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1240 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 STATCOM-Based Indirect Torque Control of Induction Machines During Voltage Recovery After Grid Faults Jon Are Suul, Marta Molinas, Member, IEEE, and Tore Undeland, Fellow, IEEE Abstract—This paper proposes a control method for limiting the torque of grid-connected cage induction machines during the recovery process after grid faults, by using a static synchronous compensator (STATCOM) connected at the machine terminals. When a STATCOM is used for transient stability improvement, common practice is to design the control system to keep reactive current at maximum level until the voltage has returned to its initial value. This will result in high torques during the recovery process after grid faults. The control method proposed in this paper is intended to limit such torque transients by temporarily defining a new voltage reference for the STATCOM control system. As torque is controlled through the voltage reference of the STATCOM, the method is labeled indirect torque control (ITC). The presented concept is a model-based approach derived from a quasi-static equivalent circuit of the induction machine, the STATCOM and a Thévenin representation of the power system. For illustration and verification, time-domain simulations of a wind power generation system with a STATCOM at the terminals of an induction generator, are provided. As the objective of limiting the torque of the induction machine is achieved, the derivation of the concept proves to be reasonable. The approach is presented in its most general form, oriented to torque limitation of induction machines both in generating and motoring mode, and is not restricted to the presented example. Index Terms—Grid voltage recovery, induction machine stability, induction machine torque, low-voltage ride through (LVRT), static synchronous compensator (STATCOM). I. INTRODUCTION PERATION of induction machines directly connected to the power system has been an issue of investigations in stability studies for a long time [1]–[6]. The characteristics of induction motor loads and how their transient behavior influence the voltage stability of power systems is well known, and the most relevant solution to improve system stability is often reactive compensation close to the source of instability [7]–[10]. As wind turbines based on induction generators have been introduced into the power system to an extent where their influences on the grid can not always be considered negligible, the issue of voltage stability studies involving induction machines has regained interest. This has attracted attention to investigations O Manuscript received February 28, 2009; revised July 18, 2009. Current version published May 7, 2010. Recommended for publication by Associate Editor J. Kokernak. The authors are with the Department of Electric Power Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2009.2036619 of static voltage stability limits of induction generators and the need for reactive power compensation to allow for introduction of large-scale wind power production in the presence of grid limitations [11]–[14]. Dynamic stability limits and transient stability of induction machines has also been investigated, especially with respect to low-voltage ride through (LVRT) capability of wind turbines [15]–[22]. This has led to increased focus on reactive power compensation for induction generators based on power electronic solutions, for improvement of transient stability and LVRT capability [10], [23]–[33]. Solutions based in induction machines directly connected to the grid still have a large share of the installed ratings in large scale power systems, both as industrial motors and as generators for distributed generation systems like wind turbines and small hydropower units [8], [34]–[36]. Therefore, shunt reactive power compensation for stability improvement of induction machines will continue to be of significant importance with respect to several aspects of power system operation. For improvement of transient stability, a static synchronous compensator (STATCOM) will be the power electronic solution with the best performance at low voltages, and will, therefore, contribute the most to increase the capability of LVRT [9], [10], [28], [31], [33], [37]. Increasing the LVRT capability by reactive power compensation will, however, increase the torque capability of the induction machine at speeds outside the normal operating range, resulting in higher maximum torque, and correspondingly higher stresses on the drive-train during the recovery process after the fault [24], [30], [31]. This will be the case since common practice is to let the system operate with controllers running into saturation, and thus controlling the STATCOM to provide maximum reactive current through a grid fault and until the voltage is recovered. Maximum reactive power compensation is only needed to keep the system stable as long as the speed of the machine is close to the stability limit, and therefore, it can be possible to reduce the level of compensation after stability is ensured to relieve the torque stresses on the drive train. With the purpose of limiting the maximum torque of an induction machine during the recovery process after a grid fault, this paper suggests a new way of setting the voltage reference during the recovery process for the commonly used control structure of a STATCOM originally designed to increase the LVRT capability of a grid connected induction machine. The proposed method is a model-based approach implemented by temporarily redefining the voltage reference for the STATCOM as a function of the speed of the induction machine. The method is labeled indirect torque control (ITC) since the torque is indirectly controlled by 0885-8993/$26.00 © 2010 IEEE Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS Fig. 1. System under study with an induction machine connected to the grid through a transformer and with a STATCOM connected at the terminals. influencing the terminal voltage of the induction machine. An application of torque control by a STATCOM to a realistic wind turbine system has been briefly presented in [38], while this paper is providing the theoretical basis and the derivation of the ITC concept in the most general way. Since the proposed control approach will only be active during the recovery process after a grid fault, the normal operation of the STATCOM and the induction machine will not be influenced. Therefore, the presented concept can be considered to provide transient torque control as an add-on feature of a STATCOM initially designed for reactive power support and improvement of transient stability. The main disadvantage of this additional control feature will be that the recovery process after a fault is made longer due to the limitation imposed on the machine torque by the controller. II. SYSTEM MODEL The system under consideration is sketched in Fig. 1 and consists of an induction generator directly connected to the grid through a transformer, and a STATCOM connected at the terminals of the induction machine. It should, however, be noted that a system with an induction motor can be considered in the same way. The derivation of the suggested control method is based on a quasi-static approach, neglecting the flux transients of the induction machine and the transient response of the grid. This leads to the use of the well known per phase equivalent circuit of the induction machine [11], [17], [18], [24], [30], [31], [33], [39]. Although this approach is well established both for steady-state calculations and for evaluation of static and dynamic stability limits, it has not been previously used together with a STATCOM for designing a dynamic control method. The validity of this approach will be discussed later, but can basically be justified because the objective of the presented control method is to limit the torque and by that the acceleration of the machine. It should also be noted that accuracy of control is not of critical importance, as long as the objective of limiting the maximum torque is achieved. The quasi-static equivalent circuit representation of the system under study is shown in Fig. 2. In addition to the induction machine equivalent, the circuit consists of a simplified representation of the grid by a Thevenin equivalent, and the STATCOM represented as a controllable source of reactive current. In the figure, v g , v 1 , and v m are phasors for grid voltage, induction machine terminal voltage, and internal voltage at the magnetizing reactance, while ig , iSTATCOM , i1 , im , and i2 are line, STATCOM, stator, magnetizing, and rotor current phasors. The 1241 Fig. 2. Quasi-static equivalent circuit for derivation of the control method suggested during the recovery process after a grid fault. The model consists of the traditional induction machine equivalent circuit, the STATCOM modeled as a controllable reactive current source, and a Thevenin-equivalent of the grid. grid impedance is given by rg + jxg while r1 , r2 are stator and rotor resistance and x1 , xm , x2 are stator, magnetizing, and rotor reactance. The model is expressed in per unit (pu) quantities, with all parameter values referred to the stator of the induction machine. As long as quasi-static considerations are reasonable, the model in Fig. 2 can represent the system both before and after a grid fault. During a fault, the voltage at the generator terminals is assumed to be very low, such that the influence from the STATCOM current on the response of the induction machine can be considered negligible. The location of the fault is not of specific importance, since the focus of the suggested approach is the recovery process after a short circuit fault in the grid is cleared. For simplicity, the fault is assumed to be at the terminals of the machine when simulating the system for investigating the validity of the presented control method. The STATCOM is assumed to be current controlled with high bandwidth current control loops, and to have a fast voltagecontrol loop acting on the reactive current reference [31], [32], [40], [41]. However, the type of control system, the modulation technique and the practical implementation of the inner control loops have no significant influence on the proposed concept, as long as the control structure can be tuned to obtain a fast dynamic response. The torque of the induction machine in per unit can be found from simple calculations to be given by (1) [7]. With the reference directions indicated in Fig. 2, positive values for torque τ em , slip s, and rotor current i2 correspond to motor operation of the induction machine, while negative values of the same variables correspond to generator operation r2 (1) τem = |i2 |2 . s III. INDIRECT TORQUE CONTROL CONCEPT By phasor calculations on the equivalent circuit from Fig. 2 and application of (1), it is possible to calculate the quasi-static conditions needed to obtain a specified torque at a specified speed. In [31] and [33], it has been shown how this can be used to estimate the rating of a compensation device needed to maintain stability of the system as a function of the speed of the machine when a fault is cleared. In the following sections, it will be shown how the same approach can be used dynamically during the recovery process after a grid fault, to indirectly control the torque of the induction machine by controlling the terminal voltage with the STATCOM. The focus will be on Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. 1242 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 derivation, explanation, and proof of concept, with verification and illustration provided by detailed time-domain simulations. A. Derivation of Voltage Reference Signal for the ITC The starting point of the suggested control approach will be to specify a torque reference that can be input to (1). This torque reference should be selected with respect to known characteristics, measurements or estimations of the mechanical torque as a compromise between limiting the torque and length of the recovery process. Solving for the rotor current i2 as a function of the slip of the machine will result in (2), where the solution with the positive sign should be chosen for motor operation while the negative solution will be valid for generator operation τem ,ref s . (2) i2 = ± r2 By using the current i2 as the reference for phasor calculations, the stator current i1 corresponding to the calculated rotor current will be given by (3). The full expression for the stator voltage that corresponds to a specified torque reference will then be given as a function of the slip by (4) x2 r2 i1 = i2 + im = +1−j (3) i2 xm sxm x2 r2 r2 x1 + + 1 r1 + v 1 (s) = s xm sxm x2 τem ,ref s r2 r1 + j x2 + + 1 x1 − ± xm sxm r2 (4) v ref ,STATCOM (s) = |v 1 (s)|. (5) Defining the absolute value of the voltage from (4) as a speed dependent reference voltage for the STATCOM control system as given by (5), it is possible to indirectly control the torque of the machine in the high-speed region towards a specified value. This is only relevant after a grid fault, when the speed of the machine is outside the normal operating range and the machine will have to pass through the speed range around the pullout torque during the recovery process. B. Verification of ITC Concept by Time-Domain Simulation To verify and illustrate the functionality of the suggested ITC concept, a system with an induction machine directly connected to the grid and a STATCOM connected at the machine terminals R /EMTDCTM software [42]. The is simulated with the PSCAD simulation model can be considered to represent a wind turbine generator with rating in the range of 2 MW, and the main parameters of the simulated system are given in the Appendix [33]. The R /EMTDCTM model includes a full fifth-order dynamic PSCAD model of the induction generator, the simple grid equivalent and a STATCOM with a control system based on voltage oriented vector current control [31], [41], [43]. The main control loops of the STATCOM are included in the simulation model, but for simplicity and speed of simulation, an average model of the voltage source converter is used instead of simulating the Fig. 3. Structural block diagram of control system for STATCOM with ITC modifying the voltage reference when the induction generator is operating in the high-speed region during the recovery process after a grid fault. pulsewidth modulation (PWM) switching pattern [44]. The proposed control concept is included in the simulation model by implementing the ITC equations and using the voltage reference calculated from (5) as the reference value for the voltage control loop of the normal STATCOM control structure when the induction generator is operating in the high speed region. This is shown in Fig. 3, where the block to the left of the figure indicates how the ITC functionality is allowed to define a temporary, speed-dependent, value for the grid voltage reference. Under normal STATCOM operation, the voltage reference will be close to 1.0 pu as indicated in the figure. The ITC concept is only overriding this reference value during the recovery process after a fault, when the induction generator is operating in the high-speed region. Three cases have been simulated; one reference case with only constant capacitor compensation to keep nominal voltage under normal operating conditions, a second case with a STATCOM for voltage control and LVRT capability, and the third case to show how the STATCOM based ITC can be achieved as an additional functionality. In all the simulations, the mechanical input torque is considered to be constant during the simulation time. In the case with ITC, the system is set to limit the torque of the induction machine below 1.1 pu Simulation results are shown for 10 s when the system is starting from stationary conditions and is exposed to a 350 ms three-phase fault at the terminals of the generator after 1 s of simulation time. The main results from the simulations of the three cases are collected in Fig. 4. The curves in Fig. 4(a) show the torque– speed trajectory of the system for the different cases as starting from steady state, through the fault and during the recovery process. This figure clearly shows that the case with capacitor compensation is unstable, while the results with normal STATCOM control and with ITC are identical up to the point when the ITC comes into operation during the recovery process. Fig. 4(b) is included, to illustrate the influence of the ITC more clearly by focusing on the recovery process without showing the Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS 1243 Fig. 4. Obtained results from the three selected cases of simulation. Parts (a)–(c) show how the torque during the recovery process can be limited by the ITC, and part (d) shows how this results in an almost linear reduction of speed during parts of the recovery process. Parts (e) and (f) show the resulting voltages in the three different cases. (a) Simulated Torque–speed trajectories for the three selected cases. (b) Zoom of simulated torque–speed trajectories together with the calculated torque–speed curve for 1.5 pu STATCOM current. (c) Electrical torque before, during, and after the fault for the three selected cases. (d) Speed of the machine before, during, and after the fault for the three selected cases. (e) Voltage at the machine terminals before, during, and after the fault for the three selected cases. (f) Simulated voltage-speed trajectories for the three selected cases. Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. 1244 influence from the torque transients when the fault occurs. This figure also includes the torque–speed curve calculated from the quasi-static equations of the system, to show the influence of the flux dynamics on the system with normal STATCOM control. An arrow indicates how the ITC comes into operation when the torque of the machine reaches the set-point value. Fig. 4(c) shows the torque as a function of time for the three different cases and further illustrates how the ITC effectively limits the peak torque during the recovery process, while Fig. 4(d) is showing the resulting speed as function of time. Fig. 4(e) is showing the voltage at the generator terminals as a function of time, and here it can be clearly seen that the system is not able to recover the voltage in the case with only capacitor compensation. It can also be seen that the voltage is actively reduced by the ITC during the recovery process to limit the torque, but only after stability is ensured and the machine has started to decelerate. This operation of the ITC as a secondary control objective after stability is ensured is what makes the approach reasonable, and is, therefore, a central point of the proposed concept. The trajectory of the voltage at the generator terminals with respect to the generator speed is shown in Fig. 4(f), and in the case of ITC this trajectory corresponds to the voltage reference calculated from (4) and (5) during the recovery process. The results plotted in Fig. 4 illustrate both the general behavior of a system with an induction machine and a STATCOM and the specific influence of the presented ITC method, as can be explained stepwise in the following points. 1) Before the fault, the system is in normal operation, and the voltage at the terminals of the induction machine is close to the nominal value as seen in Fig. 4(e). For the cases with STATCOM, the voltage control structure of the STATCOM is operating in the normal way and the STATCOM is operating in the capacitive region to provide reactive power to the induction generator. 2) When a fault occurs, there will be short circuit torque transients in the induction machine as seen clearly from Fig. 4(a) and 4(c). The STATCOM is not able to influence these torque transients, and they are not the focus of this paper. Because of the serious fault with a low remaining voltage, the reactive current of the STATCOM will have limited influence on the system voltage and on the operation of the generator during the fault. Because of the large voltage drop, the maximum current limit of the STATCOM will be reached, and the STATCOM running into saturation will operate as a constant source of reactive current. 3) During the fault, the short circuit transients of the induction generator are damped, and afterwards the electrical torque is almost negligible because of the low remaining voltage, as seen in Fig. 4(a)–(c). Since the average electrical torque during the fault is close to zero, the applied mechanical torque is causing an almost linear increase in generator speed as can be seen in Fig. 4(d). 4) When the fault is cleared, the STATCOM will keep maximum current since the system is not capable of recovering the voltage immediately due to the increased speed of the generator shaft. The simulation with only reactive com- IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 5) 6) 7) 8) 9) pensation by constant capacitors results in the lowest voltage after the fault is cleared, leading to voltage collapse as can be seen from Fig. 4(e). In this case, the system is seen to be clearly unstable since it is not possible to recover the voltage and return to the initial conditions. In the two cases with STATCOM, the voltage after the fault is cleared can be kept high enough for the system to be stable. The two cases with the STATCOM give identical results during and immediately after the fault is cleared. Since the system is stable in these cases, the generator starts to decelerate after the fault is cleared as can be seen in Fig. 4(a), (b), and (d), but as the speed of the generator is decreasing, the torque capability of the machine is increasing. With normal STATCOM control, the system will recover under maximum reactive compensation from the STATCOM as shown by the blue dashed lines in Fig. 4, and this result in a high transient torque during the recovery process. As can be seen in Fig. 4(b), and as discussed in [33], the dynamic recovery of the generator is resulting in a torque capability that is slightly reduced compared to the torque–speed curves that can be obtained from quasi-static calculations, but still the torque is significantly higher than the rated torque. In the case of recovery with ITC, the prioritized control objective of the STATCOM will change when the torque of the machine reaches the set point of the indirect torque control algorithm. The point when this condition is reached and the ITC comes into operation is marked with an arrow in the torque–speed trajectory of Fig. 4(b). Then the voltage reference for the STATCOM control system will be adjusted as a function of the speed of the generator according to (5). The influence on the torque is clearly seen by the red lines in Fig. 4(a)–(c), where the torque is kept almost constant, and as a result the speed in Fig. 4(d) is decreasing almost linearly. As long as the indirect torque control is active, the torque will be limited below the set-point value that has to be kept larger than the applied mechanical torque. The influence of the dynamic response of the machine and the grid, that are not accounted for in the ITC equations, is resulting in a torque that is slightly below the set point during the recovery. This slight reduction in torque can be noticed in Fig. 4(a), but can be better identified in the zoom of Fig. 4(b). Although much smaller, the influence of the flux transients of the machine in the case of ITC is similar to the difference between the calculated quasi-static torque– speed curve in Fig 4(b) and the simulated torque trajectory of the system during recovery with normal STATCOM control. The ITC is, however, intended to limit the torque and this result in a slower deceleration of the rotor and by that reduced influence of the transients in the machine and in the grid. The assumptions made to derive the equations of the ITC, therefore, prove to be valid, because the torque of the machine is limited by applying the proposed control concept. As soon as the speed of the machine is recovered close to its initial value before the fault and the voltage reaches the Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS reference value of 1.0 pu, the main control objective of the STATCOM with ITC will be shifted back the normal voltage control. 10) The resulting influence on the voltage when limiting the torque during the recovery process is shown in Fig. 4(e) and (f). Although this reduced voltage at the machine terminals will be the main drawback of the presented approach, the influence on the grid voltage will be less than what can be seen in Fig. 4(e) because of the transformer inductance between the generator and the point of common coupling (PCC). Since the control is limiting the torque of the machine to a value that must be higher than the applied mechanical torque, the reduced voltage will not represent any risk of instability originated by the induction generator. The validity and accuracy of calculations on such a system based on quasi-static phasor analysis is briefly investigated in [31] and [33], respectively, for the assessment of stability limits and requirements for reactive compensation in wind turbine applications. As shown by the curves in Fig. 4, the influence from the flux transients of the induction machine is similar in this case as in the case described in [33], both for the conditions around the stability limit and during the recovery process when the speed returns to the initial conditions. Since the objective of the ITC concept is to limit the torque of the induction machine during the recovery process, the deceleration will be slowed down compared to the case of recovery with maximum reactive compensation. This will result in reduced influence from the flux dynamics of the machine and the transient response of the grid. Slower deceleration will also reduce the influence of the response time of the STATCOM control system. When the torque reference is set close to the mechanical torque, the recovery process will be slow and the machine will operate close to stationary conditions, so that only a small influence of the flux dynamics and the controller response can be expected. This set of arguments support the validity of using a quasi-static model as the basis for deriving the ITC concept, and shows how it is the implementation of the control method itself that makes the assumptions to be valid. The simulation results shown in Fig. 4 also verify this by illustrating the functionality of the proposed concept. IV. ANALYSIS OF STATCOM CURRENT INJECTION WITH ITC As observed in Fig. 4(e) and (f), the suggested control approach will reduce the voltage reference for the STATCOM during the recovery process after a fault, to limit the torque of the induction machine. This will result in a longer recovery process, and more reactive power drawn from the grid. Depending on the parameters of the system and the torque reference used to calculate the voltage reference for control of the STATCOM, the STATCOM can even be controlled into inductive operation. This corresponds to actively controlling the STATCOM to Aeq,ST + jBeq,ST = j 1245 consume reactive power for reducing the voltage at the machine terminals, to slow down the recovery process. Although the proposed ITC concept is introducing a new control objective to the operation of a STATCOM, investing in a STATCOM only for this purpose will not be a relevant option. As presented in the premises for the investigation, the ITC should, therefore, mainly be considered as an add-on feature of an already existing STATCOM intended for reactive power support and improvement of transient stability or LVRT capability. Still, it will be important to know the current range needed for the indirect torque control or to investigate what torque limitation can be achieved with a certain rating and a specified set of system parameters. The required current as a function of speed and the torque reference should, therefore, be derived from the system model to verify the operational range of the STATCOM when applying ITC during the recovery process. Since losses of the STATCOM are neglected, the phasor of the SATCOM current can be expressed by (6), where the constants Aeq,ST and Beq,ST originates from (4) as given by (7), at the bottom of this page. v1 iSTATCOM = j |iSTATCOM | |v 1 | = (Aeq,ST + jBeq,ST )|iSTATCOM |. (6) With the current directions indicated in Fig. 2, the grid current will be the sum of the stator current of the machine and the STATCOM current. The simple expression relating the currents and the terminal voltage of the machine to the grid voltage is given in (8) v g = v 1 + (rg + jxg )(i1 + iSTATCOM ). (8) The power system is represented by a Thevenin equivalent, where the voltage source is assumed to have a known, fixed magnitude, and by substituting from (3), (4), and (6) into (8), the only unknown variable for a specific speed will be the magnitude of the STATCOM current. By defining equivalent resistances and reactances as given in (9), (8) can be brought into the form of (10), and by solving for |iSTATCOM |, the result is a second-order equation as given by (11). The minimum solution to (11) will result in the required STATCOM current to obtain the specified torque as a function of the slip or the speed of the machine x2 r2 r2 + + 1 (r1 + rg ) + (x1 + xg ) req,i 2 = s xm sxm x2 r2 xeq,i 2 = x2 + + 1 (x1 + xg ) − (r1 + rg ) xm sxm req,STATCOM = rg Aeq,ST − xg Beq,ST xeq,STATCOM = xg Aeq,ST + rg Beq,ST (9) v g = (req,i 2 + jxeq,i 2 )i2 + (req,STATCOM + jxeq,STATCOM )|iSTATCOM | (10) −(x2 + ((x2 /xm ) + 1)x1 − (r2 r1 /sxm )) + j((r2 /s) + ((x2 /xm ) + 1)r1 + (r2 r1 /sxm )) v1 = . |v 1 | ((r2 /s) + ((x2 /xm ) + 1)r1 + (r2 r1 /sxm ))2 + (x2 + ((x2 /xm ) + 1)x1 − (r2 r1 /sxm ))2 (7) Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. 1246 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 Fig. 5. Simulation results showing the reactive current from the STATCOM and illustrating the difference between operation with normal voltage control and operation with ITC during the recovery process. (a) STATCOM current–speed trajectories from simulation together with calculated characteristics of ITC. (b) Simulated reactive current from the STATCOM with normal operation and with ITC. seen in the current trajectory since the current is kept at the same value during both the acceleration and the deceleration of the machine. In the case with ITC, the modification of the voltage (req,i 2 i2 )2 + (xeq,i 2 i2 )2 − |v g |2 × |iSTATCOM | + 2 = 0. reference for the STATCOM is starting to act on the system req,STATCOM + x2eq,STATCOM as soon as the torque capability of the induction machine is reaching the specified set-point value and the STATCOM cur(11) rent is a result of this modified voltage reference. Therefore, the STATCOM current follows the trajectory of the red curve in The same approach has been used to estimate the required Fig. 5(a) until the system has returned to the initial state before rating of compensation devices in [31] and [33] for obtaining the fault. Comparing this current trajectory resulting from the LVRT. The main contribution of the presented concept is that the simulation of the ITC and the result obtained by plotting the calculations are used dynamically for implementing the indirect solution of (11) as a function of speed, only a small difference torque control as a model-based control concept that is shown to is observed and this difference is mainly caused by the flux dybe reasonable through the recovery process of the system after a namics of the machine and the delay in response caused by the fault. Therefore, the characteristics obtained from (11) must be PI-controllers of the STATCOM control structure. considered for the whole speed range of the induction machine, From the presented results, it is seen that the ITC is coneven if the result is corresponding to inductive operation of the trolling the STATCOM into inductive operation for limiting the STATCOM. torque when the machine is passing through the speed region Fig. 5 shows the STATCOM current resulting from the simwith the highest torque capability. Assuming that the current ulation of the two cases with STATCOM that were presented rating of the STATCOM has been determined by LVRT requirein Fig. 4. The trajectories of the STATCOM current with rements and that the current limit for operation in the inductive spect to the generator speed in the cases with and without ITC region is equal to the capacitive current limit, it is seen that are shown in Fig. 5(a), while Fig. 5(b) shows the simulated the ITC is operating well within these limits. Since the ITC is STATCOM currents as function of time. Fig. 5(a) also shows proposed as an additional feature that has relevance only during the calculated STATCOM current as a function of speed, resultthe recovery after a fault, the most realistic approach will be to ing from solving (11) with the same torque reference as used implement the ITC to operate within the current limits set by the for the simulations. main design criteria. The implementation of the ITC as an addInspecting the results in Fig 5(a) and (b), it can be seen how on functionality of a STATCOM can then provide additional the STATCOM current both with and without ITC is immevalue to an investment made for other purposes, as one among diately controlled to the maximum available rating when the other incremental software features giving advantages to supplifault occurs. When the grid fault is cleared, there is a transient ers intending to further exploit the potential of the STATCOM response in the STATCOM due to the grid transients, but the technology. current is quickly settled at the maximum value and the current is still identical for both cases since the torque of the machine V. IMPACT OF GRID PARAMETERS ON ITC is lower than the reference value specified for the ITC. For the The reactive current from the STATCOM needed to achieve case with the normal STATCOM control, maximum reactive current is kept until the system is recovered, and this is barely ITC during the recovery process depends on the system |iSTATCOM|2 + 2i2 (req,i 2 req,STATCOM + xeq,i 2 xeq,STATCOM) 2 req,STATCOM + x2eq,STATCOM Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS 1247 Fig. 6. STATCOM current as function of generator speed for different grid inductance values. (a) Required STATCOM current at stability limit as function of speed. (b) Required STATCOM current as function of speed with ITC and torque reference of 1.1 pu. parameters, and the widest relevant parameter range can be expected for the grid impedance. Since the grid impedance is determined by the strength and the R/X-ratio of the grid at the point of connection for the induction machine, it is of importance to estimate how different grids will influence the operation of the suggested control method. The largest variation can be expected in the grid inductance, and the influence on the current required for ITC is, therefore, investigated for a range of different values of the grid reactance xg , while all other parameters of the systems are kept constant at the values given in the Appendix. As a starting point, Fig. 6(a) is showing the STATCOM current as a function of speed when (11) is solved with a torque reference equal to the mechanical torque of 1.0 pu for different values of the grid reactance. This corresponds to operation at the stability limit of the system, in a similar way as the current profiles calculated in [31]. Fig. 6(b) shows the results when (11) is solved for a torque reference value of 1.1 pu, and gives the STATCOM current needed for the ITC for 5 different per unit values of the grid reactance. By comparing the results in Fig. 6(a) and (b) it can be seen that the current needed to obtain the specified torque is always more capacitive than the current calculated at the stability limit. This indicates how the ITC only can have priority as a control objective after stability of the system is ensured. Studying the curves in Fig. 6, it can also be seen that the curves for the different grid inductances are crossing each other at high speeds. The point of intersection indicates the speed where the terminal voltage needed to obtain the required torque will be higher than the grid voltage, and to obtain this condition reactive power has to be delivered to the grid from the point where the STATCOM is connected. In that case, the required capacitive current will be highest for strong grids, where the influence from reactive current on the voltage is low. For speeds below this point of intersection, the STATCOM current needed to keep the specified torque is less capacitive when the grid reactance is reduced. This corresponds to the stability consideration from [31], where less reactive compensation is needed to keep the system stable when the grid reactance is low because a stronger grid is capable of delivering more reactive power to the induction machine. With respect to torque control, this shows that more inductive current is needed to limit the peak torque during the recovery process in a strong grid, while little current is needed in a weak grid that is less stable without reactive compensation. The influence of the grid reactance on the most inductive current needed to limit the torque below the set-point value during the recovery process is illustrated clearly by the plot in Fig. 7(a) that shows the maximum inductive current needed to limit the torque to 1.1 pu, plotted as a function of the grid inductance. As seen, the required inductive current goes towards infinity when the grid inductance goes towards zero, while the current at the peak torque becomes capacitive for large grid inductances. The situation with a capacitive current in Fig. 7(a) corresponds to a situation where the peak torque of the machine is lower than the specified torque reference, and in this case the system would be close to the stability limit or even unstable without reactive compensation from the STATCOM in normal operation. Another result illustrating the same tendency is seen in Fig. 7(b), that shows the speed at the peak torque as a function of grid inductance. The influence from the grid inductance on the peak torque is also indirectly indicated by the curves in Fig. 6, where it can be seen how the current required to limit the torque will be reduced, and also that the speed at the pull-out torque of an induction generator will be reduced, when the grid inductance is increased. In case of an induction generator in a wind turbine, or a large induction motor for an industrial load, the connection to the grid will usually be through a dedicated transformer. If this transformer is directly connected to a typical voltage level for distribution systems like 11 or 22 kV, the transformer inductance is usually in the range of 5–6% referred to the transformer rating. For the system configuration in Fig. 1, the transformer impedance will be the minimum grid impedance if the system is connected directly to a strong grid. A grid reactance of 0.06 pu Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. 1248 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 Fig. 7. Peak inductive STATCOM current for ITC as function of grid reactance and corresponding speed where peak inductive current occurs. (a) Minimum (most inductive) STATCOM current needed to obtain ITC with 1.1 pu torque, as a function of grid reactance. (b) Speed at the point of maximum torque, where the most inductive STATCOM current is needed to obtain ITC during the recovery process. is, therefore, considered as a realistic minimum value, and used as the minimum value for the plots in Fig. 6. Still, such a low grid inductance would require a very large reactive current to limit the torque, and this will also have as a consequence that large reactive power will flow from the grid. On the other side, it can be seen from Fig. 7(a), that when the grid reactance is increasing towards 0.20 pu, the induction machine will require support of reactive current from the STATCOM even around the peak of the torque–speed curve. For higher reactances, reactive power compensation will be needed to keep the system stable even in normal operation, and it will be difficult to ensure transient stability of the system with respect to grid faults. At the same time, the grid inductance and the flux transients of the induction machine might dominate the response of the system after a fault is cleared and the control of the STATCOM itself can be challenging. According to the presented results, the most relevant range of grid reactance for implementation of the presented ITC concept can be considered to be between 0.10 and 0.20 pu. However, the parameters of the induction machine might influence this range, since a machine with lower inductances or higher losses, and correspondingly higher peak torque, will be more stable. Also, the resistance of the grid will influence the stability of the system, although the expected range of variation for grid resistance will be lower than for the grid inductance. VI. CONCLUSION A control concept for limiting the torque of a grid-connected induction machine during the recovery process after a grid fault by use of a STATCOM has been suggested. The proposed concept is a model-based approach derived from a quasi-static model of the induction machine, the STATCOM and the grid, and was presented as a secondary control objective of a STATCOM intended to improve the stability of an induction machine directly connected to the grid. The suggested method for indirect torque control was tested by detailed timed-domain simulations when applied to a model of a wind generation system consisting of an induction generator with a STATCOM connected at the terminals. In case of grid faults, it was shown how the full current capacity of the STATCOM can be first utilized to extend the stability limit of the induction generator, before the indirect torque control comes into operation. It was further demonstrated how the proposed method controls the STATCOM to limit the maximum torque of the generator during the recovery process after the fault. The initial control objectives of the STATCOM operation for voltage regulation in normal operation and improved LVRT capability in case of grid faults are not influenced and the simulation results show how the system returns to normal operation when the speed of the induction machine is back to the initial value before the fault. The presented control method was shown to make the STATCOM capable of indirectly controlling and limiting the torque of an induction machine during the recovery after a grid fault, by modulating the terminal voltage and the flow of reactive power in the investigated system. By comparing results from the detailed time-domain simulations with calculations based on the model used to derive the proposed concept, it has been shown that the influence of the neglected dynamics of the induction machine and the grid is a slight reduction of torque. The accuracy of the torque limitation will, therefore, be increased by setting the torque reference closer to the applied mechanical torque, but this will also increase the length of the recovery process. It should, therefore, be clear that it is the torque limitation introduced by the ITC method that gives validity to the quasi-static model used for the derivation of the concept. Analysis of the operating range of the STATCOM needed to obtain the Indirect Torque Control is presented in the paper, and the influence of the grid impedance is investigated. It is shown that for most conditions, the STATCOM is required to operate both in the capacitive and inductive region and that the maximum inductive current will decrease by increasing grid inductance. For very strong grids, the suggested method will, therefore, require a high inductive current from the STATCOM and result in a large flow of reactive power from the grid. The main drawback of limiting the torque of the induction machine in the suggested way is the lengthened recovery process, since the machine shaft will need longer time to return to Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS the initial speed when the torque is controlled to be closer to the mechanical torque. It should, however, be noted that the ITC concept mainly requires software modifications with respect to a normal STATCOM control system, and it should, therefore, be considered as a possible add-on feature that can increase the functionality and value of a STATCOM installed with another main purpose. Although this might currently be most relevant for wind generation systems with induction generators, the concept presented in this paper is general and can be applied for torque limitation of induction machines operated both as generators and as motors. For a possible practical implementation, there should be a tradeoff between the maximum torque and the length of the recovery process. In cases where the method can be considered relevant, it should also be investigated together with other practical aspects of the considered application. APPENDIX TABLE I MAIN PARAMETERS OF INVESTIGATED SYSTEM REFERENCES [1] D. S. Brereton, D. G. Lewis, and C. C. Young, “Representation of induction motor loads during power system stability studies,” AIEE Trans., vol. 76, pp. 451–461, Aug. 1957. [2] M. A. Merkle and A. M. Miri, “Modelling of industrial loads for voltage stability studies in power systems,” in Proc. Can. Conf. Electr. Comput. Eng., 2001, vol. 2, pp. 881–886. [3] J. Faiz and A. Keyhani, “Performance analysis of fast reclosing transients of induction motors,” IEEE Trans. Energy Convers., vol. 14, no. 1, pp. 101–107, Mar. 1999. [4] R. Stern and D. W. Novotny, “A simplified approach to the determination of induction machine dynamic response,” IEEE Trans. Power App. Syst., vol. PAS-97, no. 4, pp. 1430–1439, Jul. 1978. [5] N. Gunaratnam and D. W. 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Undeland, “A simple method for analytical evaluation of LVRT in wind energy for induction generators with STATCOM or SVC,” in Proc. 12th Eur. Conf. Power Electron. Appl., EPE2007, pp. 1–10. [34] B. C. Mecrow and A. G. Jack, “Efficiency trends in electric machines and drives,” Energy Policy, vol. 36, no. 12, pp. 4336–4341, Dec. 2008. [35] A. D. Hansen and L. H. Hansen, “Wind turbine concept market penetration over 10 years (1995–2004),” Wind Energy, vol. 10, no. 1, pp. 81–97, 2006. [36] W. Freitas, J. C. M. Vieira, A. Morelato, L. C. P. da Silva, V. F. da Costa, and F. A. B. Lemos, “Comparative analysis between synchronous and Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply. 1250 [37] [38] [39] [40] [41] [42] [43] [44] IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010 induction machines for distributed generation applications,” IEEE Trans. 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Blasko and V. Kaura, “A new mathematical model and control of a threephase AC-DC voltage source converter,” IEEE Trans. Power Electron., vol. 12, no. 1, pp. 116–123, Jan. 1997. D. Maksimović, A. M. Stancović, V. J. Thottuvelil, and G. C. Verghese, “Modeling and simulation of power electronic converters,” Proc. IEEE, vol. 89, no. 6, pp. 898–912, Jun. 2001. Jon Are Suul received the M.Sc. degree from the Norwegian University of Science and Technology, Trondheim, Norway, in 2006. He is currently working toward the Ph.D. degree in the Department of Electric Power Engineering, Norwegian University of Science and Technology. From 2006 to 2007, he was with SINTEF Energy Research, Trondheim, Norway, where he was engaged in simulation of power electronic systems. In 2008, he was a guest Ph.D.-student for 2 months at the Energy Technology Research Institute of the National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan. His current research interests include control of power electronics converters in power systems and for renewable energy applications. Marta Molinas (M’94) received the Diploma degree in electromechanical engineering from the National University of Asuncion, Asuncion, Paraguay, in 1992, the M.Sc. degree from Ryukyu University, Okinawa, Japan, in 1997, and the Doctor of Engineering degree from Tokyo Institute of Technology, Tokyo, Japan, in 2000. She was a Guest Researcher with the University of Padova, Padova, Italy during 1998. From 2004 to 2007, she was a Postdoctoral Researcher with the Norwegian University of Science and Technology (NTNU), Trondheim, Norway. She is currently with the Department of Electric Power Engineering at NTNU as full Professor since 2008. From 2008 to 2009, she was a JSPS Research Fellow for 10 months with the Energy Technology Research Institute at the National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan. Her research interests include wind/wave energy conversion systems, and power electronics and electrical machines in distributed energy systems. Dr. Molinas is actively engaged as a Reviewer for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and IEEE TRANSACTIONS ON POWER ELECTRONICS. She is an AdCom member of IEEE Power Electronics Society. Tore Undeland (M’86–SM’92–F’00) received the M.Sc. degree and the Ph.D. degree in electrical engineering from the Norwegian University of Science and Technology (NTNU), Trondheim, Norway, in 1970 and 1977, respectively. He has been with the Department of Electric Power Engineering at NTNU as full-time Professor since 1984. He has also been Adjunct Professor at Chalmers University of Technology, Göteborg, Sweden, since 2000, and is a Scientific Advisor to SINTEF Energy Research, Trondheim, Norway. His research interests include power electronics and wind energy systems. He is the coauthor of the well-known book Power Electronics, Converters, Applications and Design. Mr. Undeland has been the President of the European Power Electronics Society and a Member of the Norwegian Academy of Technological Sciences, Trondheim. Authorized licensed use limited to: Norges Teknisk-Naturvitenskapelige Universitet. Downloaded on June 14,2010 at 18:21:38 UTC from IEEE Xplore. Restrictions apply.