Power balanced control of rectifier permanent magnet generator sets

Abstract

With the wide application of electric drive equipment and variable frequency load, the power supply system based on the DC grid has attracted much attention because of its high energy density and simple control, and the operation mode of rectifier AC synchronous generators operating in parallel is often adopted. The available topology structures of the rectifier permanent magnet (PM) generator sets are analyzed in this paper, the parallel operation principle of uncontrolled rectifier PM generator sets is analyzed in theory. The parallel operation characteristics of the generator sets are summarized when the voltage-stabilizing and power balanced measures are not taken, and the influence factors of power balancing among parallel operation generators are analyzed. The power-balanced method of rectifier generator sets operating in parallel based on a master-slave control strategy is proposed, which can realize power balanced with the closed-loop control of the DC side output current. The simulation and experiment results show that the proposed method can realize the power balanced control of rectifier generator sets operating in parallel well. The output power of each generator set can be distributed according to capacity. The rationalization proposal of how to matching generators’ parameters in the power supply system of rectifier PM generator sets operating in parallel is given.

Keywords

PM generator uncontrolled rectifier operating in parallel power balanced control mobile power supply

1 Introduction

Compared with the traditional internal combustion engine drive, electric drive has the advantages of convenient control, fast response, and a good economy. It is widely used in electric propulsion ship, electric vehicle, high-speed railway, truck, oil and gas drilling, and other fields [1, 2]. The rapid application and development of the electric drive system cannot be separated from the support of the mobile power supply with high reliability and high performance. With the increasingly high demand for mobile power supply in various fields, the conventional power frequency generator set with diesel or gasoline as fuel is difficult to meet the requirements of capacity and power density [3]. Because the electric drive system is mostly variable frequency load, the generator sets only need to output DC power to meet the needs of the inverter, and it is no longer limited to the power frequency AC power [4]. Compared with the DC generator, the AC generator has obvious advantages in high speed and high power field [5]. The rectifier AC generator set eliminates the frequency limit of the generator and can be driven directly by a gas turbine with high speed. Which can meet the demand for capacity and power density, and the use of clean energy natural gas as a fuel has unparalleled economic and environmental benefits [6]. To improve the reliability, economy, and capacity expansibility of the mobile power supply, the power supply type of several generator sets operating in parallel is usually adopted [7].

Rectifier AC synchronous generator set adopts a high-speed prime mover and generator, which can greatly increase the power density of the power supply, and reduce the volume of the power supply. The system can operate on the optimal fuel consumption curve by adjusting the speed of the prime mover according to the load change [8]. The mobile power supply based on the DC grid has attracted more and more attention. For example, ABB has launched the DC power grid for ships, and SIEMENS has introduced the DC electric propulsion system BlueDrive PlusC [9]. The research on the operation characteristics, parallel operation conditions, and power balance measures of the AC power supply system operating in parallel has been very mature. However, the relevant research of the rectifier AC generator sets operating in parallel is still in the initial stage. To promote the rapid popularization and application of the power supply system of rectifier generator sets operating in parallel, a control strategy with high reliability, good economy, and easy operation is essential [10].

If the rectifier generator sets operating in parallel does not take effective power balanced measures, there are some inevitable differences between the parameters of the generator sets, which will result in the power generator sets can’t distribute the power according to their capacity and affect the stability of the power supply system. Depending on the difference of prime mover type, generator type, rectifier method, and voltage regulation measure, the rectifier generator set has a variety of topologies, and the strategies for power balanced control under different topologies are different [11]. In references [12, 13], the PWM rectifier method is analyzed and improved, and the output voltage and current waveforms of the generator are very sinusoidal. In references [14, 15], the power supply system of PM generators operating in parallel is studied, the PWM rectifiers are connected to the DC grid, and the control strategy based on vector control technology is adopted. The stability of power supply system operating in parallel is studied in reference [16], it shows that there may be interaction shock and load oscillation in this kind of system, and the stability criterion is given. In reference [17], aiming at the topology of uncontrolled rectifier electric excitation synchronous generator operating in parallel, the influence factors of the power balance are analyzed, and the method of regulating the generators’ output voltage by adjusting the excitation current is used to adjust the power distribution ratio between the generators. In references [18-19], the influence of the master-slave control strategy on the output characteristics of the power supply system is studied for controlled rectifier generators operating in parallel. In references [20-21], the principle of current sharing control in parallel operation DC-DC chopper circuit is analyzed, and the method of current sharing control is given.

The available topology of the rectifier PM generator set is analyzed in this paper. In different topologies, the influence of generator parameters on the output power balance of the generators is studied. For the uncontrollable rectifier topology, the power balanced method for rectifier generator sets operating in parallel based on master-slave control strategy by adjusting the speed of the slave generator set is proposed, and the power balanced is realized by the closed-loop control of the DC side output current.

2 The topology of rectifier pm generator set

According to whether the output voltage of the generator is constant, the voltage-stabilizing methods of the rectifier generator set can be divided into single port voltage-stabilizing control and dual-port voltage-stabilizing control [22]. To obtain stable DC power, the AC side voltage-stabilizing control can be realized by the self-control of the generator, and the DC side voltage-stabilizing control can be realized by the control of power electronic device [23, 24]. When DC side voltage-stabilizing control is adopted, there is no need to maintain the output voltage of the generator constant, which promotes the wide application of PM generator with simple structure, high power density, and high efficiency [25]. This paper takes the rectifier PM generator set as the research object, according to the difference of voltage-stabilizing control measures, the available topologies of the rectifier generator set are shown in Fig. 1.

The PWM rectifier voltage-stabilizing topology shown in Fig. 1 (a), compared with the electric excitation generator, the PM generator is difficult to voltage-stabilizing by itself. To achieve voltage-stabilizing, the method of hybrid excitation or space vector control technology is needed. Due to the hybrid excitation that will result in the generator with complex structure and poor reliability, the latter method is generally used to realize voltage-stabilizing control. PWM rectifier can realize the maximum torque per ampere control of the PM generator, and the output voltage and current waveforms of the generator with good quality. The shortcomings of the PWM rectifier method mainly reflected in two aspects, one is that its control circuit is complex and dependent on the parameters of the generator, the other is that the required 6 sets of high-power full-controlled devices still need to be imported, which will greatly increase the cost of the system [26].

Fig. 1

The topology of rectifier PM generator set.

When the prime mover running at a constant speed and the uncontrollable rectifier circuit is adopted, to realize the DC side voltage-stabilizing control of the generator set, the DC-DC converter is often added. The voltage-stabilizing topology with DC-DC converter is shown in Fig. 1(b). This topology has the advantages of simple control and output voltage stability, which is widely used in wind power generation systems. However, the system still needs a few high-power full-controlled devices, and the introduction of large-capacity capacitance and inductance components increase the complexity and cost of the system [27].

The voltage-stabilizing topology by adjusting the speed of the prime mover is shown in Fig. 1(c). Due to the existence of the rectifier, no need to maintain the output frequency of the generator as constant, and the DC side output voltage can be kept constant by adjusting the speed of the prime mover. As the interior PM generator with reverse salient features, reasonable design can make it with a low voltage regulation rate. The DC side voltage-stabilizing can be achieved by a small range change of the prime mover speed. When using this topology, the system has the advantages of simple structure, convenient control, and low cost. This paper takes this topology as an example to analyze the output characteristics and power balanced control method of the rectifier PM generator sets operating in parallel.

3 Principle of rectifier pm generator sets operating in parallel

The structure of the mobile power supply type of PM generator sets operating in parallel is shown in Fig. 2, which is a power supply system based on the DC power grid. To ensure the reliability of the power supply system, it is necessary to research the output characteristics of the generator sets when the operation frequency, RMS of output voltage, phase of output voltage, and other parameters are different.

Fig. 2

Diagram of rectifier generator sets operating in parallel.

The equivalent circuit of two rectifier generator sets operating in parallel without the filtering and stabilizing measures is shown in Fig. 3. To simplify the equivalent model of the generator, this paper takes the non-salient pole PM generator as an example in the equivalent circuit. Meanwhile, assume that the no-load air gap magnetic field of the generator is sinusoidal distribution, and the influence of armature reaction magnetic field on excitation magnetic field is neglected, that is, the back EMF of the generator is sine waveform and its amplitude is constant. The symbols E, u, i, L, R and R_L in Fig. 3 represent the generator’s back EMF, output phase voltage, output phase current, synchronous inductance, stator phase resistance, and load resistance respectively.

Fig. 3

Equivalent circuit of rectifier generator sets operating in parallel.

From Fig. 3, we can see that the difference of generators’ back EMF, stator phase resistance, and synchronous inductance will affect the balance of generators’ output power, and the difference of the back EMF involves its frequency, RMS, and phase. To ensure the stability of the rectifier generator operating in parallel, it is necessary to research the influence of the difference of the above parameters on the balance of generators’ output power.

In the small-capacity power supply system, the influence of synchronous inductance can’t be ignored. Even the pure resistance load, the existence of synchronous inductance will lead to the existence of a commutation overlap angle, and the commutation process can’t be completed instantaneously. According to the symmetry of the circuit structure, there are three operating states of the two rectifier generator sets operating in parallel, as shown in Fig. 4. The operating state is shown in Fig. 4 (a) represents each of the two generators has two phases conduction, according to the equivalent circuit, the voltage equation is

$\begin{matrix} E_{A 1} - E_{B 1} - 2 L \frac{d i_{a 1}}{dt} - 2 i_{a 1} R_{1} \\ = E_{A 2} - E_{B 2} - 2 L \frac{d i_{a 2}}{dt} - 2 i_{a 2} R_{2} \end{matrix}$ (1)

Fig. 4

Operating states of two rectifier generator set operating in parallel.

Because the resistance voltage drop is far less than the inductance voltage drop, neglecting the influence of the resistance voltage drop in the above formula. The phase difference of the back EMF is expressed by symbol ψ, and assume that L = L₁ = L₂, the difference between the output current of the two generators is $\begin{matrix} i_{a 1} - i_{a 2} = \frac{\sqrt{6} (E_{A 1} - E_{A 2})}{2 L} \times \\ [sin (ω t - \frac{π}{3}) - sin (ω t + ψ - \frac{π}{3})] \end{matrix}$ (2)

The operating state is shown in Fig. 4(b) represents one of the generators has two phases conduction, and the other has three phases conduction, according to the equivalent circuit, the voltage and current equations are

${\begin{matrix} E_{A 1} - E_{C 1} - L \frac{d i_{a 1}}{dt} + L \frac{d i_{c 1}}{dt} = E_{A 2} - E_{B 2} - 2 L \frac{d i_{a 2}}{dt} \\ i_{a 1} = - i_{b 1} - i_{c 1} \\ E_{C 1} - L \frac{d i_{c 1}}{dt} = E_{b 1} - L \frac{d i_{b 1}}{dt} \end{matrix}$ (3)

From the above formula can be obtained that

$\frac{d (i_{a 1} - i_{a 2})}{dt} = \frac{E_{A 1} - (E_{B 1} + E_{C 1}) / 2 - (E_{A 2} - E_{B 2})}{2 L}$ (4)

The operating state is shown in Fig. 4(a) represents each of the two generators has three phases conduction, according to the equivalent circuit, the voltage and current equations are

${\begin{matrix} E_{A 1} - E_{C 1} - L \frac{d i_{a 1}}{dt} + L \frac{d i_{c 1}}{dt} = E_{A 2} - E_{C 2} - L \frac{d i_{a 2}}{dt} + L \frac{d i_{c 2}}{dt} \\ i_{a 1} = - i_{b 1} - i_{c 1} i_{a 2} = - i_{b 2} - i_{c 2} \\ E_{C 1} - L \frac{d i_{c 1}}{dt} = E_{B 1} - L \frac{d i_{b 1}}{dt} \\ E_{C 2} - L \frac{d i_{c 2}}{dt} = E_{B 2} - L \frac{d i_{b 2}}{dt} \end{matrix}$ (5)

From the above formula can be obtained that $\begin{matrix} \frac{d (i_{a 1} - i_{a 2})}{dt} \\ = \frac{2 E_{A 1} - (E_{B 1} + E_{C 1}) - 2 E_{A 2} + (E_{B 2} + E_{C 2})}{4 L} \end{matrix}$ (6)

According to the above formulas, the difference between the output current of the two generators is related to the difference of their synchronous inductance, RMS of the back EMF, and phase of the back EMF. The instantaneous difference value of the generators’ output current in the full cycle can be obtained by formula (2), formula (4), and formula (6).

Using the circuit shown in Fig. 3 for circuit simulation, when the RMS of the two generators’ back EMF is different, the output current waveforms and their RMSs of the generators are shown in Fig. 5. When the phase of the two generators’ back EMF is different, the output current waveforms and their RMSs of the generators are shown in Fig. 6. According to the simulation results, it can be seen that the output current waveforms of the generators are distorted seriously. Whether the RMS or the phase of the generators’ back EMF is different, the output current of the two generators is unbalanced. The difference of the generators’ RMS of the back EMF has a great influence on the balance of the two generators’ output power. To ensure the output current of the generators is always the same, the rated parameters and running speed of the two generators are required to be the same, and the output voltage of the generators is kept in the same phase. The difference of any parameter will break the balance, which leads to the unbalanced of generators’ output current.

Fig. 5

Current waveforms at different RMS of back EMF.

Fig. 6

Current waveforms at a different phase of back EMF.

4 Output characteristics of rectifier generators operating in parallel

According to the above analysis, when using the power supply system of the rectifier generator sets operating in parallel shown in Fig. 3, the condition of achieving the aim of current sharing control is very harsh, and the DC side voltage-stabilizing can’t be realized. The inductance and capacitance filter elements are often added to suppress the impact of current and reduce the fluctuation of DC output voltage. The study in this paper found that the power supply system of rectifier PM generator sets operating in parallel with good output characteristics and operation stability after adding the inductance and capacitance filter elements in the location shown in Fig. 7. The inductance L_d can reduce the impact of the generator’s output current and the capacitance C can reduce the fluctuation of DC side output voltage.

Fig. 7

Rectifier generator sets with LC filtering circuit.

Using the circuit shown in Fig. 7 for circuit simulation, when the RMS of the two generators’ back EMF is different, the output current waveforms and their RMSs of the generators are shown in Fig. 8. When the phase of the two generators’ back EMF is different, the output current waveforms and their RMSs of the generators are shown in Fig. 9. The simulation results show that the output current waveform of the generators has been improved obviously after the LC filter elements are added. The difference between the RMS of back EMF still affects the balance of the generators’ output current, while the influence of the phase difference on the output current balance of the two generators is very small, which can be ignored. To more clearly understanding the influence of the difference between the RMS of back EMF on the balance of the two generators’ output power, the relationship between the ratio of the output current and the ratio of the EMF’ RMS is simulated, as shown in Fig. 10. Because the DC side output voltage of the two generators is the same, so the ratio of the output current is the ratio of the output power.

Fig. 8

Current waveforms at different RMS of back EMF.

Fig. 9

Current waveforms at a different phase of back EMF.

Fig. 10

Relationship between the ratio of output current and the ratio of back EMF’ RMS.

According to the above simulation results, we know that when taking the circuit structure shown in Fig. 7, there is no need to maintain the phase of the two generators’ output voltage consistent. The equal RMS of the two generators’ output voltage can make the output power of them equal. Therefore, maintaining the equal of the two generators’ output voltage can achieve the power balanced control. It can be found that the reasonable ratio of the RMS of the two generators’ back EMF can balance the output power of the two generators. Due to the inevitable difference between the rated parameters and external characteristics of the generators, and the balance of the generators’ output power is very sensitive to the RMS of the output voltage. Without appropriate measures of power balanced, it is difficult to ensure that the output power of each generator is distributed according to capacity.

5 Power balanced strategy of rectifier generators operating in parallel

5.1 Principle of master-slave control based on speed regulation

According to the system structure and output characteristics of the rectifier, generator sets operating in parallel shown in Fig. 7 [28], the RMS of the generator’s output voltage can be adjusted by adjusting the speed of the prime mover, to realize the purpose of controlling the output power of each generator set according to its capacity. In this paper, the master-slave control strategy based on the speed regulation of the slave generator set is adopted, and the larger capacity generator set is selected as the master, and other generator sets are used as the slave. By changing the speed of the master, the DC side output voltage can be adjusted. The ratio of generator sets’ output voltage can be adjusted by changing the speed of slave so that each generator set can distribute power according to its capacity.

The structure diagram of the master-slave control system based on the speed regulation of the slave is shown in Fig. 11. The balance of the generators’ output power can be realized by the closed-loop control of the slave’s DC side output current. The id1and id2 in the figure represent the DC side output current of the master and the slave, respectively. The id1 is given as the DC side output current of the slave after low-pass filtering. The output of the PI regulator is used as the control signal of the fuel regulator to adjust the speed of the slave and then change the RMS of the slave’s output voltage to achieve power balanced control. The ratio of the two generators’ output power can be adjusted by changing the value of GAIN.

Fig. 11

Structure diagram of master-slave control system.

5.2 Simulation research of master-slave control based on speed regulation

The field circuit coupling simulation circuit of the rectifier PM generator sets operating in parallel is shown in Fig. 12, the master-slave control strategy based on the speed regulation of the slave generator set is adopted. The simulation model of two generators is established according to the rated parameters of the prototype. The rated parameters of the two 7.5 kW PM generators are shown in Table 1. Because the two generators with the same rated power, the GAIN value is set to 1. Prototype 1 is selected as the master, and its speed is constant at the rated speed. The simulation results of the field circuit coupling simulation circuit shown in Figs. 13 and 14. The output voltage waveforms and their RMSs of the generators, the output current waveforms, and their RMSs of the generators are shown in Fig. 13. The output speeds and their average values of the generators, the output current waveforms of DC side output current after low-pass filtering, and their RMSs of the generators are shown in Fig. 14.

Fig. 12

Field circuit coupling simulation circuit.

Fig. 13

Output voltage and current waveforms of generators.

Fig. 14

Speeds and DC side output currents of generators.

As shown in Figs. 13 and 14, the master-slave control strategy based on the speed regulation of the slave generator set has a good load sharing effect. The output power of the slave is closely related to the power of the master, and the running speed of the slave is higher than the rated speed with a small range of fluctuates. The RMS of the two generators’ output voltage and current is equal.

5.3 Experimental research of master-slave control based on speed regulation

To verify the validity of this research, the load-balanced effect of the master-slave control strategy based on the speed regulation of the slave generator set is measured. In the process of measurement, using the circuit structure shown in Fig. 7 to build the experimental platform, and the resistance box is used as the load. The PM generator is driven by frequency conversion PM motor respectively. The rated parameters of the two 7.5 kW PM generators are the same as Table 1. The back EMF waveforms and their RMS of the two generators at the rated speed are shown in Fig. 15.

Table 1
Rated parameters of prototypes

No. Frequency Speed Back EMF End inductance Phase resistance

1 100Hz 3000r/min 242V 0.429mH 0.469Ω

2 100Hz 3000r/min 220V 0.339mH 0.363Ω

No.	Frequency	Speed	Back EMF	End inductance	Phase resistance
1	100Hz	3000r/min	242V	0.429mH	0.469Ω
2	100Hz	3000r/min	220V	0.339mH	0.363Ω

Fig. 15

No-load back EMF waveforms of prototypes.

The RMS of the back EMFs of the master and slave is 242 V and 220 V, respectively, a difference of 1.1 times. The running speed of the slave is increased by about 1.1 times than the rated speed, then fine-tune the running speed of the slave to equal the output current of the generators. After achieving load sharing, the output voltage waveforms and their RMSs of the generators are shown in Fig. 16, the output current waveforms and their RMSs of the generators are shown in Fig. 17.

Fig. 16

The output voltage of generators after load sharing.

Fig. 17

The output current of generators after load sharing.

The experimental results of Figs. 16 and 17 show that the simulation analysis in this paper is in good agreement with the experimental results, which shows the feasibility of the research methods in this paper. The power balanced can be achieved by adjusting the ratio of the RMS of the two generators’ output voltage.

6 Conclusion

The research in this paper found that for the mobile power supply type of rectifier PM generator sets operating in parallel, the influence of synchronous inductance, RMS of output voltage, and phase of output voltage on the power balance of mobile power supply is different under different topology. When no load sharing measure is taken, any small difference between generators may lead to an unbalance of power distribution. After adding the LC filter circuit, it is not necessary to keep the phase of each generator’s output voltage consistent, because it is almost unaffected by the phase difference of the generators’ output voltage. The power balanced can be achieved by adjusting the ratio of the RMS of the two generators’ output voltage. The control structure of the power supply system is simple and has a good prospect of application.

The power balanced method of master-slave control strategy based on the speed regulation of the slave is proposed, the output voltage of the slave is changed by adjusting its speed, and then the ratio of the output power between the master and the slave is adjusted. Using the closed-loop control of the DC side output current of the slave, the generator sets can distribute power according to their capacity by changing the GAIN value. The validity of the proposed method in this paper is verified by field circuit coupling simulation and experiment. The research of this paper has the guiding and reference significance for the application of the mobile power supply of rectifier PM generator sets operating in parallel.

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Power balanced control of rectifier permanent magnet generator sets

Abstract

Keywords

1 Introduction

2 The topology of rectifier pm generator set

5.1 Principle of master-slave control based on speed regulation

Table 1 Rated parameters of prototypes No. Frequency Speed Back EMF End inductance Phase resistance 1 100Hz 3000r/min 242V 0.429mH 0.469Ω 2 100Hz 3000r/min 220V 0.339mH 0.363Ω

References

Table 1
Rated parameters of prototypes

No. Frequency Speed Back EMF End inductance Phase resistance

1 100Hz 3000r/min 242V 0.429mH 0.469Ω

2 100Hz 3000r/min 220V 0.339mH 0.363Ω