Dynamic Operation Loss Minimization for Permanent Magnet Synchronous Generator Based on Improved Model Predictive Direct Torque Control

Abstract

During permanent magnet synchronous generator (PMSG) operation, aside from improving the rapid response of torque and reducing the rippling of torque and flux to guarantee the operational reliability, the loss of the PMSG itself cannot be ignored either. Aiming at this problem, an improved model predictive direct torque control (MPDTC) method is proposed, which suppresses the torque ripple and achieves PMSG efficiency optimization. Firstly, based on the conventional MPDTC and the loss model of PMSG, the predicted stator active current is determined, which is utilized for obtaining the predicted torque. Secondly, combined with the generator loss model, the set value of the stator energetic current is obtained; combined with the wind power system maximum power point tracking method, the set value of generator torque is obtained. Thirdly, by converting the torque control error and current control error into a per unit value, the influence of the weight coefficient in the cost function on the control effect is reduced. Finally, the key results verified the effectiveness and superiority of the proposed control scheme by simulation and experiment.

1. Introduction

The wind power system has advantages such as a clean, short construction period, and low operation cost, it has already drawn worldwide attention in recent years. The various speed constant frequency (VSCF) generation system generates small impact and high-power factor, which is developing fast and replacing the conventional constant speed constant frequency (CSCF) system [1,2,3,4]. Since there is no gearbox and field winding loss in the generator, compared with a doubly-fed induction generator-based wind power system, the direct-driven PMSG-based wind power system has relatively high stability and efficiency, which makes it a primary generator type of the VSCF system [5,6].

The PMSG extracts the maximum wind power by controlling the rotational speed. The most popular maximum wind power point tracking methods include the tip speed ratio (TSR) control, perturbation and observation control, and power signal feedback control [7]. In the TSR control, as the speed of the winds changes, the rotational speed must be changed accordingly to maintain the optimal tip speed ratio at all times, despite its promising features including fast response speed and simplicity, the TSR control needs kind of sensors to measure the speed. The key to perturbation and observation control is located in the choice of step length, which can hardly consider both rapid response and stable output power. The power signal feedback control can implement the maximum wind power point tracking method by controlling the optimal power curve or optimal torque curve, which avoids wind speed measurement and gains high stability output power. This method can also reach a relatively high conversion rate on small and medium-size generators.

The high-performance control scheme of PMSG includes vector control (VC) and direct torque control (DTC). The DTC eliminates the complex coordination transformation, which can estimate the optimal torque according to the generator speed directly [8,9]. This method has a rapid response for both torque and speed, and it can precisely trace the maximum power point by combining it with power signal feedback control [10].

Since the conventional DTC with a switching table adopts a hysteresis controller, changes in speed and load will lead to unstable switching frequency, bus voltage fluctuation and stator resistance variation, which causes apparent rippling in torque and flux [11]. Therefore, several control methods have been proposed to improve the performance of DTC, including DTC based on torque angle, DTC based on space vector PWM, deadbeat DTC, and model predictive DTC [12,13,14,15]. In [16], a novel MPDTC scheme based on PWM modulation is proposed. Firstly, the cost function of model predictive control is used to replace the hysteresis comparator. According to the torque and flux error of the current control cycle, the voltage vector that minimizes the torque and flux error in the next control cycle is found in the six non-zero voltage vectors, and the duration of the effective voltage vector is calculated. Then, in the current control cycle, the calculated duty cycle generates a PWM wave according to the idea of vector modulation, that is, the combined voltage vector of two zero voltage vectors and the selected effective voltage vector controls the inverter to turn on. In [17], aiming at the problems of strong parameter dependence and a large amount of calculation in the traditional MPDTC algorithm, an improved PMSG MPDTC is designed. Firstly, the full order sliding mode observer is used to observe the equivalent back electrodynamic force in the static coordinate system, and then the stator flux and torque in the static coordinate system are predicted according to the observed equivalent back electrodynamic force and the sampled stator current, which avoids the complex coordinate transformation operation, improves the parameter robustness and improves the dynamic characteristics of the system.

In [18], the PMSM predictive torque control method based on deadbeat theory is designed, which reduces the amount of calculation to a certain extent, but the weight coefficient still needs to be designed, and the loss of the motor is not considered. In [19], the loss model of interior PMSM is established based on the rotor flux-oriented vector control, and then, the optimal direct axis stator current value is put forward under control of minimum loss. Feedforward compensation is also introduced, which is commonly used in servo motor control to solve the problem caused by the efficiency optimization control algorithm with the slow dynamic response of the motor control system. However, the control efficiency of this method will be affected by the precision of generator parameters, and it does not consider ways to reduce torque rippling. In [20], the MPC-based method toward PMSG, provided a cost function with multi-target control and adjustable weight, which can reduce the switching loss. However, this method has not proposed a way to quantify the loss, and the system operation efficiency cannot be improved steadily either. Through the above analysis, the real-time minimum loss control for the system based on torque rippling reduction is still a problem confronted by the efficiency improvement of PMSG.

This paper, based on the maximum wind power tracking method of PMSG implemented by power signal feedback control, proposed an efficiency optimization MPDTC without a weight coefficient scheme for the PMSG to further improve the operation efficiency and control precision of PMSG. In the beginning, the PMSG loss model is established. A method to predict generator electromagnetic torque by predicting stator active current is provided based on the analysis of active and reactive current in the stator, electromagnetic torque of the generator and the stator flux. Moreover, the relation between turbine torque and generator speed is deduced, and the power signal feedback method to implement maximum wind power tracking based on MPDTC is discussed. In advance, by studying the relationship between the total loss of the generator and the stator active current, developed a cost function to replace the stator flux in the conventional MPC cost function with the stator active current, which can make the generator operate at a minimum loss. In order to reduce the influence of weight coefficient on the control effect, torque control error and current control error are converted into per unit value, on this basis, the cost function is redesigned. In the end, the scheme is analyzed and verified on the experiment platform.

Compared with the existing algorithms, firstly, the optimized efficiency MPDTC acquires the predictive value of the electromagnetic torque of the generator by predicting the active current of the stator, which improves the accuracy of the torque prediction; secondly, combined with the generator loss model, the set value of the stator energetic current is obtained, and the real-time minimum control for PMSG loss is implemented based on the reduction in torque rippling; thirdly, by converting the torque control error and current control error into per unit value, the influence of the weight coefficient in the cost function on the control effect is reduced.

2. MPDTC for PMSG

MPDTC significantly improves the concept of DTC, by replacing the lookup table with an online computational stage. The conventional MPDTC for PSMG is shown in Figure 1.

The stator current at k in dq reference frame can be obtained by transforming the three-phase AC current through a 3 s/2 r transformation. Then, the predicted current at k + 1 can be predicted by the prediction module according to the stator current at k, and the torque and flux at k + 1 can be reached either. Subject to the principle of reducing the rippling in torque and flux, the cost function is chosen as follows:

$$g={\left(T_{\mathrm{e}}^{*}-T_{\mathrm{e}}(k+1)\right)}^2+\eta {\left({\psi }_{\mathrm{s}}^{*}-{\psi }_{\mathrm{s}}(k+1)\right)}^2$$

(1)

where η are weights for torque term and flux term, respectively. ${\psi }_{\mathrm{s}}^{*}$ is the flux reference; $T_{\mathrm{e}}^{*}$ is torque reference.

3. Efficiency Optimized MPDTC

3.1. Loss Model of PMSG

The PMSG loss contains core loss, copper loss, mechanical loss and stray loss, the mechanical loss and stray loss will alter along with the operation condition, which belongs to the uncontrollable losses [21,22]. Improving the operation efficiency is the primary control objective of the generator side. The MPPT only boosts the efficiency of maximum wind power input, this paper proposed an optimization strategy, which further improves efficiency by combining generator loss and MPDTC.

By taking into account the core loss and copper loss, an equivalent circuit with a series-parallel structure is introduced, as shown in Figure 2 [23,24].

The R_s is the resistance of stator winding; R_c is the resistance of equivalent core loss, which can be obtained by the searching method; L_d = L_q = L is the equivalent inductance in dq reference frame; n_p is the pole pairs; Ψ_f is the rotor flux; i_d and i_q are stator current components in dq reference frame, respectively; U_d and U_q are stator voltage components in dq reference frame, respectively; i_wd and i_wq are the active component of stator current in dq reference frame, respectively; i_cd and i_cq are the equivalent core loss component of current in dq reference frame.

From Figure 2, the steady-state voltage and current in dq reference frame of PMSG can be represented as

$$\{\begin{array}{l}{u}_{\mathrm{d}}=R_{\mathrm{s}}{i}_{\mathrm{d}}-\omega L{i}_{\mathrm{wq}}\hfill \\ u_{\mathrm{q}}=R_{\mathrm{s}}{i}_{\mathrm{q}}+\omega (L{i}_{\mathrm{wd}}+{\psi }_f)\hfill \end{array}$$

(2)

$$i_{\mathrm{cd}}=-\frac{\omega n_{\mathrm{p}}L{i}_{\mathrm{wq}}}{R_{\mathrm{c}}}$$

(3)

$$i_{\mathrm{cq}}=\frac{\omega n_{\mathrm{p}}(L{i}_{\mathrm{wd}}+{\psi }_f)}{R_{\mathrm{c}}}$$

(4)

$$i_{\mathrm{wd}}=i_{\mathrm{d}}-i_{\mathrm{cd}}$$

(5)

$$i_{\mathrm{wq}}=i_{\mathrm{q}}-i_{\mathrm{cq}}$$

(6)

The stator flux in dq reference frame Ψ_d and Ψ_q can be represented as

$${\psi }_{\mathrm{d}}=L{i}_{\mathrm{wd}}+{\psi }_f$$

(7)

$${\psi }_{\mathrm{q}}=L{i}_{\mathrm{wq}}$$

(8)

The electromagnetic torque

$$T_{\mathrm{e}}=\frac{3}{2}{n}_{\mathrm{p}}{i}_{\mathrm{wq}}{\psi }_f$$

(9)

The core loss and copper loss can be described as

$$\begin{array}{ll}{P}_{\mathrm{cu}}& =\frac{3}{2}{R}_{\mathrm{s}}(i_{\mathrm{d}}^2+i_{\mathrm{q}}^2)\\ & =\frac{3}{2}{R}_{\mathrm{s}}\cdot \left\{{(-\frac{\omega n_{\mathrm{p}}L{i}_{\mathrm{wq}}}{R_{\mathrm{c}}}+i_{\mathrm{wd}})}^2+{\left[\frac{\omega n_{\mathrm{p}}(L{i}_{\mathrm{wd}}+{\psi }_f)}{R_{\mathrm{c}}}+i_{\mathrm{wq}}\right]}^2\right\}\end{array}$$

(10)

$$\begin{array}{ll}{P}_{\mathrm{Fe}}& =\frac{3}{2}{R}_{\mathrm{c}}(i_{\mathrm{cd}}^2+i_{\mathrm{cq}}^2)\\ & =\frac{3}{2}{R}_{\mathrm{c}}\left\{{\left(-\frac{\omega n_{\mathrm{p}}L{i}_{\mathrm{wq}}}{R_{\mathrm{c}}}\right)}^2+{\left[\frac{\omega n_{\mathrm{p}}(L{i}_{\mathrm{wd}}+{\psi }_f)}{R_{\mathrm{c}}}\right]}^2\right\}\end{array}$$

(11)

According to Equations (10) and (11), the loss of PMSG can be described as

$$P_{\mathrm{loss}}=P_{\mathrm{Cu}}+P_{\mathrm{Fe}}$$

(12)

according to Equation (9)

$$i_{\mathrm{wq}}=\frac{2T_{\mathrm{e}}}{3n_{\mathrm{p}}{\psi }_f}$$

(13)

Combining Equation (13) with Equations (10)–(12), we have

$$\begin{array}{ll}{P}_{\mathrm{loss}}& =\frac{3}{2}{R}_{\mathrm{s}}{\left(-\frac{2\omega L{T}_{\mathrm{e}}}{3R_{\mathrm{c}}{n}_{\mathrm{p}}{\psi }_f}+i_{\mathrm{wd}}\right)}^2+\frac{3}{2}{R}_{\mathrm{s}}{\left[\frac{\omega ({\psi }_f+L{i}_{\mathrm{wd}})}{R_{\mathrm{c}}}+\frac{2T_{\mathrm{e}}}{3n_{\mathrm{p}}{\psi }_f}\right]}^2\\ & +\frac{3{\omega }^2}{2R_{\mathrm{c}}}\left[{\left(\frac{2T_{\mathrm{e}}L}{3n_{\mathrm{p}}{\psi }_f}\right)}^2+{({\psi }_f+L{i}_{\mathrm{wd}})}^2\right]\end{array}$$

(14)

3.2. MPPT Method

According to Betz’ Law, wind power can be measured and has its limit range [25]. The output power of wind turbine P_w is described as follows:

$$P_{\mathrm{w}}=\frac{1}{2}\rho \pi R^2{C}_{\mathrm{p}}(\lambda ,\beta )v_{\mathrm{w}}^3$$

(15)

$$v_{\mathrm{w}}=\frac{\omega R}{\lambda }$$

(16)

where ρ is the air density; R is the radius of the turbine blade; ω_r is the mechanical angular velocity; C_p is the wind power utilization coefficient, which is a function of tip ratio λ and pitch angle β; v_w is the wind speed.

The torque of the wind turbine can be represented by P_w and ω_r, combining Equation (15) with Equation (16), we have

$$T_{\mathrm{w}}=\frac{1}{2{\lambda }^3}\rho \pi R^5{C}_{\mathrm{p}}(\lambda ,\beta ){\omega }^2$$

(17)

Figure 3 is the relation curve of C_p and λ. When wind speed changes, the maximum wind energy utilization coefficient C_pmax can be reached by keeping the tip ratio λ at the extreme point λ_opt.

Based on the above analysis and Equation (17), the maximum output torque of the wind turbine is:

$$T_{\max }=\frac{1}{2{\lambda }_{\mathrm{opt}}^3}\rho \pi R^5{C}_{\mathrm{pmax}}{\omega }_{\mathrm{ropt}}^2=k_{\mathrm{opt}}{\omega }_{\mathrm{ropt}}^2$$

(18)

where, $k_{\mathrm{opt}}=\frac{1}{2{\lambda }_{\mathrm{opt}}^3}\rho \pi R^5{C}_{\mathrm{pmax}}$ and ω_ropt is the optimized wind turbine rotational speed corresponding to the maximum output torque.

Figure 4 shows the output characteristics of the wind turbine. The relationship between the maximum output torque T_max and the generator speed ω can be learned from the figure. During the wind speed change, the maximum wind power tracking can be implemented by keeping the wind turbine operating at the dotted line.

3.3. The Optimization Algorithm of MPDTC

By considering the dynamic losses of the generator, the predicted stator active current can be defined, and the predicted torque and flux can then be acquired by the current prediction value.

If T_s is small enough, then

$$\frac{d{i}_{\mathrm{w}}{}_{\mathrm{d},\mathrm{q}}}{dt}=\frac{i_{\mathrm{w}}{}_{\mathrm{d},\mathrm{q}}(k+1)-i_{\mathrm{w}}{}_{\mathrm{d},\mathrm{q}}(k)}{T_{\mathrm{s}}}$$

(19)

Active voltage equations corresponding to Equation (2) can be described as

$$\{\begin{array}{c}{u}_{\mathrm{d}}=R_s{i}_{\mathrm{d}}+L\frac{\mathrm{d}{i}_{\mathrm{wd}}}{\mathrm{d}t}-\omega L{i}_{\mathrm{wq}}\\ u_{\mathrm{q}}=R_s{i}_{\mathrm{q}}+L\frac{\mathrm{d}{i}_{\mathrm{wq}}}{\mathrm{d}t}+\omega (L{i}_{\mathrm{wd}}+{\psi }_f)\end{array}$$

(20)

Combining Equation (19) with Equation (20), we have a discretization equation corresponding to Equations (5) and (6) at k

$$\{\begin{array}{l}{i}_{\mathrm{wd}}(k+1)-i_{\mathrm{wd}}(k)=\frac{T_{\mathrm{s}}}{L}[u_{\mathrm{d}}(k)-R_{\mathrm{s}}{i}_{\mathrm{d}}(k)+\omega (k)L{i}_{\mathrm{wq}}(k)]\\ i_{\mathrm{wq}}(k+1)-i_{\mathrm{wq}}(k)=\frac{T_{\mathrm{s}}}{L}[u_{\mathrm{q}}(k)-R_{\mathrm{s}}{i}_{\mathrm{q}}(k)-\omega (k)L{i}_{\mathrm{wd}}(k)-\omega (k){\psi }_f]\end{array}$$

(21)

The current can be deduced from Equations (3)–(6)

$$\left[\begin{array}{c}{i}_{\mathrm{wd}}(k)\\ i_{\mathrm{wq}}(k)\end{array}\right]=A\left[\begin{array}{c}{i}_{\mathrm{d}}(k)\\ i_{\mathrm{q}}(k)\end{array}\right]+B{\psi }_f$$

(22)

where, $A=\left[\begin{array}{cc}\frac{1}{1-\gamma }& 0\\ 0& \frac{1}{1+\gamma }\end{array}\right]$, $B=-\left[\begin{array}{c}0\\ -\frac{\gamma }{L(1+\gamma )}\end{array}\right]$, $\gamma =\frac{\omega n_{\mathrm{p}}L}{R_{\mathrm{c}}}$.

By combining Equations (21) and (22), the active current at k + 1 can be predicted.

According to Equations (7)–(9), the predicted torque and flux at k + 1 can be described as follows

$${\psi }_{\mathrm{d}}(k+1)=L{i}_{\mathrm{wd}}(k+1)+{\psi }_f$$

(23)

$${\psi }_{\mathrm{q}}(k+1)=L{i}_{\mathrm{wq}}(k+1)$$

(24)

$$T_{\mathrm{e}}(k+1)=\frac{3}{2}{n}_{\mathrm{p}}{\psi }_f{i}_{\mathrm{wq}}(k+1)$$

(25)

To improve the control precision and improve efficiency from the aspect of reducing generator loss, the cost function needs to be chosen by considering torque rippling reduction and loss minimization.

The ω and T_e are constant values in the steady operation state. From Equation (18), the total loss in a steady operation state is only related to active current i_wd. Through the above analysis, we have

$$\frac{d{P}_{\mathrm{loss}}}{d{i}_{\mathrm{wd}}}=0\Rightarrow i_{\mathrm{wd}}=-\frac{{\omega }^{2}L{\psi }_f(R_{\mathrm{s}}+R_{\mathrm{c}})}{{\omega }^2{L}^2(R_{\mathrm{s}}+R_{\mathrm{c}})+R_{\mathrm{s}}{R}_{\mathrm{c}}^2}$$

(26)

The i_wq from Equation (26) is a reference value of active current in the d-axis, the cost function is designed as follows

$$J={\left(T_{\mathrm{e}}^{*}-T(k+1)\right)}^2+g{\left(i_{\mathrm{wd}}^{*}-i_{\mathrm{wd}}(k+1)\right)}^2$$

(27)

where, g is the weights for torque term and active current term, which are designed to balance the importance of the two control targets in the evaluation function. The torque set value $T_{\mathrm{e}}^{*}$ can be obtained by Equation (18), where it is provided by the output of the MPPT module instead of the PI controller. There is no flux control term in the cost function, since the two squared terms of errors have been determined by the active current in the dq frame, and the flux values in the dq axis are defined correspondingly.

According to Equations (21)–(25), the torque and flux prediction values at k + 1 can be carried out. However, the weight coefficient in Equation (27) has a great impact on the torque and current control effect, and the weight coefficient can only be obtained by trial. Therefore, in order to avoid weight coefficients design and simplify the complexity of the PMSG predictive torque control system, a cost function design method without weight coefficient based on dynamic normalization of torque and flux prediction error is proposed in this paper.

Firstly, two cost functions of torque and current are defined, respectively, to meet the requirements:

$$\{\begin{array}{l}{J}_{\mathrm{T}}=\left|T_{\mathrm{e}}^{*}-T(k+1)\right|\\ J_{\mathrm{i}}=\left|i_{\mathrm{wd}}^{*}-i_{\mathrm{wd}}(k+1)\right|\end{array}$$

(28)

In the process of torque predictive control of PMSG, eight different cost function values J_Tn and J_in (n = 1, 2,…, 8.) can be calculated according to the Equations (11)–(17). Then, the maximum and minimum values of J_T and J_i can be obtained. The maximum and minimum values of J_T are J_Tmax and J_Tmin, respectively, and the maximum and minimum values of J_i are J_imax and J_imin, respectively.

Set a new cost function G:

$$G=G_{\mathrm{T}}+G_{\mathrm{i}}$$

(29)

where

$$G_{\mathrm{T}}=\frac{J_{\mathrm{T}}{}_n-J_{\mathrm{T}}{}_{\min }}{J_{\mathrm{T}}{}_{\max }-J_{\mathrm{T}}{}_{\min }}$$

(30)

$$G_{\mathrm{i}}=\frac{J_{\mathrm{i}}{}_n-J_{\mathrm{i}}{}_{\min }}{J_{\mathrm{i}}{}_{\max }-J_{\mathrm{i}}{}_{\min }}$$

(31)

J_Tn and J_in are corresponding torque and stator flux cost function values when the voltage vector is applied.

It can be seen from Equations (30) and (31) that G_T and G_i are of an order of magnitude, and the variation range is 0~1, therefore, the weight coefficient of the cost function can be set to 1, and no need for complex weight coefficient design. The smaller G, the smaller the prediction error of torque and flux. The voltage vector that minimizes G can be selected as the optimal vector through online comparison, so as to realize the weightless coefficient torque predictive control of PMSG.

The efficiency optimization MPDTC system is shown in Figure 5.

4. Simulation Verification

Simulation studies are carried out in Simulink to validate the proposed scheme and compared it with the conventional MPDTC method. The parameters of PMSG are stator resistance R_s = 1.66 Ω, equivalent core loss resistance R_c = 53.51 Ω, inductance L_d = L_q = 9.1 mH, permanent magnet flux Ψ_f = 0.4 Wb, number of pole pairs n_p = 2. Moreover, the DC side RC filter parameters include the filter resistance R = 80 Ω, and the filter capacitor C = 190 μF.

Simulation of efficiency optimization MPDTC start-up process is first investigated on PMSG. In this test, the speed of PMSG is set as 3000 r/min, the torque is set as −2.5 N·m. The simulation results are shown in Figure 6. Speed and torque reach a stable value at about 0.07 s. The results all show good reference tracking performance.

In order to simulate the operation of the generator when the wind speed changes, the torque setting value is changed from −2.5 N·m to −5 N·m at 0.4 s after steady-state operation of the system. The speed will not change instantaneously due to the inertia of the system. The speed setting value is altered from 3000 r/min to 3700 r/min at 0.8 s, and the results are shown in Figure 7.

When the system makes the torque step response, the system achieves a new steady-state torque value of −5 N·m in 1.8 ms, and the influence of step on the speed is negligible. After adding the step speed setting value, the speed reaches a new steady-state value of 3700 r/min in 20 ms, and the torque also returns to the steady-state value, the torque fluctuation can be stabled at 0.3 N·m. These results indicate the good steady-state performance and strong robustness in the face of perturbations.

From the perspective of torque rippling reduction and efficiency optimization, a comparison of torque and loss between the conventional MPDTC and the efficiency optimized MPDTC is performed. The set values of speed and torque are consistent with those in Figure 6, and the simulation results are shown in Figure 8.

In Figure 8, (a) are conventional MPDTC, and (b) are efficiency optimized MPDTC simulation curves. After comparison and analysis, the torque ripple of conventional MPDTC is 1.5 N·m, and the system reaches a steady state at 0.13 s. However, by using the efficiency optimized MPDTC, the torque ripples are 0.6 N·m, and the system reaches a steady state at 0.08 s. The generator copper loss and core loss have also been reduced in the steady state as well. The proposed MPDTC strategies which consider the generator loss factors have a much smaller torque ripple and exhibit good dynamic and steady-state performance. In the performance cost function, the stator active current is directly predicted and controlled, which shortens the adjustment time.

The total generator output power P_out is characterized by the product of torque and speed. The operation efficiency can be described as

$$\mu =\frac{P_{\mathrm{out}}}{P_{\mathrm{out}}+P_{\mathrm{cu}}+P_{\mathrm{Fe}}}$$

(32)

Figure 9 shows that, compared with the traditional MPDTC, the efficiency optimization MPDTC system can be used to improve the efficiency of the PMSG.

5. Experimental Verification

A 1.5 kW prototype is established with the same parameters as the simulation parameters. The real experimental system is shown in Figure 10, the system parameters are shown in

Table 1. System parameters.

Parameters	Values	Parameters	Values
Rated Power	1.5 kW	Permanent magnet flux/Ψf	0.4 Wb
Rated torque	25 N·m	Number of pole pairs/np	2
Equivalent core loss resistance/Rc	53.51 Ω	Stator resistance/Rs	1.66 Ω
Inductance/Ld, Lq	9.1 mH	Rectifier switch frequency	30 kHz

. In the test, an asynchronous motor which is powered by Siemens SINAMICS S120 inverter, and the PMSG are connected through a mechanical coupling. The control algorithms are implemented on a TMS320F28335 DSP controller board from the PC to the DSP controller board through the XDS510 emulator, and then, the DSP controller board generates switch signals S_abc.

Figure 11 presents the dynamic state performance achieved by the two MPC strategies. During the experiment, the initial value of the set speed value is 3000 r/min, and the initial value of the torque is −2.5 N·m. After the system is stabilized, the torque steps from −2.5 N·m to −5 N·m. The comparison and analysis show that, when the system has the torque step, the system by using conventional MPDTC (blue line shows ) takes 48 ms to stabilize, and the torque of the MPDTC system with optimized efficiency methods (red line shows )reaches the steady value at 28 ms, which indicates that the response time is down 41.7%. With the conventional MPDTC, the torque ripple is 1.9 N·m, and it is only 0.8 N·m by using the optimized efficiency methods. The torque rippling is obviously less than the one in the conventional method.

The system performs speed step from 3000 r/min step to 3700 r/min. The Figure 12 shows that after adding the speed step value, the system, by using traditional MPDTC (the blue line), takes 40 ms to stabilize with a large overshoot, and the optimized efficiency MPDTC (the red line) reaches the stable state in 24 ms with low overshoot. The proposed MPDTC has the advantages of rapid response, small overshoot and significantly reduced torque rippling, which indicates strong system robustness and ability of anti-interference.

In order to further verify the effectiveness of the proposed control strategy in improving PMSG efficiency, an efficiency comparison experiment was designed and carried out. At the same input power provided by the asynchronous motor, the output power of the system is analyzed to compare the power efficiency. The output power is characterized by the product of the voltage and the current on the DC side.

The experimental results are shown in Figure 13. Compared with the conventional method, the system DC bus voltage fluctuation, which by using the proposed MPDTC methods is smaller, can also suppress the fluctuation of the output power. In Figure 13a,b, the red line represents the core loss and copper loss by using conventional MPDTC, the blue line represents the core loss and copper loss by using optimized efficiency MPDTC. The output power of the PMSG by using conventional MPDTC is 760 W (Figure 13c red line shows), and the PMSG by using optimized efficiency MPDTC is 930 W (Figure 13c blue line shows). The output power is increased by 22.4% with the same input power, and the optimized efficiency method improves the PMSG efficiency.

The above experiment fully validates the reliability and effectiveness of the MPDTC strategy proposed in this paper in reducing torque rippling, improving system robustness and improving efficiency.

6. Conclusions

In order to solve the efficiency optimization problem of PMSG, this paper proposed an efficiency optimal control strategy based on MPDTC. Real-time minimum control for PMSG loss is implemented based on the reduction in torque rippling. The optimized efficiency MPDTC acquires the predictive value of the electromagnetic torque of the generator by predicting the active current of the stator, which improves the accuracy of the torque prediction, reduces the torque ripple of the system, and prolongs the service life of the wind turbine. The efficiency optimization cost function without weight coefficient designed based on the principle of minimum loss can select the appropriate switch vector, which will improve the system response speed and implement the real-time system efficiency optimization. Simulation and experimental results have verified the effectiveness of the proposed control scheme, and this scheme is simple and easy to be applied in practical engineering applications.