## 1. Introduction

Renewable energy resources, especially wind energy, are attracting great attention with the depletion of existing fossil fuel deposits and increasing concerns about CO

_{2} emissions. Since the late 1990s, variable speed constant frequency (VSCF) wind energy conversion systems (WECS) have been widely adopted in order to maximize wind energy utilization [

1,

2]. The doubly-fed induction generator (DFIG) and direct-drive permanent magnet synchronous generator (PMSG) are the most popular systems for VSCF wind energy conversion. The direct-drive PMSG has attracted more and more attention due to its advantages of high efficiency and high reliability. The configuration of a typical direct-drive WECS with PMSG is shown in

Figure 1 [

3,

4,

5]. The PMSG converts the mechanical power from the wind turbine into ac electrical power, which is then converted to dc power through a converter with a dc link to supply the dc load. By using an additional inverter, the PMSG can supply the ac electrical power with constant voltage and frequency to the power grid.

**Figure 1.**
Configuration of a direct-drive PMSG WECS.

**Figure 1.**
Configuration of a direct-drive PMSG WECS.

To maximize the use of wind energy when the wind speed is below the rated speed, the maximum power point tracking (MPPT) of the system is indispensable. The MPPT is realized by controlling the inverter which is connected to the generator. Previous research has focused on several types of MPPT methods, namely optimum tip speed ratio (TSR) control, hill climb searching (HCS) control, power feedback control and fuzzy-logic-based control [

6,

7,

8,

9,

10,

11,

12].

The TSR method regulates the generator speed to maintain the optimum TSR. The control is easy to understand but hard to achieve due to the need to know the exact wind speed and wind turbine characteristics. HCS control on the other hand does not require any prior knowledge about the system and is absolutely independent of the turbine, generator and wind characteristics [

13]. However, two serious problems with the HCS method are the speed-efficiency tradeoff and the wrong directionality under rapid wind change. The HCS strategy is optimized in some papers [

13,

14], but the algorithm and control procedure are commonly complex, which make it difficult to execute.

The power feedback control is implemented according to calculations based on the generator speed. The wind speed is not needed, but the wind turbine characteristics are indispensable [

15]. Furthermore, the power losses should be considered in order to determine the accurate given maximum power. However, the power losses change with the generator rotor speed, which makes it difficult to determine the maximum power point accurately.

The fuzzy-control-based MPPT scheme is good, but somewhat complex to implement [

8]. However, the adaptive fuzzy controller for MPPT control designed by Galdi

et al. in [

16,

17,

18] can implement sensorless peak power tracking and overcome some disadvantages of classical methods. The maximum power can be estimated through a Takagi-Sugeno-Kang (TSK) fuzzy controller by measuring the rotor speed and power generated by the generator without measuring wind speed and wind turbine parameters.

To overcome these drawbacks of the traditional HCS and power feedback MPPT methods, some effective measures are taken in this paper. Its objective is to present an effective optimum current given (OCG) MPPT method combining the advantages of the power feedback method and the HCS method without knowing the wind speed and turbine characteristics. Besides, the proposed method can extract the maximum power point more exactly and steadily than traditional HCS control, especially when the wind speed changes quickly. Furthermore, the MPPT control will not be influenced by the change of power losses through estimating the exact loss torque compared to the power feedback MPPT. The proposed MPPT method is implemented in a WECS based on a PMSG and compared with the traditional TSR control to verify the MPPT efficiency. The experimental results demonstrate the feasibility and effectiveness of the proposed strategy.

## 3. Proposed MPPT Algorithm

#### 3.1. OCG MPPT Method

The novel MPPT control strategy in this paper is proposed based on the theory of the conventional power feedback control and HCS control. According to (4), the maximum power of the wind turbine P_{max} is a cubic function of the generator speed. Traditional power feedback control meets the maximum power point by measuring the output power or the output torque and regulates it based on the cubic or square of generator speed. Although the optimal power can be calculated easily, however, the power or torque feedback loop will reduce the MPPT response speed and accuracy due to the quickly changing wind and the inertia of the mechanical system. Also, as mentioned before, the power losses which vary with the wind speed cannot be ignored and are difficult to estimate exactly.

Therefore, the optimum current given (OCG) MPPT control strategy is proposed here based on the PMSG model for improving the traditional power feedback method.

i_{d} = 0 current control strategy is commonly used for the vector control for the PMSG due to the simplicity and effectiveness [

20]. When adopting

i_{d} = 0 control, (9) can be simplified as:

Then the electromagnetic torque is only determined by the

q-axis current

i_{qs} assuming that the permanent magnet flux is constant. Therefore, the PMSG can obtain the optimum torque by giving the optimum

i_{qs}. Furthermore, the maximum power point can be achieved when the torque

versus speed meets the optimum curve shown in

Figure 3b. In other words, the MPPT can be realized when the optimum

i_{qs} is given.

The iron loss, copper loss, mechanical loss and stray loss cannot be ignored when the PMSG is in operation. As shown in (8) and (9), the copper loss has been considered in the derivation of the electromagnetic torque. Then only the iron loss, mechanical loss and stray loss are associated with the loss torque expressed as

T_{loss}. The loss torque can be divided as:

The iron loss mainly varies along with the generator speed, so the iron loss torque T_{loss_Fe}, which equals iron loss divided by speed, remains relatively constant. The mechanical loss and the stray loss only account for a small percentage of the total losses, thus the mechanical loss torque T_{loss_m} and the stray loss torque T_{loss_s} can be regarded as constant values. Therefore, the loss torque T_{loss} basically remains constant in operation.

The maximum torque of PMSG calculated by (5) is an ideal value and the actual maximum electromagnetic torque

T_{e}^{*} can be expressed as:

According to the aforementioned equations, the optimum current can be derived as:

#### 3.2. Estimation of T_{loss}

In the experiment, T_{loss} can be obtained based on the theory of dichotomy according to the characteristics of the PMSG. Based on the wind characteristics, a maximum power generated by the PMSG corresponds to a constant wind speed. The maximum loss torque T_{1} and minimum loss torque T_{2} are given first to be applied in the OCG MPPT on the basis of the experience and machine characteristics. Then the generated powers P_{1} and P_{2} by the PMSG under these two loss torques can be observed and compared. One of the next boundary loss torque values can be confirmed according to the result of comparing the two generated powers P_{1} and P_{2}.

The OCG tests will not stop until the difference between the two generated powers is less than a given constant value

ξ. Then the fairly accurate

T_{loss} can be obtained after several tests. The detailed loss torque estimation principle can be seen from the flow chart shown in

Figure 4.

**Figure 4.**
Flow chart of the T_{loss} estimation algorithm.

**Figure 4.**
Flow chart of the T_{loss} estimation algorithm.

#### 3.3. k_{opt} Obtained by HCS MPPT Method

The optimum current given control method still has the problem that the constant coefficient k_{opt} is determined by the wind turbine and therefore not so easy to measure. Furthermore, as time goes on, the wind turbine characteristics will change a little which is influenced by the external environments, then the k_{opt} will be labile.

The conventional HCS method can reach the maximum power point (MPP) without the need of

k_{opt} as shown in

Figure 5. Once the peak is detected and extracted, the coefficient

k_{opt} can be calculated and serve for the optimum current given MPPT control.

**Figure 5.**
HCS control algorithm.

**Figure 5.**
HCS control algorithm.

However, traditional HCS method cannot stop searching when the climbing reaches the MPP then the speed oscillates around the MPP as shown in

Figure 5 with the red line labels [

7]. Here two checking rules are given to ensure the MPP is detected accurately. The two checks are given as follows:

The first rule (14) means that the power variation ΔP(k) should be less than a threshold δ. The second rule (15) means that the gradient of the ω versus P curve should be less than a threshold θ. The climbing search will be stopped when both the two checks are true and then the MPP is detected. According to the actual environment of the wind fields, the improved HCS could be applied to obtain the k_{opt} for some time which will ensure the accuracy of the MPPT control.

#### 3.4. Proposed MPPT Method

After the coefficient

k_{opt} is detected the optimum current given by MPPT can be applied successfully with no need of the wind characteristics. The control configuration of the PMSG with OCG MPPT is shown in

Figure 6. The generator speed is measured to calculate the optimum torque and then obtain the optimum current. Only the double current loops are needed in this MPPT strategy. Compared to the power feedback control method which needs the power loop, the proposed method is more convenient and responds more quickly.

**Figure 6.**
PMSG control configuration with the proposed OCG MPPT.

**Figure 6.**
PMSG control configuration with the proposed OCG MPPT.

#### 3.5. Imitation of Wind Turbine

Wind turbine imitation is indispensable in the experiment for the MPPT strategy verification. In this paper, an induction machine (IM) is used to imitate the wind turbine. Based on the imitation principle of wind turbine and the direct torque control (DTC) theory [

21], the control scheme of IM can be obtained as shown in

Figure 7.

The given torque of IM is decided by the wind speed and the actual generator speed according to Equations (2), (3) and

Figure 2. The IM with direct torque control can imitate the wind turbine well due to the fast response and superior dynamics.

**Figure 7.**
Control configuration of IM with DTC control.

**Figure 7.**
Control configuration of IM with DTC control.

## 6. Conclusions

This paper proposed a novel optimum current given MPPT control method for a permanent magnet direct drive wind energy conversion system. The strategy is based on the idea of the power feedback MPPT method and traditional HCS MPPT method and combines the advantages of both of them. A method for estimating the system loss torque is proposed and the improved HCS method is adopted periodically to ensure obtaining the exact wind turbine parameters.

The traditional power feedback MPPT needs the characteristics of the wind turbines. Besides, the given optimum power which is changed due to the change of the losses varying with the generator speed which will reduce the effectiveness of the MPPT control. The HCS MPPT will deteriorate its performance under rapidly changing wind conditions. The maximum power coefficient k_{opt} is obtained by improved HCS MPPT. Then the optimum current given MPPT is adopted with no need of the wind turbine characteristics. The loss torque used in the proposed method can be regarded as a constant and the MPPT effectiveness will not be influenced by the generator speed.

For verifying the effectiveness of the proposed MPPT method, simulation models are built and experiments are carried out. Both simulation and experimental results demonstrate that the proposed MPPT method is effective under the environment with quickly changing wind speed. Furthermore, the proposed strategy is compared with the traditional TSR method in the experiment and the results show that the generated power with the proposed MPPT control is comparable with the TSR method which tracks the optimum value in real time. Besides, the output power pulsation of the proposed method is smaller than the TSR method.