Modulated Model Predictive Current Control for PMSM Operating With Three-level NPC Inverter

In finite control set model predictive control (FCS-MPC) strategy only one basic voltage vector is to be selected in per periodic time, which causes big current ripple as well as the torque ripple of permanent magnet synchronous motor (PMSM). To solve this problem, an improved model predictive control method, named modulated model predictive control (M2PC) is proposed. The proposed control strategy can produce a modulated waveform, which can reduce torque ripple and improve power quality. Simulation results verify that the proposed current controller has a better control performance than the classical FCS-MPC strategy.


I. INTRODUCTION
Multi-level converters are widely used in higher voltage range than conventional two-level converter [1]. They can reduce common mode voltages and total harmonic distortion (THD). In multi-level inverters, the three-level inverter has the least number of switches. It can be implemented easily in the technical field of a high voltage. The neutral-point-clamped (NPC) converter is often known as the three-level diode clamped converter which can improve total harmonic distortion and has bigger bandwidth than conventional twolevel converter [2]. It becomes more and more popular in many industrial application fields [3]. Finite control set model predictive control (FCS-MPC) has many advantages, such as simple structure, easy implementation and good multivariable control ability [4]. The FCS-MPC is easily extendible for different industrial applications. It has been widely concerned by academic and industrial communities [5]- [9]. More and more researchers apply MPC strategy for the multilevel converter. In [10], a finite control set model predictive control strategy was used in the five-level active neutral-point-clamped (ANPC) topology inverter for induction machine (IM). In [11], two MPC controllers are proposed for grid-side NPC inverter and generator-side converter respectively. An improved MPC controller for a high power wind energy conversion system using the three-level boost (TLB) converter and NPC inverter was proposed in [11]. In [12], a fast finite switching state MPC was proposed for T-type three-level NPC converter. However, there are still some disadvantages on this control method. The main drawback is that only one basic vector can be selected per periodic time, which causes big current ripple as well as the torque ripple of permanent magnet synchronous motor (PMSM). Another MPC control strategy named deadbeat current predictive control having a fixed switching frequency [13]- [17]. This control strategy only predictive the reference voltage in static coordinate and use the conventional space vector pulse width modulation (SVPWM) algorithm to generate the firing pulses. However, it is very complex in the calculation of switching time [4]. In order to overcome above drawbacks, a novel model predictive control strategy, named modulated model predictive control (M2PC) was proposed [18]- [20]. The M2PC control strategy adds a modulator to generate the duty cycles by selecting two active voltage vectors and zero voltage vectors, and the modulation time of each vector is calculated by minimization of the cost function. In [19], [20], the M2PC strategy was used in a seven-level H-bridge converter. In [21], the M2PC was proposed for brushless doubly fed IM control. In [2], [22], the M2PC was proposed for balancing of the DC-link capacitor voltages and regulating the load currents with a NPC converter.
M2PC for PMSM current control operating with a NPC inverter is proposed in this paper. The M2PC strategy can produce a modulated waveform by operating a cost function minimization algorithm, which can reduce torque ripple of PMSM and improve power quality. A simulation is implemented comparing with the conventional MPC strategy. The simulation results prove the effectiveness of M2PC strategy.

II. MATHEMATICAL MODEL OF THE THREE-LEVEL NPC INVERTER
The three-level NPC inverter, which is widely used in many industrial application fields [1], [12], [23]- [26], include twelve switches and six clamping diodes. The structure of three-level NPC inverter is shown in Fig.1. Switches S1x and S3x, S2x and S4x are complementary states. In the current loop of PMSM control system, the threelevel NPC inverter can produce higher switching frequency to reduce the THD than conventional two-level inverter.

A. PMSM Mathematical Model
The d-q axis mathematical model of permanent magnet synchronous motor is shown as follows: Where, d u and q u represent the d-q-axis voltages; e  is the electrical rotor speed of PMSM; d i and q i represent the dq-axis currents;  is the flux linkage of permanent magnet; d L and q L are the d-q-axis inductances and s R is the stator resistance.
The d-axis inductance and the q-axis inductance are approximately equal ( = d q L L ) in surface permanent magnet synchronous motor (SPMSM) [27].

B. Conventional FCS-MPC current control of PMSM
Assuming sampling time is Ts , the stator current derivatives can be discretized using the Euler approximation method, that is: Replacing (2) into (1), d-q axis predictive stator currents in the next sampling time can be obtained as:   Fig.3. Here, a PI speed controller is used to generate the qaxis reference current. The FCS-MPC current controller is used for tracking the d-q axis reference currents. The discretetime model of PMSM is used to predict the stator current. During each sampling period, one voltage vector that minimizes the cost function is selected from the nineteen basic voltage vectors and applied to the three-level NPC inverter.

3-level NPC Inverter
Park Clark Caculation of Angular and Velocity Fig. 3. Control diagram of classical MPC current control method with threelevel NPC inverter.
The cost function can be shown as follow: (4) Where, g is the cost function; * q i is the reference value of q-axis current, which is output by PI controller of speed loop; The task of the FCS-MPC strategy is selected the optimal switching state, which executes nineteen times (each for different basic voltage vector) to calculate the optimal cost function.

IV. MODULATED MODEL PREDICATIVE CURRENT CONTROL
FOR PMSM Same as the conventional MPC strategy, M2PC also has prediction and optimization sections. The cost function g is evaluated for each case. The only difference is the M2PC includes a suitable modulation scheme. The M2PC strategy select two adjacent active voltage vectors which minimize the cost function in each sector at every sampling time. The FOC control scheme of PMSM current control with three-level NPC inverter using M2PC strategy is shown in Fig.4. For example, two adjacent voltage vector v1 and v2 are selected in the first sector. Each prediction is calculated based on (3) and (4). 1 g , 2 g , 0 g are cost functions of voltage vectors v1,v2 and zero voltage vector, respectively. As shown in (6). The duty cycles of two adjacent active voltage vectors v1,v2 and zero voltage vector are calculated respectively.  (6), duty cycles for each vector and the parameter K can be calculated as follows: s s s d T g g g g g g g g d T g g g g g g g g d T g g g g g g g g With these above equations, the total cost function g is defined as follow: The minimum total cost function g, which is evaluated by two active voltage vectors, is applied to the three-level NPC inverter in the next sampling period.

V. SIMULATION RESULTS
To verify the performance of M2PC strategy, a simulation model is built in Matlab2018a. The parameters of the simulation are listed in table II. The simulation step is 1e-6, the current loop sampling time is 50e-6, the speed loop sampling time is same as the current loop. The speed controller is a PI controller, the proportion parameter is 0.009, and the integral parameter is 1.2. Both classical MPC strategy and proposed M2PC are evaluated in simulation.
The initial load of PMSM is 0.2N.m and target speed of PMSM is 1800rpm. In order to verify transient performance of the PMSM system, the load increases to 0.5N.m suddenly in 0.05s.
The waveforms of the d-q axis currents responses by classical MPC and M2PC are shown in Fig.5 and 6, respectively. It can be observed that the load increased suddenly at 0.05s, the q-axis current can response quickly. M2PC has a higher switching frequency than classical MPC in the same DSP interrupt time 50e-6, therefore, classical MPC strategy has a bigger ripple than M2PC strategy in the same sample time. The current THD of both methods will be discussed in details in Fig.13 and 14.  Fig. 7 and Fig. 8 show the waveforms of the three phase currents for the classical MPC and M2PC, respectively. As evident, the M2PC shows lower ripple than the classical MPC. The step response of the PMSM for both methods is shown in Fig. 9 and Fig. 10, observing again, a better performance of the speed for the M2PC strategy. It can be observed that the speed of PMSM decrease as the load increased in 0.05s, then it can restore to target speed very quickly. However, the speed fluctuation of classical MPC strategy is bigger than M2PC strategy. Similarly, Fig. 11 and Fig. 12 show the line voltages for classical MPC and M2PC. FFT analysis for the A phase current under classical MPC strategy and M2PC strategy are shown in Fig.13 and 14. The fundamental frequency is 120Hz, A phase current is analyzed in two cycles. It can be seen from the Fig.13 and 14, classical MPC strategy has a higher THD value than M2PC strategy in the same sample time 50e-6. The M2PC has a higher switching frequency than classical MPC.

3-level NPC Inverter
Park Clark Caculation of Angular and Velocity Fig. 7. Phase currents responses under classical MPC current control strategy in the presence of load torque disturbance at 1800rpm.

VI. CONCLUSIONS
A M2PC strategy for a three-level NPC inverter feeding a PMSM was proposed in this paper. Compared with the classical MPC strategy, the proposed M2PC strategy produced a modulated waveform to reduce the THD value, and has a smaller current and torque ripple. The simulation was implemented in Matlab2018a, and the results show the feasibility and effectiveness of M2PC strategy.