Topology and control algorithms for a permanent magnet synchronous motor as a part of a vehicle with in-wheel motors

This article describes an electric drive system’s topology with a permanent magnet synchronous motor for a wide speed range applications. Topology consists of a synchronous motor with permanent magnets (PMSM) and two inverters connected to the beginnings and to the ends of the PMSM’s stator windings. The first inverter is connected to a storage battery, while the other one to a floating bridge capacitor, which acts as a back-EMF compensator. The article proposes electric drive system topolo-gy and its control algorithm. Simulation modeling was implemented by the MATLAB/Simulink software package. Simulation results shows that the proposed electric drive system, in comparison with the standard topology with a «star» stator windings connection, is able to increase the maximum speed of PMSM in the field weakening mode by 17%. The maximum achievable torque on the rotor shaft at the maximum speed of the PMSM motor was increased by 16.6%. Also, developed topology allows to in-crease the speed range in the constant torque mode by 34%.


Introduction
At present, in-wheel motors usage, in the composition of vehicles, is a promising solution due to the following advantages: the rejection of mechanical energy converters (gearbox, differential, constant velocity joints), which contribute to additional losses in the system, reducing the final mass of the vehicle, its distribution and, consequently, increasing the efficiency of the system [1][2][3]. However, the main disadvantage of this solution is the need to operate the electric motor in a wide range of speeds while maintaining high values of torque on the shaft, which makes it difficult to implement in vehicle powertrains. Thus, electric motors with parameters which meets the following requirements, can be used for operation as part of in-wheel motor: high torque at low speeds; wide speed control range; high coefficient of power density. Electric motors which corresponds to mentioned above criteria are presented by the following types: asynchronous electric motor [4,5], permanent magnet synchronous motor [6,7]; brushless DC motor [8]; reluctance motor [9]. Based on the comparative analysis carried out in work [10], the permanent magnet synchronous motor (PMSM) is the most suitable type of electric motor forin-wheel motors. Both domestic and foreign authors have developed systems designed to control PMSMs at a wide range of speeds. So, in articles [11], algorithms of V/F control of a PMSM were considered.
Papers [12][13][14][15][16] are devoted to the development of field-oriented vector control and direct torque control. In [17][18][19], the possibility of weakening the magnetic field of the PMSM to achieve speeds above the nominal values was considered. In articles [20][21][22], a topology with the connection of an additional inverter to the ends of stator windings to expand the range of motor operating speeds was proposed. The use of such a connection scheme provides for: extending the speed range of the PMSM by compensating the counter-EMF of the electric motor [23]; the possibility of backup switching to the"star" mode in case of failure of one inverter when feeding the auxiliary inverter from the battery or from the common with the main converter' source [24]; availability of additional power source with a possibility of its reservation [25]; possibility to increase a voltage level applied to the PMSM in case of absence of both boost converters and additional power sources [26,27]; decrease in amplitude of current ripple [28]. Papers [29] consider the use of a floating bridge capacitor as a secondary energy source for the topology with two inverters. Based on a comparative analysis of the use of different energy sources to power the auxiliary inverter, presented in [30], the PMSM topology using a floating bridge capacitor is the most promising solution for use in a vehicle, because, in comparison with topologies using a single energy source, does not contribute to zero sequence currents, and in comparison, with systems where the auxiliary inverter is powered from an additional accumulator. In the papers [31,32], the peculiarities of selecting inverters for electric drive systems were considered. In the paper [33], the influence of the electric drive system on the source of supply voltage was evaluated. At the same time, no works have so far considered the electric drive system using permanent magnet synchronous motors with open-endstator winding and a floating bridge capacitor as a part of a vehicle using in-wheel motors.

Problem statement
For full-fledged use of PMSM topology with an open-end winding and a floating bridge capacitor in the vehicle, it is necessary to develop a control algorithm of the abovementioned electric drive system for use in a wide speed range, as well as to conduct a comparative analysis of the proposed topology and its control algorithm in comparison with the technical solutions already used for such purposes. Thus, the purpose of the study, the results of which are presented in the article, is to develop a control algorithm for a PMSM with open-endstator winding and a floating bridge capacitor in a wide range of speeds.

Research methodology
The equations for the PMSM with respect to the rotating d-q coordinate system are three basic equations which, according to [34,35], can be express ed by formulas (1 -3):  The research methodology involves the study of the transients occurring in a synchronous motor with permanent magnets, an open stator winding, and a floating bridgecapacitor based on differential equations (1 -3) using simulation methods in the Matlab/Simulink software package.

The control algorithm for a permanent magnet synchronous motor over a wide speed range
Considering a PMSM operation in a wide speed range, it is necessary to determine the limit values of speed and torque on the rotor shaft, which are limited by the maximum allowable values of currents and voltages according to formulas (4 -5): where max I is the maximum motor current; 3 max dc U U  is the maximum output voltage relative to the PMSM stator windings.
To carry out the calculations of the PMSM operation modes, as the equation of motor speed limitation as a function of voltage, equations (4 -5) must be equated with equations (7 -8), taking into account the following conditions: The solution is the equation of the PMSM velocity limit ellipse from voltage (4): where me  is the electric speed of the PMSM. Fig. 1 shows the limits of the PMSM operating characteristics, according to which the optimal current settings in the rotating coordinate system d-q, depending on the current and set values of torque and speed on the rotor shaft, can be divided into 4 main modes: MTPA, FW, MC, and MTPV. The diagram which is shown in Figure 1 was constructed based on the equations described below using the MATLAB software package.The diagram shown in Figure 1 was created by MATLAB software package using mentioned below the equations.

Fig. 1. Performance limits of the PMSM
The MTPA (maximum torque per ampere) mode is used when it is possible to achieve the highest possible ratio of output torque on a shaft with the minimum supply current in the speed range from 0 rpm to their rated value (in Fig. 1 the curve is marked with a red arrow); the MC (maximum current) mode is used when the motor's rated speed is exceeded in the case when the torque demand is equal or above the maximum allowable value (the curve is marked with a black arrow in Fig. 1); the MTPV (maximum torque per voltage) mode is optimal for deep field weakening when the MC mode is no longer optimal to achieve the necessary shaft torque values (the curve is marked with a blue arrow in Fig. 1); the FW (field weakening) mode is optimal in the speed range above the rated speed when the shaft speed and torque setting is below the limit values (the point family within the range marked with a green arrow).
The final system of equations for determining the stator currents in the rotating d-q coordinate system in MTPA mode is expressed according to equations (7 -8): where coefficients 1 1 ,   are expressed according to formulas (9 -13): Coefficients 1 1 1 1 , , , A B C D , in their turn, can be found in accordance with (14 -17): The equations for finding the control currents in the MTPV mode are: where m U is the current value of the voltage. The value MTPV  can be found by formula (22): For the FW mode, the final writing of the system of equations for determining the stator currents in the rotating d-q coordinate system according to formulas (23 -24): where coefficients 2 2 ,   are expressed in accordance with equations (25 -29): The choice of the optimal control algorithm is based on the algorithm shown in Fig. 2. According to Fig. 2, to determine the optimal control algorithm it is necessary to pre-

Control system for a permanent magnet synchronous motor with open-endstator winding.
The topology of the electric drive with the connection of inverters with independent power sources to the beginning and the end of the motor stator windings is shown in Fig. 3.

Fig. 3. Drive topology with the open-endstator winding
The resultant value of the voltage with respect to the motor windings will be the potential difference between the connected main and auxiliary source. Based on this, we can write equations (34 -36):    cos( )cos( ) sin( ) sin( ), cos( ) sin( ), sin( ) cos( ),   [37]; "Drive Controller," the block of formation of control impulses for PMSM; "Inputs," the block of formation of the task for acceleration, braking, as well as setting parameters of the roadway slope and the speed of the oncoming wind flow; "Vehicle Controller," the block of formation of the task for the moment based on the data received from the block "Inputs." Simulation of the vehicle dynamics was performed using the parameters of the electric car "Nissan Leaf," the characteristics of which are presented in [38]. The main parameters of the simulation model are shown in Table 1. To assess the effectiveness of the proposed topology, the simulation results were compared with the topology having identical parameters of the electric drive, as well as its control system with the connection of the stator winding ends according to the "star" scheme. F  Therefore, "Vehicle Dynamics" and "OWPMSM" blocks were simulated according to "Motor parameters" and "Vehicle parameters" data presented in table 1. Battery was simulated with an infinite capacity in order to exclude voltage drop influencing. That's why battery has only voltage parameter. Floating bridge capacitor data described according to "Parameters of energy storage devices" data.

Simulation results
The simulation results are shown in Fig. 6. According to Fig. 6, it can be noted that the final maximum allowable speed was increased by 1350 rpm (7700 rpm for the topology using a floating bridgecapacitor versus 6350 rpm for the topology with the connection of stator winding ends according to the "star" scheme). The maximum torque in weak field mode was increased by 10 Nm (60 Nm using the developed topology versus 50 Nm for the standard drive system topology). The PMSM rated speed has also been increased by 800 rpm (2300 rpm for the floating bridgecapacitor topology vs. 1500 rpm for the "star" scheme) to be able to achieve constant torque at the rotor shaft. a) б) Fig. 6. Diagrams of output characteristics of speed, torque on a shaft, and the capacitor voltage level of the developed and standard topology of electric drive system: a) Electric drive system with two inverters and a floating bridgecapacitor; b) Electric drive system with one inverter Fig. 7 shows the change in the driving dynamics of the vehicle. According to the figure, the vehicle using the proposed topology can speed up faster compared to the standard electric drive system topology (acceleration of the electric vehicle to 100 km/h using the developed electric drive system took 8 seconds, while the acceleration of electric vehicle using the standard topology exceeds the value of 10 seconds).

Conclusion
Based on the simulation of the electric drive system for a permanent magnet synchronous motor with a floating bridgecapacitor as a power source for an auxiliary inverter, the following results were achieved:  A model of an electric drive control system of the proposed topology in Matlab/Simulink environment was developed, a comparative analysis of the proposed topology with the topology of the electric drive with the connection of secondary winding ends according to the "star" scheme was carried out.
 Simulation results showed the possibility of increasing the final speed of the electric motor in the weakened field mode by 17%, while the torque on the rotor shaft increases by 16.6% compared to the topology of the drive with the connection of the secondary winding ends according to the "star" scheme.
 The use of the developed topology allows increasing the speed range in the mode of constant torque by 34% compared to the topology of the drive with the connection of the ends of the secondary windings according to the "star" scheme.

Discussion
Despite the fact that proposed topology helps to achieve torque-speed characteristics for PMSM motor, there are some drawbacks:  Increasingalgorithmandhardwarecomplexity  Electricdrive'stotalcostrise  Doubling the number of IGBT switches Also, it should be noted that simulations were provided excluding thermal and magnetic losses as well as switching ones. Therefore, further studies will be focused on implementation of proposed topology with finite element modelling of PMSM motor. It will be helpful to calculate overall efficiency of proposed solution.