Direct Power Control of a PWM Rectifier Fed Autonomous Induction
Transcription
Direct Power Control of a PWM Rectifier Fed Autonomous Induction
Available online at www.sciencedirect.com ScienceDirect Energy Procedia 36 (2013) 391 – 400 TERRAGREEN13 INTERNATIONAL CONFERENCE Direct power control of a PWM rectifier fed autonomous induction generator for wind energy applications Z. Boudriesa, D. Rekioua Ziania, M. Sellamib a LTII Laboratory, Departement of Elctrical Engineering, University of Bejaia, Algeria b GE Laboratory, Departement of Elctrical Engineering, University of Bejaia, Algeria Abstract In this paper, a control strategy for a stand alone induction generator (IG) driven by a variable speed wind turbine for use in remote area power supply is presented. The IG is excited simultaneously by a capacitor bank and a PWM rectifier. During the voltage build up process, there is a variation in the flux linkage of the induction generator. The variation of the magnetising inductance is taken into account due to saturation of the core. To achieve the main goal of the control system, which consists to keeping the DC link voltage constant regardless of the magnitude of the load power, a direct power control (DPC) technique is proposed. In DPC approach, the converter switching states are selected directly by a switching table based on the instantaneous errors between the controlled and estimated values of active and reactive power. The simulation calculation was achieved using MATLAB®-SIMULINK® package and results are presented to support the theoretical discussion. © Authors. Published by Elsevier Ltd. © 2013 2010The Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] Selection and/or peer-review under responsibility of the TerraGreen Academy Keywords: Direct power control; PWM rectifier; induction generator; instantaneous active and reactive power; magnetizing inductance * Z. Boudries. Tel.: +213-34-215-006; fax: +213-34-051-005. E-mail address: [email protected]. 1876-6102 © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the TerraGreen Academy doi:10.1016/j.egypro.2013.07.045 392 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 1. Introduction The trend to reduce dependency of pollutant energetic sources, such as oil and coal, has been increasing the attention given to renewable energy. The wind is a renewable energy which is clean and abundant resource. Induction generators are widely used for wind powered electric generation. For the stand-alone operating, the squirrel cage induction machine is preferred thanks to its robustness, reduced cost and low maintenance. In addition, the induction generators do not need an external power supplies to produce the excitation magnetic fields. The excitation can be provided by means of PWM converter and a capacitor bank connected to the stator windings of the induction generator. The device has to be controlled in order to maintain the DC voltage at a constant value whatever the speed and the load values as long as the wind power is sufficient to satisfy the electric needs. Several works have already dealt with the study of the autonomous induction generator and different solutions have been suggested to control the DC voltage. Field oriented control [1-9] and direct torque control [10,11] were proposed to maintain the terminal voltage constant. These strategies are robust and permits to obtain accurate control with excellent regulation of the DC voltage. With DTC, no speed-loop is needed for the controller and a true sensorless controller is naturally obtained. It, consequently, appears to be superior to vector control scheme. In this paper, the conventional direct torque control scheme for induction motor drives is extended to control directly the active power (DPC) delivered to an active load by a wind turbine driven squirrel cage induction generator (SCIG). The SCIG is interfaced to the load through an AC-DC converter (PWM rectifier). The goal of this proposed control system is to maintain the DC bus voltage at constant value independently of the variations of the load. The DPC for IG has been studied in some literatures [12, 13] and proved to have several advantages over the conventional vector control. In this control strategy, the error in the reference power and the actual power is utilized to generate the voltage control directly as in conventional DTC drives [14, 15]. This method reduces the number of PI controllers used when compared to the vector control based variable speed wind turbine generator systems. The DPC like DTC is a stator flux based control technique having the advantages of robustness and fast controls [16]. DPC has following advantages: Simpler voltage and power estimation algorithm, Easy implementation of the unbalanced and distorted line voltage compensation to obtain sinusoidal currents (low THD), excellent dynamics and no coordinate transformation is required [17] The whole control system thus obtained is simulated using MATLAB-SIMULINK software. Simulations results for a 5.5 kW induction generator are presented and discussed to verify the effectiveness of the developed control strategy. 2. System description The studied overall system is represented in Fig.1. It comprises a wind turbine, an induction generator, a PWM rectifier and an active load. The goal of the device is to keep the DC bus voltage Vdc at a constant value whatever the load variations. 393 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 3. Induction machine model The model of the induction generator in the stationary reference frame Į-ȕ is established in assumption of saturation of the core. The electrical equations are then written as follows [18]: ªVsDº «V » « sE» «0» « » ¬0¼ ª « ls « 0 0 0 ºªisD º « « » «0 Rs 0 0 »«isE » « ». Rr Z.lr Z.(.lr Lm)»«imD» « »« » «lr Rr ¼«¬imE»¼ « Rr Z.(lr Lm) « «0 «¬ ª Rs «0 « «Rr « ¬Z.lr 2 ' mD m m º i ' i .i Lm L . Lm. mD mE »ªdisD º i im »« » dt 2 »« di » ' imD.imE ' imE ls Lm. Lm Lm. »« sE » im im »« dt » (1) . 2 »«dimD» ' imD ' imD.imE 0 lr Lm Lm. Lm. »« » im im »« dt » 2 » dimE « » ' imD.imE ' imE Lm. lr Lm Lm. »«¬ dt »¼ lr im im »¼ 0 Where Rs, Rr, ls and lr are the stator and the rotor phase resistances and leakage inductances respectively, Lm is the magnetising inductance and Z n pp .: (ȍ is the rotor speed in rd/s, npp the machine poles pairs number). Besides VsĮ, isĮ, Vsȕ and isȕ are the Į-ȕ stator voltages and currents respectively. imĮ and imȕ are the magnetizing currents, along the Į and ȕ axis, defined by: i mD ®i ¯ mE i s D i rD i s E i rE (2) Where irĮ and irȕ are the Į-ȕ rotor currents. im 2 i mD i mE 2 (3) Thus the saturation effect is taken into account by the expression of the magnetizing inductance Lm with respects to the magnetizing current im defined as: To express Lm in function of im we use a polynomial approximation of degree 12 [18]. ° Lm ° ® °L m ' °¯ n ¦ a .i f ( im ) j j m j 0 dL m d im n ¦ j.a . i j j1 m j 0 This model takes account of both saturation and cross magnetizing effects. (4) 394 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 4. Model of three-phase PWM converter The converter can be expressed, in a-b-c reference frame with following equations [19]: ªVsa º «V » « sb » «¬ Vsc »¼ ªi a º ªi a º ª Va º d R ««i b »» L ««i b »» «« Vb »» dt «¬i c »¼ «¬i c »¼ «¬ Vc »¼ (5) Where L and R are the line inductance and resistance, respectively. ia, ib and ic are the AC side rectifier currents. The AC rectifiers voltages Va, Vb and Vc are defined as: Va Vb Vc Vdc 2S a S b Sc 3 Vdc Sa 2S b S c 3 Vdc S a S b 2Sc 3 (6) Sa, Sb and Sc are the switching states of the rectifier The relationship between the AC side rectifier currents ia, ib and ic and the DC bus voltage Vdc can be written as: C dc dVdc dt Sa i a Sb i b Sc i c i L (7) Where Cdc is the dc link capacitance, iL the load current. 5. Direct Power Control (DPC) system Based on the principles of DTC strategy, direct power control (DPC) is developed in this paper to control the DC voltage delivered by a PWM rectifier fed induction generator. In this strategy, there are no internal current control loops and no PWM modulator block. The converter switching states are selected by a switching table based on the instantaneous errors between the controlled and estimated values of active and reactive power and the angular flux position. Therefore, the key point of the DPC implementation is a correct and fast estimation of the reactive and active line power. A. Flux estimator Based on the measured DC link voltage Vdc and converter switching states Sa, Sb, Sc , the flux components are calculated in (Į-ȕ) coordinates system as follows [20] : 395 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 \D \E B. ³ ³ 2 1 Vdc (S a (S b S c ) L.i D 3 2 1 Vdc (S b S c ) L.i E 2 (8) Active and reactive power estimator The measured line currents ia, ib DQG WKH HVWLPDWRU IOX[ FRPSRQHQWV ȥĮ, ȥȕ are used to the power estimation [19, 20]. p Z e .(\ D i E \ E i D ) q Z e .(\ D i D \ E i E ) (9) Ze is the flux electric pulsation defined by: Ze dJ \ dt , J\ arctg \E (10) \D C. Block scheme of the DPC system Fig.1 shows the configuration of the proposed control system based on DPC method. The controller features relay control of the active and reactive power by using hysteresis comparators and a switching table. In this configuration, the DC bus voltage is regulated by adjusting the active power transmitted to the load. As shown in Fig.1, the active power control, p*, is provided from the outer PI dc voltage controller block. The reactive power control, q*, is directly given from the outside of the controller. Errors between the controlled and the estimated feedback power are input to the hysteresis comparators and digitized to the signals d p and dq defined as: dp 1 if p * p t h p , d p 0 if p * p d h p dq 1 if q * q t h q , d q 0 if q * q d h q Where hp and hq are the hysteresis band. (11) 396 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 Wind turbine Gear box Self excited Induction generator LOAD L, R Cdc PWM Rectifier C Current mesurement Instantaneous power & flux estimator Sa Sb Sc Sector selection Sa Sb Sc Vdc Switching Table dq dp Vdc * PI - p - q p* * q Fig. 1. Block scheme of DPC Also, the phasH RI WKH IOX[ YHFWRU LV FRQYHUWHG WR WKH GLJLWL]HG VLJQDO șn. For this purpose, the stationary coordinates are divided into twelve (12) sectors, as shown in Fig.2, and the sectors can be numerically expressed as: (n 2) S S d T n d (n 1) 6 6 n 1,2,...,12 Į Ĭ6 Ĭ5 Ĭ4 Ĭ3 Ĭ7 Ĭ2 Ĭ8 Ĭ1 Ĭ9 Ĭ10 Ĭ11 ȕ Ĭ12 Fig. 2. Į-ȕ plane divided into twelve sectors to detect the phase of the voltage vector (12) 397 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 The digitized variables d p, dq DQGWKHIOX[YHFWRUSRVLWLRQȖȥ DUFWJȥȕȥĮ) form a digital word, which by accessing the address of the lookup table selects the appropriate voltage vector according to the switching table I. Table 1. Switching table for direct instantaneous power control dp dq Ĭ1 Ĭ2 Ĭ3 Ĭ4 Ĭ5 Ĭ6 Ĭ7 Ĭ8 Ĭ9 Ĭ10 Ĭ11 Ĭ12 0 1 101 111 100 000 110 111 010 000 011 111 001 000 0 0 111 111 000 000 111 111 000 000 111 111 000 000 1 1 101 100 100 110 110 010 010 011 011 001 001 101 1 0 100 110 110 010 010 011 011 001 001 101 101 100 6. Simulation results To study the performances of the DPC system, the PWM rectifier with the whole control scheme has been simulated using the MATLAB SIMULINK software. The main electrical parameters of the power circuit and control data are given in table II. Table 2. Machine and power circuit parameters [18] Machine Parameters Power circuit parameters Parameter Value Parameter Value Rs 1.07131ȍ R 0.2 ȍ Rr 1.29511 ȍ L 10mH ls 0.0089382 ȍ Cdc 1mF lr 0.0048613 ȍ RL 100 ȍ npp 4 The graph presented in Fig.3 illustrates the phase voltage built up. The phase voltage value is fixed to 220V by an appropriate choice of the capacitance in the bank connected to stator winding of the induction generator (C=200P F). In Fig.4 is presented the response to step change of the controlled DC voltage (from 465V to 550V) for a value of load fixed to 100 $V FDQEHREVHUYHG WKH '& YROWDJHLV YHU\FORVH WRLWVUHIHUHQFH value that it tracks with a good accuracy and stability. Fig.5 depicts the active power waveform, in ac side, when the DC voltage step change is applied. We can note that active power changes from about 2000 W (for Vdc = 465V) to 3000 W (for Vdc = 550 V). These values correspond to the load power demand in the DC side, witch is expressed by: p Vdc2 RL 398 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 Fig.6 shows the line current evolution, when the step change to Vdc is applied. The current variation follows the power demand and there is a good agreement between the observed values and those calculated from the relation expressing the power assessment between the AC and DC side of the converter, that is given by: Vdc2 RL p 3 Vm I m 2 (13) The effect of DC load variation (Fig.7) on the operation of the system is illustrated in Fig.8,9 and 10. It can be seen that changes in load don’t affect DC link voltage which remains almost. This is due to the fact that the system acts as a voltage generator, adjusting the power demand as a function of load variations, by regulating current values according to equation (13). 150 600 550 500 465 100 400 250 Vdc(V) Vsa (V) 200 50 0 -50 300 200 -100 -150 100 -200 -250 0 0 0.2 0.4 0.6 0.8 1 0 1.2 0.2 0.4 time(s) 0.8 1 1.2 1.1 1.2 time(s) Fig. 3. A phase voltage built up 2 0.6 Fig. 4. DC voltage x 10 4 60 40 1.5 isa(A) p(W) 20 1 10 0 -10 -20 0.5 0.3 0.2 0 -40 0.6 0.7 0.8 0.9 1 time(s) Fig. 5. Active power 1.1 1.2 -60 0.6 0.7 0.8 0.9 1 time(s) Fig. 6. Current of phase a 399 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 500 110 465 400 90 350 80 75 70 300 Vdc(V) RL( 100 60 250 200 150 100 50 40 0 0.2 0.4 0.6 0.8 1 1.2 50 0 0 0.2 0.4 time(s) 0.6 0.8 1 1.2 1 1.2 time(s) Fig.7. The load variation Fig. 8. DC voltage 5000 15 4500 10 4000 isa(A) p(W) 5 3000 2000 0 -5 1000 -10 0 -15 0 0.2 0.4 0.6 0.8 time(s) Fig. 9. Active power 1 1.2 0 0.2 0.4 0.6 0.8 time(s) Fig. 10. Current of phase a 7. Conclusion A Direct Power Control (DPC) scheme is presented that directly controls the active power delivered by an induction generator to an active load. An AC-DC (PWM rectifier) is used as the power electronic interface between the load and the induction generator. To control the converter, a switching table based on the errors in instantaneous values of controlled and estimated active and reactive power is used. The simulation results agree with theoretical previsions illustrated by the by the power assessment between the Ac and DC sides of the converter, and clearly, show that the system acts as a voltage generator adjusting the power delivered by the generator to the load demand with an aim to keeping the DC bus voltage as constant value. Since constant DC voltage is achieved a DC load can use it directly, or, if required it is a matter of having an inverter to produce a constant voltage and frequency AC output. 400 Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400 References [1] John G, Erdman W, Hudson R, Sheng FC, Mahajan S. Stator flux estimation from inverter switching states for the field oriented control of induction generators. In: proceeding of the IEEE Industry Applications Conference; 1995. p. 182–188. 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