Abstract: In response to current development trends in generator systems, this paper proposes a control strategy for a permanent magnet synchronous generator system, enabling the system to operate at higher speeds. Throughout the start-up process, this control strategy employs a current loop as the inner loop and a speed loop and a bus voltage loop as the outer loops. For further expanding the speed variation range, this paper focuses on a simplified analytical field weakening control method and verifies the feasibility of the bus voltage loop under this method. Finally, simulation results show that this control strategy ensures the system operates as expected throughout the start-up process.
1 Introduction
In recent years, starters have been increasingly widely used in aviation, high-speed trains, electric vehicles, and ships, gradually becoming a core component of power generation systems. Starters not only play a major role in power supply to the power grid, but also, with the help of an external power source, can function as a starting prime mover. Combining these two functions, starters further enhance the competitiveness of power generation systems in terms of weight and size. This paper mainly explores a control strategy based on a permanent magnet synchronous starter system and addresses the need to broaden the speed variation range during the power generation phase to meet the system's development requirements.
Generally, when the starter generator operates at high speed, its output voltage increases accordingly, causing the output voltage at the DC bus to become uncontrollable. Therefore, field weakening control is needed to regulate the output voltage on the starter generator side. Traditional field weakening control methods mainly include analytical methods, voltage feedback methods, lead angle methods, and switching time feedback methods. The latter three methods all use PI regulators in the process of generating the d-axis current reference value. However, the parameter design of PI regulators becomes particularly difficult over the extended speed range. Furthermore, this paper uses a surface-mounted permanent magnet synchronous motor as the starter generator, which greatly simplifies the analytical expressions used in the analytical method. Therefore, for this study, analytical methods are more suitable for field weakening control.
When the generator reaches high speed, it enters the power generation phase. Depending on the system structure, the control strategy at this stage can use either DC bus current or voltage as the outer loop control variable. The former is typically used when the system operates in parallel with other power sources. However, this paper only considers the case of independent system operation. Since the latter has better voltage output characteristics, this paper uses bus voltage as the outer loop control variable during the power generation phase. The following section will focus on verifying the feasibility of closed-loop bus voltage control using the analytical field weakening control method over a wider speed range.
2 generator system structures
The generator system structure described in this paper consists of a permanent magnet synchronous motor, a voltage source converter, and a ±270V DC bus, as shown in Figure 1.
The complete operation process of the starter generator is shown in Figure 2. During the startup phase, the starter generator is driven by the converter to start the prime mover. Initially, the starter generator operates in constant torque mode to quickly increase the speed. When the speed reaches ωct/cp, limited by the output voltage, the starter generator will switch to constant power mode. During the power generation phase, the starter generator is driven by the prime mover and provides power to the load through the DC bus. During this process, although the output power remains constant, the speed varies within the range of ωnlg to ωmax.
3. Research on Control Strategies
In the dq-axis rotor synchronous rotation coordinate system, this section proposes a control strategy applicable to the entire start-up process. Since the purpose of this paper is to broaden the range of motor speed variation, this section will focus on the power generation stage.
3.1 Mathematical Model of Permanent Magnet Synchronous Motor and Converter
As mentioned in the previous section, the permanent magnet synchronous motor and the converter are the most fundamental components of the generator system; therefore, the control strategy must be based on the mathematical models of both. The circuit equations of the permanent magnet synchronous motor are as follows:
In the formula: Vd, Vq, id, iq, Ld, Lq are the d-axis voltage, current, and stator inductance, respectively. For a surface-mounted permanent magnet synchronous motor, Ld = Lq, denoted as LS; RS, ωe, Ψf, J, Ω, RΩ, TL, Te, P, idc, Vdc, iL are the stator resistance, rotor electric angular velocity, equivalent permanent magnet flux linkage, moment of inertia, mechanical speed, damping coefficient, load torque, electromagnetic torque, number of pole pairs, converter DC output current, bus voltage, and load current, respectively.
3.2 Start-up Phase
The main objective of the start-up phase is to drive the prime mover to start; therefore, the control strategy for the start-up phase is similar to the traditional control of a permanent magnet synchronous motor in motor mode. As shown in Figure 3, connecting the double-pole double-throw switch to terminal S constitutes the control block diagram for the start-up phase.
As can be seen from equations (3) and (4), the outer loop should use the speed loop to obtain the q-axis current reference value. For surface-mounted permanent magnet synchronous motors, the d-axis current reference value is generally set to zero to achieve the maximum torque-current ratio. In addition, the inner loops of d- and q-axis currents and space vector pulse width modulation both follow the traditional design method [9].
3.3 Design of Field Weakening Control Method
For surface-mounted permanent magnet synchronous motors, the magnetic field is generated by permanent magnets attached to the rotor surface. Due to the special setting of the rotating coordinate system, the magnetic flux generated by the d-axis current and the equivalent magnetic flux generated by the permanent magnet are on the same straight line. Therefore, the effect of weakening the magnetic field can be indirectly achieved by adjusting the d-axis current.
Once the motor reaches steady state, equations (1) and (2) will be simplified, and the magnitude of the stator voltage vector will be:
Since the operating speed is relatively high, the voltage drop across the resistor is ignored. Replacing ν with νlim in equation (7) yields the voltage limiting circle that restricts the motor's operating conditions:
When using space vector pulse width modulation, the amplitude of the stator current vector is also limited by the maximum allowable current νlim of the converter and motor.
Combining the voltage limit circle and the current limit circle, the operating range of the motor can only be located in the shaded area shown in Figure 4.
For surface-mounted permanent magnet synchronous motors, the relationship between output power, speed, and q-axis current is as follows:
In the formula: P* is the reference value of output power; n is the motor speed, in rpm.
Therefore, when the output reference power is constant, the motor's operating range will be further reduced, only including the portion of the horizontal line corresponding to the q-axis current at the current speed within the shaded area. As the motor speed increases, when the motor's operating range no longer intersects with the q-axis, id=0, and the control strategy will no longer be applicable. In other words, at this point, the d-axis current needs to be set to a negative value to weaken the magnetic flux generated by the permanent magnet. Based on the target maximum torque-to-current ratio, the motor's current vector should fall exactly at the right intersection of the horizontal line corresponding to the q-axis current and the voltage limit circle. Therefore:
3.4 Power Generation Stage
This paper mainly considers the case of resistive load, and the transfer function of the bus voltage can be obtained through equations (5) and (6):
In the formula: RL is the load resistance; md and mq are the d-axis and q-axis voltage modulation coefficients of the converter, satisfying:
When the design satisfies that the inner current loop is much faster than the outer voltage loop, the modulation coefficients will respond quickly and remain constant throughout the time constant of the entire outer loop, denoted as Md and Mq. The actual values of the d-axis and q-axis currents will also respond quickly and remain consistent with the reference values.
In the initial stage of power generation, using the id=0 control strategy, the transfer function from the q-axis current to the bus voltage can be obtained as follows:
When field weakening control is used, the expression for the d-axis current reference value is rearranged into equation (16), and substituted into equation (13), the transfer function from the q-axis current to the bus voltage can be obtained as follows:
In the formula: iq_comp is the q-axis current feedforward compensation value; k is derived from equation (10) and is determined as a constant by the output power reference value, satisfying:
Therefore, the control structure block diagram of the bus voltage loop is shown in Figure 5, where Tf is the filter time constant of the sampling feedback unit, G(s) is the transfer function from the q-axis current to the bus voltage, and K is...
R(s) is the transfer function of the controller. This paper uses a PI regulator as the controller, which can correct the bus voltage loop to a type I system, thereby ensuring the dynamic performance and stability of the system.
The open-loop transfer function of the bus voltage loop is as follows:
The design of the inner current loop during the power generation phase is completely consistent with that during the startup phase. The bandwidth of the inner current loop is designed to be 10 times that of the outer voltage loop to satisfy the assumption that the inner loop is much faster than the outer loop. As shown in Figure 3, the control block diagram for the power generation phase can be obtained by connecting the double-pole double-throw switch to terminal G.
4. Simulation Results and Analysis
Based on the system block diagram shown in Figure 3, a generator system simulation model was built in MATLAB. The system includes a surface-mounted permanent magnet synchronous motor and a three-phase full-bridge two-level IGBT converter. The motor parameters are shown in Table 1. During the power generation phase, the bus voltage is maintained at a constant 540V, and a 250kW load is connected to the bus.
During the start-up phase, the motor speed ranges from 0 to 12000 rpm, and its simulation waveforms are shown in Figures 6(a) to (c). Initially, the generator maintains a constant torque of 200 Nm. When the motor speed reaches 7000 rpm, it enters constant power mode, maintaining a constant output power of 147 kW. The simulated load torque of the prime mover is shown in Figure 6(b).
The switching point between the start-up phase and the power generation phase is set at 0.5s. The simulation waveforms of the power generation phase are shown in Figures 6(b) to (d). During the power generation phase, the torque output by the prime mover is much greater than the electromagnetic torque of the generator, making the influence of the electromagnetic torque on the prime mover speed negligible. Therefore, in the simulation model, the mechanical input of the generator is changed from load torque to speed, which varies between 12000 and 24000 rpm, as shown in Figure 6(a). As can be seen from equation (8), when the speed exceeds 17800 rpm, field weakening control is adopted. The simulation results show that field weakening control can ensure that the system continues to operate normally.
As shown in Figures 6(e) and (f), the inner loop ensures that the d-axis and q-axis currents quickly and accurately follow the reference values. As shown in Figures 6(a) and (d), the outer loop ensures the dynamic performance of the motor speed and bus voltage.
5. Conclusion
This paper proposes a control strategy for a permanent magnet synchronous generator system. This strategy employs an analytical field weakening control method to address the increasing trend in motor operating speed. Based on this field weakening control method, the feasibility and stability of the outer loop design for the bus voltage are theoretically verified. Finally, a simulation experiment of a 250kW generator system verifies the effectiveness of the control strategy, achieving a maximum speed of 24,000 rpm. Due to its simplicity and wide adaptability, this control strategy can be applied to a hardware-in-the-loop simulation platform for generator systems, used for motor parameter design. Because of its wide applicable speed range, the simulation platform can operate normally even when testing extremely demanding motor parameters.
