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Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System a
a
a
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Sofia Lalouni , Djamila Rekioua , Kassa Idjdarene & Abdelmounaim Tounzi a
Laboratoire de Technologie Industrielle et de l’Information (LTII), Faculté de Technologie, Université de Bejaia, Bejaia, Algérie b
Laboratoire d’Electrotechnique et d’Electronique de Puissance de Lille, France Published online: 11 May 2015.
Click for updates To cite this article: Sofia Lalouni, Djamila Rekioua, Kassa Idjdarene & Abdelmounaim Tounzi (2015) Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System, Electric Power Components and Systems, 43:8-10, 1028-1038, DOI: 10.1080/15325008.2014.999143 To link to this article: http://dx.doi.org/10.1080/15325008.2014.999143
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Electric Power Components and Systems, 43(8–10):1028–1038, 2015 C Taylor & Francis Group, LLC Copyright ISSN: 1532-5008 print / 1532-5016 online DOI: 10.1080/15325008.2014.999143
Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System Sofia Lalouni,1 Djamila Rekioua,1 Kassa Idjdarene,1 and Abdelmounaim Tounzi2 1
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Laboratoire de Technologie Industrielle et de l’Information (LTII), Facult´e de Technologie, Universit´e de Bejaia, Bejaia, Alg´erie 2 Laboratoire d’Electrotechnique et d’Electronique de Puissance de Lille, France
CONTENTS 1. Introduction 2. Wind Energy Conversion Subsystem 3. Simulation Results 4. Conclusion References
Abstract—Due to the instantaneous variation of wind speed, it is suitable to determine the optimal rotational speed that ensures maximum energy efficiency. This article deals with a comparison between different maximum power point tracking algorithms applied to wind energy conversion systems. The most commonly used algorithms are optimal torque control, power signal feedback, tip-speed ratio, and hill-climb search. The conventional hill-climb search method has an important drawback, which is the wrong directionality under rapid wind change. To solve this problem, using a hybrid hill-climb search method is proposed, which consists of combining the optimal torque control and hill-climb search methods. The proposed approach is applied to a wind energy conversion system based on a permanent magnet synchronous generator under a wind speed profile using a R R MATLAB -Simulink (The MathWorks, Natick, Massachusetts, USA) package to achieve the simulation calculations. The obtained results are then presented and compared to those given by classical algorithms to highlight the interest of the proposed approach in terms of efficiency and response speed.
1. INTRODUCTION
Keywords: wind energy, maximum power point tracking, optimal torque control, power signal feedback, tip-speed ratio, hybrid hill-climb search Received 22 July 2013; accepted 30 November 2014 Address correspondence to Dr. Sofia Lalouni, Laboratoire de Technologie Industrielle et de l’Information (LTII), Facult´e de Technologie, Universit´e de Bejaia 06000, Bejaia, Alg´erie. E-mail: lalouni
[email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uemp.
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Conventional energy sources produce pollution and CO2 emissions; furthermore, their known reserves are limited and their prices are continuously increasing [1]. Renewable energy sources constitute a very interesting alternative as they are clean and abundantly available in nature. In the case of electric power generation from wind energy, different generators can be used. However, due to their high power density and less maintenance, permanent magnet synchronous generators (PMSGs) are increasingly used, mainly in variable-speed operation. Almost all wind energy conversion systems (WECSs) are connected to the grid, with the main objective as the optimization of the energy captured [2–11]. Two types of converter topologies are available: one in which the converter is composed of a diode rectifier, DC chopper, DC bus, and DC/AC inverter [3, 11]; the other in which the converter is composed of
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Lalouni et al.: Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System
an insulated-gate bipolar transistor (IGBT) rectifier, DC bus, and DC/AC inverter [4]. The second topology is adopted in this article. As the output power of a wind energy system varies depending on the wind speed, the aim of the variable-speed wind turbine control consists of maximizing the extracted energy. However, due to the non-linear characteristic of the wind turbine, it is difficult to reach such a goal for all wind speed conditions. Therefore, several maximum power point tracking (MPPT) algorithms have been developed to track the maximum power point (MPP) of the wind turbine [4, 7, 12–14]. Various research has focused on several types of MPPT methods, namely tip-speed ratio (TSR) control, power signal feedback (PSF) control, optimal torque control (OTC), and hill-climb search (HCS) control. In the first algorithm, the wind and rotor speeds are measured and used to determine the optimal TSR [4, 12, 15, 16]. This method seems simple to implement, but it needs a very accurate wind speed measurement, which is very difficult to achieve [17]. The PSF method can be alternatively achieved by testing the wind turbine to find the optimal power rotation speed curve with various wind speeds [12, 15, 18]. Thus, the reference power trajectory can be mathematically written as a function of power and rotational speed and stored as a lookup table. The main drawback of this approach lies in the fact that simulations or experimental tests have to be used to obtain the maximum power characteristic [4]. The OTC adjusts the generator torque to its optimal value at different wind speeds. This method requires the wind turbine characteristics (Cpmax and λopt ) that are generally given by the manufacturer [12, 16, 19, 20]. Tracking the maximum available power of wind may cause extra fluctuations in the output power. In [21], generator output power was smoothed. Compared to those of a similar power smoothing method [22], the costs and maximum aerodynamic efficiency have been reduced, so these methods may not be economical. In [23], to maximize wind turbine output power, the optimal operation speed is determined with parameters identified. However, the operating point of maximum power control oscillates largely around the energetic maximum, which is harmful to the provided power quality and to the mechanical reliability. The perturbation and observation (P&O) algorithm or HCS, also used in power processing of photovoltaic panels [24, 25], is a promising method to achieve MPPT in wind turbines [4, 12, 26–28]. In the context of variable-speed wind energy system, this algorithm brings the operating point toward Cpmax by increasing or decreasing the rotational speed using a step. However, the choice of an appropriate step size is not an easy
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task: a large step size means a fast response but more oscillations around the maximal point and, hence, less efficiency, while a smaller step size improves the efficiency but reduces the convergence speed [12, 16]. In [12], a constant step was introduced in the perturbation process that produces ripples in the power coefficient under wind speed variations. A variable step is used in [29] by considering the variation of the tracking step, resulting in high efficiency and fast tracking speed. The HCS strategy is optimized in some works [30, 31], but the algorithm and control procedure are commonly complex, which make it difficult to execute. Many other methods have been proposed, such as slidingmode control (SMC), where Beltran et al. [32] reduced the steady-state error of tracking the optimal speed by using a highorder sliding-mode controller as a non-linear method. Neural network and fuzzy logic control have also been applied to improve the power tracking [33–40]. The fuzzy control based MPPT method has the advantages of fast convergence, parameter insensitivity, and acceptance of noisy but is somewhat complex to implement [35]. Many of the problems associated with the aforementioned methods have been solved by hybrid methods. In [41], optimal current given (OCG) control is proposed, which combines the advantages of the PSF method and the HCS method. This control needs experience and wind generator characteristic knowledge to estimate the torque loss. Raza et al. [16] merged the OTC method with HCS control to control the duty ratio of the DC/DC converter. This last method is studied herein and is applied to a WECS based on a PMSG and connected to the grid. In this article, the hybrid MPPT controller (hybrid HCS [HHCS]) is studied. It combines the benefits of OTC and HCS strategies to solve the two problems associated with conventional HCS: speed efficiency trade-off and wrong directionality under rapid wind change. It has three modes. The first mode uses the normal HCS control to search a maximum. Once the turbine operating point reaches the MPP, the second mode is activated to keep the turbine operating point at the MPP. When the wind change is detected through the change in the rotor speed, however, the system is shifted to the last mode to bring the turbine operating point quickly to a point close to the MPP. The studied WECS consists of a direct-drive variable-speed permanent magnet generator with an IGBT rectifier connected to the grid. To maximize the use of wind energy, the MPPT is realized by controlling the rectifier, which is connected to the PMSG. The reference speed is calculated by different MPPT controllers (OTC, PSF, TSR, and HHCS) to extract as much power as possible from the wind. To compare the performances of the four MPPT controllers, a WECS,
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the scope of this article, but a detailed description can be found in [4, 5, 9]. 2.1.
Wind Turbine Model
The equation governing the mechanical power captured by wind turbine blades is given by Pm =
1 C p (λ).ρ.A.vw3 , 2
(1)
where Pm is the extracted power from the wind, ρ is the air density (in kg/m3), A is the area swept by the rotor blades, vw is the wind speed (in m/s), and Cp is called the power conversion coefficient. If the pitch angle is fixed, Cp depends only on TSR λ, which is defined as the ratio of the turbine’s blade-tip speed to the wind velocity:
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λ=
ωm .R , vw
(2)
with ωm being the turbine angular speed and R the turbine radius. Then the mechanical system is represented by the following equation: FIGURE 1. WECS.
shown in Figure 1, has been simulated. As the focus is only on electric variable behavior, the conditions of the simulation are those conventionally used in electrical engineering, i.e., wind turbulence as well as mechanical stress and their effects on the wind turbine, are not considered. Thus, the simulation calculations, under different laminar wind speed conditions, are R R -Simulink (The MathWorks, carried out using MATLAB Natick, Massachusetts, USA). The results obtained with the different algorithms are compared, and they exhibit very fast performance of the proposed HHCS controller and high accuracy in sensing wind speed variations as well as maintaining its performance under variable wind conditions.
2.
J
dωm = Tm − Te − f ωm , dt
(3)
where J is the total inertia of the rotating parts in (in kg m2), Tm is the mechanical torque developed by the turbine in (in Nm), Te is the electromagnetic torque in (in Nm), and f is the viscous friction coefficient in (in Nm.s rad−1). The wind turbine characteristic used in this study is shown in Figure 2 [5]. Figure 2(a) shows that the value of Cp varies with respect to λ and reaches its maximum value at a particular λopt . The power captured by the wind turbine is then a function of the rotational speed and is maximal at λopt , and hence, for each wind velocity, maximal power can be extracted at a given rotor speed (Figure 2(b)). Therefore, the turbine speed has to be controlled to follow the optimal TSR. This is achieved by incorporating an MPPT control in the system.
WIND ENERGY CONVERSION SUBSYSTEM
The global electric scheme of the WECS adopted in this study is shown in Figure 1. It consists of a horizontal wind turbine with a fixed blade pitch angle connected to a PMSG that is connected to the distribution grid by means of a back-to-back converter. Pitch angle control of the wind turbine turns out to be another optimization problem in a WECS [10, 21, 37]. The system is designed to achieve maximum power tracking within a wide range of wind speed variation by means of an MPPT block. MPPT control is realized using the machine-side control system. The control of the grid-side inverter is out of
2.2. 2.2.1.
MPPT Techniques TSR Control
To have maximum possible power, the turbine should always operate at λopt . The TSR control method regulates the TSR to maintain it at its optimal value to extract the maximal power. This control requires the knowledge of the wind velocity, turbine speed, and reference optimal point of the TSR, which can be determined experimentally or theoretically [12]. The difference between the TSR reference and its actual value feeds the controller and gives the reference power.
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FIGURE 2. Characteristic curves of wind turbine: (a) power conversion coefficient versus TSR and (b) turbine power versus rotational speed for different wind velocities. FIGURE 4. Deviation from the MPP with the HCS algorithm: (a) under rapidly changing wind conditions and (b) operating in mode 3.
2.2.2.
PSF Control
PSF control generates a reference power signal to maximize the output power. However, it requires the knowledge of the wind turbine’s maximum power curve, which can be obtained from experimental results or simulations [18]. Then the data points for maximum turbine power and the corresponding wind turbine speed must be recorded in a lookup table [4, 16]. The PSF control method regulates the turbine power to maintain it at an optimal value so that the power coefficient Cp is always at its maximum value corresponding to the optimum TSR. 2.2.3. FIGURE 3. Principle of the P&O MPPT shown on the Pm (ωm ) characteristic.
OT Control
OTC is a slight variant of the PSF control [16]. It adjusts the generator torque to its optimal value at different wind speeds.
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FIGURE 5. Flowchart of HHCS MPPT control.
However, it requires the knowledge of the turbine characteristics (Cpmax and λopt ). If the conditions are optimal, based on Eq. (2), the optimum speed of the rotor can be estimated as vw .λopt . (4) R Combining Eqs. (1) and (2) yields the reference of the electromagnetic torque corresponding to the maximum power, which must be controlled following this equation: ωm,opt =
Te−r e f =
2 K opt .ωm,opt ,
(5)
FIGURE 6. (a) Waveforms of mechanical power and (b) zoom of the transitional state.
where K =
2.2.4.
C p max .ρ.π.R 5 2.λ3opt
.
(6)
HHCS
HCS or P&O control is usually used for the peak power of the wind turbine that will maximize the extracted energy. This Method
OTC
PSF
TSR
HHCS
Response 0.75 0.26 0.033 0.0103 time (sec) Mechanical 1872.8 1871 1872 1873.03 power (W) Efficiency 99.93 99.83 99.89 99.95 (%)
Without MPPT — 749.6 39.99
TABLE 1. Evaluation of performances of different MPPT strategies
control consists in climbing the Pm (ωm ) curve in the direction of increasing Pm by varying the rotational speed periodically with a small incremental step to reduce the oscillation around the MPP. The principle can be described as follows. As shown in Figure 3, in the ascending phase of the Pm (ωm ) characteristic and considering a positive change of the rotational speed, the tracker generates a positive change ωm > 0, which results in an increase of the delivered mechanical power and change of the operating point Xi (i = 1, 2, . . ., n – 1). In this case, the rotational speed and Pm power increase up to a new point Xi + 1 . Similar steps with the opposite direction can be done in the case of a decrease of the mechanical power by setting X = ωm ; the instantaneous rotational speed of the wind turbine follows the MPP according to a predetermined rotational speed and power values. Under these conditions, the tracker seeks the MPP permanently. At a given wind speed, the desired
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Lalouni et al.: Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System
FIGURE 7. (a) Waveforms of rotor speed and (b) zoom of the transitional state.
mechanical power is the solution of the non-linear equation given by (d Pm /dωm = 0). The magnitude of the step size is the main factor determining the amplitude of oscillations and hence the convergence rate to the final response. To overcome this trade-off, the step size of varying amplitude can be applied [4, 5, 8, 28]. The stepsize amplitude can be determined according to power variations based on the previously applied disturbance. Therefore, larger step size amplitude is selected when power is far from the MPP due to the larger magnitude of the Pm (ωm ) slope, and small amplitude is selected when power is close to the MPP. The step size is continually decreased until it approaches zero in the aim to drive the operating point to settle down at the MPP. A disadvantage of the HCS method, described by Figure 4, appears in the case of a sudden increase of wind speed, where the algorithm responds as if the increase occurred as a result of the previous perturbation of the operating speed. This wrong
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FIGURE 8. (a) Waveforms of power coefficient and (b) zoom of the transitional state.
decision leads to failure in keeping track of the MPP. The use of variable step size amplitude overcomes the trade-off between the response speed and steady-state oscillations [12]. In this article, the HHCS algorithm is presented to track the MPP, solving the two problems associated with the conventional HCS. The algorithm has three modes. • Mode 1 uses the normal HCS control to search a maximum. Here two checking rules are given to ensure that the MPP is detected accurately. The two checks are given as follows: |Pm (k)| ≤ ε1 , Pm (k) ω (k) ≤ ε2 . m
(7) (8)
The first rule (Eq. (7)) means that the power variation Pm (k) should be less than a threshold ε1 . The second rule (Eq. (8)) means that the gradient of the Pm versus ωm
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efficiency concession of a normal HCS. The direction in which the operating point travels is the direction of (ωm∗ − ωm ) (point A to B or point C to D). Mode 3 keeps in operation when the wind speed change is detected: ωm (k + 1) = α.(ωm∗ − ωm ),
(9)
∗
where ωm is the abscissa of the optimal curve corresponding to the mechanical power. The flowchart of the HHCS MPPT control is shown in Figure 5. 2.3.
PMSG Model
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The electrical equations that describe the behavior of the PMSG in the rotor (dq) reference frame are given by −Rs i d − L d didtd + ωe L q i q Vd = di Vq = −Rs i q − L q dtq + ωe (ψ f − L d i d ),
FIGURE 9. (a) Waveforms of TSR and (b) zoom of the transitional state.
curve should be less than a threshold ε2 . The climbing search will be stopped when the two checks are true, the MPP is then detected, and then Kopt is calculated through the measured power and rotational speed, and the system is switched to Mode 2. • Mode 2 sets the perturbation to zero to retain the maximum. But when the wind change is detected through the change in the rotor speed, the system is shifted to Mode 3. • Mode 3 can serve as an accurate reference to calculate ωm ∗ after coefficient Kopt is detected. For both the size and direction of the next perturbation, when the variation of wind speed is detected, the speed step can be calculated by the distance of the operating point and the optimal operating curve (Figure 4(b)); it can be calculated following Eq. (9). The perturbation size will automatically approach zero, thus eliminating the speed-
(10)
where id , iq , Vd , and Vq , are the currents and voltages in the dq reference frame; Ld and Lq are the equivalent stator inductances in the dq synchronous reference frame; Rs is the stator resistance; and ωe is the electric frequency that is related to the mechanical speed via ωe = pωm (where p is the pair pole number of the machine and ψ f is the magnetic flux produced by the rotor permanent magnets). Finally, the electromagnetic torque of the PMSG can be written under the following form: 3 (11) Te = . p(ψd .i q − ψq .i d ), 2 where ψd and ψq are the stator linkage fluxes along the d- and q-axis. They are expressed as ψd = L d i d + ψ f , ψq = L q i q .
(12) (13)
In Eq. (11), the fluxes can be replaced by their expressions in Eqs. (12) and (13) in the function of the inductances. Then, in the case of a smooth rotor PMSG, i.e., without rotor saliency (Ld = Lq ), the generator torque relation ends with Eq. (14), and the torque may be controlled by regulating current iq : 3 . p.ψ f .i q . (14) 2 A vector control strategy of a PMSG is used, the principle of which is to adjust PMSG rotational speeds according to an optimal reference speed obtained from an MPPT controller (Figure 1). In this control, the d-axis reference current is set at zero to decrease the copper losses in the stator windings. The q-axis reference current is proportional to the torque reference that is generated from an MPPT controller and varies under wind speed variations. A hysteresis-band current control technique Te =
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Lalouni et al.: Maximum Power Point Tracking Based Hybrid Hill-climb Search Method Applied to Wind Energy Conversion System
FIGURE 10. (Continued) FIGURE 10. Simulation results with HHCS controller in rapid wind change: (a) wind speed profile, (b) mechanical power, (c) rotor speed, (d) TSR, (e) power coefficient, and (f) efficiency.
is employed; i.e., the three phase line currents are compared to the three-phase reference currents applied to a hysteresis controller to generate pulse-width modulation (PWM) pulses. The provided energy by the PMSG-based variable-speed wind
turbine is transmitted on DC current and is applied to an inverter, which makes it possible to control the continuous voltage and the active and reactive powers exchanged with the grid [5].
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Electric Power Components and Systems, Vol. 43 (2015), Nos. 8–10
SIMULATION RESULTS
The proposed scheme of Figure 1 is modeled and simulated using the MATLAB/Simulink mathematical analysis software package. The simulation results are discussed in this section. The parameters used for the 2-kW PMSG model are as follows: stator resistance Rs = 5 , stator inductance Ld = Lq = Ls = 25 mH, pair pole number p = 12, flux linkage ψ f = 0.2 V.s, and total inertia J = 0.0833 kg.m2 [5]. The WECS is designed to achieve maximum power tracking. The studied MPPT methods are OTC, PSF, TSR, and HHCS. To highlight the performances of the controllers and to compare WECSs with and without MPPT control, the wind speed step is fixed to 10 m/s and is decreased and increased, respectively, after 4 and 8 sec by 10%. Figures 6–9 show the waveforms of mechanical power, rotor speed, power coefficient, and TSR in transient and steady states. The results are summarized in Table 1 for a wind speed of 10 m/s corresponding to an optimal power of 1874.03 W. The system efficiency is calculated by the following equation: η = (Pm,MPPT /Pm,opt ).100, where Pm,MPPT is the maximum mechanical power of the generator under the selected methods and Pm ,opt is the mechanical power given in optimal conditions. Without the MPPT strategy, the extracted power is only 749.6 W with a value of power coefficient (Cp ), which does not exceed 0.19 while the maximum value of this coefficient is 0.475 for the considered turbine. The HHCS controller appears to be the fastest in achieving the steady state, while the OTC and PSF controller seem to be slowest. The optimal value of power coefficient is reached, and this value is maintained even after the change in wind speed with an efficiency of 99.95%. To highlight the ability of the HHCS controller to track the maximum power in rapid wind change (Figure 10), a variable wind speed profile was applied to the PMSG wind system. Figure 10 shows the mechanical power and variation of rotor speed, which is due to the variation of wind velocity; it introduces a variation of the turbine torque. Thus, the hybrid controller has a good ability of tracking peak power point. It can be seen from the waveforms given in Figures 10(d)–10(f) that the values of the TSR and power coefficient are close to their optimal values, 7.34 and 0.475, respectively, with an efficiency of 99.95%, which shows good performances of the controller. 4.
CONCLUSION
In this article, four algorithms devoted to MPPT have been compared in a WECS. The latter is constituted of a PMSG connected to the grid by means of a back-to-back converter. The optimization algorithms are simulated in the MATLAB/
Simulink environment, and the results prove positively that the OTC, PSF, TSR, and HHCS algorithms reach the MPP. Nevertheless, the approach and stability of the MPP are not achieved within the same manner. The comparison of the obtained results shows the advantages of the HHCS strategy in terms of efficiency and response speed. It reaches the objective of extracting maximum power at any wind speed. Furthermore, it obtains the maximum value of power coefficient and the optimal TSR and maintains them at the optimal values even with changes in wind speed.
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BIOGRAPHIES
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Sofia Lalouni was born in 1979. She received her engineer degree in electrical engineering in 2002, her master’s degree in 2005, and her Ph.D. in 2009, all from University of Bejaia, Algeria. She is a lecturer at the same university. Her current research interests are modeling and control of renewable energy systems (photovoltaic, wind turbine, and hybrid systems). Djamila Rekioua was born in 1963. She received her engineer degree in electrical engineering in 1987 and her master’s degree in 1993, both from the Ecole Nationale Polytechnique, Algiers, Algeria, and her Ph.D. in 2002 from University Ferhat Abbas Setif, Algeria. Currently, she is a professor at University of Bejaia (Algeria). Her current research interests include modeling and control of AC machines and electric drives and renewable energy (photovoltaic, wind turbine, and hybrid systems).
Kassa Idjdarene was born in 1975. He received the ingeniorat and magister degrees in electrical engineering from University of Bejaia, Bejaia, Algeria, in 2002 and 2005, respectively. In 2010, he obtained his Ph.D. in electrical engineering both from University of Bejaia (Algeria) and University Lille 1 (France). He is a lecturer in the Electrical Engineering Department, University of Bejaia (Algeria). His research interests are modeling, control of AC machines, and wind energy. Abdelmounaim Tounzi was born in Casablanca (Morocco) in 1965. He graduated from University of Nancy, France (master’s degree in 1989) and Institut National Polytechnique de Lorraine (INPL), France (Ph.D. in 1993). From 1993 to 2008, he was an associate professor at University Lille 1 (USTL), France, and a member of the L2EP (Laboratory of Power Electronics and Electrical Engineering). Currently, he is a full professor at the same university and is a member of the IEEE. His research areas are the design and modeling of electromagnetic systems.
