Energy-Efficient Current Control Strategy for Drive Modules of Permanent Magnetic Actuators

Abstract

This paper proposes an energy-efficient current control strategy for drive modules of permanent magnetic actuators (PMAs) to reduce the cost and volume of DC-link capacitors. The drive module of the PMA does not receive the input power from an external power source during operation. Instead, the externally charged DC-link capacitors are used as internal backup power sources to guarantee the reliable operation even in the case of an emergency. Therefore, it is important to use the charged energy efficiently within the limited DC-link capacitors. However, conventional control strategies using a voltage open loop have trouble reducing the energy waste. This is because the drive module with the voltage open loop uses unnecessary energy even after the PMA mover has finished its movement. To figure it out, the proposed control strategy adopts a current control loop to save energy even if the displacement of the PMA mover is unknown. In addition, the proposed strategy can ensure the successful operation of the PMA by using the driving force analysis. The efficacy of the proposed strategy is verified through the experimental test. It would be expected that the proposed strategy can reduce the cost and volume of the PMA drive system.

1. Introduction

A permanent magnetic actuator (PMA) is used to operate a vacuum circuit breaker (VCB), switching it between ON and OFF states [1]. In the event of a fault in the power system, the PMA enables the VCB to rapidly disconnect the power line. Previous electromagnetic actuators before the PMA did not have a permanent magnet. They required the excitation current in the holding process, which reduced energy efficiency [2]. To figure it out, the PMA was proposed [3,4]. This electromagnetic actuator with the permanent magnet can significantly reduce the number of parts, showing advantages such as simple structure, easy maintenance, and high reliability [5].

In order to operate the PMA, a power conversion drive module is required, which has large DC-link capacitors [6]. The drive module of the PMA does not receive the input power from an external power source during operation. Instead, the externally charged DC-link capacitors are used as internal backup power sources to guarantee the reliable operation even in the case of an emergency [7]. Therefore, a large amount of energy should be charged to the DC-link capacitors when the drive module is not in operation. In other words, if the amount of energy charged in the DC-link capacitors is small, the PMA is unable to switch the state of the VCB. Meanwhile, as the application area of the PMA has expanded from low voltage to high voltage VCBs, the required energy for the DC-link capacitors has also increased [8]. Hence, it has become important to use the charged energy efficiently within the limited DC-link capacitors.

Conventional drive modules operate the PMA by simply applying a constant DC voltage to the PMA coil, which results in a variable current due to the nonlinear electromagnetic characteristics [9,10,11,12]. The problem is that the drive module uses much more energy than is actually needed to operate the PMA. The drive module is hard to know whether the PMA mover has reached the end of its mechanical stroke. Therefore, the drive module has no choice but to continuously provide the energy even after the PMA mover has finished moving to ensure the successful operation of the PMA. Like the system in [13], a displacement sensor can be installed, but it has a high cost or may interfere with the movement of the PMA mover. In addition, estimating the displacement of the PMA mover is also difficult due to the nonlinear electromagnetic characteristics.

Many researchers have tried to estimate the displacement of the PMA mover using various methods. In [14,15,16,17,18], the model analysis-based methods utilize the characteristic of the PMA where the coil inductance changes depending on the mover displacement. The coil inductance is estimated by the analyzed PMA model with the measured voltage and current, and then it is converted to the mover displacement. However, the PMA model is vulnerable to changes in parameters such as the coil resistance and back electromotive force (back-EMF), making it difficult to guarantee the accuracy when the environment changes. To solve this, the high-frequency signal injection methods [19,20,21] were proposed to measure the coil inductance by observing the response of the injected signal. The direct measurement of the coil inductance ensures the accuracy even in environmental changes. However, because the PMA operation ends within a few milliseconds, the estimation result for the mover displacement cannot be utilized due to the estimation delay. Further, the Kalman filter [22] and the sliding mode observer [23,24] are adopted to estimate the coil inductance, but there is an inevitable trade-off between the estimation speed and accuracy. In summary, the conventional drive module that applies a constant DC voltage should know the displacement of the PMA mover to reduce the energy waste, which has not yet been solved.

This paper proposes an energy-efficient control strategy for drive modules when the displacement of the PMA mover is unknown. The proposed control strategy regulates the current flowing into the PMA coil to be constant. Because the PMA that has finished its operation behaves like an inductor, it ideally does not use energy as long as the coil current remains constant. Thus, the proposed control strategy does not waste energy even if the drive module is still running after the PMA mover has finished moving. In addition, the proposed control strategy can ensure the successful operation of the PMA by using the driving force analysis. Because the driving force is closely related to the current flowing into the PMA coil, the proper level of the current can be derived through the analysis. Hence, the proposed control strategy can reduce the size of the DC-link capacitors of the drive module while ensuring the successful operation of the PMA.

The rest of this paper is organized as follows. Section 2 introduces the PMA drive system, which consists of a one-coil PMA and a drive module. In Section 3, the voltage and current applied to the PMA and resulting force are analyzed in detail. Thereafter, the proposed current control strategy is explained and verified in Section 4 and Section 5, respectively. At the end, Section 6 concludes the article.

2. System Configuration

2.1. One-Coil PMA

The PMA used in this paper is designed as a one-coil type, as shown in Figure 1. The one-coil PMA is composed of the mover, stator, permanent magnet, open spring, contact spring, coil, and so on. By applying the positive and negative voltage to the coil, the drive module can conduct the closing and opening operations, respectively. In the closing operation, the magnetic flux of the coil is generated in the same direction as that of the permanent magnet. Therefore, the magnetic flux is amplified, as shown in Figure 2a, and the mover moves downward due to the reluctance torque. When the mover reaches the end of the stroke (EOS), the holding force of the permanent magnet maintains the closed state. On the other hand, in the opening operation, the magnetic flux of the coil is generated in the opposite direction to that of the permanent magnet. Hence, the holding force is cancelled out, as shown in Figure 2b. Then, the open spring moves the mover upwards.

The contact spring is one of the key components of the one-coil PMA. It is required to satisfy the added contact force, which is specified in the datasheet of the VCB. The added contact force is provided by the compressed contact spring in the closed state, as shown in Figure 3. By pressing the contact surface with the added contact force, the VCB can prevent the electrodynamic rejection of the contacts and reduce their transient resistance [25]. Thus, in order for the mover to reach the EOS, the drive module should overcome the contact spring force at the end of the closing operation. Otherwise, the PMA may not hold and return to the open state [26].

2.2. Drive Module

The drive module of the one-coil PMA is designed as a full-bridge inverter, as shown in Figure 4. According to the Korea Electric Power Corporation (KEPCO) standard, the rated input voltage for the drive module is 125 V_DC. To provide a strong force to the PMA, the input voltage is stepped up through a switching mode power supply (SMPS). When the SMPS finishes storing energy in the DC-link capacitors, the relay disconnects the circuit to separate the full-bridge inverter from the external power source. Therefore, only the energy stored in the DC-link capacitors is used when the drive module operates the PMA.

Because the drive module is in the form of a power conversion device, the voltage applied to the coil of PMA can be implemented through a pulse-width modulation (PWM) technique. The duty ratio (D_inv) of the drive module is determined by the following equation:

$$D_{inv}={\displaystyle \frac{V_{coil}}{V_{DC}}}$$

(1)

where V_DC is the measured DC-link voltage and V_coil is the desired voltage applied to the coil of PMA. The electrical equivalent circuit of PMA coil in Figure 4 is explained in detail in the following Section.

3. Conventional Voltage Control Strategy

The conventional drive module operates by simply applying a constant DC voltage for a certain period of time. Thus, the full-bridge inverter fixes V_coil during the applied time of drive module (T_on). Then, the analysis of the current flowing through the coil (i_coil) based on the electrical circuit in Figure 4 is formulated as follows [12]:

$$V_{coil}^n=\left(i_{coil}^{n-1}-{di}_{coil}^n\right)R_c+L_i^{n-1}{\displaystyle \frac{d{i}_{coil}^n}{dt}}+L_x^{n-1}{\displaystyle \frac{{dx}_m^n}{dt}}$$

(2)

$$L_i^n={\displaystyle \frac{{\lambda }_c^n\left(i_{coil},x_m\right)-{\lambda }_c^{n-1}(i_{coil},x_m)}{{di}_{coil}^n}}$$

(3)

$$L_x^n={\displaystyle \frac{{\lambda }_c^n\left(i_{coil},x_m\right)-{\lambda }_c^{n-1}(i_{coil},x_m)}{{dx}_m^n}}$$

(4)

$${di}_{coil}^n={\displaystyle \frac{\left(V_{coil}^n-i_{coil}^{n-1}{R}_c\right)dt-L_x^{n-1}{dx}_m^n}{R_{c}dt+L_i^{n-1}}} (0\le t\le T_{on})$$

(5)

where di_coil is the increment of i_coil, R_c is the coil resistance, L_i is the coil inductance representing the transformer EMF, L_x is the inductance associated with the EMF induced by the mover’s motion, x_m is the distance of the mover moved, and λ_c is the linked flux.

Because the PMA operation involves the mechanical movements of inductor core, L_i and L_x are changed in every moment according to i_coil and x_m. In addition, R_c is sensitive to external temperature environment. Therefore, predicting i_coil is complex and requires lots of datasets and iterations. Thus, it is difficult to set proper V_coil and T_on in the conventional voltage control strategy.

3.1. Required Current for Closing Operation

To ensure successful closing operation of the PMA, the drive module should provide the sufficient closing force to the mover. Particularly, the closing force should be stronger than the force of the two springs: the open and contact springs. The directions of the forces acting on the mover are shown in the Figure 5. The conditions for a successful closing operation at the EOS can be expressed as follows [9]:

$$F_{coil}+F_{grav}+F_{bellows}\ge F_{open}+F_{contact}$$

(6)

where F_coil is the electromagnetic force from the coil, F_grav is the gravity acting on the mover, F_bellows is the spring force from the bellows of the VCB, F_open is the force from the open spring, and F_contact is the force from the contact spring.

The only force that the drive module can control is F_coil, which can be calculated as follows [11]:

$$F_{coil}={\left.{\displaystyle \frac{\partial W_{coil}}{\partial x_m}}\right|}_{i=const}$$

(7)

$$W_{coil}={\displaystyle \frac{1}{2}}{L}_i{i}_{coil}^2$$

(8)

where W_coil is the electromagnetic energy from the coil. When (8) is substituted into (7), F_coil can be expressed as follows:

$$F_{coil}={\displaystyle \frac{1}{2}}{i}_{coil}^2{\displaystyle \frac{\partial L_i\left(x_m\right)}{\partial x_m}}$$

(9)

where L_i is the function of x_m. By curve-fitting the finite element method (FEM) analysis results of the PMA used in this paper, the derivative of L_i with respect to x_m, $\partial L_i\left(x_m\right)/\partial x_m$, can be obtained as follows:

$$\begin{gathered} {\displaystyle \frac{\partial L_i\left(x_m\right)}{\partial x_m}}=3.394·{10}^9·x_m^5-3.111·{10}^8·x_m^4+1.054·{10}^7·x_m^3 \\ -1.561·{10}^5·x_m^2+1.103·{10}^3·x_m+4.091. \end{gathered}$$

(10)

The remaining forces affecting the movement of the mover in (6) are expressed as follows:

$$F_{grav}=m_{mover}\times g$$

(11)

$$F_{bellows}=k_{bellows}\times x_{bellows}$$

(12)

$$F_{open}=k_{open}\times x_{open}$$

(13)

$$F_{contact}=k_{contact}\times x_{contact}$$

(14)

where m_mover is the mass of the mover and g is the gravitational acceleration. In addition, k_bellows, k_open, and k_contact are the spring constant of bellows, open spring, and contact spring, respectively. Likewise, x_bellows, x_open, and x_contact are the compressed or stretched distance of bellows, open spring, and contact spring, respectively. When (9) and (11)–(14) are substituted into (6), the rearranged inequality for i_coil at the EOS is as follows:

$$i_{coil}\ge \sqrt{{\displaystyle \frac{2\left(F_{open}+F_{contact}-F_{bellows}-F_{grav}\right)}{\frac{\partial L_i\left(x_{stroke}\right)}{\partial x_{stroke}}}}}=I_{EOS}$$

(15)

where x_stroke is the total stroke distance and I_EOS is the minimum current at the EOS to ensure the successful closing operation. Thus, the drive module should make i_coil higher than IEOS at the EOS by tuning both V_coil and T_on in the conventional voltage control strategy.

3.2. Selection of V_coil and T_on

In the conventional strategy, V_coil and T_on are the only parameters the drive module can modulate to satisfy the required i_coil. A typical waveform of i_coil during closing operation is shown in Figure 6. If i_coil at the EOS does not exceed I_EOS due to the low V_coil, the closing operation is unable to be performed, as shown in Figure 6a. This is because F_coil is fail to overcome F_open or F_contact. Note that i_coil decreases as the mover speed increases. This is because the motional EMF term, $L_x\left(d{x}_m/dt\right)$, affects i_coil when referring to (2) and (5). Therefore, high V_coil should be selected with a sufficient margin through numerous trials and errors to obtain the desired i_coil.

Even if V_coil is selected high enough, the short T_on can make the closing operation fail, as shown in Figure 6b. This is because T_on should be long enough for the mover to reach the EOS. However, as previously mentioned, x_m is one of the difficult factors to predict. The coil temperature is changed due to both the ambient temperature and the continuous PMA operations. The changed coil temperature affects R_c, and x_m is not the same for each closing operation. Therefore, the long T_on should be selected with a sufficient margin through numerous trials and errors, same as V_coil.

However, if both V_coil and T_on are selected with a sufficient margin, a lot of energy is wasted during the closing operation, as shown in Figure 6c. Then, the large DC-link capacitors are required to prevent the DC-link voltage from dropping against the energy use. As a result, the conventional drive module, which operates with a constant DC voltage, shows a large volume and high cost. This situation becomes more severe as V_coil and T_on become higher and longer, respectively. Hence, in this paper, a new control strategy is proposed to use the energy efficiently while ensuring the successful closing operation.

4. Proposed Current Control Strategy

To achieve efficient energy use while ensuring reliable operation, the proposed control strategy adopts a current control loop, as shown in Figure 7. By using a feedback loop, the proposed current control strategy can obtain the constant i_coil despite the changes in L_i, L_x, and R_c. Thus, referring to (9), the same F_coil can be expected at the EOS for each closing operation even under the changes in environments. In addition, a voltage limiter is used to regulate the initial i_coil rise, which affects the energy use. In this paper, the voltage limit (V_limit) is set as V_coil used in the conventional strategy. After the output value of PI controller (V_PI) becomes lower than V_limit once, the voltage limiter is neglected in order not to affect the control of i_coil.

In order to control i_coil at a constant level, it is recommended to select the PI controller gain to achieve a fast control response. This is because the PMA coil has nonlinear characteristics. The equivalent circuit and current flow for each control process of the proposed strategy are shown in Figure 8. When the drive module is turned on, L_i and motional EMF (ε_x) appear, which vary with the movement of the mover. After the mover reaches the EOS, L_i and ε_x become fixed and removed, respectively. Finally, immediately after the drive module is turned off, W_coil is restored to the DC-link capacitor, which is the energy remaining in the coil. Note that the energy used for the closing operation (W_close) is calculated as follows [14]:

$$W_{close}={\int }_0^{T_{on}}{V}_{coil}·i_{coil} dt-{\left.W_{coil}\right|}_{t=T_{on}}.$$

(16)

The typical waveforms of i_coil, V_coil and x_m resulting from the conventional voltage and proposed current control strategies are shown in Figure 9a and Figure 9b, respectively. In the proposed current control strategy, the reference value of i_coil is selected as I_EOS. This allows the PMA to ensure the successful closing operation regardless of when the mover reaches the EOS. For the drive module to provide I_EOS, the following condition should be satisfied:

$$I_{EOS}\le {\displaystyle \frac{{\left.V_{DC}\right|}_{t=T_{on}}}{R_c}}.$$

(17)

Because V_DC drops as the drive module uses the energy stored in the DC-link capacitors, it is important to note that (17) should be satisfied even when t = T_on. The relationship between V_DC and the energy used from the DC-link capacitors can be expressed as follows:

$${\displaystyle \frac{1}{2}}{C}_{DC}\left\{{\left({\left.V_{DC}\right|}_{t=0}\right)}^2-{\left({\left.V_{DC}\right|}_{t=T_{on}}\right)}^2\right\}={\int }_0^{T_{on}}{V}_{coil}·i_{coil} dt$$

(18)

where C_DC is the DC-link capacitance. When (18) is substituted into (17), the rearranged condition that the drive module should satisfy to provide I_EOS is as follows:

$$I_{EOS}\le {\displaystyle \frac{1}{R_c}}\sqrt{{\left({\left.V_{DC}\right|}_{t=0}\right)}^2-{\displaystyle \frac{2}{C_{DC}}}{\int }_0^{T_{on}}{V}_{coil}·i_{coil} dt}$$

(19)

Thus, in order to apply I_EOS obtained from (15), the proper V_DC and T_on should be selected.

As shown in Figure 9b, the proposed current control strategy has no waste of energy because i_coil does not continue to rise even if the drive module is still running after the mover reaches EOS. Since the PMA that has finished its operation is identical to an inductor, it ideally does not use energy as long as i_coil keeps constant. It is noteworthy that the instantaneous change in i_coil while the mover is moving does not significantly affect the speed of the mover due to its heavy weight. In other words, the proposed current control strategy uses less W_close for the same movement of the mover, compared to the conventional strategy. Hence, the proposed current control strategy allows the efficient use of W_close to reduce the size of the DC-link capacitors while ensuring the successful closing operation.

5. Experimental Verification

To verify the energy efficiency of the proposed current control strategy, the case studies are conducted by the experimental test. Figure 10a,b show the constructed PMA and drive module. A ring-shaped permanent magnet with a rectangular cross-section is employed to form a closed magnetic circuit. In addition, the parameters of the PMA drive system are listed in

Table 1. Parameters of PMA drive system.

Parameter		Symbol	Value
Drive Module	Rated power	Prated	10 kW
	Input voltage	Vin	125 V
	Maximum output voltage	Vmax	400 V
	Maximum output current	Imax	40 A
	DC-link voltage	VDC	400 V
	DC-link capacitance	CDC	36 mF
	Switching frequency	fsw	10 kHz
	Voltage limit	Vlimit	260 V
	Applied time	Ton	110 ms
PMA	Minimum current at the EOS	IEOS	21 A
	Total stroke distance	xstroke	44 mm
	Mass of the mover	mmover	8.2 kgf
	Bellows spring constant	kbellows	18.6 kN/m
	Open spring constant	kopen	185 kN/m
	Contact spring constant	kcontact	485 kN/m
	Stretched distance of bellows	xbellows	40 mm
	Compressed distance of open spring	xopen	44 mm
	Compressed distance of contact spring	xcontact	4 mm
	Residual flux density of permanent magnet	Br	1.45 T

. Note that the large DC-link capacitors are used to successfully conduct the closing operation, as shown in Figure 10c. The total capacitance and volume of the DC-link capacitors used in this paper are 36 mF and 5581.35 cm³, respectively. The hardware setup for the experimental test is shown in Figure 10d. The VCB is emulated by the VCB simulator.

Referring to (15), I_EOS of the PMA used in this paper is calculated as 21 A, which means that the drive module should provide F_coil of 9239 N. The experimental test results by the conventional and proposed strategies are shown in Figure 11. The results include of V_DC, i_coil, V_coil, and x_m. In the conventional strategy, it is observed that i_coil at the EOS is higher than I_EOS, thereby conducting successful closing operation. However, unnecessary energy is wasted due to both high V_coil and i_coil. On the other hand, in the proposed strategy, i_coil is maintained to become I_EOS by the current control loop. Even though both V_coil and i_coil are lower than the conventional strategy, the closing operation is successfully conducted. Hence, the proposed strategy can use the energy efficiently while ensuring reliable operation.

To compare the two control strategies more directly, the overlapped graphs of x_m and W_close are shown in Figure 12. Because only the energy stored in the DC-link capacitor is used when the drive module operates the PMA, W_close can be calculated by the following equation:

$$W_{close}={\displaystyle \frac{1}{2}}{C}_{DC}(V_{DC,before}^2-V_{DC,after}^2)$$

(20)

where V_DC,before and V_DC,after are the DC-link voltages at before and after closing operation, respectively. It is noteworthy that the two control strategies use different amounts of W_close, although the results for x_m are almost same. The conventional strategy uses 669 J of energy, whereas the proposed strategy uses only 422 J. Thus, the proposed control strategy saves the energy stored in the DC-link capacitor by 36.9%. This difference becomes wider when the conventional strategy sets the higher V_coil or the longer T_on. Thus, the capacitance of the DC-link capacitor can be reduced by 36.9% by using the proposed current control strategy.

The effectiveness of the proposed current control strategy is compared in terms of cost and volume. Based on the results of the experimental test, one of the three capacitors used in this paper can be removed. The DC-link capacitors occupy a large portion of the drive module in terms of cost and volume, as shown in Figure 13a or Figure 14a. If the cost and volume of the DC-link capacitors are reduced by 33.3%, the proportion in the overall drive module can be reduced as shown in Figure 13b or Figure 14b. Hence, the energy-efficient current control strategy can be a solution to improve the product competitiveness of the drive module.

6. Conclusions

This paper proposed the energy-efficient current control strategy for the drive module of PMA to reduce the cost and volume of the DC-link capacitors. The required current for successful closing operation was theoretically analyzed, and the method for selecting control parameters was introduced. Thereafter, the practical effectiveness of the proposed current control strategy was verified by the hardware experimental test. The results showed that the energy stored in the DC-link capacitor can be used more efficiently for the same movement of the mover. It would be expected that the proposed current control strategy can reduce the cost and volume of the PMA drive system.