A new low-cost sensorless MPPT algorithm for small wind turbines

René Aubrée1,2, François Auger1 and Ping Dai1

1LUNAM Université, IREENA, Saint-Nazaire, France

2LUNAM Université, ICAM, Nantes, France E-mail: rene.aubree@icam.fr, francois.auger@univ-nantes.fr, daipinghere@gmail.com

ABSTRACT

This paper presents an original method for the sensorless Maximum Power Point Tracking (MPPT) of a small power wind turbine using a permanent magnet synchronous generator to supply a DC load. This method does neither require the knowledge of the wind speed nor the turbine parameters. After a presentation of the energy conversion chain (wind turbine, PMSM generator, rectifier and boost circuit), we first derive an analysis of its energy efficiency. This analysis shows that the highest power at the output of the turbine and the highest power supplied to the load are not obtained at the same rotor speed. This clearly shows the interest to maximize the power supplied to the load rather than to track the maximum power at the output of the turbine deduced from its theoretical power coefficient . We then describe the proposed MPPT algorithm and the speed estimator used to design a sensorless MPPT. Simulation results demonstrate the feasibility of the proposed approach.

Index Terms— Small Wind Turbines, Permanent Magnet Synchronous Generator, MPPT, Angle Tracking Observer

1. INTRODUCTION

For centuries, man converts wind into mechanical energy for its own needs. This is especially true today with the depletion of fossil fuels and the emergence of environmental issues. Increasingly large wind turbines, which are becoming more and more efficient, are now appearing. These wind turbines are grouped into large wind farms and are connected to the grid. On the other hand, there is also a need for small wind turbines (SWTs), designed to produce energy close to its consumer (remote sites, “off-grid” homes, relocatable equipment buildings, road signs, street lighting...) [6,12].

The optimal operation of a SWT is a key issue because of its low efficiency and its high initial cost. As shown in [11], the efficiency of a SWT depends on many factors. One of them is the power converter. For economic reasons, low-cost power converters are usually integrated, leading to a poor efficiency which deteriorates the reputation of SWTs. Another factor is the electric power generator. Compared to other possible generators, permanent magnet synchronous generators (PMSGs) have a higher efficiency, as the copper losses in the rotor are weak, and a larger energy density. Moreover, PMSGs may be used at low varying speeds, allowing the generator to be directly coupled to the wind turbine, without using a gearbox which would decrease the availability of the system, increase its weight and the need for maintenance [7]. However, since PMSGs are AC machines, a controlled AC/DC converter is necessary to efficiently supply a DC load. A last factor is

the operating conditions. Indeed, SWTs are usually installed at a low height (below 12 meters). At this altitude, the wind is often quickly varying both in direction and force [1].

High power horizontal axis wind turbines, which are located at an altitude where the wind is constant, are controlled by powerful computers with all the necessary sensors. On the other hand, low-cost small wind turbines must be controlled by inexpensive microcontrollers which must embed complex algorithms to get the maximum efficiency of the system. Moreover, to decrease the cost and the encumbrance of the generator, and to increase the system reliability [3], one may wish that these control algorithms do not require any mechanical sensor [17].

The aim of this paper is to present a new sensorless algorithm that can provide the highest power to a DC load. To this aim, the studied energy conversion chain is introduced in Section 2. Section 3 then presents an analysis of the performance of this chain. The proposed MPPT algorithm and the speed estimator used to provide a sensorless algorithm are presented in Sections 4 and 5 respectively. Simulation results are finally presented in Section 6 to demonstrate the feasibility of the proposed approach.

2. THE ENERGY CONVERSION CHAIN

The wind energy conversion system studied here is

made of a turbine, a direct coupled permanent magnet generator, a 6 diode rectifier and a boost circuit.

2.1. The turbine

Although the approach presented in this paper could be applied to any kind of turbine, we have considered here the use of a Darrieus vertical axis wind turbine of radius R and height H. The mechanical power PT supplied by this turbine to the generator can be expressed as [4,14]

λ 12 ρ 3 where Pw is the power supplied by the wind (W), is the area of the turbine (m2), Vw is the wind

speed (m/s) and ρ is the air density (around 1.2 kg/m3 in the usual conditions of temperature and humidity). Cp is the power coefficient of the turbine, and λ Ω ⁄ is the so-called tip speed ratio [6,16], Ω being the turbine shaft speed (rad/s). This power coefficient, which can be approximated by a fourth-order polynomial deduced from experimental measurements,

can be considered as a coefficient of performance and has a highly concentrated bell shape (see Fig. 1). As a consequence, due to variations in wind speed, the rotor speed must permanently be adjusted by a maximum power point tracking algorithm, to provide as much power as possible to the load [1].

Figure 1: Turbine power vs the turbine rotation speed Ω for different values of the wind speed .

2.2. The permanent magnet synchronous generator

To accurately reproduce its behavior during

transients, we use a dynamic model of the PMSG, expressed in the dq reference frame rotating at the same speed as the rotor. If the stator windings are supposed to be sinusoidally distributed, if the magnetic circuits are supposed to be unsaturated and if the eddy currents and hysteresis losses are supposed to be negligible, the electrical equations expressed in this frame using the Concordia transform [5,14] are

(1)

(2)

where 0 and are the no-load voltages

(obtained when 0 A), is the stator phase resistance, and are the dq inductances, is the rotor flux linkage and is the angular frequency of the electric voltages and currents. For a synchronous machine, Ω , p being the pole pairs number. The production of this electric energy at the output of the generator induces a braking electromagnetic torque. The general expression of this torque and its simplified expression in the case of a non-salient machine ( ) such as the one we considered is T (3)

Finally, the turbine torque and the electromagnetic torque are involved in a mechanical equation [15] Ω (4)

where J is the overall system inertia, f is the viscous friction coefficient and /Ω .

2.3. The AC/DC converter The final AC/DC converter is made of a 3-phase diode

bridge associated with a boost (see Figure 2).

Figure 2. AC/DC boost converter.

The boost circuit [9] is a step-up chopper made of L1, M1 and D7. It is driven by the periodic pulse width modulation (PWM) signal which controls the power switch M1 and hence the amount of power transferred to the load. Indeed, if the boost circuit is used in continuous mode, the current across the inductance never reaches zero and is a periodic piecewise linear signal, varying between a minimum and a maximum . When the switch is on (see Fig. 3), the current increases up to / (5) where is the on-state time of the switch. When the switch is off, the current decreases down to / (6) where T is the period of the PWM signal. From Eq. 5 and 6, one can deduce that [16] (7)

0 20 40 60 80 100 1200

100

200

300

400

500

600

700

800

900

Omega (rad/s)

P t

urbi

ne (

W)

Vw = 12 m/s

Vw = 4 m/s

Vw = 8 m/sVw = 6 m/s

Vw = 10 m/s

where / is the duty cycle of the PWM signal. This means that the power supplied to the load (R4) is 1

This result shows that for the diode bridge, the boost circuit can be considered as a variable resistive load with an equivalent value 1 . Since this equivalent resistance determines the current supplied by the generator, and hence the rotor speed, the duty cycle D can be used to maximize the power supplied to the load.

Figure 3. Currents and voltages inside a simulated boost circuit. From top to bottom : current across the inductance, current across the switch, current across the diode and voltages , and . Since

=60 V, V and D=0.46, Eq. 7 is satisfied in this case.

3. ENERGY EFFICIENCY ANALYSIS

When considering an energy conversion system, it

may be interesting to study its energy efficiency. This requires computing the power supplied at the output of this three-phase generator

From Eq. 2, 3 and 4, one can deduce that 12 Ω

At steady state, ⁄ ⁄ 0 A/s and Ω ⁄ 0 rad/ , so the power becomes Ω (8)

with Ω Ω 32 Ω (9) To maximize subject to the constraint given by Eq. 9, we can use the method of Lagrange multipliers. This consists in defining the Lagrange function

λΩ Ω 32 Ф Ω

And to look for a stationary point of this function, i.e. for a solution of the four equations 0, 0, 0 and

λ0.

A summary of the solution of this optimization problem is that

1) In steady state, ΩФ Ω 2) is maximized when 0 . This justifies the use

of a controlled rectifier based on the field oriented control principle.

3) is maximized when Ω is the solution of the nonlinear equation

λΩ 2 Ω λ

λ 1 32 Ф with λ

Ф

This allows defining the optimal generator power coefficient as Ω Ω

This coefficient evaluates the efficiency of the association of a wind turbine with a PMSG optimally controlled using the field oriented vector control principle, and the importance of the Joule and friction losses compared to the wind power.

Figure 4. Power coefficient of the turbine and PMSG with or without Field Oriented Control.

Fig. 4 shows a comparison of and in our case. One important point to underline is that these two curves are not at their maximum for the same abscissa. This means that when the value of the tip speed ratio for which is at its maximum is used to compute the speed reference of a vector controlled generator, the highest power at the output of the generator is not provided. This justifies to directly maximize the power supplied to the load.

4. MAXIMUM POWER POINT TRACKING

As shown in the previous section, the performance of the energy conversion chain is higher when the PMSG is controlled using the field oriented vector control principle. But this requires a three-phase inverter and a powerful microcontroller embedding a complex control algorithm. To evaluate the performances of a cheaper hardware, we have

1 2 3 4 5 6 7 8 90.1

0.15

0.2

0.25

0.3

0.35

0.4Cp vs Lambda

Lambda

Cp

Cp Turbine

Cp with FOCCp without FOC

studied how to maximize the power supplied to a DC load by a diode rectifier combined with a boost circuit. As shown in Fig. 4, the power coefficient is lower, but the initial cost reduction may compensate this. To this goal, we designed a continuous-time Maximum Power Point Tracking process close to the discrete-time ones proposed in [16,17]. This process controls the duty cycle of the PWM signal of the boost circuit. When this duty cycle is increased, the current in the load increases (as shown in Section 2.3) so the electromagnetic torque increases and the rotor speed decreases [8] (as shown in Section 2.2). As a consequence, the evolution of this duty cycle can be based on the bell shape of Ω and deduced from the evolution of the power supplied to the load, , and of the rotor speed, Ω . As shown in Fig. 5, four cases may happen. For example in the first case, the power and the speed are both increasing, which means that the power is approaching its maximum value on the left side. To proceed further, the speed must be increased, which means that the duty cycle must be decreased. The three other cases are shown in Fig. 6.

From this table, we infer that the evolution of the duty cycle, ⁄ , can be chosen proportional to Ω⁄ , with a negative proportionality coefficient: Ω ⁄Ω ⁄

where the parameter controls the rate of change of the duty cycle. Our experience showed that this parameter should be inversely proportional to the system inertia J. To avoid a division by zero in steady state, when the maximum power point is reached, we modified the previous expression to ⁄ Ω ⁄ Ω ⁄ ε

where ε is a small parameter. When Ω ⁄ is high, this expression is close to the previous one. When Ω ⁄ is low, this expression behaves like

ε⁄ Ω ⁄ , providing a small evolution of the duty cycle in the right direction. In practice, the derivatives of the power and the speed are obtained at the output of two first-order high pass filters with a large cutoff frequency compared to the rate of change of these signals.

5. SPEED ESTIMATOR We tried to further reduce the initial cost of this

energy conversion chain by removing the need of a speed sensor. For this, we used an Angle Tracking Observer (ATO) studied in [2]. This estimator is fed by the projections of the output voltages of the generator in the fixed αβ reference frame, using a Clarke transform. These projections are the coordinates of a vector rotating at the electrical rotor speed Ω . To estimate this speed, the ATO consists in making an angle evolve so as to cancel the algebraic area of the triangle formed by

the two vectors (Vα, Vβ) and (cos , sin ), which is proportional to Vβcos Vα sin . This cancellation is obtained by a classical PI controller. Figure 7 shows the block diagram of the speed and angle tracking observer.

Figure 5. The four possible cases for the evolution of the power load and the rotor speed.

Figure 6. MPPT output evolution table.

6. SIMULATION RESULTS

The performances of the proposed solution have been

evaluated by a simulation using the general purpose free full-fledged LTspice IV software [19]. We justify this choice by the ability of this software to simulate both dynamic systems and electronic circuits such as switch-mode power supplies. Fig. 8 shows a block diagram of the simulation system. The values of the parameters are given in appendix. In our case the maximum power point of the turbine is obtained for λ 4.95 (since Darrieus turbines are lift based, the speed of the apparent wind at the blade tip is greater than the speed of the real wind, so λ is greater than one). The setting of the ATO was performed as proposed in [2], with a damping factor 1.945 and a maximum permissible error of 1 degree. The proposed solution has been tested with both constant and varying wind speed. Fig. 9 shows the duty cycle, the rotor speed and the power supplied to the load for a constant wind speed equal to 6 m/s. This figure shows that the speed estimator quickly converges and the MPPT provides the value of the duty cycle that maximizes the power. For varying speed, we used the same sinusoidal wind speed model as in [13]

0 sin 2

The simulation results presented in Fig. 10 show that

Ω ⁄ < 0 > 0

< 0 2) bad direction MPPT output: 0

4) bad direction MPPT output: 0

> 0 3) good direction MPPT output: 0

1) good direction MPPT output: 0

when the proposed solution is used, the power supplied to the load has an average value of 100 W. Fig. 10 also shows that the estimated speed reaches the real shaft speed in less than 1 s. Fig. 11 shows that without boost circuit and without MPPT algorithm (passive system), the average value of the power supplied to the same load with the same wind is around 60 W. This clearly shows the significant increase of power provided by the proposed MPPT algorithm. Fig. 12 shows the results obtained when a hill-climbing system (HCS) [10,13,16] is used as MPPT algorithm. The development of this simulation was made difficult by the high inertia of our Darrieus wind turbine, which implies a very long sampling period (more than 15 s) to avoid stalling, as mentioned in [18]. Under the same conditions as in Fig. 10 and 11, the HCS delivers an average power of 74 W, which is 26 W lower than our proposed solution.

Figure 7. Block diagram of the Angle Tracking Observer.

Figure 8. Block diagram of the system simulated with LTspice.

7. CONCLUSION

In this article, a consistent modeling of a complete wind energy conversion chain has been presented. This, unfortunately, is not so easy and not so widespread. A new Maximum Power Point Tracking algorithm has been designed, that permanently controls the duty cycle of a boost circuit to maximize the power supplied to a DC load. An Angle Tracking Observer has been used to estimate the shaft speed and thus to maximize this power without using any mechanical sensor. The proposed algorithm neither requires a rotor speed sensor nor a wind velocity measurement. Simulations using LTspice have been used to demonstrate the performances of this

method. Further researches include the comparison of the proposed wind energy conversion chain with another one using a three-phase inverter and a field oriented vector control, and the validation of these algorithms on an experimental testbed.

8. APPENDIX: MODEL PARAMETERS

Wind model:

A0 =6, A1 = 0.2 m/s T1 = 60 s A2 = 2 m/s T2 = 23.5 s A3 = 1 m/s T3 = 4.8 s A4 = 0.2 m/s T4 = 1.7 s

Wind turbine: Darrieus vertical axis wind turbine Radius R = 1.0 m Height H = 2 m Ck coefficients C0 = 0.110898 C1 = -0.02493 C2 = 0.057456 C3 = -0.01098 C4 = 0.00054 Permanent magnet synchronous generator: Nominal power at 600 rpm P = 900 W Phase resistance Rs = 0.23 Ω Phase inductance Ld = 8 mH Phase inductance Lq = 8 mH PM flux linkage amplitude = 0.166 Wb Number of pole pairs 8 Shaft: Total inertia J = 5 kg.m2 Total friction coefficient f = 9.08 10-3 N.m.s/rad Maximum power point tracking :

1 ε 0.01 Angle tracking observer : Ka 57 Kb 214 Load : RL 150 Ω

9. REFERENCES [1] M. Andriollo, M. De Bortoli, G. Martinelli, A. Morini, A. Tortella,

“Control strategies for a VAWT driven PM synchronous generator”, IEEE SPEEDAM, pp. 804-809, 2008.

[2] F. Auger, O. Mansouri-Toudert, A. Chibah, “Design of advanced resolver-to-digital converters”, proc. Electrimacs conf., 2011.

[3] Z. Boulbair, M. Hilairet, F. Auger, L. Loron, “Sensorless control of a PMSM using an efficient extended Kalman filter”, ICEM, 2004

[4] J. Brahmi, L. Krichen, A. Ouali, “A comparative study between three sensorless control strategies for PMSG in wind energy conversion system”, Applied Energy, Vol. 86, No 9, pp. 1565-1573, 2009.

[5] O. Carranza, E. Figueres, G. Garcera, C. L. Trujillo, D. Velasco, “Comparative study of speed estimators applied to wind turbine with harmonic distortion in both the currents and the voltages”, ICREPQ’10, 2010.

[6] M. Drugã, C. Nichita, G. Barakat, “Performances study of direct coupled PM generator based small wind converters”, ICEM 2010.

[7] R. Esmaili, Xu Longya, “Sensorless control of permanent magnet generator in wind turbine application”, IEEE IAS conf., pp 2070-2075, 2006.

[8] M. E. Haque, M. Negnevitsky, K. M. Muttaqi, “A novel control strategy for a variable-speed wind turbine with a permanent-magnet synchronous generator”, IEEE Trans. on Indust. Elec., Vol. 46, No 1, pp. 331-339, 2010.

[9] S. Jiao, G. Hunter, V. Ramsden, D. Patterson, “Control system design for a 20 kW wind turbine generator with a boost converter and battery bank load”, proc. IEEE PESC conf., pp. 2203-2206, 2001.

[10] E. Koutroulis, K. Kalaitzakis, “Design of a maximum power tracking system for wind-energy-conversion applications”, IEEE Trans. on Industrial Electronics, Vol. 53, No 2, pp. 486-494, 2006.

[11] A.J. Mahdi, W.H. Tang, L. Jiang, Q.H. Wu, “Comparative study on variable-speed operations of a wind generation system using vector control”, ICREPQ, 2010.

[12] A. Mirecki, X. Roboam, F. Richardeau, “Architecture complexity and energy efficiency of small wind turbines”, IEEE Trans. on Industrial Electronics, Vol. 54, No 1, pp. 660-670, 2007.

[13] T. Pan, Z. Ji, Z. Jiang, “Maximum power point tracking of wind energy conversion systems based on sliding mode extremum seeking control”, Proc. IEEE Energy 2030 Conf., 2008.

[14] A. Rolãn, A. Luna, G. Vázquez, D. Aguilar, “Modeling of a variable speed wind turbine with a permanent magnet synchronous generator”, IEEE Int. Symp. on Indust. Electron., ISIE, pp. 734-739, 2009.

[15] E. Sambrata, J. Raharijaona, G. Barakat, B. Dakyo, “Modeling and test of a PM synchronous generator based small stand-alone wind energy converter”, proc. EPE-IEEE PEMC, pp. 1591-1596, 2006.

[16] T. Tafticht, K. Agbossu, A. Chériti, “DC bus control of variable speed wind turbine using a buck-boost converter”, IEEE Power Engineering Society General Meeting, 2006.

[17] J.S. Thongam, P. Bouchard, H. Ezzaidi, M. Ouhrouche, “Wind speed sensorless maximum power point tracking control of variable speed wind energy conversion systems”, proc. IEEE IEMDC, pp. 1832 - 1837, 2009.

[18] R.J. Wai, C.Y. Lin, Y.R. Chang, “Novel maximum-power-extraction algorithm for PMSG wind generation system”, IET Electr. Power Appl., Vol. 1, No 2, pp. 275-283, 2007.

[19] Linear Technology, “LTsice IV high performance simulator and schematic capture”, available at http://www.linear.com/designtools/software/#LTspice (dec. 2011).

Figure 9. Simulation results showing the output power and the (true and estimated) rotor speed obtained by the proposed system with a constant wind speed.

Figure 10. Simulation results showing the varying wind speed and the resulting rotor speed and output power obtained by the proposed system.

Figure 11. Simulation results showing the rotor speed and the output power obtained by a purely passive solution with the same wind speed model and the same load as in Fig. 10.

Figure 12. Simulation results showing the rotor speed and the output power obtained by a HCS solution with the same wind speed model and the same load as in Fig. 10.