Comparative study of four MPPT for a wind power system

Abstract

The Maximum power point tracking (MPPT) command makes it possible to find the optimal operating point of the wind generator following variations in the wind. Its principle is based on the automatic variation of the power coefficient to continuously maximize the power of the wind generator. This work is an attempt to study and discuss four most popular types of MPPT techniques such as: Perturbation and Observation (P&O), optimal torque (OT), On-Off control, and tip speed ratio (TSR). The Matlab-Simulink environment is used to analyse and then interpret the simulation results of these algorithms, and therefore show the performance and limitations of each algorithm. The comparison shows the efficiency and the superiority of the OT technique compared to the other MPPTs studied.

Keywords

Wind turbine permanent magnet synchronous generator (PMSG)maximum power point tracking (MPPT)on-off control perturbation and observation (P&O)optimal torque (OT)tip speed ratio (TSR)

Introduction

Wind power conversion systems have gained wide attention as a renewable energy source due to depletion of fossil fuel reserves and environmental concerns resulting directly from the use of fossil fuels and sources of energy nuclear energy (Manwell et al., 2010). Wind power is plentiful and varies continuously as the wind speed changes throughout the day (Manwell et al., 2010).

The more measures a strategy needs, the more equipment must be installed, which increases the cost and complexity of the control system and reduces its reliability. The amount of power produced by a wind power conversion system depends on how accurately the peak power points are tracked by the proposed controller regardless of the type of generator used (Anaya-Lara et al., 2011). In addition, correct wind speed measurements are difficult to achieve and most of the time, proper filtering techniques must be used (Anaya-Lara et al., 2011; Manwell et al., 2010). To avoid this, different strategies for controlling MPPT have been developed and are widely discussed in the literature.

The maximum power point technique (MPPT) is of the utmost importance in renewable energy conversion systems. Due to the high inertia of a wind power system, the MPPT methods studied for wind power systems are more difficult than those for the photovoltaic system (Anaya-Lara et al., 2011; Jain, 2011). The efficiency of variable speed wind turbines relies on the performance of maximum power point tracking (MPPT) techniques. However, for a certain wind speed there is only one rotor speed available which is responsible for the maximum power output known as the maximum power point (MPP) (Jain, 2011).

In general, these MPPTs can be classified into two categories. The first type is called the direct method such as Incremental Conductance MPPT (INC) and Hill Climb Search (or Perturb and observ) (Sher et al., 2015). The other type is indirect support such as speed control (TSR) (Nasiri et al., 2014), optimal torque control (OT) (Kumar and Chatterjee, 2016) algorithm, and power signal feedback (PSF) algorithm (Elbeji et al., 2020b).

In this work, four MPPTs such as TSR (Hannachi et al., 2020a), OT (Hannachi et al., 2020b), P&O (Mousa et al., 2019), and On Off (Hannachi et al., 2019) will be studied as it is presented in Figure 1. For all implemented MPPTs, the tilt angle is set to zero since we are devoting the study just to the rotor speed or torque optimization part.

Figure 1.

The wind energy conversion chain studied.

This article is organized in the following structure: Section II described the mathematical model of the studied chain which given by the wind turbine and the permanent magnet synchronous generator (PMSG) associated with a controlled rectifier. The four MPPTs TSR, OT, P&O, and On Off are respectively described in the following sections. In section VII, the results of the demonstrative simulation in the MATLAB environment are performed and compared to each other in order to show the efficiency of the proposed method. This work is finalized by a conclusion.

WECS system modeling

The proposed wind turbine conversion system consists of a three-blade horizontal axis rotor, a permanent magnet synchronous generator, and a controlled rectifier.

The mechanical power and the mechanical torque on the rotor shaft of the wind turbine, where ρ defines the air density V presents the wind speed and R is the rotor radius, are given respectively by Hannachi and Benhamed (2017):

P_{m} = P_{w} C_{p} = \frac{1}{2} ρ π R^{2} V^{3} C_{p}

(1)

T_{m} = \frac{1}{2 Ω} ρ S_{c} ν^{3} C_{p} (β, λ)

(2)

Where C_p present the coefficient of power conversion.it is calculated as a function of the blade pitch angle β and the tip speed ratio λ as given (Hannachi and Benhamed, 2017):

C_{p} (λ, β) = 0.5176 (\frac{116}{λ_{i}} - 0.4 β - 5) e^{(\frac{- 21}{λ_{i}})} + 0.006795 λ

(3)

λ_i is given by:

λ_{i} = \frac{1}{\frac{1}{(λ + 0.08 β)} - \frac{0.035}{β^{3} + 1}}

(4)

and

λ = \frac{Ω R}{V}

(5)

The dynamic of the machine is given by the following mechanical equation (Elbeji et al., 2020a):

J \frac{d Ω}{dt} + f Ω = T_{m} + T_{em}

(6)

Where J presents the total moment of inertia of the machine and f is the viscosity coefficient of friction.

The model of the permanent magnet synchronous generator in the reference d–q is presented in the following system of equations (Elbeji et al., 2020; Hannachi and Benhamed, 2017). ω is the electrical pulsation of the PMSG voltages, p is the number of pairs of poles, L_d, L_q are respectively the inductances of the direct and quadrature axis and Ψ_f inductive flux.

{\begin{matrix} u_{d} = - R_{s} i_{d} -_{s} L_{d} \frac{d i_{d}}{dt} + ω L_{q} i_{q} \\ u_{q} = - R_{s} i_{q} -_{s} L_{q} \frac{d i_{q}}{dt} - ω L_{d} i_{d} + ω Ψ_{f} \end{matrix}

(7)

Where ω is definite with:

ω = p Ω

(8)

The electromagnetic torque T_em is specified by:

T_{em} = \frac{3}{2} p ((L_{d} - L_{q}) i_{q} i_{d} - Ψ_{f} i_{q})

(9)

The machine used in this paper is with smooth poles (L_d = L_q) so T_em must be directly proportional to i_q as it is indicated in the following equation (Hannachi et al., 2020b; Hannachi and Benhamed, 2017):

T_{em} = - \frac{3 p}{2} Ψ_{f} i_{q}

(10)

The equation of controlled rectifier is given by:

c \frac{d ν_{dc}}{dt} = (S_{a} i_{a} + S_{b} i_{b} + S_{c} i_{c}) - i_{dc}

(11)

MPPT TSR strategy

This is a straightforward strategy to be executed as only the measured wind speed is required for the input of the MPPT controller. Subsequently, the rotor reference speed will be estimated for the speed controller based on information of the optimal peak speed ratio (λ_opt) and the radius of the turbine. The optimal TSR can be theoretically or experimentally determined and can be recorded as a reference (Figure 2). The objective is to keep the TSR at its optimum value by measuring the speed of the turbine and the instantaneous speed of the wind. Essentially, in order to control the optimum rotor speed, a PI type speed regulator is adjusted (Hannachi et al., 2020a; Ragheb and Ragheb, 2011).

Figure 2.

Functional diagram of the TSR control.

In order to extract the maximum power from the generator, the speed of the turbine must be changed according to the wind speed so that the optimum top speed is maintained, which ensures the optimization of the power coefficient. For the speed control of the synchronous generator with permanent magnets, the reference speed of the wind turbine is obtained by Ragheb and Ragheb (2011):

Ω_{ref} = \frac{λ_{opt} V_{ν}}{R}

(12)

MPPT OT strategy

The OT technique involves operating the wind turbine to produce the optimum torque required to there by produce optimum power (Figure 3). The reference electromagnetic torque is calculated at the optimum operating point with the pair (C_p_max, λ_op) given by Hannachi et al. (2020b) and Thongam et al. (2012):

T_{em - ref} (Ω) = \frac{0.5 ρ π R^{5} Ω^{2} C_{p max}}{{λ_{op}}^{3}}

(13)

Figure 3.

Functional diagram of the OT control.

The reference torque is proportional to the square of the speed of the generator in this form (Hannachi et al., 2020b):

T_{em - ref} (Ω) = K_{opt} Ω^{2}

(14)

With

K_{opt} = \frac{0.5 ρ π R^{5} C_{p max}}{{λ_{op}}^{3}}

(15)

MPPT P&O strategy

The Perturbation and Observation (P&O) is a mathematical optimization technique defined in reason to search for the local optimum point of a given function (Figure 4). It is generally used in wind systems to define the optimal operating point since it does not require prior knowledge of the characteristic curve of the wind turbine and it is simple (Mousa et al., 2019; Sher et al., 2015).

Figure 4.

P&O control for MPPT.

The principle of this technique is illustrated in Figure 5. We begin to disturb a control variable in small steps and observe the resulting changes in the target function until the slope becomes zero.

Figure 5.

Functional diagram of the P&O control.

The whole process starts with calculating the rotor speed and turbine power. These two values are entered for the MPPT controller to estimate the new rotor speed reference. During the calculation process, the previous values of the rotor power and speed should be saved in the memory block (Mousa et al., 2019). After that, the new speed reference will be ready for use. In this method, the wind speed measurement is not necessary, so mechanical sensors are not used. Therefore, this control method is more reliable and cost effective (Kumar, 2017).

MPPT ON-OFF strategy

This technique consists of giving a reference torque as a function of the turbine parameter (Figure 6). This desired couple is written in the form (Hannachi et al., 2019):

T_{emref} = u^{n} + u^{eq}

(16)

Where uⁿ is an alternative that switches between ±α such as α ≻ 0

Figure 6.

Functional diagram of the On–Off control.

u^eq ensures that the system is operating at the optimum point. When this point is reached, it has the function of stabilizing the behavior of the system (Kahla et al., 2015).

u^{eq} = A ν_{s}^{2}

(17)

The term A is desired by

A = 0.5 π ρ R^{3} \frac{C_{p} (λ_{opt})}{λ_{opt}}

(18)

Simulation results

Regarding this study, for the MPPT P&O we have fixed the change step at 0.05. Thus, we used the PI regulator for the MPPT OT, TSR, and On Off whose parameters associated with each technique are given in the Table 1. We set the pitch angle to zero and we study the variation of power coefficient and the speed ratio. All the parameters of the machine and the wind turbine are shown in Table 2. MPPT techniques are implemented on the SIMULINK-MATLAB. The simulation results are given in the figures below.

Table 1.

PI regulator parameter values used for each MPPT.

Regulator parameter, MPPT	Kp	Ki
OT	3	0.3
TSR	0.348	3.293
On_Off	3	0.6

Table 2.

Parameters of the wind turbine and those of the machine.

Parameter	Values
$ρ$	1.225 kg m^–3
R	2 m
P_n	3.8 kW
R ^a	0.82 Ω
L_s	15.1e^∼3.3 H
J	99e^–4 kg m²
F	10^–3 N m s rad^–1
$φ$	0.5 Wb
P	4

To compare the established MPPT strategies, for a wind speed lower than the nominal therefore in the MPPT zone, a variable wind profile is applied to the turbine of which it varies between 6 m/s and 10 m/s as shown in the Figure 7.

Figure 7.

Wind speed profile.

As soon as the optimal power point is attacked (Figure 8), each of the implemented MPPT algorithms tries to keep this operating point in order to extract the maximum power from the wind even with the variation of the wind. Both P&O and On-Off strategies give results further away from optimal conditions (Cp_max and ℷ_max) when comparing by these competitors. For MPPT TSR and OT are effective whose power coefficient value is almost equal to 0.48, which is the optimal value, with a small variation for TRS MPPT.

Figure 8.

Coefficient of power.

Figure 9 describes the variation of speed ratio which varies between 8 and 8.4 for the OT and TSR strategies and takes the value between 9 and 9.5 for P&O and On-Off MPPT. So the rotor speed always tries to keep up with the variation of the wind speed (Figure 10). In addition, the turbine torque changes in the same way as the corresponding rotor speed but each MPPT takes on a different value. The Mechanical speed is illustred in Figure 11.

Figure 9.

Tip speed ratio.

Figure 10.

Mechanical torque.

Figure 11.

Mechanical speed.

By comparing the curves obtained by the OT MPPT (Figures 8 and 9) by the optimal condition in Figure 12, we observe the efficiency and the superiority of the strategy of this technique (OT) whose power coefficient C_p is identical to the optimal value (C_p = 0.48). Thus, the speed ratio takes the value 8.1 which is the optimal value as it is indicated in Figure 12.

Figure 12.

C_p versus lambda.

At the instant t = 15 s, we make a projection and we take the values obtained for each MPPT for the power coefficient and the speed ratio of which they are present in Table 3.

Table 3.

The optimal values obtained for each MPPT.

	β	ℷ
TSR	0.47	8.3
OT	0.48	8.1
P&O	0.45	9
On–Off	0.41	9.3
The optimum values sought from the turbine	0.48	8.1

A theoretical comparative study between the strategies studied is detailed in Table 4 based on the speed of the speed response time, the need for the strategy, a measurement of the wind, requires a memory of the behavior of the wind turbine and formations prerequisites of the turbine parameter.

Table 4.

Comparative study of the MPPT strategies studied.

Characteristics	TSR	OT	P&O	On–Off
Response time	Slow	Rapid	Rapid	Slow
Necessary wind measurements	Yes	No	No	Yes
Wind turbine parameters required	Yes	Yes	Non	Yes
Requires a memory of the behavior of the wind turbine	No	No	Yes	No

Conclusion

This paper was devoted to the study and the modeling of a wind chain. first, a study for the types of MPPT is described. Four different types of MPPT algorithms TSR, OT, P&O, and On Off are presented, secondly. All theoretical background is explained, then the ideas are implemented using the MATLAB environment for varying wind speeds. Therefore, the rotor speed response of the generator and the torque responses of the generator are observed. Thirdly, a comparative study is carried out between these described techniques. The latter give generally acceptable results but with a difference in performance. The simulation results show the efficiency of OT compared to the other proposed MPPTs.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Marwa Hannachi

Omessaad Elbeji

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