Online Field Current Estimation for Brushless Synchronous Starter/Generator Considering the Rectifier Commutation Mode

The information of the field current is essential for the brushless synchronous starter/generator system, which determines the performance and health status of this system. However, since the field winding of the main machine is installed in the rotor part, the measurement of the field current in this brushless system seem impossible. Considering that, the field current might be affected by the rectifier mode, the field current estimation method in different rectifier mode is studied in this paper. The main exciter (ME) rotor currents were restructured based on the ME flux equations. With these restructured rotor currents, the field current in different rectifier commutation mode is analyzed, then the field current estimation method considering the rectifier mode can be obtained. The experiments in different rectifier modes are carried out to verify the proposed method.

SECTION I. Introduction

W ITH the development of the transportation power systems [1]–​[2], the power capacity is increasing, which makes the generator in the transportation power system have the potential to start the engine, then the integrated starter/generator (ISG) system becomes more and more popular [3]–​[5]. This ISG system based on the brushless wound field synchronous machines becomes a candidate, owing to merits of high safety [6]–​[7].

The ISG system which consists of the main machine (MM), the three-phase asynchronous main exciter (ME), the rotating rectifier (RR) and the pre-exciter (PE), is shown as Fig. 1 [8].

In this ISG, the MM, the ME and the RR are coaxially mounted, and the induced alternating current on the ME rotor is rectified as the DC current for the MM field winding through the RR [9].

Obviously, the field current plays the essential role, which determines the performance and health status of this ISG system in both starter and generator mode [10]. Obtaining the accurate information of the field current becomes one of the key problems in this ISG system. However, since the ME and the RR are coaxially mounted in the rotor part, and there is no slip and brush in this ISG system, the measurement of the field current seem impossible [11]. The requirement of estimating the field current causes great concern. The field current estimation method can be classified two categories: the MM side approaches and the ME side approaches.

Fig. 1.

Structure of the ISG with three-nhase brushless exciter.

The MM side approaches means that the field current can be estimated by the parameters of the MM, owing to the field current significantly affects the back-EMF or the inductance of the MM [12]–​[13]. However, the magnetic saturation and the variable operation state of the MM leading to the inductance parameters vary greatly [14]–​[15], thus, the MM side approaches become more complicated, the precision and dynamics of these approaches need to be improved.

The ME side approaches means that the field current can be estimated by the ME parameters, owing to the field current is the output of the ME. In most case, the ME is unsaturated, and its condition almost keep unchanged [10], [16], so the ME side approaches, might be more accurate, compare with the MM side approaches.

These ME side approaches include the numerical analytic calculation methods [17]-​[18] and online estimation methods [19]–​[22]. The numerical analytic calculation methods using the ME and RR models, through the equivalent circuit [17] or the dynamic average value model [16], then the numerical calculation of the field current can be obtained. As the online methods, the ME rotor currents or voltages are estimated first, with the rectifier model, the field current can be obtained. The difficulty of the ME side approaches is modelling the RR, in which the nonlinearity and commutation should be considered.

In [19], the current method and the voltage method of the brushless machine are proposed and compared. The performance of the current method is limited, owing to the rectifier commutation. Although the voltage method is accurate, it belongs to the MM side approach, which is not suitable for this ISG system. In [20], the parametric average value model (PAVM) of a rectifier is used for estimated the field current, and the requirement of the rotor position is avoided. But it needs large amount of data fitting for built the PAVM of the rectifier. In [21], based on the flux equations, the ME rotor current is estimated, but the field current is not discussed, and the commutation is also ignored. In [22], the frequency domain model of rectifiers is derived, and the calculation of synchronous rectification conduction time in the controller is simplified. In [23], the switching functions of the rotating rectifier is proposed, the field current is estimated by the maximum and minimum values of the switching functions.

It is well known that the rectifier has three modes, mode I, non commutation and two-phases commutation alternate state, mode II, always two-phases commutation state, mode III, two-phases commutation and three-phases commutation alternate state [24]–​[26]. The above methods are mainly focus on the field current estimation under the mode I. Unfortunately, in the brushless synchronous starter/generator, the rectifier might face the heavy current, high frequency and large inductance, the commutation time might be longer, the commutation mode of the rectifier might be changed from mode I to mode III, which the mathematical relationship among these currents also has been changed [27].

As the commutation phenomenon, the averaging method was presented to study the commutation of the rectifier. In [28], the switching model simulations of different steady-state operating points of the system were performed. In [15], [26], mathematical derivation method was used to calculate the commutation effect of rectifier. In [29], the overlap-time effect of the rectifier was studied and the optimal overlap-time distribution was presented. In [30], the commutation angle of the rectifier was studied, then the analytical model includes the rectifier was proposed for the wound field generators. In [31], by considering the commutation overlap, the simplified different frequency modeling was built and validated by simulations.

Considering that the mathematical calculation approaches are very complex [17], [29] and consumes a lot of computational resources; the switching functions approach can hardly show the current relationship during the commutation intervals [23]. The parametric average value model approach is very difficult to obtain the coefficients between input and output variables of the rectifier [20]. In addition, the existing approaches are limited to estimate the excitation current in the mode III. The accurate and effective online field current estimation for brushless synchronous starter/generator considering the rectifier commutation mode is studied in this paper.

The goal of this paper is to investigate the field current estimation method in which the commutation mode of the rectifier is considered. Based on the three-phase AC ME, the rotor current of the ME is estimated by the stator current, voltage and rotor position. The mathematical relationship between the ME rotor current and MM field current in different rectifier mode is analyzed. Then the field current estimation method can be obtained. The experiments are carried out to verify the effectiveness of the proposed method.

SECTION II. Proposed Field Current Estimation Method

To study the field current estimation method, the model of the excitation system (including the three-phase ME and three-phase bridge RR) should be built first. Here, the flux model of the ME is employed to estimate the ME rotor current. Based on a rectifier circuit, the mathematical relationship among these rotor currents is analyzed. Then the MM field current can be calculated.

A. ME Rotor Current Estimation

In this section, the ME rotor currents are restructured first. Here, the three-phase current of the exciter rotor is directly reconstructed in the a-b-c three-phase frame, instead of the $\alpha- \beta$ stationary frame, which can show the mathematical relation of the ME rotor currents intuitively and simplify the computational procedure by out of use of the coordinate transformation and inverse transformation.

Since the stator and rotor flux linkage of the ME are coupled, the rotor flux linkage can be calculated by the stator flux linkage and the mutual inductance, then the ME rotor current can be refactored. The stator voltage equation and flux linkage of the ME can be represented as (1), the coupling equations of stator and rotor flux linkage can be shown as (2).

$$\begin{align*} &\quad \begin{bmatrix} u_{\text{as}} \\ u_{\text{bs}}\end{bmatrix}=r_{\mathrm{s}}\begin{bmatrix} i_{\text{as}} \\ i_{\text{bs}}\end{bmatrix}+\frac{\mathrm{d}}{\mathrm{d} t}\begin{bmatrix}\lambda_{\text{as}} \\ \lambda_{\text{bs}}\end{bmatrix}\tag{1}\\ & \begin{bmatrix}\lambda_{\text{as}} \\ \lambda_{\text{bs}}\end{bmatrix}=L_{\mathrm{s}}\begin{bmatrix} i_{\text{as}} \\ i_{\text{bs}}\end{bmatrix}+M_{\text{sr}}\begin{bmatrix} C_{\mathrm{a}} \\ C_{\mathrm{b}}\end{bmatrix}\tag{2}\end{align*}$$ where, the $u_{\text{as}}, u_{\text{bs}}, i_{\text{as}}, i_{\text{bs}}$ are stator voltage and currents in a-b-c three-phase frame respectively. $r_{\mathrm{s}},\ L_{\mathrm{s}}$ and $M_{\text{sr}}$ represent the resistances, self-inductances and mutual inductance respectively. The $i_{a},i_{\mathrm{b}},i_{c}$ are the ME rotor currents and $C_{\mathrm{a}}$ and $C_{\mathrm{b}}$ are shown as (3). $$\begin{equation*}\begin{cases} C_{\mathrm{a}}=i_{\text{ar}} \cos \theta+i_{\text{br}} \cos \left(\theta+\frac{2 \pi}{3}\right)+i_{\text{cr}} \cos \left(\theta-\frac{2 \pi}{3}\right) \\ C_{\mathrm{b}}=i_{\text{ar}} \cos \left(\theta-\frac{2 \pi}{3}\right)+i_{\text{br}} \cos \theta+i_{\text{cr}} \cos \left(\theta+\frac{2 \pi}{3}\right)\end{cases}\tag{3}\end{equation*}$$

Considering that $C_{\mathrm{a}}$ and $C_{\mathrm{b}}$ can be derived by (1), (2) and (3), are shown as (4).

$$\begin{equation*}\begin{cases} C_{\mathrm{a}}=\frac{\int\left(u_{\text{as}}-r_{\mathrm{s}} i_{\text{as}}\right) \mathrm{d} t-L_{\text{ss}} i_{\text{as}}}{M_{\text{sr}}} \\ C_{\mathrm{b}}=\frac{\int\left(u_{\text{bs}}-r_{\mathrm{s}} i_{\text{bs}}\right) \mathrm{d} t-L_{\text{ss}} i_{\text{bs}}}{M_{\text{sr}}}\end{cases}\tag{4}\end{equation*}$$

Then the ME rotor current can be derived as (5), where $\theta_{\text{ME}}$ is the ME rotor position. Thus, the ME rotor currents can be calculated by the measurable parameter in the a-b-c three-phase frame.

$$\begin{equation*}\begin{cases} i_{\mathrm{a}}=\frac{2 C_{\mathrm{a}} \cos \theta_{\text{ME}}}{3}+\frac{2 \sqrt{3} C_{\mathrm{a}} \sin \theta_{\text{ME}}}{9}+\frac{4 \sqrt{3} C_{\mathrm{b}} \sin \theta_{\text{ME}}}{9} \\ i_{\mathrm{b}}=\frac{2 C_{\mathrm{b}} \cos \theta_{\text{ME}}}{3}-\frac{2 \sqrt{3} C_{\mathrm{b}} \sin \theta_{\text{ME}}}{9}-\frac{4 \sqrt{3} C_{\mathrm{a}} \sin \theta_{\text{ME}}}{9} \\ i_{\mathrm{c}}=-i_{\mathrm{a}}-i_{\mathrm{b}}\end{cases}\tag{5}\end{equation*}$$

B. Relationship Among the Rotor Currents

Since the ME rotor winding is inductive, the current in the rectifier should be continuous, the commutation phenomenon appears. As mentioned above, depending on the inductance and frequency of the rectifier circuit, it has three working modes. These modes can be classified by the commutation angle $\theta$. With the increasing of $\theta$, the rectifier modes move from mode I to mode III.

Mode I: Non-Commutation and Two-Phases Commutation Alternate State

In this mode, the commutation angle $\theta\in[0,\pi/3]$, it consists of the non-commutation state and two phases commutation state. The diagram of this mode is shown as Fig. 2 and Fig. 3. Where, the $U_{\mathrm{a}}, U_{\mathrm{b}}, U_{\mathrm{c}}$ are the equivalent ME three-phase voltage, respectively. $R, L$ are the ME rotor equivalent resistance and inductance, respectively. The $U_{\mathrm{f}},i_{\mathrm{f}}$ represent the rectified voltage and current on the DC side, the $R_{\text{MM}},L_{\text{MM}}$ represent the resistance and inductance of the MM field winding, the diode filled with black color represent conductive.

Fig. 2.

Non-commutation, phase AC conduction.

In Fig. 2 and Fig. 3, it can be noticed that the mathematical relation among the ME rotor currents and the MM field current can be shown as (6) and (7), respectively. Therefore, the field current can be obtained as (8).

Mode II: Always Two Phases Commutation State

In this mode, the commutation angle $\theta=\pi/3$, the commutation is continuous owing to there are always three diodes conducting.

For example, when the commutation in Fig. 3 is finished (the current of phase B lower arms commutates to phase B lower arms completely), the phase AB upper arms are commutation and phase C lower arms is conductive.

Accordingly, the currents are shown as (7), and the field current can be obtained (8), which is same with the mode I.

$$\begin{gather*}\begin{cases} i_{\mathrm{a}}=i_{\mathrm{f}}=-i_{\mathrm{c}} \\ i_{\mathrm{b}}=0\end{cases}\tag{6} \\ \begin{cases} i_{\mathrm{a}}=i_{\mathrm{f}} \\ i_{\mathrm{b}}+i_{\mathrm{c}}=-i_{\mathrm{f}}\end{cases}\tag{7} \\ \vert i_{\mathrm{f}}\vert=\frac{\vert i_{\mathrm{a}}\vert+\vert i_{\mathrm{b}}\vert+\vert i_{\mathrm{c}}\vert}{2}\tag{8}\end{gather*}$$

Mode III: Two Phases Commutation and Three Phase Commutation Alternate State

In this mode, the commutation angle $\theta\in[\pi/3,2\pi/3]$. It consists of the two phases commutation state and three phases commutation state. The current relationship under the two phases commutation state has been discussed as (7). Here, only the three phases commutation state is studied.

Fig. 3.

Two phases commutation, phase A upper arms conduction and phase BC lower arms commutation.

With the increasing of commutation angle, the commutation in Fig. 3 is not finished (phase BC lower arms commutation is not finished), the phase A upper arms are commutating to phase B upper arms, then the three phases commutation appears, shown as Fig. 4.

Fig. 4.

Three phases commutation, AB upper arm commutation and BC lower arms commutation.

Affected by the B upper arms, the $i_{\mathrm{a}}$ is not equal to the $i_{\mathrm{f}}$ any more, but less than $i_{\mathrm{f}}$, owing to the short-circuit current $i_{b1}$, compared with the (7). Then, the mathematical relation among the ME rotor currents and the excitation current of MM can be expressed as (9) and (10). The $i_{\mathrm{a}},i_{\mathrm{b}1}$ and $i_{\mathrm{f}}$ are the positive and $i_{\mathrm{c}},i_{\mathrm{b}2}$ are the negative.

$$\begin{gather*}\begin{cases} i_{\mathrm{a}}+i_{\mathrm{b} 1}=i_{\mathrm{f}} \quad i_{\mathrm{a}}, i_{\mathrm{f}} \text { and } i_{\mathrm{b} 1} \geq 0 \\ i_{\mathrm{b} 2}+i_{\mathrm{c}}=-i_{\mathrm{f}} \quad i_{\mathrm{b} 2} \text { and } i_{\mathrm{c}} \leq 0 \\ i_{\mathrm{b}}=i_{\mathrm{b} 1}+i_{\mathrm{b} 2}\end{cases}\tag{9}\\ \frac{\vert i_{\mathrm{a}}\vert+\vert i_{\mathrm{b}}\vert+\vert i_{\mathrm{c}}\vert}{2} \leq \frac{\vert i_{\mathrm{a}}\vert+\vert i_{\mathrm{b} 1}\vert+\vert i_{\mathrm{b} 2}\vert+\vert i_{\mathrm{c}}\vert}{2}=\vert i_{\mathrm{f}}\vert\tag{10}\end{gather*}$$

Here, the simple simulation of the rectifier which works in the mode III based on the MATLAB Simulink is carried out, shown as Fig. 5. The simulated field current and the calculation by the (10) are compared. It can be noticed that, the calculation result is same with the actual value in the two phases commutation state, lower than the actual value in the three phases commutation state.

Fig. 5.

Simulation in the mode III.

So that, we can obtain this conclusion: in the mode I and mode II, the field current can be calculated by (8). In the mode III, the employing of (8) might be inaccurate, the calculated result is periodic less than the field current.

C. Field Current Estimation

In fact, the accurate field current can be obtained by the (10) with the extremum method, which by finding the max value in the real-time updating data. However, this method might be easily affected by the interference or calculation error.

Considering that, the inductance of the MM field winding is large, which makes the ripple of the rectified can be ignored, shown as the simulated result in Fig. 5. So that, in the mode I and mode II the calculation result by (8) can be treated as the DC value, but in the mode III the calculation result by (10) might be the sum of the DC component and the harmonic, and the frequency of this harmonic is sixth times of the frequency of the ME rotor current, and the value of the field current can be treated as the DC component plus the RMS value of the sixth harmonic.

Considering that the frequency in this application might be changed with the rotor speed, the adaptive filter is employed here [32], and this adaptive band-pass filter is employed for the six times of the frequency of the ME rotor current, which is used to obtain the rectifier mode and compensate the calculation error in the three phases commutation state, the transfer function is shown as (11).

$$\begin{equation*} G(\mathrm{s})=\frac{0.1 \omega S}{S^{2}+0.1 \omega S+\omega^{2}}\tag{11}\end{equation*}$$

The bode plot of the band-pass filter is shown as Fig. 6, and the natural frequency is set as 2400 Hz (six times of the aircraft power supply), then the magnitude ratio of the filtered harmonic to the DC component is used to confirm the rectifier mode, and the threshold is set 3%, if the magnitude ratio is less than 3%, the rectifier works in mode I or mode II, the field current can be estimated by (8). If the magnitude ratio is larger than 3%, the rectifier works in mode III, the field current can be estimated by (8) plus the RMS value of the filtered sixth harmonic.

Fig. 6.

Bode plot of the filter.

The schematic of the proposed method is illustrated in Fig. 7. First, the ME rotor currents are estimated: the stator voltage, stator current and the rotor position are collected to the controller, based on equation (4) the ME rotor currents can be reconstituted.

Then the ME rotor currents are employed to estimate the MM field current, based on the equation (10) and (11), the sixth harmonic of the ME rotor current can be filtered, its value is compared with the preset threshold 3%. Finally, the MM field current estimation method and the rectifier mode can be obtained.

Fig. 7.

Field current estimation strategy.

SECTION III. Experiment

Since there is no brush and slip ring in the ISG system, and the MM field winding is installed at the rotor part, the measurement of the MM field current becomes impossible. Here, a brush slip ring machine is used to build the prototype experimental platform: The rotor winding is connected to the external static uncontrolled rectifier through the brush slip ring, and as the load MM field winding, the resistive inductive load is employed, with resistance value of 7.5 Ω and inductance of 0.48 mH. The experimental platform is shown as Fig. 8 and the information of the slip ring machine and driving motor are shown as Table I.

The slip ring machine is coaxial connected with the motor, which is driven by the controller. The ME is excited by the variable voltage converter. The proposed method is running in the RT lab semi physical real-time simulation system, the real-time estimated current is obtained by the D/A conversion port and the Tektronix oscilloscope. In order to verify the effectiveness of the proposed estimation method, the RR in different commutation mode under steady condition experiments are carried out, then the dynamic experiment is also carried out.

Fig. 8.

The experimental platform.

Table I The parameters of the me and driving motor

A. Steady State Experiments in Mode I

When the speed of the ME is 200 rpm, the excitation voltage and frequency are set as 29 V/50 Hz. The measured rotor currents (the cyan line and the pink line) and the field current (the blue line) of the ME are shown in Fig. 9(a). The estimated ME rotor currents (the cyan line and the pink line) and the field current (the green line) are shown in Fig. 9(b).

Then the above results are together compared in Fig. 9(c). It can be noticed that in Fig. 9(c) the measured current agrees the estimated current very well, the RMS value of the measured field current (the blue line) and the calculated field current (the green line) are both 2.4 A.

It can be noticed that in Fig. (9), the calculated phase current and field current will have a small disturbance due to the existence of interference. To eliminate the interference, the digital filter is adopted then this disturbance might be reduced.

When the experimental condition is changed, such as the excitation voltage increases to 35 V, the results are shown in Fig. 10. Then the rms value of the measured filed current and calculated field current both increase to 3 A. It is noticed that the calculated ME rotor current and the field current can still match the measured current very well.

B. Steady State Experiments in Mode III

Since the mode I of the rectifier includes the non-commutation state and two phases commutation state, the mode II only include the two phases commutation state. The experiment of mode II can be treated as one part of the experiment of mode I. Therefore, the experiment of mode II is not verified repeatedly, and the mode III is verified here.

Fig. 9.

The experiment when excitation voltage is 29 V. (a) The measured current. (b) The calculated current. (c) The comparison.

Fig. 10.

The experiment when excitation voltage increases to 35 V.

Then the excitation voltage is changed to 13 V, the excitation frequency is 400 Hz, and the load resistance is adjusted to 0.7 Ω. The calculated result of the excitation current of the ME in the third mode is shown in Fig. 11. The blue line is the measured rectifier output current, and the RMS value is 1.05 A. The green line is the calculated current, and the RMS value is 1.04 A, too. The error is less than 1%, which shows that the method proposed can obtain the high accuracy under different working modes of the rectifier.

Fig. 11.

The experiment under the third mode.

C. Dynamic Experiment

Since there are filters in the proposed method, which might produce the time delay, the dynamic experiment should be considered. In Fig. 7, it can be noticed that the dynamic performance of this method in mode I, mode II, and mode III is the same, the difference is that the whether to compensate the harmonics or not. Thus, the dynamic experiment is only carried out in mode I.

In the real application, the speed and the excitation frequency of the ME can hardly be suddenly changed. Instead, the voltage might be suddenly changed, to meet the requirement of the voltage regulation of the power supply. Thus, the dynamic performance of the proposed method is verified by the excitation voltage change, the experiment result is shown as Fig. 12.

When the motor speed is kept at 200 rpm and the excitation frequency is kept at 50 Hz, the excitation voltage increases from 15 V to 25 V, the calculated MG field current (green line) can track the measured field current (blue line), and the green line and blue line simultaneously rise from the RMS value 1 A to the RMS value 2 A with the same trajectory. When the excitation voltage drops to 15 V, the calculated MM field current and the measured field current simultaneously decrease from the 2 A to 1 A in the same trajectory again, the calculation error is less than 1%, which shows the accuracy and dynamic performance of the proposed method.

Fig. 12.

The dynamic experiment.

SECTION IV. Conclusion

A simpler and more effective field current estimation approach, considering the rectifier mode, for the brushless synchronous starter/generator is presented in this paper. Based on the flux equations the ME rotor current is calculated first, then the mathematical relationship among the ME rotor currents and MM field current in different rectifier mode is analyzed, the results show that when the rectifier works in the mode III, there might be the estimation error, owing to the commutation current. The frequency of the estimation error is six times to the frequency of AC side.

Then the adaptive bandpass filter for the sixth harmonic is employed, to confirm the rectifier mode and compensate the calculation error in the three phases commutation state. Finally, the field current estimation method can be obtained.

Since the three-phase current of the exciter rotor is directly reconstructed in the a-b-c three-phase frame, the computational procedure of the proposed method might be simplified, by out of use of the coordinate transformation and inverse transformation; In addition, the proposed method can estimate the field current in all rectifier mode and confirm the rectifier mode, is more suitable for this ISG system, and it is easier to be implemented.

The experiments are carried out in different rectifier modes, the steady and transient states experiments are also carried out, the estimation results of the proposed method match the experimental results very well.