Pitch angle control for grid-connected variable-speed wind turbine system using fuzzy logic: A comparative study

Abstract

Pitch angle control is considered as a practical technique for power regulation above the rated wind speed. As conventional pitch control commonly the proportional–integral controller is used. However, the proportional–integral type may well not have suitable performance if the controlled system contains nonlinearities as the wind turbine system or the desired wind trajectory varied with higher frequency. In the presence of modeling uncertainties, the necessity of methods presenting controllers with appropriate performance as the advanced control strategies is inevitable. The pitch angle based on fuzzy logic is proposed in this work. We are interested to the development of a wind energy conversion system based on permanent magnet synchronous generator. The fuzzy logic controller is effective to compensate the nonlinear characteristics of the pitch angle to the wind speed. The design of the proposed strategy and its comparison with a conventional proportional–integral controller are carried out. The proposed method effectiveness is verified using MATLAB simulation results.

Keywords

Wind energy permanent magnet synchronous generator pitch angle proportional–integral controller fuzzy logic controller

Introduction

Motivated by the concerns on energy availability and environmental safety, the wind system installation has been considerably increased (Rezaei and Salmasi, 2014). Commonly, wind energy conversion systems (WECSs) can be operated with constant or variable-speed operations. The variable-speed generation system is more attractive than the fixed-speed one because of its impact in the wind energy production improvement as discussed by Lin and Hong (2011). In this context, several researchers have developed the variable-speed wind turbine control strategy. In fact, to optimize the energy produced from WECS, a control system based on pitch angle regulation is generally required. The pitch angle control aims to optimize the wind turbine power output below rated wind speed as the pitch setting should be at its optimum value to generate maximum power and to minimize the fatigue loads of the turbine mechanical component. Various strategies of pitch control have been suggested in the literature. Some investigators (Jauch and Nussel, 2014) have proposed a contactless pitch angle measurement system that does not interfere with the turbine control system, while other researchers have addressed the pitch angle issue by the development of some control techniques.

In fact, Ben Smida and Sakly (2014) have compared several conventional methods of pitch angle control and their comparative performance study has shown that the control strategy where the generator power is used as the controlling variable is the most robust classical technique. The use of proportional–integral–derivative (PID) regulator has been developed by Vidal et al. (2012), while Qu and Qiao (2009) have proposed the nonlinear dynamic chattering torque control and the proportional–integral (PI) pitch angle regulator. Geng and Yang (2009) have developed a robust pitch (RP) controller for variable-speed variable-pitch wind turbine generator systems (VSVPWTGS). However, these conventional controllers require the knowledge of system’s dynamics and generally, their performance is limited by the highly nonlinear characteristics of the wind turbine. In this framework, an enormous amount of work has been devoted to investigate the pitch angle control challenge. Advanced control methods as fuzzy logic controller (FLC) are commonly employed when the system is not well known or contains nonlinearities as confirmed by Musyafa et al. (2010).

This article suggests the design of an optimal pitch angle controller based on FLC for grid-connected variable wind speed turbine. The proposed technique is studied and compared with a conventional PI controller. The studied WECS, given in Figure 1, is designed as permanent magnet synchronous generator (PMSG) connected to the grid via back-to-back pulse width modulation (PWM) converters.

Figure 1.

Overall control levels in WECS.

In our study, we started by the development of the wind turbine model, and then the different proposed pitch angle strategies are presented. Section “Simulations results” will be interested to the simulation results of the comparative study between the suggested techniques. Later on, the model of the converters and the network are developed and finally, before concluding, the performance of the grid-side control strategies is discussed using some simulation results.

Wind turbine system

Wind turbine model

The output power of the wind turbine is expressed by

P_{w} = \frac{1}{2} ρ π R^{2} V_{w}^{3} C_{p} (λ, β)

(1)

where ρ is the air density, A is the turbine swept area, and $V_{w}$ is the wind speed.

The power coefficient $C_{p}$ is a nonlinear function depending on the tip–speed ratio (TSR), λ and β blade pitch angle. It is given by

C_{p} (λ, β) = 0.53 [\frac{151}{λ_{i}} - 0.58 β - 0.002 β^{2.14} - 13.2] \times \exp (\frac{- 18.4}{λ_{i}})

(2)

where

λ_{i} = \frac{1}{\frac{1}{λ - 0.02 β} - \frac{0.003}{β^{3} + 1}}

(3)

The TSR is explicit by the following expression

λ = \frac{R Ω}{V_{w}}

(4)

Using equation (2), the typical $C_{p}$ versus $λ$ curve is shown in Figure 2.

Figure 2.

$C_{p}$ versus $λ$ .

The turbine torque is defined as the ratio of the mechanical power to the rotational speed

T_{m} = \frac{P_{w}}{Ω}

(5)

The mechanical speed of the turbine is determined from the fundamental equation of the dynamics as

J \frac{d Ω}{d t} = T_{m} - T_{e m} - f Ω

(6)

Wind turbine operating regions

The typical power control regions of wind turbine, as developed by Ben Smida and Sakly (2015), are shown in Figure 3. Three wind speeds are considered as limits of this division: the cut-in wind speed (V_cut_-in), the rated wind speed (V_rated), and the cut-out wind speed (V_cut_-out). For the wind turbine model considered in this study, the values of V_cut-in, V_rated, and V_cut-out are 6, 10, and 13 m/s, respectively.

Figure 3.

Operational modes of a wind turbine considering limitations.

In region I, the wind turbine is at stop state while the wind speed is lower than V_cut-in. Therefore, the generator torque is 0 and wind turbine cannot generate power. In this region, the pitch angle usually is set to 90°, while in the partial load region, region II, the wind speed is limited between V_cut-in and V_rated and the main objective of the control in this region is maximizing power generated by the wind turbine.

The maximum power is obtained using the maximum power point tracking (MPPT) strategy that adjusts automatically the ratio speed at its optimum value. When regulating the system under the specification of maximum power, it must be considered that turbine power must never be upper than generator rated power. The output power must be limited when generator rated power is attained at rated wind speed, $λ_{o p t}$ . The equation below, developed by Hong et al. (2013), indicates the relationship between turbine power and turbine speed at maximum power

P_{M P P T} = K_{o p t} Ω^{3}

(7)

where

K_{o p t} = \frac{1}{2} \frac{ρ π R^{5} C_{p \max}}{λ_{o p t}^{3}}

(8)

In the full load region, region III, the wind speed is higher than V_rated but lower than V_cut-out. The principle purpose of the control strategy in this region is maintaining the generator power $P_{g}$ around the rated generator power $P_{g, r a t e d}$ .

In fact, in the case of high wind, it is necessary to limit the rotational speed to avoid the damage of the turbine and the electric machine. This limitation is obtained by the control of the pitch angle $β$ . In region IV, where the wind speed is higher than V_cut-out, the wind turbine must be shut down in order to protect wind turbine against the stresses and fatigue damages. In this case, the pitch angle usually is set to 90° and power generation is stopped.

The focus of this article is on full load region (region III) to design an optimal pitch controller.

Pitch angle control

Conventional PI controller

This section is interested in the designing of a discrete conventional PI controller to adapt pitch angle in response to different power output. By linearization as a first-order system, the power output is considered proportional to pitch angle $β$ as proposed by Senjyu et al. (2006)

β_{r e f} = \frac{Δ β}{Δ P} (P_{g} - P_{g, r a t e d}) + β_{0}

(9)

where $β_{0}$ is the initial pitch angle.

Taking into consideration the blade’s orientation system, a transfer function of the first order is introduced

β = \frac{1}{1 + τ_{b} s} β_{r e f}

(10)

The control scheme of the conventional PI controller is shown in Figure 4.

Figure 4.

Control scheme of the conventional PI pitch angle controller.

The PI gain parameters are reported in Table 1.

Table 1.

Conventional PI controller parameters.

Parameter	Value
Proportional gain	1.5
Integral gain	0.07
Sampling time	10⁻³ s

Proposed fuzzy pitch angle controller

As discussed by Kasiri et al. (2012), the pitch angle is a nonlinear function of the generator power so the FLC could be a reasonable solution as it is considered as a model-free type of nonlinear control algorithms.

A FLC scheme comprises three functioning blocks, namely, fuzzification, inference engine, and defuzzification as shown in Figure 5.

Figure 5.

Block diagram of the FLC.

During the fuzzification stage, numerical input variables from the control object are converted into linguistic variables using five fuzzy levels called NL (negative large), NS (negative small), ZE (zero), PS (positive small), and PL (positive large).

The developed FLC consists of two input signals and one output signal. The difference between the active power and the rated value ΔP and the variation of the power error δ (ΔP) are used as the controller inputs, in which ΔP and δ (ΔP) are defined as

Δ P = P_{g} (K) - P_{g, r a t e d} (K)

(11)

δ (Δ P) = Δ P (K) - Δ P (K - 1)

(12)

A fuzzy PI control block is depicted in Figure 6.

Figure 6.

Control scheme of the proposed fuzzy logic pitch angle controller

The specific variable’s membership functions are given in Figure 7.

Figure 7.

The membership function of FLC: (a) membership functions of the power error, (b) membership functions of the variation of the power error, and (c) membership functions of the output $β_{r e f}$ .

In this work, the FLC inference method requires 25 fuzzy rules presented in Table 2, and these rules are applied to find the pitch angle reference

Table 2.

Fuzzy rules.

β _ref	ΔP
δ(ΔP)		NL	NS	ZE	PS	PL
	NL	NL	NL	NL	NS	PS
	NS	NL	NL	NS	ZE	PS
	ZE	NL	NS	ZE	PS	PL
	PS	NS	ZE	PS	PL	PL
	PL	NS	PS	PL	PL	PL

Generator model

The dynamic equations of the PMSG stator currents in the Park model are given by

{\begin{cases} \frac{d i_{s d}}{d t} = \frac{1}{L_{s}} (v_{s d} - R_{s} i_{s d} + L_{s} p Ω_{t} i_{s q}) \\ \frac{d i_{s q}}{d t} = \frac{1}{L_{s}} (v_{s q} - R_{s} i_{s q} - L_{s} p Ω_{t} i_{s d} - p Ω_{t} φ) \end{cases}

(13)

The electromagnetic torque is derived from the following equation

C_{e m} = p φ i_{s q}

(14)

Simulations results

A series of simulation tests were performed using MATLAB/SIMULINK software.

During 40 s, we have applied to the wind turbine model a variable wind profile between 4 and 13 m/s with an average value of 10 ms⁻¹. This sequence is obtained by adding a turbulent component to a slowly varying signal represented in Figure 8. The wind turbine is dimensioned to provide a nominal power at a nominal speed of 10 ms⁻¹. Beyond this wind, it is necessary to protect the wind turbine against mechanical failures; therefore, we must limit its speed. This limitation will be obtained by the variation of the pitch angle illustrated in Figure 9. The more the pitch angle increases, the more the power coefficient decreases as given in Figure 10.

Figure 8.

Wind profile.

Figure 9.

Pitch angle variation for different methods.

Figure 10.

C_p variation for different methods.

The mechanical speed response and the generator output power variation are illustrated in Figures 11 and 12 for the studied methods. It is clear that next to the use of FLC technique, both the speed and power responses present less fluctuation ripples and are widely smoother in comparing with PI pitch angle controller’s responses.

Figure 11.

Generator speed variation for different methods.

Figure 12.

Generator power variation for different methods.

In order to analyze the comparative performance of the suggested techniques, three performance indices are considered in this study: the mean square error (MSE), the mean absolute error (MAE), and the mean percentage error (MPE). The results are tabulated in Table 3.

Table 3.

Performance comparison with various control methods.

	MPE (%)	MAE (%)	MSE (%)
FLC	0.0088	29.02	0.33
PI controller	0.018	65.8	1.83

The converters model

For the studied system, AC/DC/AC converters are connected between the wind generator and the grid side. The groups of two insulated gate bipolar transistors (IGBTs) associated to the same phase constitute the converter leg, and a switching function $γ_{k}$ is defined for each power switch as developed in Melício et al. (2011)

γ_{k} = {\begin{cases} 1, (S_{1 k} = 1 and S_{2 k} = 0) \\ 0, (S_{1 k} = 0 and S_{2 k} = 1) \end{cases} k \in {1, \dots, 6}

(15)

The index $k$ with $k \in {1, 2, 3}$ identifies a leg for the rectifier and $k \in {4, 5, 6}$ identifies the inverter one.

As ideal power switches are considered

\sum_{i = 1}^{2} S_{i k} = 1 k \in {1, \dots, 6}

(16)

The bus voltage $V_{d c}$ is expressed by

\frac{d V_{d c}}{d t} = \frac{1}{c} (\sum_{k = 1}^{3} γ_{k} i_{k} - \sum_{k = 4}^{6} γ_{k} i_{k})

(17)

The model and the control of the grid side

The grid model

The dynamic model of the grid in the Park model as developed in Zhang et al. (2011) is expressed by

{\begin{cases} V_{g_{d}} = V_{i_{d}} - R_{g} i_{g_{d}} - L \frac{d i_{g_{d}}}{d t} + ω l_{g} i_{g_{q}} \\ V_{g_{q}} = V_{i_{q}} - R_{g} i_{g_{q}} - L \frac{d i_{g_{q}}}{d t} - ω l_{g} i_{g_{d}} \end{cases}

(18)

where $U_{i_{d}}$ and $U_{i_{q}}$ are the (d–q) inverter voltage components, $L_{g}$ is the grid inductance, and $R_{g}$ is the grid resistance.

The active and reactive powers injected into the grid are calculated using equations (19) and (20)

P = \frac{3}{2} (V_{g_{d}} i_{g_{d}} + V_{g_{q}} i_{g_{q}})

(19)

Q = \frac{3}{2} (V_{g_{q}} i_{g_{d}} - V_{g_{d}} i_{g_{q}})

(20)

If d-axis of synchronous frame has aligned absolutely on the grid voltage, $U_{g_{q}}$ will be set at 0 and the powers will be expressed by

P = \frac{3}{2} V_{g_{d}} i_{g_{d}}

(21)

Q = - \frac{3}{2} V_{g_{d}} i_{g_{q}}

(22)

The basic structure of active and reactive powers (PQ) inverter control is shown in Figure 13; two PI controllers are proposed to control the injected power flow. A d-axis PI controller is used to control active power, and a q-axis PI controller controls reactive power. The d-axis reference is generally obtained from DC-link voltage controller, and the q-axis reference is set to 0 to get unity power factor.

Figure 13.

Block diagram of PQ inverter controller.

The parameters of the PI controllers are chosen to attain a fast and well-damped response of the DC-link voltage and active power.

The grid-side simulation results

As confirmed by section “Simulation results,” the suggested FLC technique is more robust to the wind profile variation than the PI method; so taking into consideration the wind profile given by Figure 7, the simulation of the fuzzy pitch angle controlled variable wind turbine connected to the grid is carried out in this section.

The bus voltage response is illustrated in Figure 14 while Figure 15 gives the grid voltages for the studied situation. Simulation results show that the bus voltage tracks its reference (1000 V) and the grid voltages adapt the wind speeds change continuously. Figure 16 gives the response of the grid currents as it can be deduced that the injected currents are sinusoidal with a constant frequency (50 Hz). The reactive power is kept at 0 (unity power factor) as shown in Figure 17. However, Figure 18 confirms that the active power is proportional to the wind speed.

Figure 14.

Bus voltage.

Figure 15.

Grid voltage.

Figure 16.

Grid currents.

Figure 17.

Reactive power.

Figure 18.

Active power.

Conclusion

In this article, a grid-connected WECS based on PMSG was proposed. In order to maximize the exploited power from the wind, an MPPT technique was developed and a comparative study between a fuzzy logic and a conventional PI pitch angle controller was suggested. The main purposes of the proposed pitch angle controller are to regulate output power during above rated wind incidents and smooth wind power fluctuations during below rated wind incidents by dynamic pitch actuation. The grid-side control was also dealt in this study and simulation results demonstrate that the three-phase PWM inverter controlled the DC-link voltage and allowed delivering only the active power into the grid with unit power factor, thus exploiting maximum wind power.

Footnotes

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.

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