https://doi.org/10.6113/JPE.2018.18.4.1067

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

Control of Motor Drives Fed by PFC Circuits without DC-Link Electrolytic Capacitors

Kwang-Man Kim^*,**, Eung-Ho Kim^**, and Jong-Woo Choi^†

^*Department of Electrical Engineering, Kyungpook National University, Daegu, Korea

^**LG Electronics, Changwon, Korea

^†Department of Electrical Engineering, Kyungpook National University, Daegu, Korea

Abstract

This paper presents a control method for variable-speed motor drives that do not use a DC-link electrolytic capacitor. The proposed circuit consists of a power factor correction converter for boosting the DC-link voltage, an inverter for driving the motor, and a small DC-link film capacitor. By employing a small DC-link capacitor, the proposed circuit that is small, and a low cost and weight are achieved. However, because the DC-link voltage varies periodically, the control of the circuit is more difficult than that of the conventional method. Using the proposed control method, an inverter can be controlled reliably even when the capacitance of the DC-link capacitor is very small. Experiments are performed using a 1.5-kW inverter with a 20-μF DC-link capacitor, and the experimental results are analyzed thoroughly.

Key words: Capacitor-less, Inverter drive, PFC

Manuscript received Aug. 18, 2017; accepted Mar. 1, 2018

Recommended for publication by Associate Editor Zheng Wang.

^†Corresponding Author: cjw@knu.ac.kr Tel: +82-53-950-5515, Kyungpook National University

^*Dept. of Electrical Engineering, Kyungpook National University, Korea

I. INTRODUCTION

Conventionally, single-phase PFC converters for motor drive systems have been used in home appliances to boost the DC-link voltages to values higher than those obtained using passive converters. Moreover, appliances with power factor correction (PFC) converters can meet harmonic regulations such as the IEEE 61000-3-2 regulation, since the converter maintains the input current in a sinusoidal shape. The DC-link capacitors of these systems are typically large electrolytic capacitors, which can reduce the DC-link voltage ripple and decouple the converter and the inverter. Therefore, with a large DC-link capacitor, the converter and inverter can be controlled independently. However, systems with large capacitors tend to be bulky and expensive.

Recently, in an effort to reduce the cost, size and weight of drive systems, motor drives with small DC-link capacitors have been studied in [1]-[21]. The authors of [1] suggested a control method for a three-phase power input. The converter in [1] was a passive rectifier. Instant power control for the motor input power and active damping were suggested to stabilize the DC-link voltage. By employing instant power control and active damping, the resonant current between the input inductor and the DC-link was effectively decreased. However, the instant power control that occurs in [1] could increase the disturbance in the current control and make the tuning of the current controller difficult. The study in [2] used an additional circuit referred to as a DC-link shunt compensator. This could improve the quality of the input current and stabilize the DC-link voltage. However, the additional cost for implementing the additional hardware circuit was a problem. The authors in [3] suggested a control method for the drive systems in air conditioners that did not use an electrolytic capacitor. Although this control method demonstrated good performance for three-phase inputs, applying this method to motor drives with a single-phase input source was difficult.

The authors of [4] and [5] suggested a control method for single-phase motor drives. Although a PFC circuit was not used in the circuit, the harmonic regulations were satisfied. With this scheme, the average DC-link voltage was lower than that in the case of passive converters. Since the input voltage of the motor was limited by the DC-link voltage, the operating region was severely reduced. Moreover, due to the low DC-link voltage, the motor periodically operated in the flux-weakening region. Therefore, the efficiency of the motor was reduced.

In this paper, a variable-speed motor drive system fed by a PFC circuit without a DC-link electrolytic capacitor is proposed. To extend the operation region of the speed control and to enhance the motor efficiency, the proposed circuit uses a boost PFC circuit at the source side. The major application of the proposed circuit is in air conditioners, where the main control target is the motor speed. Since bulky DC-link electrolytic capacitors are eliminated, it can be used in applications that require a low cost, small size and long life. Furthermore, experimental results show that the efficiency of the proposed circuit is acceptable in most cases and that the operation region is higher than the inverter without an electrolytic capacitor or PFC converter. This implies that the proposed inverter drive can replace the conventional drives in many applications to reduce the cost and weight. To control the motor reliably, new control methods are proposed for the converter and inverter. The proposed algorithm shows good performance even when the electrolytic capacitor is eliminated.

The remainder of this paper is organized as follows. The proposed topology and principle of the control are presented in Section II. The control method for the proposed circuit is explained and analyzed in Section III. Experimental results are presented and compared with those of conventional circuits with large capacitors in Section IV. Some conclusions are presented in Section V.

II. PROPOSED TOPOLOGY AND PRINCIPLE OF CONTROL

In this section, a new circuit is proposed, and the working principle is described.

The proposed motor drive circuit shown in Fig. 1 is applied to an inverter driving an air conditioner. It consists of a converter part and an inverter part. As mentioned before, the bulky DC-link electrolytic capacitor is replaced with a film capacitor with a capacitance below several tens of microfarads. The converter boosts the DC-link voltage and regulates the input current to the required shape. The peak of the DC-link voltage is usually below 400 V. Thus, the voltage ratings of the power devices are usually 600 V. An inverter employing the vector control algorithm controls the speed of the interior permanent magnet synchronous motor (IPMSM) required by air conditioners.

Fig. 1. Proposed motor drive circuit.

Fig. 2 shows an equivalent circuit for explaining the principle of the control in the proposed circuit, and Fig. 3 shows simulated waveforms. Since the capacitance of the DC-link capacitor is small, the converter controls the DC-link voltage v_dc with an average value of v_dc. Therefore, the converter controller updates the input current command with respect to the DC-link voltage once in a half-period of the input source v_in. Because a DC-link voltage ripple is caused by the difference between the DC-link input P_{dc_in} and the motor input P_{motor_in}, it may be impossible to control P_{motor_in} constantly, as in the conventional motor control. If P_{motor_in} is constant, the difference between P_{dc_in} and P_{motor_in} is very large, and the voltage peak of the DC-link may be over the rated voltage of the power devices. In this paper, the inverter controls the motor input power, similar to a resistance load, to stabilize the DC-link voltage. If the motor is operated similar to a resistance load, the difference between P_{dc_in} and P_{motor_in} is relatively small, and the ripple in the DC-link voltage may be at an allowable level, as shown in Fig. 3.

Fig. 2. Equivalent circuit for the control principle.

Fig. 3. Simulated waveforms: (a) Without the third harmonic of the input current; (b) With the third harmonic of the input current (I₃ = 0.25I₁) (From top to bottom: input voltage, input current, DC-link voltage, DC-link input power (red), motor input power (blue)).

(a)

(b)

Fig. 3 shows simulated waveforms of the proposed circuit. Waveforms in the case of maintaining the input current i_s in a sinusoidal shape are shown in Fig. 3(a), and waveforms in the case of maintaining i_s in a sinusoidal shape including the fundamental and third harmonic currents are shown in Fig. 3(b). Note that the third harmonic of the input current does not affect the average power from the input source.

The input voltage is given as:

  (1)

If the input current has a third harmonic component, it is expressed as:

          (2)

where I₁ and I₃ are the peak values of the fundamental component and the third harmonic component, respectively. By neglecting the power loss of the circuit and the stored energy of the boost inductor L_b, the instantaneous power P_{dc_in} from the converter to the DC-link can be obtained as:

          (3)

From (3), P_{dc_in} can be plotted with respect to the amplitude of I₃, as shown in Fig. 4.

Fig. 4. Plot of P_{dc_in} with respect to the amplitude of I₃ for I₁ = 8 A and E = 311 V.

In Fig. 4, the peak of P_{dc_in} may be decreased by over 20% when I₃ is approximately 0.25I₁. By injecting the third harmonic into the input current command, the peak of P_{dc_in} and the peak voltage of the DC-link can be reduced as shown in Fig. 3(b).

The output power P_{motor_in} can be expressed as:

   (4)

where R_eq is the equivalent resistance of the motor load. Furthermore, the differential equation can be obtained as:

   (5)

where i_Cdc is the current flowing to the DC-link capacitor C_dc. Since (5) is nonlinear, the simulated waveform of v_dc is also nonlinear, as shown in Fig. 3. It is shown that the peak voltage of v_dc is decreased by over 10% after the third harmonic is added to the input current i_s. In practice, the peak value of the DC-link is important in the case of using 600 V rated switches in the inverter. Due to the parasitic inductances inside the power device, the PCB pattern, etc., the peak of the DC-link voltage is usually controlled to be approximately below 400 V. In addition, the size of the third harmonic is limited by harmonic regulations. As per the IEC 61000-3-2 Class A standard, the third harmonic should be suppressed to below 2.3 A. Moreover, when the third harmonic increases, the losses in the converter may increase. Hence, the value of the third harmonic should be determined considering the above mentioned factors.

III. PRACTICAL CONTROL OF THE PROPOSED INVERTER DRIVE

In this section, the block diagram of the proposed control shown in Fig. 5 is explained. Since the capacitance of the DC-link capacitor is very small, the converter controls the DC-link voltage every half period. In addition, the inverter controls the motor power, similar to a resistance load, to easily stabilize the DC-link voltage. When compared to the conventional motor driving algorithm, the q-axis current control is replaced by a new algorithm, referred to as 1-cycle power control, to instantly control the motor input power. The command of the 1-cycle power control is the motor input power, and is proportional to the square of v_dc, for operating as an equivalent resistance load.

Fig. 5. Block diagram of the motor drive control for: (a) Converter control; (b) Inverter control.

(a)

(b)

A. Converter Control

If the DC-link voltage is assumed to be constant during a switching period T_s, the average inductor voltage during T_s is:

    (6)

where Δi_L is the inductor current variation, and D is the duty ratio of the switch S_b. Rearrangement of both sides yields:

  (7)

where:

       (8)

The control duty D_c can be obtained from a proportional- integral (PI) controller. Since the DC-link voltage fluctuates periodically, the gain of the PI controller is set to be inversely proportional to v_dc. This technique is referred to as gain scheduling.

The DC-link voltage controller controls every half-period and decides the amplitude of the current reference. Since the response of this controller is updated every half-period, the DC-link voltage should be stabilized by the inverter during the half-period. The stabilizing methods are explained in the next section.

B. Motor Control

Assuming steady-state operation and neglecting the loss of the motor, the input power of the motor P_{motor_in} can be written as:

      (9)

where ω_e is the angular velocity, φ_m is the back-EMF constant, and i_d and i_q are the phase d–q currents in the synchronous frame. From (9), the power reference P^* can be obtained as:

          (10)

where v_dc,average is the average value of v_dc over a long period of time. It is difficult to calculate the optimal i_d that maximizes the efficiency since analysis in a transient state is required. In many cases, φ_m＞＞(L_d – L_q)i_d is true. Therefore, to simplify the problem, (L_d – L_q)i_d can be ignored. Subsequently, the i_q current is proportional to the motor input power in the steady state. To control the motor input power, similar to a resistance load, the i_q current reference should be:

      (11)

To maintain the ratio of the phase d–q currents during a half-period of the input source, the d-axis current reference is given in (12).

        (12)

Experimentally, this shows good performance. The input power of the motor can be written as:

         (13)

where v_d and v_q are the output voltages of the inverter. Thus, the q-axis voltage reference can be obtained as:

   (14)

The 1-cycle power control proposed in (14) replaces the conventional q-axis PI current controller. It can control the motor input power within one or two switching periods. Therefore, the proposed 1-cycle power control is faster than the conventional PI control. This is very useful when direct control of the motor input power is needed. A weak point of the proposed 1-cycle power control occurs when i_q is very small. This weak point can be easily improved by switching to the conventional PI control during very light loads.

Generally, if the line-to-line back EMF of a motor is higher than v_dc, the power flows from the motor to the DC-link. This may cause the DC-link voltage to rise above the desired value. The proposed 1-cycle power control is effective in avoiding this unwanted situation since the inverter output power is decided directly by (14). In practical implementations, the power command can be realized after a 1-cycle PWM period. Therefore, v_d^* is the output of the d-axis current control, which is applied after a PWM period. Thus, the currents i_d and i_q should be predicted from the sensed currents one cycle after the next.

Since the DC-link capacitor is very small, the DC-link voltage becomes periodically lower than the value needed to operate in the maximum torque per ampere (MTPA) region. Thus, the dynamic over-modulation algorithm is very important for controlling the d-axis current in a stable manner [23]. In this paper, a new over-modulation method is presented, which is shown in Fig. 6. In the over-modulation region, the difference between the d-axis current controller output v_d^* and its realized voltage v_d might become a major hindrance to the d-axis current controller. The proposed over-modulation method is designed to decrease the gap between v_d^* and v_d. The q-axis voltage reference can be simply limited in the synchronous frame due to the absence of PI control. Afterwards, the d–q reference voltages are projected to the nearest side of the voltage hexagon in the stationary frame as shown in Fig. 6. The proposed over- modulation scheme provides a more reliable d-axis current control under fluctuating DC-link voltages.

Fig. 6. Proposed over-modulation method: (a) First step in the synchronous reference frame; (b) Second step in the stationary frame.

(a)

(b)

IV. EXPERIMENTAL RESULTS

In this section, experimental results are presented, and the performance is analyzed.

The proposed circuit and control logic are tested in an air conditioner, as shown in Fig. 7(b). A test board without bulky DC-link capacitors is shown in Fig. 7(a). The test board drives a twin rotary compressor. The speed command for the compressor is determined by the room and outdoor temperatures. The phase currents of the motor are calculated from the voltage across a 1-shunt resistor, while the position of the rotor is predicted by a position sensorless logic.

Fig. 7. Test environment: (a) Test board; (b) Air conditioner outdoor unit with the test board.

(a)

(b)

The specifications of the test drive and motor are listed in Table I.

TABLE I EXPERIMENT SPECIFICATIONS

Drive	Input voltage vs	220 V/60 Hz
	PWM Frequency (converter)	45 kHz
	PWM Frequency (inverter)	5 kHz
	Boost Inductance Lb	300 µH
	DC-link Capacitance Cdc	20 µF
	DC-link Target Voltage	310 V
	Third Harmonic I3	0.25I1
Motor	Mechanical Frequency	55 Hz ((a) - (e)) 90Hz ((f) - (g))
	D-axis Inductance Ld	7 mH
	Q-axis Inductance Lq	11 mH
	Back EMF Constant	0.354 V/(rad/s)
	Pole Number	6

From Fig. 8(a) to (e), waveforms are measured at 800W drive input and 55Hz mechanical frequency. Fig. 8(f) and (g) are measured at 1.5kW and 90Hz. Fig. 8(a) and (b) show that the waveforms are similar to the simulated results presented in the previous section. Fig. 8(c) shows that the DC-link voltage is periodically lower than the desired value. From Fig. 8(d) and (e), it is observed that the motor input power is periodically limited, and that the d-axis current i_d is controlled in a stable manner by the proposed control algorithms. Fig. 8(f) and (g) show that the proposed drive can be operated in the high speed operation region.

Fig. 8. Experiment waveforms of the proposed circuit: (a) Input current (blue), input voltage (red) and DC-link voltage (green); (b) DC-link voltage (green) and phase currents (yellow, red and blue); (c) DC-link voltage (green), measured DC-link voltage (red) and × amplitude of the inverter output voltage (yellow); (d) DC-link voltage (green), reference of the 1-cycle power controller (yellow) and measured motor input power (red); (e) Reference of the d-axis PI current controller (yellow) and the measured d-axis current (red); (f) Input current (blue), input voltage (red) and DC-link voltage (green) at 1.5kW drive input, 90Hz (5400rpm) mechanical frequency; (g) DC-link voltage (green) and phase currents (yellow, red and blue), at 1.5kW drive input, 90Hz (5400rpm) mechanical frequency.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Fig. 9(a) is measured at 2.2 Nm load conditions and shows the total efficiency of the drive and motor. Fig. 9(a) shows that the efficiency of the proposed circuit is slightly lower, when compared with that of the conventional circuit. However, this difference is very small and may be acceptable in most cases. In comparison with inverters without electrolytic DC-link capacitors and PFC circuits [4], [5], the proposed circuit has a higher efficiency and a wider operation region. Therefore, the proposed inverter may be used more widely. Fig. 9(b) shows that the drive satisfies IEC 61000-3-2 Class A harmonic regulation standards.

Fig. 9. Measured performances: (a) Efficiency comparison of cases with/without a DC-link electrolytic capacitor and PFC converter (drive and motor); (b) Limit and measurement results of harmonics.

(a)

(b)

V. CONCLUSION

In this paper, a control method for variable-speed motor drives without using DC-link electrolytic capacitors was proposed. By employing a small DC-link film capacitor, a proposed drive system that is small, and low in cost and weight, was achieved. To control the system reliably, certain new control methods were proposed. First, third harmonics were injected into the input current to minimize the peak value of the DC-link voltage. Secondly, the controller operated the motor, similar to a resistance load. Finally, to control the motor, similar to a resistance load, a 1-cycle power control was proposed. Experimental results showed that the measured performances were reasonably good even when the system was driven without DC-link electrolytic capacitors.

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Kwang-Man Kim was born in Busan, Korea. He received his B.S. degree from Pusan National University, Busan, Korea, in 1999; and his M.S. degree from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2008. Since 2001, he has been a Research Engineer for LG Electronics, Korea. His current research interests include circuit design and the control of converters and inverters for air conditioners.

Eung-Ho Kim was born in Jeju, Korea, in 1977. He received his B.S. degree from Hanyang University, Seoul, Korea, in 2003; and his M.S. and Ph. D. degrees from the Pohang University of Science and Technology, Pohang, Korea, in 2005 and 2009, respectively. Since 2009, he has been a Research Engineer for LG Electronics, Korea. His current research interests include circuit design and the control of converters and inverters for home appliances.

Jong-Woo Choi was born in Daegu, Korea. He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Seoul National University, Seoul, Korea, in 1991, 1993 and 1996, respectively. From 1996 to 2000, he worked as a Research Engineer for LG Industrial Systems Co., Korea. Since 2001, he has been a Professor in the Department of Electrical Engineering at Kyungpook National University, Daegu, Korea. His current research interests include static power conversion and electric machine drives.