Research Article  Open Access
Mingming Huang, Quanzhen Huang, Yang Zhang, Xinjun Guo, "A Comprehensive Optimization Control Method for Hybrid Excitation Synchronous Motor", Mathematical Problems in Engineering, vol. 2020, Article ID 1390650, 11 pages, 2020. https://doi.org/10.1155/2020/1390650
A Comprehensive Optimization Control Method for Hybrid Excitation Synchronous Motor
Abstract
Hybrid excitation synchronous motor (HESM) offers the advantages of a convenient flux regulation and a wide range of available speeds. As such, it may be conveniently employed in the fields of electric vehicle and aerospace. In this paper, based on a suitable control strategy for vector and speed partition, we put forward a speed control method for HESM which shows optimal efficiency. On the one hand, our method aims at minimizing the copper loss by an optimal configuration of the qaxis current, the daxis current, and the excitation current under the constraint voltage at the armature end. On the other hand, we conduct a comprehensive analysis of the effects of the fluxweakening speed coefficient on the operating performance of the motors and suggest a selfadaptive control method to regulate that coefficient and further improve the overall performance of the motors, including their speedrange regulation, their efficiency, and their dynamical properties. The proposed fluxweakening control method has been assessed by simulations and HESMdriven experiments. Results have confirmed the feasibility and optimality of our method.
1. Introduction
Hybrid excitation synchronous motor (HESM) represents a novel class of motors based on the permanent magnet synchronous motor (PMSM) and is characterized by a wider range of available speeds [1–3]. There are two magnetic potential sources in this kind of motor, with the permanent magnet providing a nearly constant magnetic field in the air gap and the excitation winding providing a magnetic field with variable magnitude and direction. The HESM is thus endowed with a large torque with small speed and may access a wide range of speeds. Therefore, HESM has extensive applications in the areas of electric vehicle, machine tools, and aerospace [4, 5].
The electromagnetic torque generated by the HESM is a nonlinear function of the daxis current, the qaxis current, and the excitation current [6, 7]. Therefore, a given electromagnetic torque may be generated by different current partitions, each one leading to a different total copper loss [8]. In order to enhance the performance of the motor, the control method of maximum torque per ampere (MTPA) used for PMSM is often adopted [9–11] to realize the optimal configuration of the armature and excitation currents. However, there is one more controllable excitation current in the HESM than in the PMSM, and thus the MTPA control method only provides copper loss minimization control for HESM [12], leaving room for further improvement.
For the hidden pole or the approximate hidden pole of the HESM, the authors of [8, 13] have proposed a vector control method based on the daxis current i_{d} = 0 combined with the copper loss minimization control strategy to optimize the motor efficiency. The disadvantage of the method is that, during the fluxweakening regulation, when the motor is operating at high speed, the fluxweakening effect on the daxis current is not fully exploited, resulting in a limitation of the available motor speed range. The authors proposed a piecewise optimization control algorithm [14], which combines fuzzy control with particle swarm optimization to enhance the motor efficiency and stability. The shortcoming here is that, during the fluxweakening, the basespeed coefficient is constant and cannot maintain the optimal working point when the motor operating state changes. The fluxweakening method may be also applied while keeping constant the back electromotive force (back EMF) [13], and this makes the motor able to show a satisfactory operating performance, though the stability problem of [12] is not solved.
In this paper, an innovative efficiency optimization control method is proposed, which is combined with the vector control and speed partition control principles [14, 15]. Our method aims at minimizing the copper loss by the motor, and it consists in exploiting two different control methods depending on the speed of the HESM. Upon splitting the possible values of the speed into two intervals, we employ the copper loss minimization control method with i_{d} = 0 for “low speed,” whereas for “high speed,” the fluxweakening basespeed coefficient is adjusted by the selfadaptive method to realize the optimal configuration of the excitation and armature currents, as well as to achieve the efficiency optimization control. We also present a set of simulations and motordriven experiments to show the validity and the efficiency of the proposed control method.
2. Mathematical Model of HESM
In a generic HESM, the dqaxis coordinate is established by adopting the directional control method of the rotor magnetic field, whose air gap magnetic field is generated by the permanent magnetic body, daxis current of the armature coil, and the current of the excitation coil. The effects of temperature fluctuations, iron loss, stray loss, magnetic field saturation, and other influences inside the motor are neglected. The HESM excitation current is assumed to have the same phase of the air gap magnetic flux generated by the permanent magnetic body. With these assumptions, the equivalent circuit model of the motor at the steady state is shown in Figure 1.
Based on the equivalent circuit model shown in Figure 1, the following basic equations of the HESM can be derived [14].
The circuit equations are
Flux linkage equations are
Torque equations arewhere the meanings of the symbols are the following: u_{d}, u_{q}, i_{d}, and i_{q} are the voltage and current components of the d and qaxes, respectively; ψ_{pm}, ψ_{d}, and ψ_{q} are the permanent magnet flux linkage and the flux linkages of the d and qaxes, respectively; u_{f} and i_{f} are the voltage and current of the excitation coils; R_{s} and R_{f} are the resistances of armature and excitation winding, respectively; L_{d}, L_{q}, and M_{sf} are the armature d and qaxes inductance and the mutual inductance between the armature and the excitation winding, respectively; and ω_{r} is the angular velocity, p is the pole pairs of the motor, and T_{e} is the electromagnetic torque.
3. Speed Partition Optimization Control of the HESM
3.1. Introduction of the Control Strategy
In analogy with the PMSM motor, the speed range may be divided into two regions, as shown in Figure 2, in which the partition control method is adopted. Region I (ω_{r} ≤ ω_{N}, where ω_{r} is the motor speed and ω_{N} is the rated speed of the motor) is the lowspeed region, where the control method of fluxstrengthening or noexcitation is applied. The motor in this speed range can obtain the excess electromagnetic torque without exceeding the current limit. Moreover, when the motor speed is less than or equal to the fluxstrengthening basespeed ω_{M}, the maximum output electromagnetic torque reaches T_{max}, above which the output torque will decrease linearly due to the voltage limitation on the motor. Region II (ω_{r} > ω_{N}) is the highspeed region, in which the back EMF of the motor is kept constant. By suitably adjusting the excitation current and the daxis current, we can implement the fluxweakening speed regulation, making the motor able to operate at speed much higher than the rated speed.
3.2. Control Method in the LowSpeed Region (ω_{r} ≤ ω_{N})
According to the HESM electromagnetic properties, if there is noexcitation current, the reference torque current i_{Tref} at the output of the speed controller is exactly the torque component of the armature current. In other words, in the lowspeed region, an HESM is equivalent to a PMSM with a similar structure and the vector control method with i_{d} = 0 may be used. Upon exploiting the torque equilibrium relation, we have that when the HESM is under the control of fluxstrengthening, the reference value of electromagnetic torque is given bywhere i_{fref} is the reference value of the excitation current and i_{qref} is the reference value of the qaxis current. The basic current distribution may be obtained from (4) as follows:
By inspecting (4), we see that when the fluxstrengthening excitation current and the qaxis current take the values i_{fref} = 0 and i_{qref} = I_{qN} or i_{fref} = I_{fN}and i_{qref} = I_{qN} (where I_{fN}, I_{qN} are the excitation current and the rated qaxis current), the reference electromagnetic torques at the speed controller are the rated value and the maximum value, respectively:
In (5), since i_{qref} and i_{fref} are both unknown, one more constraint equation should be added to obtain the unique value of the current distribution of the HESM in the lowspeed region. In this study, we take the minimization of the copper loss by the motor as the other constraint condition to solve the two reference values of the current. Upon considering the i_{d} = 0 vector control method, the equation of the copper loss for the HESM is given by
The Lagrangian multiplier method is then adopted to determine the minimum value of P_{cu}. By combining (4) and (7) and letting i_{q} = i_{qref}, i_{f} = i_{fref}, we obtain the Lagrangian function as follows:
Taking the derivatives of (8) with respect to i_{qref} and i_{fref} and setting them to zero, we can eliminate λ and get the relation between i_{qref} and i_{fref} when the minimum copper loss condition is satisfied:
By substituting (5) into (9), we obtain the following equation after straightforward algebra:
Equation (10) is a quartic equation with one unknown variable which can be solved numerically, e.g., by Newtonian iteration. When the HESM is operating in the lowspeed region, the motor has only two states: the fluxstrengthening and noexcitation states. We thus have i_{fref} ≥ 0, and we may assume i_{fref} = 0.5I_{fN} without loss of generality. Simulations and experiments both verify that four iterations are enough to obtain the approximate solution of i_{fref} with a relative error lower than 1%. Therefore, the realtime operation requirement can be satisfied when using the DSP to control the HESM. Finally, by substituting the value of i_{fref} into (5), we find i_{qref}.
In the above calculations, since the speed is low, the fluxstrengthening is not leading to a very large back EMF and, in turn, there is no need to consider the limitation of bus voltage. On the other hand, when the speed exceeds ω_{M} and the system enters into subRegion 2 (see Figure 2), the torque current reference value should be limited in order to prevent overloading. By combining (5) and (6), we obtain ω_{M}, as well as the value of the maximum torque current reference I_{Tmax}:where P_{N} is the rated power of the HESM.
3.3. Control Method in the HighSpeed Region
3.3.1. Basic Algorithm
In the design of the HESM control system, the fluxweakening control in the highspeed region is a challenging crucial step. When the motor speed reaches the rated speed ω_{N}, its back EMF approaches the voltage value at the armature end, and to further increase the speed, the fluxweakening control should be applied. In this condition, the regulation of the HESM armature current and excitation current are constrained by the voltage limit cycle, as it happens with the fluxweakening speed regulation mode in the constant power region of the PMSM. Under the steady operating condition, the voltage vector amplitude should satisfywhere U_{lim} is the limiting value of the voltage vector due to the back EMF at the motor side. Neglecting the resistance of the armature coil, the dq back EMF components for a steadystate motor are given by
Substituting (13) into (12), we obtain
Upon inspecting the above formula, it is straightforward to see that applying the fluxweakening control on the HESM, the current distribution is limited by U_{lim}, while the qaxis component of the back EMF is given by
By combining (14) and (15), we have that when the HESM is operating at noload speed, i_{q} ≈ 0 and (14) can be simplified to
Overall, the principle of the fluxweakening speed regulation of HESM is very much similar to the PMSM one, and we only need to keep E_{q} smaller than or equal to U_{lim} when applying the fluxweakening control.
It can be seen from (15) that when i_{d} = i_{f} = 0, ω_{r} depends linearly on E_{q}. As a consequence, when the normal vector control is applied, the maximum noload speed ω_{max} at the noexcitation current is linearly dependent on the DC bus voltage U_{dc}. The fluxweakening basespeed ω_{Bdec} is limited by ω_{max}, whose value can be obtained by the i_{d} = i_{f} = 0 vector control under the noload experimental condition. After collecting experimental data of bus voltage and maximum noload speed, we build a linear fittingwhere is the ratio of the maximum speed over the voltage; ω_{0} is the speed offset value; and k_{b} is the fluxweakening basespeed coefficient. In order to simplify calculation, we may set the fluxweakening base speed to ω_{Bdec} = ω_{N}, so k_{b} = ω_{N}/ω_{max}.
In the process of fluxweakening speed regulation, a control strategy to keep the back EMF invariant should be adopted. This is in order to ensure that the back EMF of the motor is smaller than the voltage of the power source and, in turn, to prevent the saturation of the current controller and the loss of control on the speed. To this aim, a strategy similar to the fluxweakening control in the PMSM may be employed. The back EMF base value E_{base} is approximately
From (15), the motor back EMF may be approximated by
To maintain the back EMF nearly constant in the highspeed region and under the fluxweakening speed regulation, the estimated value of the back EMF should satisfy
Combining (18)–(20) and setting the daxis current and excitation current at their reference values, respectively, i.e., i_{d} = i_{dref}, i_{f} = i_{fref}, we can obtain the voltage constraint equation of the HESM fluxweakening speed regulation. After some algebra, we arrive at
Obviously, (21) is different from the analogue voltage limit equations of the normal PMSM because it is an approximate equation. Its precision and the practical control effect are determined by the value of ω_{Bdec}. We will discuss this point later.
In the operating process of fluxweakening, to control and minimize the copper loss of the HESM, the limitation of the loading torque and the inverter output voltage should be satisfied simultaneously. That is, under the condition posed by (3) and (21), we need to find the value of the current reference needed to minimize the copper loss of the motor by solving the corresponding loss equation:
Combining equations (3), (21), and (22) and setting P_{cu}, i_{d}, i_{q}, and i_{f} to their reference values, i.e., P_{cu} = P_{cu_ref}, i_{d} = i_{dref}, i_{q} = i_{qref}, and i_{f} = i_{fref}, we can construct the Lagrangian function as follows:where λ_{1} and λ_{2} are the Lagrangian multipliers. Upon eliminating the multipliers, we arrive at the following equation:
In addition, by combining (3) and (21) and using an iteration method [13], we may find all the current reference values i_{dref}, i_{qref}, and i_{fref} leading to the minimization of the copper loss by the motor.
Equations (3), (21), and (24) form a system of equations with three unknown variables. Although it can be solved via the iteration method, the calculation process may be involved, and in practical engineering applications, a simplified control algorithm for the minimization of copper loss may be better adopted.
3.3.2. Simplified Control Algorithm
According to (2) and (19), the larger is the fluxweakening current, the weaker is the air gap magnetic field and the smaller is the back EMF. Overall, this results in a larger qaxis current required at a given load, and, therefore, to realize the copper loss minimization control, the fluxweakening current should be reduced as much as possible to make the back EMF as close as possible to the terminal voltage. The qaxis current reference value is given by the speed controller and can be adjusted automatically according to the variation of the load and speed:where T_{eref} is the reference electromagnetic torque output by the speed controller and k_{i} is the ratio coefficient of the current over the torque, i.e., a constant determined by the HESM electromagnetic properties.
Since i_{d}, i_{q}, and i_{f} are fully decoupled, they do not need a unified calculation. Therefore, when applying the control algorithm for the copper loss minimization, we can use the incomplete copper loss equation in place of (22) to conduct the calculation; that is,leading to a simplified algorithm of the copper loss minimization control. The differences between this algorithm and the original one are about the current calculation process. In the present algorithm, only the voltage constraint in (21) is used while the torque equation is not included. Needless to say, this considerably simplifies calculations. Combining equations (21) and (26) and setting P_{cu}, i_{d}, and i_{f} to their reference values, we obtain the following Lagrangian function:
Using (21) and taking the derivatives of the above equation with respect to i_{dref} and i_{fref}, we get the following solution:which, by using the notationcan be rewritten as
From (30), we see that the fluxweakening currents i_{dref} and i_{fref} decrease when ω_{Bdec} increases, which in turn leads to a decrease of the motor flux weakening. Therefore, by increasing or decreasing the value of ω_{Bdec}, one may tune the motor fluxweakening speed and the copper loss magnitude.
3.3.3. SelfAdaptive Regulation of FluxWeakening BaseSpeed Coefficient
From the above theoretical analysis, we know that ω_{Bdec} influences the operating properties of the HESM fluxweakening control. Those effects may be summarized as follows: (1) when ω_{Bdec} is too large, the fluxweakening current is too small, thus leading to an insufficient fluxweakening. In this case, the HESM speed cannot reach the set value, i.e., we have a limitation on the speed range; (2) when ω_{Bdec} is too small, the fluxweakening current is too large, leading to overweakening of the flux in the motor and, in turn, to an increase of the copper loss, resulting in a low efficiency. Therefore, in order to ensure optimal control of the motor fluxweakening speed regulation, further analysis on the influence of ω_{Bdec} should be performed, possibly leading to a suitable choice of its value.
From (17), we know that the magnitude of ω_{Bdec} is determined by the fluxweakening basespeed coefficient k_{b}. Therefore, we may describe the relationship among the variables as follows:
In other words, the crucial ingredient to determine the optimal ω_{Bdec} value and to jointly realize the optimizations of the motor speed range and the efficiency is the choice of the value for k_{b}.
In order to assess the influence of k_{b} on the HESM efficiency, we may use the system simulation analysis while changing its value. In the simulation, all the electrical parameters are set according to the prototype practical parameters [14]. The simulation result is presented in Figure 3, which indicates that the motor efficiency increases monotonically with k_{b}.
To gain a deeper insight into the influence of k_{b} on the HESM speed range and dynamical properties, we have performed a set of simulated experiments by setting different k_{b} values in the HESM control system. The behavior of the speed as a function of time is illustrated in Figure 4 for different values of k_{b}. Results have been obtained by setting the load at 0.5 Nm and the reference speed at 6000 rpm, and they indicate that the larger is k_{b}, the lower is the maximum speed that the motor may reach. When k_{b} ≥ 0.9, the maximum speed is smaller than 1500 rpm. The value k_{b} also influences the dynamical properties of the motor fluxweakening speed regulation. In particular, the larger is k_{b}, the slower is the speed rising and the longer is the starting time.
In conclusion, we have that decreasing k_{b} may enhance the HESM speed range and dynamical properties, however at the expense of reducing the efficiency. On the contrary, by increasing k_{b}, we reduce the copper loss of the motor and enhance its efficiency, but the speed range decreases, and the fluxweakening speed regulation dynamical properties degrades. In particular, when k_{b} exceeds a certain threshold value, the fluxweakening base speed becomes too high and the motor becomes unable to switch to the fluxweakening speed regulation region, resulting in a large decrease of the speed range. In other words, we have that keeping k_{b} constant when the motor is operating does not guarantee the optimality of its performance under different working conditions.
In order to solve these issues, this paper proposes an HESM control method which may selfadaptively adjust the fluxweakening basespeed coefficient k_{b} according to the working condition, thus resulting in an enhancement of the motor overall performance. The principle is to split the HESM operating regimes in the highspeed region into three regions, which are the region of transient state, the region of quasisteady state, and the region of steady state, respectively. The three regions are determined by the difference between the set speed and the practical speed and are illustrated in Figure 5. According to the changes in the motor state, we can dynamically adjust the coefficient k_{b} to optimize the motor overall performance, as shown in Figure 6. The regulation method for k_{b} in each region is illustrated below.
The region of transient state corresponds to ∣ω_{r} − ω_{ref}∣ > Δω_{ust}, where Δω_{ust} is the error upper limit in the region of quasisteady state. The parameters k_{b,}stable, and up are initialized and kept constant in this region. Since to improve the HESM speed range and dynamic property, the initial value k_{bmin} should not be too large, we set it at k_{bmin} = 0.5.
The region of quasisteady state corresponds to the range Δω_{st} < ∣ω_{r} − ω_{ref}∣ ≤ Δω_{ust}, where Δω_{st} is the error upper limit in the region of the steady state. In this region, according to the values of stable, up and the magnitude of ω_{r}, one may decide whether to make an adjustment of k_{b} or not.
The region of the steady state corresponds to ∣ω_{r} − ω_{ref}∣ ≤ Δω_{st}: this region may be further divided in two subcases according to the value of stable, which indicates whether the optimization is complete or not. If it is equal to 1, then the regulation of k_{b} is completed and the value should be kept unchanged. If instead it is equal to 0, then the optimization is not completed and k_{b} should be increased, along with the flag set to up = 1, indicating that the adaptive control should be continued.
In the process of selfadaptive regulation of k_{b}, the HESM is kept in the steady operating state until k_{b} exceeds the upper limit, then the motor is forced to lower its speed and leave the steady state. Therefore, the k_{b} regulation step length, termed Δk_{bu}, cannot be too large to avoid the generation of large overshoot. At the same time, the regulation time period should be properly set according to the motor electrical and mechanical properties. This is in order to keep the armature current and excitation current variation amplitude small and smooth and also to keep the output electromagnetic torque nearly constant in the whole regulation process.
During the operating process of the HESM, due to the influence from the set speed, load variation, or other external factors, the motor is forced to leave the region of steady state, go across the region of quasisteady state, and finally reach the region of transient state, where k_{b} should be reset to a small initial value k_{bmin}. On the other hand, when the motor reaches again the steady state, k_{b} should be automatically adjusted to optimize the motor efficiency.
4. Analysis of the Experimental Results
4.1. Control System Modeling
The HESM vector control system model, resulting from the above theoretical analysis based on the speed partition and vector control principle, is shown in Figure 7. This control system model is similar to the regular PMSM vector control one, however with three more functional modules (contained in the dashed ellipses). The three modules are the current distributor, the excitation current pulse width modulation, and the excitation drive module. Among them, the current distributor is the core module of the HESM control system, and it is designed according to the speed partition control principle. Its main function is to estimate the armature current and the excitation current and then output the reference currents i_{dref}, i_{qref}, and i_{fref}.
4.2. Analysis of the Experimental Results
Figure 8 illustrates the results of the experiments performed with the HESM control system. The experiment adopts the expert system TS7700, from the Japanese Ono Measurement Device, for the torque workstation equipped with the torque sensor MT6425, the eddy current brake, and so forth. This series of test devices can be used to measure the different parameters influencing the motor properties, including the speed, torque, input and output power, and efficiency. We employ the HESM prototype with a claw pole structure, which includes the TAMAGAWA OIH482500 increment photoelectric encoder. The parameters of HESM are given in Table 1. The control board is a hardware circuit based on the TMS320F2812 + AT89C55WD architecture, along with the two driver boards of armature and excitation, and a circuit board of buttons and display. The computer and the control board are connected to the DSP simulator by the JTAG interface. By applying the debugging software CCS3.3, we may also record the variation of the relevant electric parameters which are not accessible by other devices.

Figure 9 reports the experimental waveforms of HESM during the starting process. Figure 9(a) is the variation of speed and fluxweakening basespeed coefficient with time. Figure 9(b) shows the relationship between copper loss and time. In the experiment, the speed is set at 3000 rpm, and the load is set at 1 Nm. After the motor is switched on, as well as before the speed reaches the steady state, k_{b} is kept nearly constant at the value k_{b} = 0.5. After a transient time of about 2 s, the motor enters the region of steady state and k_{b} begins to linearly increase with time. In this regime, the speed is kept constant and the motor copper loss decreases as k_{b} increases. After about 3.7 s, k_{b} reaches its peak. At this time, due to the overdecreasing of the excitation current and the daxis current, the motor fluxweakening degree is insufficient, resulting in the increase of the motor back EMF and the saturation of the qaxis current controller, which will further force the speed to decrease and the motor to enter into the region of quasisteady state. After decreasing k_{b} slightly, the motor returns to the steady state, and then the speed stays constant. The motor copper loss is instead slightly increasing during the callback of k_{b}. The results of this experiment indicate that the copper loss is about 60 W before the regulation of k_{b} and about 40 W after the regulation of k_{b}, i.e., a reduction ratio of about 1/3.
(a)
(b)
Figure 10 shows the experimental waveforms of the Aphase current and excitation current when the HESM is starting. In this experiment, the motor speed is set at 2500 rpm and the load torque is given by 1.5 Nm. In order to enhance the motor performance when it starts up, we apply an excitation current to increase its starting torque 0.5 s before the motor is switched on. With the increase of the speed, i_{f} quickly drops to 0, and when the speed exceeds n_{Bdec}, i_{f} becomes negative and the flux weakening is activated. When the motor speed enters the region of steady state, due to the gradual increasing of k_{b}, the excitation current and armature current decrease accordingly. Two seconds after the motor is started, a fluctuation with the duration of 0.5 s appears in the armature current and excitation current. This fluctuation is caused by overregulation of k_{b}, which leads to a decrease of the speed and drives the motor to the region of quasisteady state. At last, when we shut down the motor drive system because of the high operating speed, we need to slightly postpone the shutdown of the excitation current, in order to prevent an excessive response of the back EMF caused by the shutting down of the deep flux weakening. Therefore, as it may be seen in Figure 10, the armature current is shut down 0.3 s before the excitation current.
Figure 11 shows the current waveforms of the Aphase current and excitation current when HESM is operating in the steady state. The motor speed is here set at 2500 rpm and the load torque is given by 1.5 Nm. i_{f} is equal to 0.8 A; it shows very small fluctuations, and it is relatively smooth. The phase current amplitude is 2.4 A; it shows an almost sinusoidal waveform, and it has negligible harmonic components.
5. Conclusion
HESM represents a class of highorder, nonlinear, and strongcoupling systems with multiple variables. In this paper, upon building on the vector control method, we put forward a control algorithm which combines the copper loss minimization control algorithm with a selfadaptive method to dynamically regulate the fluxweakening basespeed coefficient and to further improve the motor’s overall operation properties. We have assessed and verified the validity and efficiency of the proposed HESM control strategy by means of numerical simulations and experiments. The conclusions may be summarized as follows:(1)For the HESM with salient pole (also effective for the hidden pole), we have proposed a basic copper loss minimization control algorithm. The calculations are relatively complex, but since we suitably exploit the regulation functions of armature current and excitation current on the torque and magnetic field, the motor efficiency optimization control may be still realized.(2)Starting from the HESM electrical properties, we have proposed a simplified copper loss minimization control algorithm, which may largely simplify the calculation of the reference current. The method is similar to the basic copper loss minimization control algorithm.(3)We have suggested a selfadaptive regulation of the fluxweakening basespeed coefficient for the motor operating in the steady state to optimize the control method of the fluxweakening current and, at the same time, to minimize the copper loss and enlarge the speed range. In this way, we have solved the problems arising when the HESM speed range, efficiency, and dynamical property cannot be simultaneously taken care of due to the constant fluxweakening basespeed coefficient. The overall performance and dynamical properties of the motor are significantly enhanced.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the Natural Science Foundation of Henan Province (182300410224), the National Natural Science Foundation of ChinaHenan Joint Fund (U1804162), the Fundamental Scientific and Technological Research Funds of Henan Science and Technology Agency (192102210072 and 202102210109), and the Key Scientific Research Projects of Colleges and Universities in Henan Province (17A470008).
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Copyright © 2020 Mingming Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.