Key words: wind power generation; MPPT con-trol; permanent magnet synchronous generator; sensorlesscontrol; current vector control.
1. Introduction
Efficient utilization of natural energy has attractedmuch attention recently in the context of depletion ofenergy sources and other environmental problems. In par-ticular, wind power generation systems have been devel-oped and implemented due to the renewability andcleanness of wind energy. Since wind energy fluctuatesgreatly over time, its stable efficient use is an important
problem [1, 2]. Usually, wind power systems employ induc-tion generators with constant speed or double speed (bychanging the number of poles); however, recently, variable-speed systems capable of suppressing power fluctuationsrelated to wind speed have been developed, and their con-trol algorithms have been researched [3, 4]. In addition,permanent magnet synchronous generators (PMSG), whichwere previously employed for small wind power turbines,are now used in large-scale power plants of several hundredkilowatts, and variable-speed systems are under develop-ment [1, 5, 6].
This study deals with a variable-speed power genera-tion system using PMSG. In particular, a new PMSG con-trol system is proposed for maximally efficient utilizationof wind energy to assure maximum output. For the samepurpose, Ref. 7 presents a maximum output tracking controlin which the optimum references for generator speed andd-axis current are found as a function of wind speed, andthe PWM converter is controlled by using feedback. Incontrast, the method proposed in this study has the follow-ing features. Maximum power point tracking (MPPT) isimplemented without using wind speed data; instead, thetorque is controlled appropriately according to the gener-ator’s speed [8]. With torque control, the maximum outputis achieved by minimization of generator loss while takingPWM converter capacity into account and performing cur-rent vector control depending on the operating conditions[8–10]. In addition, position and speed data are required forconventional PMSG control, but here high-performancesensorless control is used for this purpose [9, 10]. Thecharacteristics of the proposed system are studied experi-mentally to demonstrate its effectiveness.
2. Generation Control System
2.1 Configuration of power generation system
The configuration of the wind power generation sys-tem considered in this study is shown in Fig. 1.
Electrical Engineering in Japan, Vol. 150, No. 2, 2005Translated from Denki Gakkai Ronbunshi, Vol. 123-B, No. 12, December 2003, pp. 1573–1579
Contract grant sponsor: Supported in part by a JSPS Grant-in-Aid forFundamental Research (C(2) 14550271).
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The wind turbine shaft is connected to the PMSG viaa speed-up gear (gear ratio G) so that the wind energybecomes the mechanical input of the generator. The PMSGis connected to a PWM converter, and optimum currentvector control is applied to the PMSG current. The DCoutput rectified at the converter is supplied to a battery or aDC load, or is released to a network via an inverter. Sincethis study aims at maximization of the generated power, theconverter output (DC power) is assumed to be absorbed andconsumed completely.
2.2 MPPT control irrespective of wind speed
The output of a wind turbine can be found as follows[4, 11]:
Here ρ is the density of air, A is the wind turbine swept area,Vw is the wind speed, and Cp is the power coefficient.
The power coefficient is a function of the tip speedratio λ provided that the pitch angle is unchanged:
Here R is the wind turbine radius, and ωw is the wind turbineangular speed.
Wind energy can be utilized most efficiently as gen-erator input when the power coefficient is highest, and thetip speed ratio λopt meeting this condition is determineduniquely irrespective of the wind speed. This condition isreferred to as the maximum power condition in this study,and is denoted by the subscript “opt.” In addition, the speedand torque values discussed below pertain to the generatorshaft unless specified otherwise. At the maximum powercondition, the generator’s angular speed, input torque, andinput power (turbine output) can be represented by func-tions of the wind speed as shown below:
Here Kw, Kt, and Kp are coefficients specific to the windturbine.
In addition, the generator’s speed, torque, and powerat the maximum power condition are interrelated as fol-lows:
Fig. 1. Configuration of wind power generation system.
(1)
(2)
(3)
(4)
(5)
Fig. 2. Characteristics of wind turbine.
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A polynomial or another approximation is used to representthe power coefficient Cp that governs the turbine charac-teristics; for example, when Eq. (8) [11] is applied, thecharacteristics shown in Fig. 2 are obtained. Here the pa-rameters given in Table 1 are used in the calculations:
Here γ is the wind speed to generator’s speed ratio[mph/(rad/s)]. The power coefficient in Eq. (8) reaches itsmaximum Cp-opt = 0.4176 at γopt = 11.5 mph/(rad/s) = 5.14(m/s)/(rad/s).
In Fig. 2(a), the curve connecting the maximumpower points at various speeds (marked by circles) corre-sponds to Eq. (7). The torque is represented by the optimumtorque curve [see Fig. 2(b)], which shows the relationshipbetween the generator’s speed and the torque required toobtain the maximum output from the turbine, which corre-sponds to Eq. (6).
Maximum power point tracking can be implementedby controlling the generator’s speed or torque according tothe wind speed by using Eqs. (3) or (4). When a wind speedsensor is installed, wind speed data can be used for efficientcontrol. In this study, however, MPPT control is imple-mented without using the wind speed. Equation (6) is usedto control the generator’s torque Tg as a function of thespeed ωg:
This control operation is illustrated by Figs. 2(b) and 3.Suppose that at wind speed Vw3 (7 m/s), the generator’storque Tg and turbine’s torque Tw coincide at the optimumoperating point A in Fig. 2(b). When the wind speedchanges to Vw2 (9 m/s) at t = 0.1 s as shown in Fig. 3, Tw
changes abruptly and moves to point B; however, the
change of speed wg is impeded by inertia, and the gener-ator’s torque Tg is maintained at point A. The generator isaccelerated by the torque Tw – Tg so that the speed increases,and the torque Tg controlled in accordance with Eq. (9)increases along the optimum torque curve. On the otherhand, the turbine’s torque drops with increasing generatorspeed so that Tw and Tg eventually reach the same value(point C). This is the maximum power point at wind speedVw2. Hence, MPPT control can be implemented withoutusing wind speed sensors. Figure 3 also illustrates the casein which the wind speed drops from Vw2 to Vw3. In this case,too, the characteristic converges to the optimum operatingpoint (point A) in a similar way.
3. PMSG Control
3.1 Configuration of control system
The configuration of the PMSG control system isshown in Fig. 4. In the position/speed estimation unit, theestimated generator position θ̂ (electrical angle) and speedω̂ (electrical angle) are calculated from the currents iγ, iδobtained by converting the detected generator currents iu, ivinto γδ coordinates at estimated position θ̂, and the voltagereferences vγ
∗, vδ∗. In the MPPT control unit, the generator’s
torque reference T g∗ is generated from the estimated speed
(6)
(7)
Table 1. Specifications of wind turbine
(8)
(9)
Fig. 3. Dynamic responses in MPPT control.
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ω̂g (mechanical angle) by means of Eq. (9). In the optimalcurrent vector unit, the optimal current vector referencesid∗, iq
∗ are generated from the torque reference and the esti-mated speed according to the operating conditions, andfeedback control is applied to the PWM converter. Eachcontrol unit is described in detail below.
3.2 PMSG model and optimal current vectorcontrol
The mathematical model for a permanent magnetsynchronous generator (PMSG) is basically the same as thatfor a permanent magnet synchronous motor (PMSM). Theequivalent circuits (for the d- and q-axes) and the torqueequation of the PMSM with regard to iron loss are given inFig. 5 and Eq. (10), respectively:
Here Pn is the number of pole pairs, ψa is the armature fluxlinkage due to PM, and Ld, Lq are the d- and q-axis induc-tances.
In Fig. 5, Rc is the equivalent loss resistance repre-senting iron loss. This loss is taken into consideration inmaximum efficiency control (described below), but is dis-regarded in other control algorithms for the sake of simplic-ity. In the latter case, the circuits in Fig. 5 become the mostcommon equivalent circuits of the PMSM.
Generator operation (Tg > 0) takes place when controlis applied so that the motor’s torque Tmot becomes negative.MPPT control can be implemented by applying a torquereference output by the MPPT unit to the generator’s torque.However, as is evident from Eq. (10), there is some freedomin choosing the current to generate the same torque. There-fore, appropriate setting of the current vector is importantin order to maximize performance. Since this study aims at
maximization of the generated output, two control schemesare designed: one to minimize generator losses, and theother to obtain maximum output with regard to the capacityof the PWM converter.
1. Maximum efficiency control
The authors have shown that the optimal currentvector at a given generated torque can be calculated as afunction of torque and speed with regard to iron loss asshown in Fig. 5 [12]. In this study, considering the specificimplementation for torque control, the current referencesfor d- and q-axes are approximated as
Here K0, K1, K2, K3 are first-order functions of ω.The locus of the optimum current vector i(id, iq)
specified by Eqs. (11) and (12) is shown in Fig. 6 as themaximum-efficiency curve. As the wind speed rises, thetorque reference increases. Therefore, the current vectorshifts along the maximum-efficiency curve toward point A[as shown by (1) in the diagram].
2. Control with regard to converter capacity
As stated above, the generator’s speed and torqueincrease with the wind speed. As a result, the generator’sterminal voltage and current increase so that the maximum
Fig. 4. Configuration of the PMSG control system.
Fig. 5. Equivalent circuits of PMSM.
(10)
(11)
(12)
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voltage and current values governed by the converter’scapacity and generator’s ratings are surpassed. Therefore,the following control algorithm is applied to the operatingarea where the limit values are exceeded.
When the current Ia (= | i |) surpasses the limit Iam, thecurrent vector is adjusted in phase so as to obtain greatertorque at the same current compared to the maximumefficiency control. In other words, when the current vectorreference during maximum efficiency control goes beyondpoint A in Fig. 6 (Ia = Iam), the q-axis current is increasedalong the negative direction of the current limit circle, andthe current vector is shifted toward point B [shown by (2)in the diagram]. Point B is associated with the current vectorproducing maximum torque at Ia = Iam, being defined asfollows [13]:
In the speed area in which the generator’s voltageexceeds its limit value, flux-weakening control [13] isapplied so that the induced emf Vo does not exceed its limitvalue Vom. The following equation is obtained by ignoringiron loss in the equivalent circuit in Fig. 5:
From the conditions Vo = Vom and Ia = Iam, the d-axis currentreference can be found in the following way. The d-axiscurrent reference is obtained from the d-axis current refer-ence in Eq. (16) by using Eq. (14):
The current vector shifts along the current limit circle as thespeed increases [shown by (3) in the diagram] so that thecurrent and voltage are kept within their limits.
3.3 Sensorless control of PSMG
Position and speed data are required for control of apermanent magnet synchronous generator (PSMG); hencethe need for sensors. In this study, however, the requireddata are estimated from the current and voltage, thus pro-viding sensorless control. In particular, a control algorithmis used that was previously proposed by the authors forinterior permanent magnet synchronous motors [14]. Theestimation of position and speed is briefly explained below.
The electric system model of the PMSG in estimatedcoordinates (γδ coordinates) that rotate at the electricalangular speed ω̂ while lagging by the electrical angle θe
(= θ − θ̂) behind the dq coordinates (the rotating referenceframe of PMSG), is expressed as shown below [14]:
where
Based on Eq. (17), eγ and eδ are estimated by the disturbanceobserver. Assuming that the speed estimation error ωerr (=ω – ω̂) in Eq. (18) is sufficiently small, the estimatedextended emf [the first term on the right-hand side in Eq.(18)] indicates that the position estimation error θe is
Using PI compensation, the estimated angular speed ω̂(electrical angle) is found, and is then integrated to obtainthe estimated position θ̂:Fig. 6. Locus of optimum current vector.
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
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In the proposed method, position and speed cannot beestimated at standstill or in low-speed operation. However,this is a sensorless control method providing position/speedestimation by a relatively simple control configurationwithout any special additional signals, and thus is suitablefor PMSG in a wind power system with no stoppages orlow-speed operation.
4. Experimental Study of Characteristics
4.1 Configuration of experimental system
Experiments were performed on the proposed systemas shown in Figs. 1 and 4. However, an AC servomotor (2kW, 2000 min–1) was employed instead of a wind turbineto drive the experimental PMSG. The specifications of thePMSG are listed in Table 2.
Since the q-axis inductance varies depending on themagnetic saturation, the following model is used in theposition/speed estimation unit and control units:
The coefficient in Eq. (9) for the MPPT control unit was setto Kopt = 2.52/(188.52) = 7.09 × 10–5 Nm/(rad/s)2 accordingto the rated torque and speed. Proceeding from the gener-ator specifications given in Table 2, the coefficients in Eq.(11) for the d-axis current reference in maximum efficiencycontrol were set as follows [12]:
The gains for speed estimation in Eq. (21) were setto K1 = 45, K2 = 2025. All processing in the control block
shown by the dotted line in Fig. 4 was performed by a DSP(TMS320C32) at a sampling period of 0.1 ms. In addition,PWM control of the converter was performed by compari-son with a triangular carrier, with a carrier frequency of 10kHz and a DC link voltage Vdc of 150 V.
(21)
(23)
(22)
Table 2. Specifications of tested PMSG
Fig. 7. Steady-state characteristics as a function ofgenerator speed.
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4.2 Steady-state characteristics
The experimental steady-state characteristics versusthe generator speed are shown in Fig. 7.
In panel (a), the d- and q-axis currents are varied withthe speed to obtain the optimal current vector. In the speedarea below ω1, both the voltage and current are within theirlimits, as shown in panel (c); therefore, maximum effi-ciency control is implemented, and the generator’s torqueis kept on the optimal torque curve [see panel (b)]. Whenωg = ω1, the current Ia reaches its limit value (set to the ratedcurrent 8.66 A). As the speed increases further, Ia is keptconstant, and the torque is increased by advancing thecurrent’s phase. When ωg = ω2, the voltage also reaches itslimit (98 V); therefore, at higher speeds, flux-weakeningcontrol is performed by applying a negative d-axis current,which makes high-speed operation possible while keepingthe voltage and current within limits [see panel (c)]. As aresult, the generator’s torque becomes unable to follow theoptimal torque curve as soon as the speed exceeds its rating.However, nearly the rated torque can be generated, so thatthe output increases [see panels (b), (d)]. Thus, the energyof the wind turbine can be utilized as efficiently as possibledue to the optimal current vector control.
4.3 Transient characteristics
Figure 8 presents the dynamic response when thegenerator speed is varied as 1400 → 2200 → 1400 min–1
using the AC servomotor.Current vector control is switched among the three
algorithms near 1800 min–1. The speed estimation error inthe transition is small, amounting to 10 min–1 at most.Regarding the position estimation characteristic shown inpanel (b), an error of up to 20° occurs during acceleration.However, the characteristic converges rapidly, providingbasically good results without steady-state error. The gen-erator’s current and the d- and q-axis currents are shown inpanel (c). Due to switching among control algorithms ac-cording to speed, the actual d- and q-axis currents followtheir respective references properly. As is evident from theelectrical output shown in panel (d), stable output controlin the presence of varying speed is realized.
5. Conclusions
This study has dealt with a wind power generationsystem using a permanent magnet synchronous generator.In particular, a control method for PMSG was proposed inorder to maximize the utilization of wind energy. MPPTcontrol was implemented by maintaining the optimal rela-tion between the generator’s speed and the torque. In addi-tion, a current vector control algorithm was proposed tominimize generator losses while keeping the voltage andcurrent within limits with regard to the capacity of thePWM converter (used to drive the PMSG), thus maximiz-ing the output power. The proposed control scheme was
Fig. 8. Dynamic responses of proposed system.
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implemented without any sensors. The performance of theproposed system was examined and estimated experimen-tally, using an AC servomotor instead of wind turbine, andgood characteristics were confirmed. In this study a con-stant pitch angle was assumed, but the proposed method canalso be applied to a system with a pitch angle controller.Specifically, one needs only to adjust the MPPT coefficientsaccording to the power coefficient (a function of the pitchangle). The proposed method does not require wind turbinecharacteristics beyond the rated wind speed, and hencethere is no direct effect of pitch angle control. However, theoperating characteristics may be improved by combiningpitch angle control with the proposed method.
In the future, the authors plan to thoroughly examinethe performance of the proposed method under realisticconditions of a wind power system (e.g., variation of windspeed), and to apply it to a real system.
Acknowledgment
The present study was supported in part by a JSPSGrant-in-Aid for Fundamental Research (C(2) 14550271).
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AUTHORS (from left to right)
Shigeo Morimoto (member) completed the M.E. program at Osaka Prefecture University in 1984, became a researchassociate there in 1988, and has been an associate professor since 1994. His education and research interests are motor drivesystems and motion control. He holds a D.Eng. degree, and is a member of IEEE, SICE, ISCIE, and JIPE.
Tomohiko Nakamura (student member) completed the first term of his doctorate at Osaka Prefecture University in 2003and is now employed by ST Microelectronics. His student research dealt with wind power systems using permanent magnetsynchronous generators.
Yoji Takeda (member) completed the M.E. program at Osaka Prefecture University in 1968, joined the faculty as a researchassociate, and has been a professor since 1993. His education and research interests are variable-speed motor control and linearactuators. He holds a D.Eng. degree, and is a member of IEEE, ISCIE, and JIPE.
