Novel Hybrid Observers For A Sensorless MPPT Controller And Its Experiment Verification Using A Wind Turbine Generator Simulator

Transcription

1 Novel Hybrid Observers For A Sensorless MPPT Controller And Its Experiment Verification Using A Wind Turbine Generator Simulator A. J. Mahdi Department of Electrical Engineering, College of Engineering, University of Kerbala, Kerbala, Iraq Tel: , a3mahdi@gmail.com Abstract A robust sensorless maximum power point tracking (MPPT) controller has been proposed for maximizing the output power of a wind turbine generator (WTG) system, which is based on a permanent magnet synchronous generator (PMSG). It includes two novel observers, which are: first, an adaptive slidingmode observer (SMO) for estimating rotor speeds and second, an adaptive perturbation and observation (P&O) algorithm for estimating reference rotor speeds and optimal duty cycles based on turbine coefficient errors and rotor speed errors, respectively. The adaptive P&O algorithm uses an adaptive perturbation step size and an adaptive observation period. The purpose of adopting adaptive parameters is to decrease steady-state oscillations around optimal operating power points, increase the tracking speed and keep the perturbation tracking in the right direction with small rotor speed overshoots under fast wind speed variations. A cost-effective switch-mode rectifier (SMR) with an input filter for harmonic mitigation is employed for implementing the proposed sensorless MPPT controller using a WTG simulator. The experimental results show that the proposed sensorless MPPT controller obtains high MPPT efficiencies and small steady-state speed ripples under variations of wind speed and load. A comparison between the proposed sensorless MPPT controller and the conventional MPPT controllers, which use PI controllers and classic P&O algorithms, has been made. Index Terms Wind turbine generator system, permanent magnet synchronous generator, switch-mode rectifier, slidingmode observer, perturbation and observation algorithm. I. INTRODUCTION The power delivered by a WTG system is dependent on the swept area of a wind turbine, wind speeds, power coefficients of a wind turbine and the current drawn from a generator. The only controllable factor is the power coefficient, which varies with operating tip speed ratios (TSR). For each wind speed, there is an optimal TSR that keeps the power coefficient at its maximum value. In order to achieve the optimal TSR, it is required to control rotor speeds of a WTG system to follow a reference rotor speed, which can be produced by a TSR controller based on measurements or estimation of wind speeds. Basically, mechanical sensors (i.e. an anemometer, an encoder or a resolver) are required for implementing a MPPT controller for a WTG system. These mechanical sensors measure wind speeds and rotor speeds or positions, which are used as feedback signals for a speed controller [1]. There are many drawbacks of using mechanical sensors such as low reliability, high maintenance requirements, high cost and adding DC offsets in measured signals [2]. Sensorless MPPT controllers are a practical solution to overcome these problems. Rotor speeds can be estimated by only measuring the terminal voltage and line currents of a generator, which are used as input signals to a speed observer. Thus the performance of these sensorless MPPT controllers mainly depends on the estimation accuracy and the range of rotor speeds. Various MPPT algorithms, for WTG systems, have been investigated by many researchers. Among these algorithms, the P&O algorithm, also known as a hill climbing searching algorithm has been widely used, which doesn t require any previous knowledge of wind turbine and generator characteristics. In spite of these advantages, it has some problems, which considerably decrease its dynamic performance. These problems are the steady-state oscillations around a maximum power point (MPP), a slow tracking speed, a perturbation process in a wrong direction [3] and a high rotor speed overshoot under fast wind speed variations. To overcome these problems, it is desirable to use an adaptive perturbation step size and an adaptive observation period. In [4], a powerful method for estimating a perturbation size was presented. In that paper, a perturbation step size was parted into eight steps, i.e. the first perturbation step size is the smallest and the eighth perturbation step size is the largest. If a power operating point is not near the MPP, the perturbation step size is increased slowly until it achieves the MPP. When a power operating point is around the MPP, the perturbation step size is reduced to its smallest value in order to reduce the amplitude of oscillations. In [5], a robust power peak detection algorithm was developed for estimating the optimal power line of a WTG system for all wind speeds. The perturbation step size was estimated from a dynamic error, which is the difference between a power operating point and its corresponding optimal value. An intelligent rotor speed observer was also developed to avoid using mechanical sensors. In [5], the electrical frequency and consequently, rotor speeds were estimated by detecting the number of zero crossings of a phase current during one period. In this paper, an adaptive sensorless MPPT controller for a WTG system using a PMSG has been proposed to improve its dynamic performance and avoid instability. The proposed sensorless MPPT controller is based on two novel observers, i.e. an adaptive SMO and an adaptive P&O algorithm. The former is used to estimate rotor speeds using an adaptive PMSG

2 model in the stationary reference frame, an adaptive sliding gain and an adaptive cutoff-frequency LPF. The purpose is to eliminate the chattering effect (which occur in conventional SMOs) and decrease estimation errors. The adaptive P&O algorithm has been employed to estimate a reference rotor speed and an optimal duty cycle based upon turbine coefficient errors and rotor speed errors, respectively. It uses adaptive variables compared to some existing P&O algorithms, which use an adaptive perturbation step size but a fixed observation period. The adaptive variables are: (i) a perturbation step size, which decreases steady-state oscillations around optimal operating power points and (ii) an observation period, which increases the tracking speed and ensures that MPPT is always executed in the right direction with small rotor speed overshoots under fast wind speed variations. This paper is organized into six parts. Section II presents the configuration of a WTG simulator, which consists of a wind turbine model, a PMSG model and a state-space model of a SMR. Sections III and IV present the two novel observers, i.e. an adaptive SMO for estimating back-emfs and rotor speeds, and an adaptive P&O algorithm for estimating reference rotor speeds and optimal duty cycles. Experimental results are discussed in Section V based on test measurement of the WTG simulator. Finally, Section VI summarizes the findings of this paper. II. CONFIGURATION OF A WIND TURBINE GENERATOR SIMULATOR For implementing the proposed sensorless MPPT controller, the mechanical characteristics of a WTG system must be obtained in order to validate its performance. In this work, a WTG simulator is constructed in order to implement the proposed sensorless MPPT controller. A. Wind Turbine Model The output power of a wind turbine, P wt, is given by a well-known expression: P wt (C p (λ), V w, r) =.5ρπr 2 C p (λ)v 3 w, (1) where ρ is the wind density (e.g kg/m 3 ), r the length of a blade of a wind turbine, V w the wind speed, C p (λ) the power coefficient and λ TSR, defined as the ratio of a tip speed ω r r (where ω r is the rotor speed) to a wind speed. Equation (2) is a nonlinear empirical expression of C p (λ) as a function of λ for the horizontal-axis wind turbine (HAWT) used in this research. C p (λ) =.13λ λ λ (2) To avoid the negative values of C p (λ), λ is limited in the range between and 1. From (1) and (2), mechanical characteristics, i.e. P wt versus ω r, is illustrated in Fig. 1, where A, B, C, D and E are various operating power points. It is seen that the range of wind speeds is chosen between 6 m/s and 12 m/s, which matches with the range of the rotor speed of the WTG simulator. Equation (1) can be expressed in the terms of C p (λ) and λ by replacing V w with ω r r/λ as follows: P wt (k wt, ω r ) = k wt ω 3 r, (3) Fig. 1. Wind Turbine Power (W) m/s 8 m/s 1 m/s 12 m/s MPPT Line A B Rotor Speed (rad/s) C D E Wind turbine characteristics of a WTG simulator. where k wt is the turbine coefficient k wt =.5ρπr 5 C p(λ) λ 3. (4) For any given wind speed, there is a reference rotor speed, ω ref, which ensures the optimal tip speed ratio, λ opt, and consequently the optimal power coefficient, C p-max. At C p-max, a maximum wind turbine power, P wt-max, can be extracted [6]. In this paper, the values of λ opt and C p-max are calculated from the wind turbine specifications as shown in Fig. 1, which are 6.29 and.34, respectively. Substituting these values in (3), yields P wt-max (ω ref ) = k opt ω 3 ref, (5) where k opt is the optimal turbine coefficient k opt =.5ρπr 5 C p-max λ 3. (6) opt It is worth noting that k opt has a unique value, i.e. k opt =.71, for all wind speeds regarding the WTG system used in this research. B. Dynamic Model of a PMSG An important step of designing a sensorless MPPT controller is to obtain an accurate PMSG model with its measured parameters. In this work, a voltage model of a PMSG in the stationary reference frame, α-β, is adopted (instead of a d-q model) for estimating a back-emf and then a rotor speed. The α-β model is independent of rotor positions, and it has no cross-coupling terms between the α- axis and β- axis [7]. Hence, the voltage model of a surface-mounted PMSG, where its α-β inductances are equal and independent to rotor positions, can be represented in (7), which is derived from the standard phasor model by using the Clarke transformation: V = M( R s I + d Λ), (7) dt Λ = M( L s I + 2λ pm Θ), (8) where R s is the stator resistance per phase, L s the stator inductance per phase, λ pm the permanent magnet flux linkage,

3 V the voltage vector [v α v β ] T, I the current vector [i α i β ] T, Λ the stator flux linkage vector [λ α λ β ] T, Θ the electrical angle vector [cos(pθ r ) sin(pθ r )] T, p the number of pole pairs, θ r the rotor position and M the 2 2 identity matrix. As well-known, electromagnetic torque T e of a PMSG can be computed using following equation. v ab,v bc i a, i b L s R s k s T e = 3 2 p(λ αi β λ β i α ), (9) i s-est i s III. ESTIMATION OF BACK-EMF AND ROTOR SPEED USING AN ADAPTIVE SLIDING-MODE OBSERVER SMO has been widely applied for controlling and state variable estimation for electrical machines due to the following features: (i) insensitive to variations of physical parameters; (ii) robustness to external disturbances and (iii) fast transient responses. In spite of these advantages, SMO has some drawbacks, such as the chattering effect (i.e. high frequency oscillations) caused by its switching mechanism and the high sliding gain, which increases estimation errors. In this research, these problems are tackled by using an adaptive sliding gain and an adaptive cutoff-frequency. An adaptive SMO has been developed for estimating the back-emfs using the α-β model of a PMSG and rotor speeds without the knowledge of rotor positions. The configuration of the proposed adaptive SMO is described in Fig. 2, where, [v ab,v bc ] are the measured generator line-to-line voltages, [i a,i b ] the measured generator line currents, Î the estimated generator line currents, Ê the estimated back-emfs, I the AC current error vector, e s-est the magnitude of the back-emfs, i s the magnitude of a generator line current; i s-est the magnitude of an estimated generator line current, ω est the estimated rotor speed, sign the signum function, k s the sliding gain and f c the cutoff-frequency of a LPF. It can be seen from Fig. 2 that the proposed adaptive SMO comprises two main sub-blocks: (i) an adaptive current model of a PMSG, which is used to estimate generator line currents; and (ii) an adaptive LPF, which is used to estimate back-emfs using the discontinues signals generated from a sliding surface. The dynamic model of the developed adaptive SMO is derived from the α-β model of a PMSG, which is discussed in section II-B. Substituting (8) into (7), the voltage model of the PMSG is derived as: d V = M( R s I L s dt I + d 2 λ pm Θ) (1) dt It can be noted from (1) that the only state variables are I and the third term on the right-hand side represents back- EMFs, which is proportional to the rotor speed (dθ r /dt) and θ r. Thus the current model of the PMSG can be obtained by re-arranging (1) as follows: I = 1 M ( R s I + E V)dt, (11) L s where E is the back-emf vector [e α e β ] T, e α equals to k e ω r sin(θ e ), e β equals to ω r k e cos(θ e ) and k e is the back- EMF constant 2pλpm. In conventional speed controllers, the back-emf feedback signals are calculated by directly Fig. 2. f c Block diagram of the developed adaptive SMO. measuring rotor speeds and rotor positions using mechanical sensors. As mentioned before, these speed sensors are impractical for speed control applications, because they have some disadvantages such as a low reliability and high cost. In this work, the back-emfs are estimated by integrating the discontinues signals, k s sign( I), using an adaptive LPF. Equation (12) is derived from a classic transfer function of a LPF, which has been modified using an adaptive cutofffrequency. Ê = f c (k s sign( I) Ê)dt, (12) where I = Î I. Î can be obtained by substituting Ê in (11) as: Î = 1 M ( R s Î + Ê V)dt. (13) L s Equation (14) is adopted for estimating L s, which varies during generator operations due to magnetic saturation. It is assumed as a function of the estimated phase current i s-est. p e s est L s = c 1 i s-est + c 2, (14) where c 1 and c 2 are constants determined from experiments and bounded in the range between a low rotor speed 1 rad/s and a high rotor speed 1 rad/s. As shown in Fig. 2, k s and f c are automatically tuned in order to eliminate the chattering effect and decrease estimation errors. For example, if the value of k s is selected too high, the estimation errors are rapidly minimized, but high overshoots occur in discontinuous signals. These overshoots may lead to instability [8]. The chattering effect can be reduced by designing an advanced switching function using a continues switching function, i.e. a saturation function or a sigmoid function [9]. As clearly indicated in Fig. 2, f c is directly proportional to an estimated electrical frequency and k s is identified via a PI controller based on the magnitude of a current errors, i s = i s-est i s, as follows: k s = k ps i s + k is i s dt, (15) where k ps and k is are the coefficients of a sliding PI controller. Finally, in conventional speed observers, rotor speeds are estimated by integrating rotor positions, which are calculated from arctan(e β-est /e α-est ). There are two well-known problems of this strategy i.e. first, the DC drift problem, which k e est

4 occurs because of using a pure integrator and second, the singularity problem due to using an inverse tangent function, which converges to ±2π when an angle diverges to infinity. In this paper, the rotor speed is calculated directly as follows: ω est = e s-est k e, (16) where k e is accurately derived based on the measured λ pm. E n k th2 E n E n k th1 IV. ESTIMATION OF REFERENCE ROTOR SPEEDS AND DUTY CYCLES USING AN ADAPTIVE P&O ALGORITHM A P&O algorithm is one of the most popular MPPT methods, which can be applied for a WTG system without having the knowledge of its characteristics. As well-known that the main drawbacks of a classic P&O algorithm are: first, the speed ripple and vibration, which are caused due to using a fixed perturbation step size and second, a wrong perturbation direction under rapid variations of wind speeds, which is caused by a fixed observation period. As a result, to improve the performance of a classic P&O algorithm, the perturbation step size and the observation period should be automatically tuned. In this work, a new P&O algorithm has been developed based on a classic P&O algorithm as shown in Fig. 3, where E(n) is the input error, which is either turbine coefficient error, k, or the rotor speed error, ω, x(n) the control variable; x the perturbation step size and n the number of samples; k th1 and k th2 the predetermined thresholds; k 1 and k 2 the weight factors, which are used to adjust a perturbation step sizes; k 3 and k 4 the weight factors for adjusting the observation period T o ; k t the termination factor; f saw (t) the periodic sawtooth signal with unity amplitude and t the discontinuous time, which is generated by a digital clock in every T s. It should be noted that the parameters of the proposed adaptive P&O algorithm were estimated from experiments and off-line data analysis. An optimization algorithm, e.g. particle swarm optimization, could be applied to obtain these parameters. The perturbation process of the improved P&O algorithm can be summarized in the following steps: (i) E(n) and its absolute value, E(n), are calculated; (ii) E(n) is compared with k th1 to calculate x as x = k E(n), where k is either k 1 or k 2 and k 1 >> k 2 in order to increase the tracking speed at transients and decrease the amplitude of oscillation at steady-state; (iii) x(n) is calculated as follows: x(n) = x(n 1) sign(e(n)) xk t, (17) where the sign of x depends on the sign of E(n) and (iv) the perturbation process is terminated, i.e. x(n) = x(n 1), when k(t) equals to zero. As shown in Fig. 3, the perturbing process period is only one sample, T s, while the observation process period is varied with E(n). The objective is to decrease overshoots under fast wind speed variations. The main difference between the proposed P&O algorithm and the classic one is the latter is based on calculating the gradient of the wind turbine characteristics, which requires to compute the turbine power variation within a sampling time. Under windgust disturbances, the perturbation process leads to wrong tracking directions because the sampling time is generally Fig. 3. k 3 k 4 T o T o E n E n k t f saw t,t o T s f saw t,t o The improved P&O algorithm. k t TABLE I x k 1 E n x n x n E n x k t EVALUATION OF A REFERENCE ROTOR SPEED OBSERVER. Power Point ω r (rad/s) P wt (W) k wt k A (Left side) < B (Left side) < C (MPP) = D (Right side) > E (Right side) > T o T o x k 2 E n less than the mechanical time constant of a WTG system. To address this problem, a P&O algorithm should be updated within a period greater than or equal to a mechanical time constant of a WTG system. The objective is to keep the rotor speed and the duty cycle of the WTG system stable during a perturbation process. As illustrated in Fig. 3, k 3 and k 4 have been chosen to obtain a good compromise between the small peak overshoots and fast tracking speeds. Also, the pulses with adaptive observation periods are generated by comparing a variable-frequency sawtooth signal, which is given by (18), with the sampling period of data acquisition. f saw (t, T o ) = 1 T o ( mod(t,t o )). (18) As mentioned previously, the proposed adaptive P&O algorithm is used for estimating the reference rotor speed at a given wind speed. Consider different power points at the rated wind speed 1 m/s as shown in Fig. 1, which are randomly chosen in the left and the right sides of a MPP. TABLE I lists the values of k wt and k = k opt k wt, for all power points. It is seen that k depends on the location of a power point. If k is negative, it means that ω r is less than ω ref and the direction of a perturbation process must be continued in the same direction. While, if k is positive, it means that ω r is greater than ω ref, and the direction of a perturbation process must be reversed. The procedures of estimating a reference

5 rotor speed, i.e. k is considered as an input error E(n), can be summarized as follows: first, the mechanical power of a PMSG is computed by multiplying the magnitude of its electromagnetic torque, which is calculated from (9), by the estimated rotor speed; second, k wt is calculated from (4); third, k is calculated; forth, a reference rotor speed (which is considered as a control variable) is perturbed, which is either increased or decreased (by x) depending on the value of k and finally, a perturbation process is terminated when the value of k is equal to zero. This procedure ensures small rotor speed overshoots under fast wind speeds in comparison with existing P&O algorithms, in which a perturbation process is terminated when the value of E(n) is less than or equal to a pre-defined value. Typically, a conventional MPPT controller, which is based on PI controllers and measurements of an output DC voltage and a wind speed is used to generate a reference rotor speed. It includes two main control loops, i.e. an outer speed loop and an inner DC voltage loop. The former loop is adopted to generate a reference DC voltage by controlling rotor speed errors via a PI controller. The calculation of rotor speed errors require an optimal speed, which is calculated by a TSR controller by measuring wind speeds. The DC voltage loop is then employed to generate an optimal duty cycle by controlling voltage errors via another PI controller. The main disadvantages of this technique are that its parameters are highly sensitive to the changes of wind speed and a load and it needs an additional voltage sensor and an anemometer in comparison with sensorless MPPT controllers. To address these disadvantages, the proposed adaptive P&O algorithm is adopted to estimate an optimal duty cycle, d, without measuring the DC voltage or wind speeds. d is proportional to the input DC voltage V av based on a well-known voltage expression of a DC-DC boost converter, V av = V o (1 d), and a rotor speed according to (??). Finally, in order to apply the proposed adaptive P&O algorithm for estimating duty cycles, the speed error, ω = ω ref ω est, and d have been considered as an input error and a control variable, respectively. V. EXPERIMENTAL SETUP AND RESULTS A. A Wind Turbine Generator Simulator A WTG simulator is an effective solution for a real-time implementation of a MPPT controller, as it can conduct and repeat experiments under controlled wind speeds. In this work, a WTG simulator has been constructed, which includes the following main components: (i) a three-phase induction motor; (ii) a three-phase direct-connected surface-mounted PMSG (model GL-PMG-5A); (iii) a SMR, which includes a threephase bridge rectifier and a DC-DC boost converter and (iv) a dspace system (model DS114), which is used for digital data acquisition and implementing the proposed sensorless MPPT controller in real-time. Figure 4 shows a photograph of the WTG simulator used for experiments. B. Step Change of Wind Speed The proposed sensorless MPPT controller is also tested under the changes of wind speed, i.e. from 6 to 8 m/s, from 8 Fig. 4. A photograph of a WTG simulator, where (1) an AC driver, (2) an induction motor, (3) a PMSG, (4) an LC filter, (5) a diode rectifier, (6) an IGBT, (7) a diode, (8) an IGBT driver, (9) voltage and current sensor boards, (1) an encoder, (11) a dspace controller and (12) a resistive load. to 1 m/s and from 1 to 12 m/s. Moreover, the load resistance is varied from 1 to 2 Ω. The purpose of this test is to validate the ability of the developed optimal speed observer based on the adaptive P&O algorithm for tracking maximum power points. Figure 5(a) shows the experimental characteristics of the WTG simulator with and without the proposed sensorless MPPT controller. It can be observed that the experimental MPPT line using the proposed sensorless MPPT controller is very close to the theoretical MPPT line with small oscillations around MPPs. Clearly, the experimental characteristics without optimized using a MPPT controller diverge from the MPPT line due to operating the WTG simulator at fixed speeds. For a comparison, the experimental MPPT line is also obtained using the conventional MPPT controllers (a classic P&O and a PI controller, which is based on self adjusting parameters) as shown in Fig. 5(b). It can be seen that large overshoots and oscillations occur especially in case of using a classic P&O algorithm with fixed optimal parameters. TABLE II provides a summary of the experimental results of the steady state of MPPT efficiencies, η mppt, and the percentage speed errors, E ω. It is seen that the maximum η mpp and the minimum E ω are obtained by using the proposed sensorless MPPT controller compared with other controllers. For comparison purposes, the WTG simulator is operated without a MPPT controller in order to demonstrate the advantage of the proposed sensorless MPPT controller. It can be seen that the mechanical power is increased by 29.51% and 4.84% at loads of 1Ω and 2Ω, respectively. It can be also observed that the average MPPT efficiencies in the case of using a conventional PI controller and a classical P&O algorithm are also high in comparison with the case without MPPT. But their dynamic responses are poor in terms of vibrations and noise, and their percentage speed errors are high in comparison with the proposed sensorless MPPT controller, which relatively provides smooth speed control with small percentage speed errors, i.e. under 1%, for all operating power points.

6 Wind Turbine Power (W) Wind Turbine Power (W) Characteristics Proposed Without MPPT Rotor Speed (rad/s) (a) With and without a MPPT controller. Characteristics Classic P&O PI Controller Rotor Speed (rad/s) (b) Using conventional MPPT controllers. Fig. 5. Experimental characteristics of the WTG simulator under step changes at various wind speeds, i.e. from 6 to 8 m/s, from 8 to 1 m/s and from 1 to 12 m/s. TABLE II COMPARISON RESULTS UNDER WIND SPEED VARIATIONS. Wind Load Proposed Without MPPT Speed (Ω) (Sensorless MPPT) (Fixed speed operation) (m/s) η mpp% E ω% η mpp% E ω% Average Wind Load PI Controller Classic P&O Speed (Ω) (Self adjusting and (Using optimal fixed (m/s) using an encoder) x and T o) η mpp% E ω% η mpp% E ω% Average VI. CONCLUSION In this paper, a novel sensorless MPPT controller has been developed and implemented in real-time using a WTG simulator. It includes three novel observers, i.e. a rotor speed observer, a reference rotor speed observer and an optimal duty cycle observer. An adaptive SMO is employed to estimate the rotor speed, which is only based on the measurements of two phases of terminal voltages and line currents of the PMSG by using a PMSG model in the stationary reference frame. Moreover, an adaptive P&O algorithm is also adopted for the estimation of a reference rotor speed and a duty cycle by minimizing turbine coefficient errors and rotor speed errors, respectively. The experimental results show that the proposed sensorless MPPT controller has small overshoots and steady-state ripples around maximum power points. It has improved MPPT efficiencies, i.e. above 99%, and decreased speed errors, i.e. under 1%, for all operating power points under variations of wind speed and load in comparison with various conventional MPPT controllers. REFERENCES [1] J. Brahmi, L. Krichen, and L. Ouali, A comparative study between three sensorless control strategies for pmsg in wind energy conversion system, Applied Energy, vol. 86, no. 9, pp , 29. [2] T. Senjyu, Y. Ochi, Y. Kikunaga, M. Tokudome, A. Yona, E. Billy, N. Urasaki, and T. Funabashi, Sensor-less maximum power point tracking control for wind generation system with squirrel cage induction generator, Renewable Energy, vol. 34, no. 4, pp , 29. [3] D. Hohm and M. Ropp, Comparative study of maximum power point tracking algorithms using an experimental, programmable, maximum power point tracking test bed, in Photovoltaic Specialists Conference, 2. Conference Record of the Twenty-Eighth IEEE, 2, pp [4] D. Petreus, T. Patarau, S. Daraban, C. Morel, and B. Morley, A novel maximum power point tracker based on analog and digital control loops, Solar Energy, vol. 85, no. 3, pp , 211. [5] S. Kazmi, H. Goto, G. HaiJiao, and O. Ichinokura, A novel algorithm for fast and efficient speed-sensorless maximum power point tracking in wind energy conversion systems, Industrial Electronics, IEEE Transactions on, vol. 58, no. 1, pp , jan 211. [6] K. Raza, H. Goto, H. Guo, and O. Ichinokura, A novel speed-sensorless adaptive hill climbing algorithm for fast and efficient maximum power point tracking of wind energy conversion systems, in Sustainable Energy Technologies. IEEE International Conference, 28, pp [7] P. Vas, Sensorless Vector and Direct Torque Control. Oxford University Press, [8] F. Yorgancolu and H. Kmurcugil, Single-input fuzzy-like moving sliding surface approach to the sliding mode control, Electrical Engineering (Archiv fur Elektrotechnik), vol. 9, pp , 28. [9] J. Lee, J. Son, and H. Kim, A high speed sliding mode observer for the sensorless speed control of a pmsm, Industrial Electronics, IEEE Transactions on, no. 99, pp. 1 1, Dec. 21.