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Wind Speed Sensorless Maximum Power Point Tracking Control of Variable Speed Wind Energy Conversion Systems J. S. Thongam1, Member IEEE, P. Bouchard1, H. Ezzaidi2, Member IEEE and M. Ouhrouche2, Member IEEE 1 Department of Renewable Energy Systems, STAS Inc., 1846 Outarde, Chicoutimi, QC, Canada, G7K1H1 Department of Applied Sciences, University of Quebec at Chicoutimi, Chicoutimi, QC, Canada, G7H2B1 [email protected] 2 Abstract-A maximum power point tracking (MPPT) controller for variable speed wind energy conversion system (WECS) is proposed. The proposed method, without requiring the knowledge of wind speed, air density or turbine parameters, generates at its output the optimum speed command for speed control loop of rotor flux oriented vector controlled machine side converter control system using only the instantaneous active power as its input. The optimum speed commands which enable the WECS to track peak power points are generated in accordance with the variation of the active power output due to the change in the command speed generated by the controller. The concept is analyzed in a direct drive variable speed permanent magnet synchronous generator (PMSG) WECS with back-to-back IGBT frequency converter. Vector control of the grid side converter is realized in the grid voltage vector reference frame. Simulation is carried out in order to verify the performance of the proposed controller. Keywords-Wind energy conversion system, permanent magnet synchronous generator, wind speed sensorless, maximum power point tracking control. I. INTRODUCTION Wind is an abundant source of energy that will never run out. It is also the world’s fastest growing energy source which is available free, and once the wind turbine generator is installed, the running cost is very small consisting only of routine maintenance and repairs. Therefore, wind generation systems are attracting great attention all over the world. In recent years, fixed speed wind energy conversion systems, due to poor energy capture, stress in mechanical parts and poor power quality have given way to variable speed systems. These systems have reduced mechanical stress and aerodynamic noise, and can be controlled in order to enable the turbine to operate at its maximum power coefficient over a wide range of wind speeds, obtaining a larger energy capture from the wind [1]-[4]. Wind power, even though abundant, varies continually as wind speed changes throughout the day. Maximum power which a wind turbine can deliver at a certain wind speed depends upon certain optimum value of speed at which the shaft rotates. Extracting maximum possible power from the available wind power is of utmost importance, because, only then we can have efficient use of equipment and available 978-1-4244-4252-2/09/$25.00 ©2009 IEEE energy source; therefore, MPPT control is an active research area [5-20]. Wind speed sensor normally used in conventional WECS [5]-[6] for implementing MPPT control algorithm reduces the reliability of the WECS in addition to inaccuracies in measuring the wind speed. Therefore, some MPPT control methods estimate the wind speed; however, many of them require the knowledge of air density and mechanical parameters of the WECS [7]-[11]. Such methods, requiring turbine generator characteristics result in custom-design software tailored for individual wind turbines. Air density, on the other hand, depends upon climatic conditions and may vary considerably over various seasons. Therefore, a lot of research efforts are focused on developing wind speed sensorless MPPT controller which does not require the knowledge of air density and turbine mechanical parameters [12]-[18]. In [12], MPPT control is achieved using stator frequency derivative and power mapping technique. The maximum power curves for power mapping are established by running several simulations or offline experiments at various wind speeds. In [13], [14] simple hill-climb search type algorithms are proposed in for tracking peak power point. Hill-climb search type algorithm proposed in [15] for tracking the peak power point uses the principle of search-remember-reuse process. The method uses memory for storing maximum power points obtained during training process which are used later for tracking peak power points. Optimum power search algorithm is proposed in [16] which uses the fact that dPo/dω=0 at peak power point. The algorithm dynamically modifies the speed command in accordance with the magnitude and direction of change of active power. In [17], [18] fuzzy logic based MPPT controllers are proposed. The MPPT controllers proposed in these works generate optimum speed command for the speed control loop of the machine side converter control system enabling optimal power tracking. In this paper, a simple wind speed sensorless MPPT controller for variable speed WECS is proposed. The proposed method of tracking maximum power point does not require the knowledge of turbine parameters or air density in addition to not requiring the knowledge of wind speed. The algorithm requires only the instantaneous active power as its input and generates at its output the optimum reference speed for the 1832 vector controlled machine side converter control system in order to enable the system to track maximum power point. Performance of the proposed controller is verified by simulation; work for complete experimental verification of the proposed method is underway. III. THE PMSG MODEL The dynamic model of the surface mounted PMSG in magnetic flux reference frame is vsd = − Rs isd − Ls disd / dt + ω Ls isq II. WIND TURBINE vsq = − Rs isq − Ls disq / dt − ω Ls isd + ωφr . The torque produced by a wind turbine is given by 3 Tm = 0.5πρC p (λ ) R2vw / ωr (2) In order to compute CP, a look up table of turbine power coefficient as a function of tip speed ratio and pitch can be effectively used without much loss of accuracy [19]. Alternatively, CP can also be calculated as shown in [20] using the relation C p = 0.5176[116 / λi − 0.4 β − 5]e −21/ λi + 0.006795λi (3) where λi = [1/(λ + 0.08β ) − 0.035 /( β 3 + 1)]−1 . The dynamic equations of the wind turbine is given as d ω / dt = (1 / J ) ⎡⎣Tm − TL − Fω ⎤⎦ (4) where ω is the turbine-generator angular speed, J is the moment of inertia and F is the viscous friction coefficient. Fig. 1 shows the power coefficient C p as a function of tip speed ratio λ . The power coefficient and hence the power is maximum at a certain value of tip speed ratio called optimum tip speed ratio λopt . In order to have maximum possible power, the turbine should always operate at λopt . This is possible by controlling the rotational speed of the turbine so that it always rotates at the optimum speed of rotation. Fig. 1 Power coefficient vs. tip speed ratio. (6) The electromagnetic torque is given by (1) where R is the turbine radius, v w is the wind speed, ω is the turbine angular speed. The tip speed ratio is given by λ = ω r R / vw . (5) T = (3 / 2) pφr isq . (7) IV. THE CONTROL SYSTEM A. Machine Side Converter Control A vector control approach is used where control is exercised on the rotor flux reference frame. The block schematic of the machine side converter control system is shown in Fig. 2. The proposed MPPT controller generates ω * , the reference speed which when set as the command speed for the speed control loop of the machine side converter control system, maximum power points will be tracked by the WECS. The details of the controller will be discussed in the next section. The required d-q components of the machine side converter voltage vector are derived from two PI controllers: one of them controls the d-axis component of the current and the other, the q-axis component. For fast dynamic control capability COMPd and COMPq are added to the direct and quadrature axis current regulator outputs respectively to form command d and q voltage [21]. Space vector PWM generates the switching pulses for the converter power devices. B. Maximum Power Point Tracking Control The power that can be extracted from a turbine at a certain wind speed is maximum at a certain optimum speed of rotation of the rotor. The MPPT controller computes this optimum speed using information on magnitude and direction of change in power output due to the change in command speed. The flow chart in Fig. 3 shows how the proposed MPPT controller is executed. The operation of the controller is explained below: The active power Po(k) is measured, and if the difference between its values at present and previous sampling instants ΔPo(k) is within a specified lower and upper power limits PL and PM respectively then, no action is taken; however, if the difference is outside the this range then certain control action is taken. The control action taken depends upon the magnitude and direction of change in the active power due to the change in command speed. • If the power in the present sampling instant is 0 either due to found to be increased i.e. ∆ an increase in command speed or command speed remaining unchanged in the previous sampling instant i.e. Δω* ( k − 1) ≥ 0 then, the command speed is incremented. 1833 COMPd = Ls ω isq * isd COMPq = − Ls ω isd + ωφr Po MPPT CONTROLLER _ + + COMPd * isq ω* + v*sd1 + v*sd + _ v*sq1 + _ _ dq v*sβ S V P W M GENERATOR SIDE CONVERTER + isd isq ω + v*sq αβ v*sα COMPq isa , isb dq ← αβ ← abc 1/s PMSG Fig. 2 Block diagram of the machine side converter controller. MPPT Control Set initial values of power and command speed Read power Δ ω * ( k − 1) = ω * ( k − 1) − ω * ( k − 2 ) Δ Po ( k ) = Po ( k ) − Po ( k − 1) Yes No ∆ Yes Yes Δ ω * ( k − 1) ≥ 0 Δ ω * ( k ) =| Δ P ( k ) | * C ω * ( k ) = ω * ( k − 1) ∆ 0 No Yes No Δ ω * ( k − 1) ≥ 0 No Δ ω * ( k ) = − | Δ P ( k ) | *C i.e. ∆ 1 0 then, the command speed is decremented. • Further, if the power in the present sampling 0 instant is found to be decreased i.e. ∆ either due to a constant or increased command speed in the previous sampling instant i.e. then, the command speed is Δω* ( k − 1) ≥ 0 decremented. • And, if the power in the present sampling instant 0 due to a is found to be decreased i.e. ∆ decrease in command speed in the previous sampling instant i.e. ∆ 1 0 then, the command speed is incremented. The magnitude of change, if any, in the command speed in a control cycle is decided by the product of magnitude of power error ΔPo ( k ) and C, whose values are determined by the speed of the wind. During the maximum power point tracking control process this product decreases slowly and finally equal to zero at the peak power point. In order to have good tracking capability at both high and low wind speeds the value of C should change with the change in the speed of the wind. The value of C should vary with variation in wind speed, however, as the wind speed is not measured, the value of command rotor speed is used to set its value. As the change in power with the variation in speed is lower at low speed, the value of C used at low speed is larger and its value decreases as speed increases. In this work, its values are determined by running several simulations with different values and choosing the ones which show best results. C. Grid Side Converter Control The grid side converter is vector controlled in grid voltage reference frame. In grid voltage vector reference frame the dynamic model of the grid connection is given by ω * ( k ) = ω * ( k − 1) + Δ ω * ( k ) Fig. 3 Flow chart of MPPT controller. • If the power in present sampling instant is found to be increased i.e. ∆ due to reduction in command speed in the previous sampling instant vd = vid − Rid − Ldid / dt + ω Liq (13) vq = viq − Riq − Ldiq / dt − ω Lid (14) where L and R are the grid inductance and resistance, respectively, vid and viq are the inverter voltage components. 1834 θg id * Vdc id* + _ Vdc iq* + ia , ib dq ← αβ ← abc _ vd*1 + vd* + iq + vab , vbc ANGLE COMPUTATION COMPgd _ vq*1 + vq* θg αβ dq vα* v*β S V P W M GRID SIDE CONVERTER + COMPgq _ + Fig. 4 Grid side converter control scheme. With the reference frame oriented along the supply voltage, the grid voltage vector is v = vd + j 0 (15) Then the active and reactive power may be expressed as P = (3 / 2 )vd id (16) Q = (3 / 2)vd iq . (17) The block diagram of the grid side converter control scheme is shown in Fig. 4. Active and reactive power control is achieved by controlling direct and quadrature current components respectively. Two control loops are used to control the active and reactive power. An outer dc voltage control loop is used to set the d-axis current reference for active power control. This assures that all the power coming from the rectifier is instantaneously transferred to the grid by the inverter. The second channel controls the reactive power by setting a q-axis current reference to a current control loop similar to the previous one. The current controllers provide a voltage reference for the inverter that is compensated by adding rotational emf compensation terms COMPgd = ω Liq + ed (18) COMPgq = −ω Lid . (19) V. SIMULATION RESULTS Simulation is carried out in order to verify the effectiveness of the proposed method. The block diagram of the direct drive PMSG WECS incorporating the proposed algorithm used for simulation is shown in Fig. 5. The details of the WECS used in this work are given in Appendix. The values of C as mentioned above are determined by running several simulations using different values and selecting the ones which give best results. In this work, C used in implementing the control algorithm are computed by performing linear interpolation of 1.1 at 0 rad/s, 0.9 at 10 rad/s, 0.6 at 20 rad/s, 0.32 at 30 rad/s 0.26 at 40 rad/s, 0.25 at 50 rad/s and 0.24 at 55 rad/s. During the simulation, the d axis command current of the machine side converter control system is set to zero; whereas, for the grid side converter control system, the q axis command current is set to zero. Simulation is carried out for two speed profiles applied to the WECS incorporating the proposed MPPT controller. First, a rectangular speed profile with a maximum of 9 m/s and a minimum of 7 m/s is applied to the WECS. The wind speed, rotor speed, power coefficient and active power output are shown in Fig. 6. Then, a real wind speed profile is applied to the WECS. The wind speed, rotor speed, power coefficient and active power for this case are shown in Fig. 7. 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