mode control. The following diagram shows the structure of a Grid-Imposed Frequency VSC System. The abc reference frame equations are given as follows: (1) (2) (3) Where Transformer inductance seen from primary side or inductance Transformer resistance seen from primary side or resistance Inverter output voltage (x =a, b, c) Grid voltage seen from primary side (x =a, b, c) 3 3 The following Park transformation will be used to convert abc to dq synchronous reference frame: ( ) ( ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ) ( ) (4) Transforming the following equations into dq synchronous reference frame, we have: (5) (6) The active and reactive powers are given as follows: [ ] (7) [ ] (8) Using a PLL (Phase Locked Loop) where in steady state (9) (10) Voltage-Mode Control Substituting from (9) and (10) into (5) and (6), we have: ( ) ( ) ( ) (11) ( ) ( ) ( ) (12) For both powers in kW, we have: ( ) ( ) (14) 4 4 ( ) ( ) (15) Where ( ) ( ) Thus, the PI controllers that control both powers are calculated using the IMC (Internal Model Control) and are given as follows: ( ) ( ) (16) Where Power response time constant Switching frequency A feed forward compensation is done in order to calculate and Current-Mode Control Using (5) and (6), we have: Since , the above equations can be written as follows: (17) (18) Where 5 5 Thus, the PI controllers that control both currents are calculated using the IMC (Internal Model Control) and are given as follows: Where Current time constant Switching frequency A feed forward compensation is done in order to calculate and 1.2. Diagram blocks The diagram block of Voltage-Mode Control 6 6 The diagram block control of Current-Mode Control 2. PROCESSES DATA Example I Grid Voltage (cosine wave) Inverter: IGBT with snubber Transformer Yy 0 degree Initially the active and reactive powers are set to zero. At t = 0.02 s, active and reactive powers jump respectively to 500 kW and 250 kVAr. 7 7 At t = 0.15 s the active power jumps to 1080 kW and t = 0.30 s the reactive power jumps to 520 kVAr. Example II Grid Voltage (cosine wave) Inverter: IGBT with snubber RL impedance Initially the active and reactive powers are set to zero. At t = 0.002 s the active power is set to 2500 kW and 1000 kVAr at t = 0.06 s. At t = 0.1 s the active power jumps to -2500 kW. Example III A three phase voltage source supplies an AFE three phase rectifier that feeds the inverter of example II. Initially the inverter active and reactive powers are set to zero. At t = 0.02 s the active power is set to 2500 kW and 500 kVAr at t = 0.1 s. At t = 0.18 s the active power jumps to -2500 kW. The DC voltage is set to 1250 Volts. The IGBTs are modeled by ideal switches in parallel with diodes. The capacitor . The AFE is designed in abc reference frame. The IGBTs are triggered by a hysteresis control which is set to . The following parameters are used for the controllers: PLL PI controller Voltage Controller 8 8 3. CONTROLLERS DESIGN Example I Voltage-Mode Control Design First of all, we have to calculate the impedance of the transformer seen from the primary side. From the transformer parameters, we have: Hence, the impedance of the transformer seen from the primary side is calculated as follows: Second of all, we have to calculate the grid voltage seen from the primary side of the transformer. Using a PLL (Phase Locked Loop) where in steady state , we have: √ √ Where Turn ratio of the transformer For a time constant , PI controllers that control both powers are calculated using the IMC (Internal Model Control) and are given as follows: ( ) ( ) The cross coupling terms for feedforward compensation are: ( ) 9 9 ( ) Current-Mode Control Design Using the parameters calculated for Voltage-Mode Control, we have: For a time constant , PI controllers that control both currents are: The cross coupling terms for feedforward compensation are: Example II Voltage-Mode Control Design Using a PLL (Phase Locked Loop) where in steady state , we have: √ √ Where Turn ratio of the transformer For a time constant , PI controllers that control both powers are calculated using the IMC (Internal Model Control) and are given as follows: ( ) ( ) The cross coupling terms for feedforward compensation are: 10 10 ( ) ( ) Current-Mode Control Design Using the parameters calculated for Voltage-Mode Control, we have: For a time constant , PI controllers that control both currents are: The cross coupling terms for feedforward compensation are: Example III Use controllers of current-mode 4. SIMULATION PARAMETERS The simulation was run in time domain with sample time of 5. PROCESSES REPRESENTATION IN ES V6 See the end of the document 11 11 6. ENGINEERING SUITE V6 RESULTS Example I: Voltage-Mode Control 12 12 13 13 14 14 Example I: Current-Mode Control 15 15 16 16 17 17 Example II: Case of Current-Mode Control 18 18 19 19 20 20 Example III: AFE feeds VSC System in Current-Mode Control 21 21 22 22 23 23 24 24 Conclusion This document shows how to design controllers for grid-imposed frequency VSC system in voltage-mode control and current-mode control. 7. REFERENCE BOOK 1. Voltage-Sourced Converters in Power Systems. Modeling,Control, and Applications. A. Yazdani / R. Iravani. 3 3 A I a Φ I a I b Φ I b I c Φ I c 3 V V a Φ V a C T V b Φ V b V c Φ V c 3 Vdc / 2 GRID-IMPOSED FREQUENCY VOLTAGE SOURCED CONVERTER (VSC) SYSTEM: CONTROL IN dq FRAME Qref K K Vid Viq ∑ 3 Yn Yn 3 3 K Δ Δ ITL ITL ∑ K d 0 a Φ b c q ∫ s b b s a a s G 1 0 1 0 ) ( ∑ C Phase Locked Loop To dq/abc transform a b c d Φ q 0 C P 3 Pref sbb saasG 10 10 )( sbb saasG 10 10 )( 3 1 a b c 3 A Ia Φ Ia Ib Φ Ib Ic Φ Ic ≥ ≥ ≥ ma mb mc C ÷ ÷ ÷ Voltage-Mode Control ∑ ∑ 3 1 a b c 3 3 3 A I a Φ I a I b Φ I b I c Φ I c 3 V V a Φ V a C T V b Φ V b V c Φ V c 3 ≥ ≥ ≥ P 3 d 0 a Φ b c q Δ Pref Qref ∑ Vdg Vq PI regulator Id_Ref Iq_Ref Δ d 0 a Φb c q ÷ ÷ a b c d Φ q 0 C sbb saasG 10 10 )( sbb saasG 10 10 )( ∑ ∑ K sbb saasG 10 10 )( sbb saasG 10 10 )( KK -wL K 2 / 3 ÷ ÷ ∑ C C -2 / 3 Id Iq C Ud Uq K K Transform kW to W Transform kVAr to VAr wL ∫ s b b s a a s G 1 0 1 0 ) ( ∑ C Phase Locked Loop To abc/dq and dq/abc transforms Vdc / 2 Avoid zero division Avoid zero division PI regulator Feed-forward filter ma mb mc md mq 3 A I a Φ I a I b Φ I b I c Φ I c 3 Yn Yn 3 GRID-IMPOSED FREQUENCY VOLTAGE SOURCED CONVERTER (VSC) SYSTEM: CONTROL IN dq FRAME Current-Mode Control K Voltage turn ratio K K K Current turn ratio Current turn ratio ∑ ∑ 3 1a b c 3 3 3 3 3 A I a ΦI a I b ΦI b I c ΦI c 3 V V a Φ V a C T V b Φ V b V c Φ V c 3 ≥ ≥ ≥ P 3 d 0 a Φ b c q Δ Pref Qref ∑ Vd Vq PI regulator Id_Ref Iq_Ref Δ d 0 a Φb c q ÷ ÷ a b c d Φ q 0 C sbb saasG 10 10 )( sbb saasG 10 10 )( ∑ ∑ K THREE PHASE BOOST RECTIFIER & GRID-IMPOSED FREQUENCY VOLTAGE SOURCED CONVERTER (VSC) SYSTEM: CONTROL IN dq FRAME sbb saasG 10 10 )( sbb saasG 10 10 )( KK -wL K 2 / 3 ÷ ÷ ∑C C -2 / 3 Id Iq Ud Uq ∑ K K Transform kWto W Transform kVAr to VAr wL ∫ s b b s a a s G 1 0 1 0 ) ( ∑ C Phase Locked Loop To abc/dq and dq/abc transforms Vdc / 2 Avoid zero division Avoid zero division PI regulator Feed-forward filter ma mb mc md mq V Φ VC T V X Δ ∑ K K ∫ Δ X Δ A/D A/D Δ A/D X Vdc measured PI controller Current phase a template Current phase b template Current phase c template Hysteresis control P 3 3 3 3 A I a ΦI a I b ΦI b I c ΦI c 3 1 a b c d 0 a Φ b c q ∫ s b b s a a s G 1 0 1 0 ) ( ∑ C Vabc to Vdq PLL 3 V Va ΦVa C T Vb ΦVb Vc ΦVc 3 3 a b c d Φ q 0 C C C Iq=0 Id=1 I0=0 C Hysteresis control Hysteresis control K