Output Power Capacity Improvement Based on Three-Phase Current Balance Control for the Doubly Salient Electromagnetic Generator System

Abstract

The doubly salient electromagnetic generator (DSEG) has the advantages of flexible control, high robustness, and low cost. Since multiple stator poles share a common set of field windings, the magnetic circuit of each phase is asymmetrical, which limits the output performance of the DSEG. The three-phase current balance control for the DSEG system was proposed. By investigating the current waveform under the angular position control (APC), a three-phase current prediction method was proposed. The conduction angle of the power switches in the active rectifier was predicted to make the three-phase current balanced. Based on the analysis and experiment, the current waveform was further analyzed, and the effectiveness of the three-phase current balance control was verified. Compared with the APC method, the output power capacity was improved using the three-phase current balance control under a limited winding current density. The maximum potential of the DSEG was explored, and the electromagnetic load capacity of the DSEG was fully released.

1. Introduction

The doubly salient electromagnetic generator (DSEG) was developed from the switched reluctance generator (SRG) with a similar structure [1,2]. The DSEG has a wide range of application fields, such as an aircraft generator and wind turbine generator [3,4,5], due to its simple structure, high control flexibility, low cost, and strong fault tolerance [6].

However, the DSEG and SRM have great differences in their working principle and control method [7]. Due to the parallel stator pole structure, the three-phase magnetic circuits in the DSEG are inherently asymmetric, which leads to unbalanced three-phase currents.

Although control methods for three-phase balance were reported, the available balance control methods are not ideal for DSEG systems. A power and voltage balance control scheme for a solid-state transformer (SST) based on a cascaded H-bridge multilevel inverter was proposed [8]. The research focused on the application of three-phase SST and their controllers to distribute renewable energy flow to the grid under unbalanced conditions, and ultimately inject pure sinusoidal balanced three-phase current into the AC grid. The controller adopts the moving floating neutral control algorithm to realize the power balance of the three-phase AC side.

In a distribution network system, three-phase unbalance leads to transformer losses and lower motor efficiency [9]. A three-phase unbalance regulation method based on improved k-means clustering was proposed. The Frénchet distance was first used to measure the resemblance between different load curves. Then, the k-means clustering method was used to cluster the loads with similar variation rules. The loads in all phases were evenly distributed to achieve a strong three-phase balance. Since this method can only change the three-phase unbalance caused by unbalanced load distribution, it is not applicable to the problem caused by a DSEG.

Predictive current control was adopted to improve the tracking dynamic response of compensating current, and the effect of compensating harmonic current was optimized. The simulation results show that the active power filter method based on model predictive control can suppress the harmonic current effectively [10].

Due to the errors in generator manufacture and drift in diode parameters, the currents of paralleled diodes in the same bridge arm or branch currents in the same phase are not consistent [11]. There is also a fixed unbalanced current between the paralleled components. The inherently unbalanced current of the rectifier parallel structure was smaller. However, the method cannot suppress the three-phase current unbalance of a DSEG caused by parallel stator poles.

Since the structure of the DSEG is quite different from other motors, the three-phase current unbalance caused by parallel poles needs to be studied.

The stator of the DSEG with distributed field windings (DSEG-DF) has a radial pole structure. A set of field windings is installed around each pole and the phase magnetic circuit is symmetrical. Therefore, the DSEG-DF can solve the problem of an asymmetric three-phase magnetic circuit inherent in the DSEG with concentrated field windings (DSEG-CF). However, the DSEG-CF performs better than the DSEG-DF with regard to electromagnetic vibration due to the thicker yoke and higher-order spatial EMF harmonics [12]. Therefore, the DSEG-DF does not improve the three-phase unbalance without affecting the performance.

The main causes of three-phase unbalance include the structural asymmetry, load unbalance, and errors generated by the production process. Due to the unique structure of the DSEG, there is an unbalance in three-phase currents, and the output performance is affected.

In [13], a DC-link voltage regulation method was proposed based on capacitor energy control for the DSEG system. In the outer loop, the stored energy in the DC-link capacitor was used as the control target. The dynamic performance was optimized. A current self-injection-based position sensorless control method was proposed for a DSEG with an active rectifier [14]. The control method improved the performance of the DSEG through the coordinated control of armature current and field current. In [15], the angular position semi-control method was proposed to increase the output power of the DSEG in the low-speed range. However, the method is not applicable to all working conditions. The model predictive current control for the doubly salient electromagnetic machine was proposed in [16]. A predictive current model was derived and an objective function for current ripple reduction was constructed to suppress current ripples and improve the torque performance.

The relationship between the control parameters and the three-phase current in the DSEG system is the theoretical fundamental of performance optimization control. The three-phase current balance control is an effective method for improving the output power capacity in full working condition.

A three-phase current balance control method based on phase current prediction was proposed. In order to improve the output capacity of the DSEG system in the limited state and extend the service life of power electronic components, the three-phase current waveform was analyzed based on angular position control (APC). A mathematical model was established to predict the current waveform and to calculate the APC conduction angle that balances the phase currents. The three-phase current balance control method was applied to the DSEG system under different working conditions. The experimental results showed that the proposed method was effective. Compared with the conventional control method, the proposed control method could achieve a three-phase current balance and effectively improve the output capacity of the DSEG system over a wide operation range.

This paper is organized as follows. In Section 2, the reasons for the three-phase current unbalance, the DSEG active rectifier system, and the APC method are discussed. In Section 3, the output power capacity improvement based on three-phase current balance control for the DSEG system is proposed and discussed, along with the simulation tests. In Section 4, the results of the experiments are used to verify the effectiveness of three-phase current balance control for the DSEG system. In the last section, a summary of the work is presented. The application areas of the proposed method are given.

2. Characteristics of the DSEG System

2.1. Reasons for the Three-Phase Current Unbalance

The DSEG-CF with concentrated field windings and DSEG-DF with distributed field windings are the common structures of the DSEG. The structure of a DSEG-CF is shown in Figure 1. Each of the three stator teeth is surrounded by a concentrated field winding [17]. Each stator pole of the DSEG-DF has a field winding with a symmetrical magnetic circuit. The three-phase unbalance is suppressed in the DSEG-DF. However, the DSEG-DF brings problems such as a large mutual inductance of the armature windings, high magnetization frequency of rotor poles, and larger core loss [18]. Therefore, the control method to suppress the three-phase unbalance is an important issue to improve the performance of the DSEG-CF.

In order to increase the slot fill factor of the field windings, the DSEG-CF stator adopts a parallel pole structure, and each of the three stator poles shares a set of field windings. The field windings generate two pairs of pole excitation magnetic fields, showing the characteristics of concentrated excitation potential in the circumference direction of the air gap. The armature windings are placed around the stator teeth and the field windings are placed around the three-phase windings, as shown in Figure 1. The salient pole structure is employed in the rotors, and the rotors have neither windings nor permanent magnets. The simple structure produces high reliability.

Due to the asymmetric phase magnetic circuit inherent in the DSEG, each excitation component is wrapped around the three-phase armature windings, while the magnetic circuits passed by the three-phase windings are asymmetric. The distance between the armature windings and the field windings is different in the phases. The B-phase and C-phase windings are closer to the field element, and the magnetic circuit is relatively short. The A-phase winding is farther away from the field element and the magnetic circuit is longer. The asymmetry of the magnetic circuits in three phases leads to the unbalanced output power capacity of the three-phase windings and the unbalanced currents of the three phases.

The flux linkage of each phase will constantly change with the electrical degree. In each 360° electrical cycle, the phase flux linkage can be divided into three regions: the rising region, the falling region, and the constant value region, with each occupying 120°.

As shown in Figure 2a, when the rotor is in the A-phase rising zone, the corresponding rotor pole just starts to slide into the A-phase stator pole. The engagement between the rotor pole and the stator pole is small and the mutual inductance saturation between the field winding and the armature winding is low. The changing rate of the flux linkage around the armature winding is large and the back-EMF amplitude is large. As shown in Figure 2b, when the rotor is in the A-phase falling zone, the corresponding rotor pole is about to completely slide into the A-phase stator pole. The engagement between the rotor pole and the stator pole is large and the mutual inductance between the field winding and the armature winding is close to saturation. Both the changing rate of the flux linkage around the armature windings and the back-EMF amplitude are small. Therefore, it can be seen that the changing rate of the magnetic chains of the armature windings is not consistent at the minimum and maximum values. There will be a distortion in the back-EMF, which can cause three-phase unbalanced currents during steady-state operation of the DSEG.

The A-phase current reaches saturation first, while the B- and C-phases are not fully used, which limits the output power capacity of the DSEG. Meanwhile, due to the asymmetric structure of the three-phase magnetic circuit, the current stresses of the three-phase windings are different, and the currents carried by the switches in the active rectifier are also different. As the A-phase current is relatively large, the temperature is higher and the current stress is larger. The power switches connected to the A-phase are relatively easy to damage. When the three-phase currents are balanced, the three-phase heat dissipation is balanced, and the power electronic components are sharing the same current stress. The three-phase windings reach the current density limit at the same time.

The DSEG system is composed of a 12/8 pole DSEG, an asymmetric H-bridge driving the field windings, a three-phase converter, a digital signal processor (DSP), a filter capacitor, etc. As shown in Figure 3, the sensors feed the DC-link voltage U_DC and the field current in real time back to the DSP. In order to maintain the DC-link voltage at 270 V, the double closed-loop proportion–integral–derivative (PID) controller is used. The outer loop controls the DC-link voltage and the inner loop controls the field current. The output result of the PID controller is the duty cycle of the PWM, which is used to control the field current and regulate U_DC.

2.2. The APC Method for the DSEG System

Due to the similar structure of the SRG and DSEG, the control method and optimization strategy of the DSEG can refer to the SRG [19,20,21].

APC is an effective method for improving the performance of the DSEG system. Figure 4 shows the three-phase electromotive forces and the three-phase self-inductances. The conduction principle of APC is also demonstrated. In each electrical cycle, the phase self-inductance can be divided into three zones with 120° equal widths, namely, the rising zone, the falling zone, and the constant value zone. β° is defined as the conduction angle.

Taking 120°~240° as an example, the B-phase is in the falling zone, the C-phase is in the rising zone, and the insulated gate bipolar transistors (IGBTs) of the C-phase upper bridge arm and B-phase lower bridge arm are conducting and then turned off after β°, as shown in Figure 5a. In 120°~120 + β°, the B-phase voltage is negative and the C-phase voltage is positive. e_b and e_c are the back-EMFs of the B- and C-phases, respectively. The phase windings are connected to the capacitor in reversed direction through T₅ and T_6. The filter capacitor provides the required current i_DC for the load and generates the current i_back to the B- and C-phases. The discharge current of the filter capacitor is i_cap:

$$i_{cap}=i_{back}+i_{DC}$$

(1)

In 120 + β°~240°, the B- and C-phases are connected to the capacitor through D₃ and D₂, as shown in Figure 5b. The phase current i_out charges the filter capacitor while providing current to the load, and i_cap is the charge current of the filter capacitor. In this case, i_out is the sum of i_cap and i_DC.

$$i_{out}=i_{cap}+i_{DC}$$

(2)

The APC effectively reduces the overlapping phenomenon during the phase change and accelerates the change of phase currents.

3. Three-Phase Current Balance Control

Since the three-phase currents of DSEG systems are affected by various factors, such as speed and load, the prediction is relatively complex and difficult. A three-phase current balance method was proposed and the conduction angle required to achieve three-phase current balance under different working conditions was calculated. Based on the phase current prediction, the three-phase current balance control method increased the power of the DSEG in the extreme state. The three-phase windings can be used to the current density limit and the service life of power electronic components can be extended appropriately.

3.1. Single-Phase Conduction Modes Analysis

In order to balance the RMS values of three-phase currents, the single-phase conduction mode was investigated. Taking 120°~120 + β° as an example, when the electrical degree is between 120°~120 + β°, T₅ and T₆ are conducting. The B-phase and C-phase windings are serially connected to the filter capacitor with reversed polarity. The filter capacitor not only charges the B-phase and C-phase windings but also provides current to the load side. In the range of 120 + β°~240°, the B-phase and C-phase windings are connected to the capacitor through D₃ and D₂, respectively. The DSEG output current (i_out) charges the filter capacitor while providing current to the load. Assuming that when the RMS value of the B-phase current (i_brms) is small, the conduction time ∆β₆° of T₆ is extended appropriately. As shown in Figure 6, in β°~β + ∆β_i°, T₆ on the lower bridge arm is switched on, T₅ in the upper bridge arm is turned off, and D₂ is conducting. The B-phase and C-phase windings form a series circuit through T₆ and D₂, respectively, and the filter capacitor charges the load to form a separate closed circuit:

$$\{\begin{array}{c}{i}_b=-i_c\\ i_{cap}=i_{DC}\end{array}$$

(3)

It was verified by simulation that the capacitor current i_cap was equal to the load current i_DC. There was no current flowing from the three-phase winding to the filter capacitor and load. Therefore, the current in the B- and C-phases increased. As the C-phase current increased, the commutation rate slowed down. The A-phase and B-phase currents decreased in the next 120° zone, in which the A- and C-phases worked simultaneously. Therefore, through conduction modes analysis, the three-phase current balance control method was proposed.

3.2. Three-Phase Current Balance Control Method

There is a complex nonlinear relationship between the DSEG three-phase current i and conduction angle β. Due to the influence of the working conditions, it is necessary to establish a mapping relationship between i and β. The relationship of the predicted current is established according to the working condition and β which can make the three-phase current balance is calculated.

The accurate prediction of the current waveform is the basis of realizing the three-phase current balance and improving the output power capacity of the DSEG to the current density limit. By detecting the RMS values of the three-phase currents in the last electrical cycle, the unbalance degree ε is calculated:

$$\epsilon =\frac{i_{rms\max }-i_{rms\min }}{i_{rms\min }}\times 100\%$$

(4)

The maximum of the three-phase currents (i_arms, i_brms, i_crms) is defined as i_rmsmax, and i_rmsmin is the smallest of i_arms, i_brms, and i_crms. i_a(θ), i_b(θ), and i_c(θ) are defined as the currents of the A-, B-, and C-phases under APC, respectively. i’_a(θ), i’_b(θ), and i’_c(θ) are defined as the currents of the A-, B-, and C-phases, respectively, under the three-phase current balance control method.

Compared with the APC method, there is no significant drop in the DC-link voltage and back-EMF, and the structure of the DSEG is not changed. From the analysis above, taking the B-phase current waveform as an example, in β°~∆β_i°, i_b (θ) and i’_b(θ) can be further expressed as (5) and (6), respectively:

$$i_b\left(\theta \right)=\frac{e_b-e_c+270}{2r}$$

(5)

$${i_b}^{\prime }\left(\theta \right)=\frac{e_b-e_c}{2r}$$

(6)

where r is the equivalent winding resistance [13]. The derivatives of i_b(θ) and i’_b(θ) are (7) and (8), respectively:

$$\frac{\mathrm{d}{i}_b\left(\theta \right)}{\mathrm{d}\theta }=\frac{1}{2r}\ast \frac{\mathrm{d}(e_b-e_c+270)}{\mathrm{d}\theta }=\frac{1}{2r}\ast \frac{\mathrm{d}(e_b-e_c)}{\mathrm{d}\theta }$$

(7)

$$\frac{\mathrm{d}{i_b}^{\prime }\left(\theta \right)}{\mathrm{d}\theta }=\frac{1}{2r}\ast \frac{\mathrm{d}(e_b-e_c)}{\mathrm{d}\theta }$$

(8)

It can be seen from (7) and (8) that the derivatives of i_b(θ) and i’_b(θ) are equal. Therefore, it can be assumed that the slope of the waveform is the same before and after changing the conduction angle. ∆β_i is defined as the increased conduction angles of the ith IGBT T_i. In β + ∆β_i°~240°, i_b(θ) can be further expressed as (9):

$$i_b\left(\theta \right)=\frac{e_b-e_c-270}{2r}$$

(9)

$$e_x=\frac{\mathrm{d}{\phi }_x}{\mathrm{d}t}=\frac{\mathrm{d}{L}_{\mathrm{x}}}{\mathrm{d}t}{i}_x+\frac{\mathrm{d}{i}_x}{\mathrm{d}t}{L}_x$$

(10)

where e_x and φ_x are the back-EMF and flux linkage of the xth phase, respectively.

Based on the analysis above, it can be idealized that L is linear. Taking 120° to 240° as an example, L_b and L_c can be expressed as (11) and (12), respectively:

$$L_b\left(\theta \right)=k\theta +b$$

(11)

$$L_c\left(\theta \right)=-k(\theta -360)+b$$

(12)

where k and b are constants. To convert time quantities into angular quantities, a constant D is set:

$$D=\frac{\mathrm{d}\theta }{\mathrm{d}t}$$

(13)

Since i_b = -i_c, by combining (9) to (13), i_b(θ) can be expressed as follows:

$$i_b\left(\theta \right)=\frac{D\left[2k{i}_b+\frac{\mathrm{d}{i}_b}{\mathrm{d}\theta }(L_b+L_c)\right]-270}{2r}=C_1{e}^{-\frac{(2r-2Dk)\theta }{360\mathrm{k}+2b}}-\frac{270}{2r-2Dk}$$

(14)

where C₁ is constant which can be obtained by substituting the special solution i_b(β).

Similarly, i’_b(θ) can be expressed as follows:

$${i_b}^{\prime }\left(\theta \right)=\frac{D\left[2k{i}_b+\frac{\mathrm{d}{i}_b}{\mathrm{d}\theta }(L_b+L_c)\right]-270}{2r}=C_2{e}^{-\frac{(2r-2Dk)\theta }{360\mathrm{k}+2b}}-\frac{270}{2r-2Dk}$$

(15)

where C₂ also can be obtained by substituting the special solution i_b’(β + Δβ_i).

Based on the analysis of the waveform, the shapes of i’(θ) and i(θ) are similar, and the waveform of i’(θ) can be obtained from i(θ). Taking T₆ as an example, the conduction angle is extended from β° to β + Δβ₆°. Taking the B-phase current waveform at an instance, as shown in Figure 7, the following formula can be obtained in one electrical cycle:

$${i_b}^{\prime }\left(\theta \right)=\frac{{{\displaystyle C}}_2}{{{\displaystyle C}}_1}(i_b\left(\theta \right)+\frac{270}{2r-2Dk})-\frac{270}{2r-2Dk}$$

(16)

$$\Delta i_{brms}={i_{brms}}^{\prime }-i_{brms}$$

(17)

Since i_brms is a constant, ∆i_brms can be expressed as follows:

$$\begin{array}{cc}\Delta i_{brms}& ={i_{brms}}^{\prime }-i_{brms}=\sqrt{\frac{{\displaystyle \sum _{k=1}^n{i}_{bk}{}^2}}{n}}-i_{brms}\hfill \\ & =\sqrt{\frac{{{\displaystyle \sum _{k=1}^n\left[i_{bk}\left(\theta -\Delta {\beta }_6\right)-\Delta i_b\right]}}^2}{n}}-i_{brms}\hfill \end{array}$$

(18)

where Δi_brms is the increased RMS value of the B-phase current under three-phase balance control. n is the number of steps taken to calculate the RMS value of the current. θ is the electrical degree, as shown in Figure 7. First, i(θ) is obtained with the APC method. The RMS values and ε of the three-phase currents are calculated. If ε is higher than 5%, adopt the three-phase current balance control method (Figure 8). Taking the A-phase current as a standard, the B- and C-phase currents are adjusted. ∆β_i is estimated using (18).

The current RMS value (i_rms’) is fed back and calculated in real time, and the unbalance degree is calculated again. If ε is less than 5%, stop adjusting the conduction angle. When the unbalance degree is larger than 5%, continue to predict the conduction angle that makes the three-phase current balance. The RMS values of currents are calculated and repeated until the unbalance degree is less than 5%.

To verify the three-phase current balance control, the simulation was performed according to the control flow in Figure 9. The simulation platform of the DSEG active rectifier system was established to compare the three-phase current unbalance degree under the conventional control method and the three-phase current balance control method. The output power capacity of the DSEG was improved and the three-phase windings reached the current density limit at the same time, verifying the effectiveness of the three-phase current balance control. Considering the limit of the current density and the structure of the armature windings, the limit of three-phase currents was set to 20 A. The RMS values of three-phase currents were unbalanced with the conventional method. When the RMS value of the A-phase current reached the upper limit, the output power capacity of the DSEG system was limited. The field current was generated by an independent excitation source, and double closed-loop control was adopted to keep the DC-link voltage stable at 270 V. As shown in Figure 10a, the three-phase current unbalance degree was 31.9% with the diode rectifier (DR). The RMS values for the A-, B-, and C-phase currents were 20.54 A, 15.57 A, and 17.54 A, respectively. The RMS value of the A-phase current reached the limit of the current density, while the B-phase and C-phase currents only reached 77% and 87% of the maximum current density, respectively.

The three-phase unbalance was serious due to the inherent three-phase magnetic circuit asymmetry, limiting the output power capacity of the DSEG system.

The A-phase current reached saturation first. The temperature was high, and the stress on the power electronic equipment of the A-phase was relatively high. Therefore, the power electronic components connected to the A-phase were easily damaged. The B-phase and C-phase windings could not be used to their limits. When β was 10°, at a fixed and uniform conduction angle, as shown in Figure 10b, the unbalance degree was still relatively high. The RMS values of the three-phase currents were i_arms = 20.04 A, i_brms = 16.27 A, and i_crms = 17.74 A. The unbalance degree was 21.0%.

When the three-phase currents were balanced, the heat dissipation was balanced, which can effectively extend the life of the electronic components. According to the original waveforms of the three-phase currents and (18), the influence of the conduction angle ∆β_i was predicted, and the conduction angle required for the three-phase current balance was calculated. As shown in Figure 11, the conduction angles of the six IGBTs could be controlled to achieve the three-phase current balance. The three-phase currents were relatively balanced so that the RMS values of three-phase currents could reach the upper limit at the same time. The output power capacity of the DSEG system was improved to 6.075 kW, and the RMS values of the A-, B-, and C-phase currents were 20.54 A, 19.23 A, and 19.66 A, respectively. The unbalance degree was 4.9%. Compared with the conventional control method, the output power capacity of the three-phase current balance control method based on current prediction was improved by 7.9%.

4. Experimental Verifications

Based on the balance control of the three-phase current, the parameters were collected by the sensors and fed back to the DSP. The data was processed in the DSP and the conduction angles were calculated. The field current was controlled by a double closed-loop PID controller that included an external voltage loop and an internal field current loop. The DC-link voltage U_DC was controlled at 270 V.

In order to validate the proposed method, comparison experiments were conducted at several common speeds to analyze the output capacity of different control methods. The experimental platform is shown in Figure 12. The operating speed n, load r_L, phase current i_p, and DC-link current i_DC were used to evaluate the load capacity of the DSEG. First, experiments with a diode rectifier were carried out to record the phase currents, DC-link voltage, and DC-link current. The RMS values of the three-phase currents were calculated in real time. The difference between the three-phase currents was calculated, and ∆β_i° was calculated with (18). The corresponding lower bridge arm conduction angle β was selected by the controller. The RMS values of three-phase currents were balanced so that the maximum output power capacity was improved.

Based on the diode rectifier, when the speed was 4000 r/min and the maximum output power capacity was 3.71 kW, the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 13. The A-phase current was much higher than the B-phase current, and the three-phase currents are extremely unbalanced. The RMS values of the A-, B-, and C-phase currents were 16.2 A, 11.6 A, and 12.8 A, respectively. The field current i_f was 5.98 A, and the DC-link voltage U_DC was 261 V. Due to the limitation of the output capacity at the speed used, the DC-link voltage did not rise to 270 V, and the unbalance degree ε was 39.6%, and thus, relatively high.

Based on the diode rectifier, when the speed was 5000 r/min and the output power capacity was 3.64 kW, the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 14. i_arms, i_brms, and i_crms were 15.7 A, 12 A, and 12.7 A, respectively. i_f, U_DC, and ε were 3.45 A, 270 V, and 30.8%, respectively. The unbalance degree ε was relatively high. Due to the limited output performance of the diode rectifier, the phase current was smaller and the output power capacity was lower.

Based on the APC method (β = 30°), when the speed was 3000 r/min, the output power capacity was 3.37 kW, and the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 15. i_arms, i_brms, and i_crms were 20.6 A, 15 A, and 19.4 A, respectively. i_f, U_DC, and ε were 2.94 A, 270 V, 37.3%, respectively. The A-phase current was much higher than the B-phase current and the unbalance degree was relatively high.

Based on the APC method (β = 50°), when the speed was 4000 r/min, the output power capacity was 4.32 kW, and the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 16. i_arms, i_brms, and i_crms were 20.2 A, 15.6 A, and 19 A, respectively. i_f, U_DC, and ε were 3.05 A, 270 V, and 19.2%, respectively. The A-phase current was much higher than the B-phase current. The unbalance degree was relatively reduced, but the B- and C-phases could not be fully used.

Based on the proposed three-phase current balance control method, when the speed was 3000 r/min, ∆β₆ was 17° and ∆β₂ was 5°. The conduction angle of the other IGBTs remained unchanged, and the three-phase currents were balanced. When the B-phase current increased and the output power capacity increased to 3.75 kW, the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 17. i_arms, i_brms, and i_crms were 19.7 A, 19.6 A, and 19.4 A, respectively. i_f was 2.96 A and ε was 1.5%. The output power capacity increased by 11.2% and the three phases could be fully used.

Based on the proposed three-phase current balance control method, when the speed was 4000 r/min, ∆β₆ was 14° and ∆β₂ was 9°. The conduction angle of the other IGBTs remained unchanged, and the three-phase current was relatively balanced. When the B-phase current increased and the output power capacity increased to 4.83 kW, the waveforms of i_a, i_b, i_c, U_DC, i_DC, and i_f are shown in Figure 18. i_arms, i_brms, and i_crms were 19.5 A, 19.8 A, and 19.9 A, respectively. i_f was 3.01 A and ε was 2.0%. The output power capacity increased by 11.8% and the three phases could be fully used.

In Figure 19 and Figure 20, the performance of the three control methods is compared under different operating speeds. The diode rectifier was used as the reference scheme. Compared with the two conventional control methods, the APC method could slightly improve the three-phase current unbalance but the three phases could be fully used. The proposed method could effectively reduce the unbalance of the three-phase currents and improve the output power capacity of the DSEG to the current density limit. As the speed increased, the increasing effect of the APC and the proposed method of the maximum output power was gradually weakened. The reduction effect of the two methods on the unbalance degree increased, while the reduction effect on the field current gradually decreased. The output capacity of the proposed method was consistently better than the APC method at different speeds.

5. Conclusions

A three-phase current balance control method was proposed based on the three-phase current prediction. According to the unbalance degree of the three-phase current in the previous cycles, the three-phase current balance control method was employed to compensate for the smaller current in the three-phase current. The conduction angle for the three-phase current balance was calculated to realize the balance control of the three-phase current in the next cycle. When the three-phase current was balanced, the output power capacity of the DSEG was appropriately increased. The upper limit of the RMS values of three-phase currents was restricted in accordance with the conventional control method. The feasibility of the proposed method was verified under various working conditions. Based on the closed-loop control of the field current to stabilize the DC-link voltage, the goal of realizing the three-phase current balance by using the optimized active rectifier control method was realized. In a wide operation range, the output power capacity of the DSEG system was improved to the limit of the current density.

The influence of three independent variables, namely, speed, load, and conduction angle, on the power generation system was studied. With six conduction angles as independent variables and the phase currents as the dependent variables, a three-phase current balance control method was obtained, and the obtained data were tested.

The control method was verified via experiment, and the prediction method was further optimized according to the experience obtained from the actual situation. The corresponding relation between the conduction angle and the phase current in all working conditions was obtained. The system three-phase balanced conduction angle was selected according to the practical application requirements.

The results showed that under different working conditions, the conduction angle for the three-phase current balance could be obtained by the three-phase current balance method. The proposed method offers valuable insights into increasing the output power capacity of the DSEG.