Maximum ef ﬁ ciency control of six- and three-phase two-motor drives

: In this study, a method for loss minimisation of six- and three-phase two-motor drive systems is presented. In two-motor drive systems (or multiphase multi-motor drive systems), currents of one motor pass through the other motor(s), which lead to increment of copper loss. In the proposed method for loss minimisation of six- and three-phase two-motor drive systems, extra copper loss of the six-phase motor, caused by reference currents of three-phase motor, is considered in loss-minimisation equations of three-phase motor; therefore the total controllable loss (including copper and iron losses) of whole system will be minimised in a uni ﬁ ed form. In this paper, amount of ef ﬁ ciency improvement of proposed method for a system of two six- and three-phase motors in different speeds and load torques are compared with a conventional method of nominal ﬂ ux. Also experimental results verify performance of the proposed method.

Nomenclature V d , V q d-and q-axis components of stator voltage i d , i q d-and q-axis components of current i cd , i cq d-and q-axis iron loss components of current L m magnetising inductance L ls ,L lr stator and rotor leakage inductances R s stator resistance R c iron loss resistance P cu−s , P cu−r stator and rotor copper loss P Fe iron loss v r rotor mechanical speed v electrical frequency P pole pairs T e electromagnetic torque

Introduction
In many applications, such as electric vehicle/hybrid vehicle (EV/HV), railway traction, more electric aircraft and electric ship propulsion, multiphase machines are utilised due to advantages including reduction of the inverter per-phase rating, less noise pollution, higher efficiency, reduced torque pulsations, greater tolerance to open-circuit faults and so on [1][2][3][4]. In addition to these benefits, two or more multiphase machines can be controlled by increasing phase number to at least five or more from a single current-controlled voltage source inverter (VSI) [5]. This advantage extends the applicability of multiphase multi-motor systems to a variety of applications which require more than one motor such as locomotive traction, heating, ventilation and air-conditioning (HVAC) and so on [6]. Main idea and connection diagram of multiphase multi-motor systems are presented in [7,8] for odd and even phase numbers, respectively. Based on this idea, two components of current are required for vector control of each multiphase motor; therefore the remaining degrees of freedom can be used for controlling the other motors which are to be connected in series with the first motor [5]. Accordingly, motors should be connected with an appropriate phase transposition from one motor to the other.
In [9], steady-state modelling of five-phase and six-phase twomotor drives is presented. It is shown in this paper that the specific winding connections results in less dc-link voltage requirement in comparison to the situation that the windings have been connected directly in series. Also, in [6,10], dynamic modelling of two-motor drives is discussed.
In [11], a method for voltage control of two six-and three-phase motor drives is presented. It is shown that how to achieve independent feedforward voltage control and to evaluate the switched voltage profile in the motors' windings and their behaviour.
In multiphase multi-motor systems, utilising different types of motors (including induction, synchronous reluctance, permanent magnet synchronous motors etc.) is possible. In [12], two induction and synchronous reluctance motors, and in [13], two induction and permanent magnet synchronous motors are connected in series in two six-and three-phase motor drive system. It is experimentally verified in these references that in addition to independent control of the two motors, there is no negative impact on the transient performance of both motors.
Increased copper loss in multiphase multi-motor systems leads to decrement of efficiency to some extent. As stated in [12],   one of the best applications of these systems is wider application. However, efficiency improvement of these systems can have great importance.
There are different methods for loss minimisation of a single induction motor. Generally, these methods can be divided into three main groups of search-based, model-based and hybrid methods.
In search-based control methods, the control variable would be perturbed by a specified process in order to minimise input power. In [14], output voltage in a scalar method would be changed in such a way that stator current will be minimised. In general, main advantage of search-based methods is motor parameter independency and its simplicity in implementation. However, the drawbacks of these methods are low dynamic response and oscillating around operating point. These drawbacks limit utilisation of search-based methods in some applications which model-based methods should be utilised in.
In model-based methods [15][16][17][18][19][20][21], loss minimisation is based on motor model. In [15], the loss-minimisation condition is obtained by differentiating controllable loss equation (sum of copper and iron losses) with respect to d-axis current and equating the derivative to zero. In [16], an analysis is done on loss minimisation of induction motors. Based on experimental results of [16] on two different motors with power ratings of 22 and 90 kW, it is not critical if the converter losses are neglected in the control system for loss minimisation. Therefore, from the view point of efficiency, there is not considerable difference between the case of 'considering converter loss' and the case of 'not considering converter loss', because their operating points are close together. Generally, the main advantage of model-based methods is fast dynamic response to reach optimum operating point.
In hybrid methods [22,23], a combination of model-based and search-based methods is utilised. In [23], a ripple correlation control (RCC) approach is utilised as a hybrid method. In this method, extremum-seeking control is done by using inherent ripple in power electronics. However, RCC requires a rotor flux estimate, which is dependent on motor parameters.
In this paper, at first, two six-and three-phase motor seriesconnected drive systems are discussed. In Section 3, lossminimisation control of a single induction motor is investigated. Later, in Section 4, proposed loss-minimisation control method of two six-and three-phase motor drives is presented. The effect of using proposed method in comparison with nominal flux control method is discussed in Section 5. Finally, experimental results are presented in order to verify the performance of the proposed methods.
2 Two six-and three-phase motor series-connected drives In two six-and three-phase motor series-connected drive systems, both motors can be controlled independently via single inverter.
Connection diagram of this system has been established in [8] which is shown in Fig. 1. Also block diagram of the control system is shown in Fig. 2. This block diagram is utilised for each of the two motors in order to obtain current references of each motor. Then phase current references of the motors are added with each other based on (1) to obtain phase current references of the inverter. Finally, inverter current references will be applied to the motor via hysteresis current controller (1) In model-based maximum efficiency control method of induction motors, at first, total controllable loss, including copper loss and iron loss, should be differentiated with respect to d-axis current and equating the derivative to zero. Controllable loss components are as follows: Condition of maximum efficiency control of induction motors, which is concluded by differentiating sum of controllable losses with respect to d-axis current and equating the derivative to zero [15] i 4 Maximum efficiency control of two six-and three-phase motor drives In two six-and three-phase motor systems, each phase current of three-phase motor comes from two phases of six-phase motor, while currents of six-phase motor do not pass from three-phase motor windings. Total copper loss of each motor is as follows: Therefore, extra copper loss produced in six-phase motor, caused by reference currents of three phase motor, should be considered in maximum efficiency control of three phase motor. Therefore, in maximum efficiency control of these two motors, the following equations should be used in maximum efficiency control of each motor: In fact, the term of 6 · R s−6w · (i 3w /2) 2 = 3 · (R s−6w /2) · (i 2 3w ) is a component of copper loss of six-phase motor, but this term is controlled by reference currents of three-phase motor. Therefore, in maximum efficiency control of three-phase motor, this term should be added to copper loss of three-phase motor. In better words, stator resistance of three-phase motor should be considered equal to R s−3w + (R s−6w /2) in maximum efficiency control of three-phase motor, and also stator resistance of six-phase motor should be considered equal to R s−6w in maximum efficiency control of six-phase motor.
5 Comparison of proposed maximum efficiency control method with nominal flux control method A consideration on the effect of utilising proposed lossminimisation control method is carried out on the system of two six-and three-phase motors in this section. Parameters of threephase and six-phase motors are shown in Tables 1 and 2. In this investigation, proposed loss-minimisation and nominal flux control methods are compared with each other in terms of copper loss, iron loss and efficiency. In the first case, for different values of load torques, speed of three-phase motor and six-phase motor are 200 and 1400 rpm, respectively. In Fig. 4,e f ficiency, copper loss, iron loss and phase current as a function of load torque for three-phase motor, six-phase motor and whole of two motors are illustrated. Load torque values of three-phase motor are shown on top axis; and load torque values of six-phase motor are shown on bottom axis in Fig. 4. As illustrated in Fig. 4b,u p to about 32% improvement in efficiency is obtained in light loads.
In the second case, two methods are compared in different speeds. In this situation, load torque of both of three-phase and sixphase motors is 10 N m. Also, efficiency, copper loss, iron loss and Fig. 7 Control of two six-and three-phase motors with nominal flux method (experimental result) aI d , i q and speed of three-phase motor and inverter phase 'a' current bI d , i q and speed of six-phase motor phase current as a function of speed for three-phase motor, sixphase motor and whole of two motors are illustrated in Fig. 5. Speed values of three phase motor are shown on top axis; and speed values of six-phase motor are shown on bottom axis in Fig. 5. As illustrated in Fig. 5b, up to about 7% improvement in efficiency is obtained using proposed method.
As in nominal flux method, flux level of the motor would be adjusted based on optimum value in nominal speed and load, therefore the difference between efficiency of the methods decreases by increasing the load torque.

Experimental results
A laboratory setup is constructed in order to verify proposed method applicability. Test setup configuration and experimental setup are illustrated in Fig. 6. Six-and three-phase motors parameters, incorporated in experimental setup, are listed in Tables 1 and 2. A Microchip dsPIC microcontroller is utilised in experimental setup. As shown in Fig. 6b, six-phase motor is coupled to dc generator as load. Results are sampled via an Advantech USB-4711A data acquisition apparatus.
Effectiveness in loss reduction of proposed method in comparison with nominal flux method under different conditions is investigated experimentally. Also motor losses which are obtained via calculation and experimental results are compared with each other for both methods.
In the experimental test, six-phase motor is coupled to dc generator as load; and three-phase motor operates in no-load condition. In this test, three-phase motor accelerates from standstill to 700 rpm, then at t = 1 s, motor decelerates to 200 rpm; also six-phase motor accelerates from zero to 1400 rpm; afterwards, a load of 10 N m is applied to motor at about t =4s.
Results of nominal flux method are shown in Fig. 7; and results of proposed method are shown in Fig. 8 which includes i q , i d and speed of three-and six-phase motors, and also inverter phase current.
For calculating motor losses in a specified speed and torque, motor steady-state equations are utilised by using i d , i q and motor parameters. Also, Table 3 shows motor loss including copper, iron and mechanical losses for both methods obtained from calculation and experiments which have good accordance with each other.

Conclusion
In this paper, a method is proposed for loss minimisation of two sixand three-phase drive systems. In two six-and three-phase motor systems, each phase current of three-phase motor comes from two phases of six-phase motor, while currents of six-phase motor do not pass from three-phase motor windings. Therefore, in order to maximum efficiency control of two six-and three-phase motor systems, it is just required to consider extra copper loss produced in six-phase motor, caused by currents of three phase motor in maximum efficiency control of three phase motor, because currents of six-phase motor does not pass through windings of three-phase motor. Therefore, stator resistance of three-phase motor should be considered equal to R s−3w + (R s−6w /2) in maximum efficiency control of three-phase motor, and also stator resistance of six-phase motor should be considered equal to R s−6w in maximum efficiency control of six-phase motor. Also, simulation and experimental results verified effectiveness of proposed method in loss reduction. Table 3 Total loss of whole system for both control methods obtained from calculation and experimental resultsthree-phase motor is no-load; and speed of three-phase motor and six-phase motor are 200 and 1400 rpm, respectively