Design and Control of Brushless DC Motor Drives for Refrigerated Cabinets

Abstract

The purpose of this study is to develop a variable frequency brushless DC motor drive for the compressors of refrigerated cabinets. It is based on the microcontroller unit (MCU) produced by Renesas Co., Ltd. using the space vector pulse width modulation (SVPWM) for the modulation of the inverter. In addition, at the AC power supply side of the inverter developed, a circuit for suppressing electromagnetic interference (EMI) and a power factor corrector (PFC) are integrated to control the power factor (PF) at the AC power supply side to be above 0.95, which is far better than the commercially available inverters with a power factor of only 0.5. Finally, an intelligent variable frequency control approach based on the extension theory is designed to classify the rotational speed difference and the rate of change in rotational speed difference between the rotational speed commands and the actual rotational speed of the compressor into 20 zones. Then, for the rotational speed difference and the rate of change in rotational speed difference actually measured, their correlations to the 20 zone categories are calculated to determine an appropriate rotational speed command. The temperature of the refrigerated cabinets can quickly be determined to reach the set target value. The proposed extension speed control is simple in computation and does not require much learning data, making it easy to implement. Furthermore, the drive developed is verified by actual testing and its performance is compared to the compressor drives of the refrigerated cabinets commercially available. It is proved that the performance of the drives developed is indeed far better than that of the drives commercially available.

1. Introduction

Motors are the essential equipment in many industrial or household electrical products, among which refrigeration equipment is the most widely used. The induction motors used on the compressors of the refrigeration equipment in the past have been replaced gradually by brushless DC motors. However, considering the costs and the technologies, most of the drives of refrigeration equipment on the market still adopt six-step square-wave driving, resulting in poor driving performance. To improve the driving performance, a space vector pulse width modulation (SVPWM) controlled inverter [1,2] can be used to reduce the vibration and noise when the compressor is running.

In addition, since the inverter of the electrical equipment uses high-frequency modulation, the high-frequency noise and signals generated will disturb the peripheral equipment, even making the power factor drop. The main cause is that the distortion on the input current waveform will lead to a large number of high-frequency harmonics, which will affect the power factor, increase the reactive power and thus increase the line losses. In this case, the power supply side has to supply more electricity, resulting in an increase in electricity cost. Therefore, a compressor drive for the refrigerator cabinet incorporating an EMI suppression circuit and PFC should be developed. The EMI suppression circuit is located on the AC side of the input end. A PFC is configured to correct the input current waveform into a sine wave with the same phase as the input voltage to increase the power factor at the AC input side.

The conventional proportional-integrated (P-I) controller cannot be applied to all operating points for well-performed control [3,4]. Therefore, many intelligent controllers [5,6,7] have been proposed. However, the architectures of such controllers are complicated, and the computation time required is long, so these control rules are not easy to implement, and the control performance is not as good as expected. Thus, this study proposed an intelligent variable frequency control technique, using a variable frequency control approach based on the extension theory [8]. The frequency of the inverter is determined to control the rotational speed of the compressor so that the set temperature of the refrigerated cabinets can be reached quickly. The control approach takes the rotational speed difference and the rate of change in rotational speed difference between the actual rotational speed and the rotational speed commands of the compressor as the system characteristics and determines the appropriate speed command with extension theory. To determine the command value of the rotational speed, the two characteristic values of the rotational speed difference and the rate of change in rotational speed difference are classified into several zones according to their magnitude ranges. Then, the classical domain and the neighborhood domain of the extension theory [8] are used to build an extension model and the weights are defined according to the importance of the two characteristics [9,10]. The correlation degree of each rotational speed difference and each change in rate of rotational speed difference to the zone categories is computed. Then, they will be classified into the zone category with the maximum value of correlation degree to them to calculate the corresponding rotational speed command of a such category, so that the temperature of the refrigerated cabinet can quickly reach the set value. This study will use the drive developed to control the commercially available compressors (embraco_VEGT11HB) [11] and the performance will be compared with the drive originally equipped on the commercially available compressor.

2. Architecture of Drive Control System for Refrigerated Cabinets

The refrigeration cycle system mainly consists of four processes: compression, condensation, throttling, and evaporation [12]. Among them, the compression process is the most important one. Thus, the compressor’s performance and the compressor’s drive are critical, which will determine the cooling performance of the refrigerated cabinets. Currently, the temperature control system of the refrigerated cabinets commercially available consists of a temperature controller and a compressor drive, and its system architecture is shown in Figure 1. In particular, the temperature controller receives the temperature value set (${\mathrm{T}}_{\mathrm{set}}^{*}$) by the temperature display panel and then feeds back the temperature value (T) measured by the temperature sensor in the refrigerated cabinet. The P-I controller computes according to the difference between the actual temperature and the set temperature and issues the corresponding rotational speed command $({\omega }_r^{*})$ to control the temperature inside the refrigerated cabinet. As for the rotational speed controller, in this paper, an intelligent controller is built based on extension theory.

2.1. Design of Compressor Drives

The main configuration of the compressor drive developed includes EMI suppressor, power factor corrector and inverter, as shown in Figure 2.

2.1.1. EMI Suppressor

The X capacitor C_x, Y capacitor C_Y, and common choke L₁ and L₂ are used on the AC input side of the drive developed to construct the EMI suppressor shown in Figure 3. The main purpose is to suppress the differential mode and common mode of EMI [13]. For the drive developed, 0.33 μF is selected for the X capacitor C_x, 1000 pF is selected for the Y capacitor C_Y, and 4 mH is selected for the common choke L₁ and L₂, complying with FCC PART 15B [14], the regulation established by U.S. Federal Communications Commission (FCC). The EMI limits for each frequency band in the regulations are shown in

Table 1. FCC PART 15B regulation [14].

Frequency (MHz)	Limit db (μV/m)
30–88	40
88–216	43.5
216–960	46.0
960 and above	54.0

.

2.1.2. Power Factor Corrector

The active power factor corrector (PFC) [15] is used for the drive developed. The circuit diagram is shown in Figure 4. A bridge rectifier with a boost converter are used to realize the PFC, which is simple in control and the cost is low. For the PFC control IC, L4984D from STMicroelectronics is used, which has a control mode of fixed-off time-continuous conduction mode (FOT-CCM) [16]. Its operating principle is to use a resistor to divide voltage. The raised voltage V_out is fed back to the error amplifier (VA). Then, it is compared to V_REF to generate an error signal V_C that will be fed into the multiplier and multiplied by the sine wave voltage VMULT, the voltage divided by the resistor after full-wave rectification. The V_CSREF output from the multiplier is a sine wave after full-wave rectification, used as the PWM modulation reference signal. V_CSREF is sent to the inverting input of the PWM comparator to be compared with the voltage V_CS generated by the current flowing through the detection resistor R_sense when the MOSFET is in ON-state. Then, its output is sent to the PWM latch RS flip-flop and the PWM signal is generated after computing with the FOT (fixed off time) generator, achieving the intention of power factor correction.

2.1.3. Space Vector Pulse Width Modulation of Inverter

Due to the high utilization rate of the DC link voltage in the space vector pulse width modulation approach, which has lower current harmonics and is easy to be implemented through digital control [17,18,19,20], it is now widely used in the modulation techniques for the output of the sine wave inverters. Thus, such a modulation approach is also used in the inverter developed in this study to control the ON- and OFF-state of the six power semiconductors in the inverter, as shown in Figure 5, to have an output of three phase balanced sine wave AC voltage.

2.2. Sensorless Speed Estimation of the Inverter

For this study, the micro-controller is used as the core control [21] to form a closed-loop control for various subsystems under the sensorless speed control architecture, including the motor phase current detections, coordinate system transformation, rotor position estimations, space vector pulse width modulation, P-I controller for current loops and the extension speed controller, etc. The control architecture is shown in Figure 6.

After rearranging the magnetic flux vector formula of the brushless DC motor, Equations (1) and (2) can be obtained [22].

$$x={\lambda }_m^{}\cos (\widehat{\theta })={\lambda }_{\alpha }^{}-L_s{i}_{\alpha }={\lambda }_{\alpha 0}^{}+{\displaystyle {\int }_0^t(v_{\alpha }^{}-R_s^{}{i}_{\alpha }^{})dt-L{i}_{\alpha }^{}}$$

(1)

$$y={\lambda }_m^{}\sin (\widehat{\theta })={\lambda }_{\beta }^{}-L_s{i}_{\beta }^{}={\lambda }_{\beta 0}^{}+{\displaystyle {\int }_0^t(v_{\beta }^{}-R_s^{}{i}_{\beta }^{})dt-L{i}_{\beta }^{}}$$

(2)

After taking the arctangent functions of Equations (1) and (2), the angles can be estimated $\widehat{\theta }$ [23].

$$\widehat{\theta }={\tan }^{-1}(\frac{x}{y})$$

(3)

The angle $\widehat{\theta }$ obtained from Equation (3) is differentiated with respect to time, then the rotational speed estimation ${\widehat{\omega }}_r^{}$ can be obtained, as expressed in Equation (4).

$${\widehat{\omega }}_r^{}(t)=\frac{d}{dt}\widehat{\theta }(t)$$

(4)

3. Drive Control for the Compressor of Refrigerated Cabinet

For the closed-loop control of the refrigerated cabinet drive system, firstly, the error value between the temperature feedback from the inside of the refrigerated cabinet and the temperature settings of the refrigerated cabinet is calculated. A rotational speed command is obtained after P-I controller processes the error value. Then, such rotational speed command is compared with the actual speed of the compressor, obtaining the rotational speed difference, and the rate of change in rotational speed difference. Next, the rotational speed difference and the rate of change in rotational speed difference are used as the system characteristics and introduced into the extension theory to obtain a command suitable for the drive frequency of the inverter $f^{*}$, which is used to control the rotational speed of the compressor. The overall control architecture is shown in Figure 7.

3.1. Extension Theory

3.1.1. Extension Matter-Element Model

In daily life, people, matters and things can be referred to as “matters” in general. To distinguish the difference between matters, the designation N is used for definition. Matters have characteristics c, which describe their different forms, functions, properties, matters, and relationships between matters and styles. Additionally, these characteristics have their corresponding quantity values v, to describe the range, degree and amount of the characteristics. “Characteristic”, “designation”, and the corresponding “quantity value” of the characteristic are the three elements used to describe a matter. Thus, they are expressed as a matter-element model [8] in Equation (5).

$$R=(N,c,v)$$

(5)

In particular, if a matter has multiple characteristic points, the matter N can be described by x characteristics c₁, c₂, …, c_x and their corresponding quantity values v₁, v₂, …, v_x. Thus, the matter-element model [8] can be expressed as Equation (6).

$$\mathit{R}=\left[\begin{array}{c}{R}_1^{}\\ R_2^{}\\ ⋮\\ R_x^{}\end{array}\right]=\left[\begin{array}{ccc}N,& c_1^{},& v_1^{}\\ & c_2^{},& v_2^{}\\ & ⋮& ⋮\\ & c_x^{}& v_x^{}\end{array}\right]$$

(6)

3.1.2. Definition of Classical Domain and Neighborhood Domain in Extension Theory

If the quantity value of a characteristic is a range value, such a range is defined as the classical domain $F_0^{}=<a,b>$ of such a characteristic and included in a neighborhood domain $F=<d,e>$, i.e., $F_0^{}\in F$ [8]. If point $f$ is any point in interval F, then the matter-element corresponding to $F_0^{}=<a,b>$ can be expressed as Equation (7).

$$R_0^{}=(F_0^{},c_i^{},v_i^{})=\left[\begin{array}{ccc}{F}_0^{},& c_1^{},& <a_1^{},b_1^{}>\\ & c_2^{},& <a_2^{},b_2^{}>\\ & ⋮& ⋮\\ & c_x^{}& <a_x^{},b_x^{}>\end{array}\right]$$

(7)

where c_i is the characteristic of F₀, and v_i is the quantity value of characteristics c_i, i.e., its classical domain. Additionally, the matter-element R_F corresponding to F can be expressed as Equation (8) [8]. Where $c_j^{}$ is the characteristic of F, and $v_j^{}$ is the quantity value of characteristics $c_j^{}$, i.e., its neighborhood domain.

$$R_F^{}=(F,c_j^{},v_j^{})=\left[\begin{array}{ccc}F,& c_1^{},& <d_1^{},e_1^{}>\\ & c_2^{},& <d_2^{},e_2^{}>\\ & ⋮& ⋮\\ & c_x^{}& <d_x^{},e_x^{}>\end{array}\right]$$

(8)

3.1.3. Distance and Rank Value

In classical mathematics, it is the distance relationship between points. While in extension theory, it is the distance relationship between one point $f$ on real domain and an interval $F_0^{}=<a,b>$. If it is expressed as a function, it can be expressed as Equation (9).

$$\rho (f,F_0^{})=\left|f-\frac{a+b}{2}\right|-\frac{b-a}{2}$$

(9)

In addition to considering the correlation between point and interval, the relationship between points and the relationship between intervals is also considered. Therefore, if $F_0^{}=<a,b>$ and $F=<d,e>$ belongs two intervals, respectively, in a real domain, and the interval $F_0^{}$ is within $F$, then the rank values of point $f$, interval $F_0^{}$ and interval $F$ can be expressed as Equation (10) [8].

$$D(f,F_0,F)=\{\begin{array}{ll}\rho (f,F)-\rho (f,F_0)& ,f\notin F_0\\ -1& ,f\in F_0\end{array}$$

(10)

3.1.4. Correlation Function

Assume $F_0^{}=<a,b>$, $F=<d,e>$, $F_0^{}\subset F$, and there is no common endpoint, then the correlation function can be expressed as Equation (11) [8].

$$K(f)=\frac{\rho (f,F_0^{})}{D(f,F_0^{},F)}$$

(11)

In particular, when $f=(a+b)/2$, its function value is the maximum value, then such a correlation function is referred to as an elementary correlation function and its schematic is shown in Figure 8. In addition, when $K(f)<-1$, it indicates that point $f$ is outside the interval $F$. When $K(f)>0$, it indicates that point $f$ is within interval $F_0^{}$. Additionally, $-1<K(f)<0$ indicates that point $f$ is within the extension domain.

3.2. Selection of the Extension Variable Frequency Control Characteristics for Refrigerated Cabinet

To make the response of temperature control for the refrigerated cabinet more rapid and stable, the rotational speed control based on extension theory is adopted in this study. The control rule is to divide the rotational speed difference ($e(n)\triangleq {\widehat{\omega }}_r^{}(n)-\stackrel{}{{\omega }_r^{*}}(n)$) and the rate of change in rotational speed difference ($\dot{e}\left(n\right)\triangleq e(n+1)-e(n)$) between the actual rotational speed $({\widehat{\omega }}_r^{})$ range (from 1800 rpm to 4500 rpm) operable of the refrigerated cabinet compressor and the rotational speed command $({\omega }_r^{*})$ into 20 zones (i.e., 20 categories). Figure 9 shows the dynamic analysis of 20 categories divided from the rotational speed errors $(e)$ and the rate of change in rotational speed errors $(\dot{e})$ between the rotational speed command of the compressor and the actual rotational speed. Figure 9 shows that Category A1–A4 has a larger oscillation on the wave amplitudes due to the largest difference between the actual rotational speed and the rotational speed command. For Category A17–A20, the oscillation on the wave amplitudes is smaller, since the rotational speed difference is smaller. As for Category A1–A4, A5–A8, A9–A12, A13–A16, and A17–A20, there is no significant difference regarding the rate of change in rotational speed errors. Taking Zone A1 as an example, its $e>0,\dot{e}>0$ and $e$ becomes larger. Even though $\dot{e}>0$, its value becomes smaller. Additionally, $\dot{e}=0$ at point m₁, yet, at this moment, $e$ is the largest. Therefore, when the rotational speed difference $e$ becomes larger (i.e., the actual rotational speed is much higher than the rotational speed command) and the rate of change in rotational speed difference $\dot{e}$ is positive, the actual rotational speed has to be reduced significantly to make the actual rotational speed match the rotational speed command. Thus, the frequency command of the rotational speed has to be reduced until it is the same as the rotational speed command. The same approach can be applied to the rest zones to perform the dynamic analysis. Therefore, for the dynamic analysis shown in Figure 9, according to extension matter-element theory, the matter-element model for the classical domain of its 20 zone categories can be built based on the two characteristics, rotational speed difference $(e)$ and the rate of change in rotational speed difference $(\dot{e})$. Additionally, $\Delta Freq$ is the frequency command variation in the rotational speed command corresponding to the matter-element model of 20 classical domains individually. The results are shown in

Table 2. Extension matter-element models of 20 categories and frequency variations $\Delta Freq$.

Zones	Extension Matter-Element Model	Frequency Command Variations $\Delta \mathit{F}\mathit{r}\mathit{e}\mathit{q}$
A1	$R_1^{}=\left[\begin{array}{lll}{F}_1^{}& e& <0,2700>\\ & \dot{e}& <0,162650>\end{array}\right]$	−50
A2	$R_2^{}=\left[\begin{array}{lll}{F}_2^{}& e& <0,2700>\\ & \dot{e}& <-162650,0>\end{array}\right]$	−50
A3	$R_3^{}=\left[\begin{array}{lll}{F}_3^{}& e& <-2700,0>\\ & \dot{e}& <-162650,0>\end{array}\right]$	50
A4	$R_4^{}=\left[\begin{array}{lll}{F}_4^{}& e& <-2700,0>\\ & \dot{e}& <0,162650>\end{array}\right]$	50
A5	$R_5^{}=\left[\begin{array}{lll}{F}_5^{}& e& <0,2400>\\ & \dot{e}& <0,144578>\end{array}\right]$	−40
A6	$R_6^{}=\left[\begin{array}{lll}{F}_6^{}& e& <0,2400>\\ & \dot{e}& <-144578,0>\end{array}\right]$	−40
A7	$R_7^{}=\left[\begin{array}{lll}{F}_7^{}& e& <-2400,0>\\ & \dot{e}& <-144578,0>\end{array}\right]$	40
A8	$R_8^{}=\left[\begin{array}{lll}{F}_8^{}& e& <-2400,0>\\ & \dot{e}& <0,144578>\end{array}\right]$	40
A9	$R_9^{}=\left[\begin{array}{lll}{F}_9^{}& e& <0,2100>\\ & \dot{e}& <0,126506>\end{array}\right]$	−30
A10	$R_{10}^{}=\left[\begin{array}{lll}{F}_{10}^{}& e& <0,2100>\\ & \dot{e}& <-126506,0>\end{array}\right]$	−30
A11	$R_{11}^{}=\left[\begin{array}{lll}{F}_{11}^{}& e& <-2100,0>\\ & \dot{e}& <-126506,0>\end{array}\right]$	30
A12	$R_{12}^{}=\left[\begin{array}{lll}{F}_{12}^{}& e& <-2100,0>\\ & \dot{e}& <0,126506>\end{array}\right]$	30
A13	$R_{13}^{}=\left[\begin{array}{lll}{F}_{13}^{}& e& <0,1800>\\ & \dot{e}& <0,108433>\end{array}\right]$	−20
A14	$R_{14}^{}=\left[\begin{array}{lll}{F}_{14}^{}& e& <0,1800>\\ & \dot{e}& <-108433,0>\end{array}\right]$	−20
A15	$R_{15}^{}=\left[\begin{array}{lll}{F}_{15}^{}& e& <-1800,0>\\ & \dot{e}& <-108433,0>\end{array}\right]$	20
A16	$R_{16}^{}=\left[\begin{array}{lll}{F}_{16}^{}& e& <-1800,0>\\ & \dot{e}& <0,108433>\end{array}\right]$	20
A17	$R_{17}^{}=\left[\begin{array}{lll}{F}_{17}^{}& e& <0,1500>\\ & \dot{e}& <0,90361>\end{array}\right]$	−10
A18	$R_{18}^{}=\left[\begin{array}{lll}{F}_{18}^{}& e& <0,1500>\\ & \dot{e}& <-90361,0>\end{array}\right]$	−10
A19	$R_{19}^{}=\left[\begin{array}{lll}{F}_{19}^{}& e& <-1500,0>\\ & \dot{e}& <-90361,0>\end{array}\right]$	10
A20	$R_{20}^{}=\left[\begin{array}{lll}{F}_{20}^{}& e& <-1500,0>\\ & \dot{e}& <0,90361>\end{array}\right]$	10

. In Table 2, the rotational speed difference $e$ and the rate of change in the rotational speed difference $\dot{e}$ are used as the two characteristics of the extension theory and they are divided into 20 classical domains. Among them, the minimum value of the characteristics in the 20 classical domains of the rotational speed difference $e$ is −2700 and the maximum value is 2700, so the neighborhood domain of the characteristic value of the rotational speed difference $e$ is <−2700, 2700>. In the same way, the minimum value of the eigenvalues in the 20 classical domains of the rotational speed difference change rate $\dot{e}$ is −162,650, and the maximum value is 162,650, so the neighborhood domain of the eigenvalues of the rotational speed difference $\dot{e}$ is <−162,650, 162,650>. Therefore, the neighborhood domain established by the maximum and minimum values of the classical domain of each characteristic is shown in Equation (12).

$$R_F^{}=(F,c_j^{},v_j^{})\left[\begin{array}{lll}F& e& <-2700,2700>\\ & \dot{e}& <-162650,162650>\end{array}\right]$$

(12)

3.3. Rotational Speed Control by Extension Theory

To allow a rapid and stable response of the rotational speed control for the compressor, in this study, the two characteristic values, the rotational speed difference and the rate of change in rotational speed difference between the compressor rotational speed command and the actual rotational speed are input into the extension theory to calculate the correlation degree. The category with the highest correlation degree to such characteristic value is identified and such characteristic data will be classified into that category. Then, the frequency command value of the inverter corresponding to the rotational speed command will be determined. Since the embraco_VEGT11HB compressor [11] used in this study has the lowest rotational speed of 1800 rpm and the highest rotational speed of 4500 rpm, the setting range of the rotational speed command for classification is from 1800 rpm to 4500 rpm. The corresponding control frequency command of the inverter is 60 Hz to 150 Hz. The characteristics are the rotational speed difference and the rate of change in rotational speed difference between the rotational speed command and the actual rotational speed, i.e., $e\triangleq {\widehat{\omega }}_r^{}-{\omega }_r^{*},\dot{e}\triangleq de/dt$. The process of the extension rotational speed command control is described below.

Step 1:

Build the matter-element model of the characteristics for each category of the rotational speed difference and rate of change in rotational speed difference.

$$R_g^{}=(F,c,v)=\left[\begin{array}{lll}{F}_0& e& <a_1^{},b_1^{}>\\ & \dot{e}& <a_2^{},b_2^{}>\end{array}\right],g=1,2,\dots ,20$$

(13)

Step 2:

Input the two characteristics to be classified, the rotational speed difference $e$ and the rate of change inrotational speed difference $\dot{e}$, and the matter-element model is built as

$$R_{NEW}^{}=\left[\begin{array}{lll}{F}_{NEW}^{}& e& v_{NEW1}^{}\\ & \dot{e}& v_{NEW2}^{}\end{array}\right]$$

(14)

Step 3:

For the rotational speed difference $e$ and the rate of change in rotational speed difference $\dot{e}$, use Equation (11) to calculate their correlation functions with each zone category.

Step 4:

Set the weights $W_1^{}$ and $W_2^{}$ for each characteristic, to represent the importance of each characteristic. For this study, both weights $W_1^{}$ and $W_2^{}$ are set to 1/2, and $W_1^{}+W_2^{}=1$.

Step 5:

Calculate the correlation degree between each category’s characteristic values to be measured.

$${\lambda }_g^{}={\displaystyle \sum _{j=1}^2{W}_j^{}{K}_{gj}^{},g=1,2,\dots ,20}$$

(15)

Step 6:

After calculation, the rotational speed difference $e$ and the rate of change in rotational speed difference $\dot{e}$ to be classified will be classified into the category with the highest correlation degree and the frequency variation $\Delta Freq$ will be determined based on the category it belongs to. The new rotational speed frequency command $Fre{q}_{new}^{}$ is recalculated, i.e.,

$$Fre{q}_{new}^{}=Fre{q}_{old}^{}+△Freq$$

(16)

where $Fre{q}_{old}^{}$ is the rotational speed frequency value for the highest correlation degree calculated in the previous cycle.

Step 7:

The correlation degree of each classified category is normalized by using Equation (17) to have a correlation degree within the range of <−1,1>, which improves the sensitivity of the correlation degree to facilitate the classification.

$$\{\begin{array}{l}{\lambda }_g^{\prime }=\frac{{\lambda }_g^{}}{\left|{\lambda }_{\max }^{}\right|}, if {\lambda }_g^{}>0\\ {\lambda }_g^{\prime }=\frac{{\lambda }_g^{}}{\left|-{\lambda }_{\max }^{}\right|}, if {\lambda }_g^{}<0\end{array}$$

(17)

where ${\lambda }_{max}^{}$ and $-{\lambda }_{max}^{}$ are the maximum value and minimum value of the correlation degrees for each category classified, respectively.

4. Experiment Results

The compressor drive and intelligent controller designed in this study are developed to verify the performance of the compressor drive and controller, as shown in Figure 10. Additionally, the refrigerated cabinet shown in Figure 11 is used for testing.

The compressor of refrigerated cabinets used in this paper is manufactured by embraco_VEGT11HB, which belongs to the DC brushless motor type and its detailed specifications are listed in

Table 3. Specifications of compressor of refrigerated cabinets.

Electrical Parameter	Value
Rated voltage	AC 230 V
Rated current	AC 3.3 A
Rated power	429 W
Rated rotational speed	4500 rpm
Input frequency range	60–150 Hz
Poles	4

. The specifications of the developed inverters are shown as

Table 4. Inverter Specifications.

Electrical Parameter	Parameter Value
Input rated voltage	AC 230 V
Input rated current	AC 2.39 A
Three-phase output AC rated voltage	240 Vrms
Three-phase output AC rated current	10 A
Output rated power	500 W
Switching frequency	20 kHz

. The input AC voltage is 230 V. The input voltage goes through the EMI suppressor and is converted to DC with a rectifier. Then, it adopts PFC control IC L4984D to control the boost converter circuit, stabilize the DC link output voltage at DC 400 V and control the Power Factor (PF) of the AC input end to near 1.0. The DC link output capacitor adopts 450 V/680 uF, inductor adopts 1.48 mH, and power semiconductor switch component adopts R6020KNX/20 A/600 V. As to the power semiconductor switch component for the inverter adopts, the rated value of 20 A/600 V of intelligent power module (IPM) made by Mitsubishi Ltd. (Chiyoda, Tokyo, Japan). All the related component specifications are shown in

Table 5. Component specifications used in the developed inverter.

Component Name	Model/Specifications
X capacitor	0.33 uF/300 VAC
Y capacitor	1000 pF/400 V
Common choke	4 mH/3.7 A
Rectifier	GBJ2510/25 A/1000 V
DC link output voltage	DC 400 V
DC link output current	1.25 A
DC link capacitor	450 V/680 uF
PFC control IC	L4984D
PFC power MOSFET	R6020KNX/20 A/600 V
PFC inductor	1.48 mH/3.5 A
Intelligent power module	PSS20S92F6A-AG/20 A/600 V

. The micro-controller unit (MCU) adopts the chip of Renesas factory model RX24T as the control core. Its specifications are shown in

Table 6. Specifications of Micro-controller unit Renesas RX24T.

Item	Specifications
Bit count	32 Bits
Maximum Operating Frequency	80 MHz
A/D converter	12 bits
D/A converter	8 bits
PWM control number	4
Operating voltage	2.7 V~5.5 V
ROM capacity	512 Kbytes
RAM capacity	32 Kbytes
Flash RAM capacity	8 Kbytes

.

In order to verify the performance of the designed compressor drive and intelligent controller, the equipment shown in

Table 7. Experimental equipment and measurements used.

Instrument Name	Manufacturer/Model	Measure Signal
Power analyzer	Vitrek Corporation/PA900	Voltage, Current, Frequency, Apparent power, Real power, Power factor, Total harmonic distortion
Spectrum analyzer (including near field probe)	Rohde-Schwarz Ltd./FPC1000 (Rohde-Schwarz Ltd./HZ-15)	Electromagnetic interference (EMI)
Oscilloscope	Agilent Technologies Ltd./MSO-X 3034A	Voltage waveform, current waveform

is used in this paper to conduct electrical measurements, where the PA900 power analyzer produced by the Vitrek Corporation is used to measure the voltage, current, power, power factor and total harmonic distortion of the drive, etc. The Rohde-Schwarz Ltd. (Harvest Cres, Fleet, UK) factory FPC1000 spectrum analyzer, together with HZ-15 near field probe is used to measure electromagnetic interference (EMI). As for the MSO-X3034A oscilloscope manufactured by Agilent Technologies, it is used to measure the output voltage and current waveforms of the inverter, as well as the input voltage and current waveforms of the AC side of the power factor corrector (PFC).

4.1. EMI Emission Suppression at the AC Input Side

A circuit to suppress the EMI noise is incorporated at the drive’s AC input side developed. It is tested according to the FCC PART 15B regulations stipulated by U.S. Federal Communications Commission (FCC). In order to analyze the different degrees of EMI on the circuit board, the test method is to divide the drive developed into 12 parts and numbered, as shown in Figure 12. Since Figure 12(A1–C1) are close to where the power transistor module is located, the high-frequency switching of the power transistor will make these blocks subject to a stronger emission interference. Therefore, when the compressor of the refrigerated cabinet is driven to a rotational speed of 4500 rpm by the drive, the spectrum analyzer is used together with the near field probe to conduct a test for each block. The EMI spectrogram measured at Figure 12(A1–C1) are shown in Figure 13, Figure 14 and Figure 15, respectively. From the spectrograms, it can be seen that for each block, the interference in dB with the maximum magnitude generated due to EMI at 34.923 MHz is 34.59 dB, 22.83 dB and 30.10 dB respectively. All meet the FCC PART 15B regulation indicated in Table 1.

4.2. Power Quality Improvement at AC Input Side

Under the same input voltage conditions, the input voltage waveforms and the input current waveforms of the commercially available drive and the drive developed are measured, respectively. Figure 16 is the waveforms of the commercially available drive’s input voltage and input current. Figure 17 is the waveforms of the drive’s input voltage and input current developed. Since the drive developed is equipped with PFC and the commercially available drive is not equipped, from Figure 16 and Figure 17, the input current waveform of the commercially available drive is distorted due to the capacitor used for filtering the rectifier output.

4.3. Comparison of Power Factor and THD

Under the same load, Figure 18 shows the apparent power, real power, and power factor value measured on the commercially available drive, which is 724.24 VA, 365.56 W, and 0.5048, respectively. Figure 19 shows the total harmonic distortion (THD), which is up to 167.67%. Figure 20 shows the apparent power, real power, and power factor value measured on the drive developed, which is 488.69 VA, 486.99 W, and 0.9965, respectively. Its THD is only 5.905%, according to Figure 21. The comparison results of the two drives demonstrate that since the drive developed is equipped with PFC, the input current can be corrected into a sine wave the same as that of the input voltage, so that the power factor can be corrected to be close to 1 and its THD is reduced significantly. Thus, the power factor on the AC side can be improved.

4.4. Power Factor on the Output Side of the Drives

4.4.1. Comparison of the Output Line Voltage and Phase Current of the Drives

Under the frequency command of 150 Hz at the same rotational speed (i.e., rotational speed command of 4500 rpm), the output 3-phase line voltage and phase current waveform of the commercially available drive and the drive developed are measured, respectively, for comparison. Figure 22 and Figure 23 are the 3-phase output line voltage and current waveform of the commercially available drive, respectively. Figure 24 and Figure 25 are the 3-phase output line voltage and current waveform of the drive developed. In Figure 22 and Figure 23, the measured frequency of the output 3-phase line voltage and phase current of the commercially available drive is around 125 Hz, which cannot reach the exact 150 Hz of the rotational speed frequency command. Additionally, both the output line voltage and phase current waveforms are distorted. While in Figure 24 and Figure 25, the measured frequency of the output 3-phase line voltage and phase current of the drive developed is 150 Hz, which reaches the exact 150 Hz of the rotational speed frequency command. Additionally, both the output line voltage and phase current waveforms are the more stable waveform of sinusoidal pulse width modulation, making it easier for filtering.

4.4.2. Comparison of the Output Current THD of the Drives

Next, the power analyzer is used to measure the output current. The total harmonic distortion of the output current measured on the commercially available drive and the drive developed are compared. The higher the total harmonic distortion of the current, the poorer the power quality of its power supply. Figure 26 shows the measured data of the total harmonic distortion of the current for the commercially available drive at the rotational speed frequency command of 150 Hz (i.e., rotational speed command of 4500 rpm). From Figure 26, it can be found that the total harmonic distortion of the output current is up to 19.96%. As for the drive developed, the measured data of the total harmonic distortion of the output current at the rotational speed frequency command of 150 Hz (i.e., rotational speed command of 4500 rpm) is shown in Figure 27. From Figure 27, it can be found that the total harmonic distortion of the output current is only 5.079% when the drive developed is at a rotational speed of 4500 rpm. For easy comparison with the total harmonic distortion of the output current between the commercially available drive and the drive developed, the data are summarized in

Table 8. Comparison with the output current THD_i of two types of drives.

Rotational Speed Command		Commercially Available Drive		Drive Developed
Frequency	Corresponding rotational speed	Output frequency	THDi	Output frequency	THDi
150 Hz	4500 rpm	125 Hz	19.96%	150 Hz	5.079%

.

4.5. Responses of the Refrigerated Cabinet Temperature Control under Different Ambient Temperatures

The conventional P-I controller and the proposed controller based on extension theory are installed on the refrigerated cabinet separately for testing. First, the temperature controller inside the cabinet of the refrigerated cabinet is set to 5 °C and the refrigerated cabinet temperature is adjusted to 13 °C, 11 °C, and 9 °C, respectively. Then, the conventional P-I controller and the extension controller are used to compare the control performance. The temperature sensor here uses a thermistor. The relationship between the temperature Temp and the resistor R_Temp of the thermistor is listed in

Table 9. The relationship between the temperature and the thermistor [24].

Temp	RTemp	Temp	RTemp
1 °C	310.764 kΩ	11 °C	189.8841 kΩ
2 °C	295.4121 kΩ	12 °C	181.0559 kΩ
3 °C	280.9084 kΩ	13 °C	172.6881 kΩ
4 °C	267.2014 kΩ	14 °C	164.754 kΩ
5 °C	254.2428 kΩ	15 °C	157.229 kΩ
6 °C	241.9877 kΩ	16 °C	150.0898 kΩ
7 °C	230.394 kΩ	17 °C	143.3144 kΩ
8 °C	219.4224 kΩ	18 °C	136.8825 kΩ
9 °C	209.0361 kΩ	19 °C	130.7749 kΩ
10 °C	199.2007 kΩ	20 °C	124.9734 kΩ

[24]. Then, the resistor of the thermistor relative to the temperature is converted into a voltage using the circuit in Figure 28, which is expressed as Equation (18).

$$V_{Temp}^{}=VDD\times \frac{R_{Temp}^{}}{R_{Temp}^{}+100k}$$

(18)

The F/V conversion circuit between voltage and frequency is shown in Figure 29, and their relationship is expressed as Equation (19) [25].

$$V_{Freq}^{}=Freq\times 2.09\times \frac{R_L^{}}{R_s^{}}\times (R_t^{}{C}_t^{})$$

(19)

The test results are shown in Figure 30, Figure 31, Figure 32, Figure 33, Figure 34 and Figure 35 and summarized in

Table 10. Comparison of the response speed of the temperature control under different ambient temperatures between the conventional P-I controller and the extension controller when the temperature is set to 5 °C.

Operating Condition of the Temperature Control inside the Refrigerated Cabinet	Response Time of the Conventional P-I Controller	Response Time of the Proposed Extension Controller
13 °C$\to$5 °C	434 s	367 s
11 °C$\to$5 °C	371 s	303 s
9 °C$\to$5 °C	267 s	219 s

. From the results measured, it is found that the proposed extension controller can carry out continuous variable frequency control and can rapidly and stably control the temperature inside the refrigerated cabinet to the setting of 5 °C.

4.6. Responses of the Refrigerated Cabinet Temperature Control under the Instantaneous Change in Loads

To test the temperature control performance of the conventional P-I controller and the proposed extension controller when the items inside the refrigerated cabinet are increased suddenly, first, the setting of the temperature inside the cabinet of the refrigerated cabinet is set to 5 °C. Then, the cabinet door is open for 5 s and closed to simulate the situation that the items inside the refrigerated cabinet increased suddenly. Through the actions of opening and closing the door of the refrigerated cabinet, it is equivalent to the change in the number of items placed in the refrigerated cabinet. The main reason is that when the user picks up and puts the items in the refrigerated cabinet, the door must be opened first and then closed after taking and placing. Air is exchanged, causing the temperature in the cabinet to rise, and the degree of temperature change is much greater than the increase or decrease in the number of items in the cabinet. In this paper, the controller test is used mainly to test the control response of the developed intelligent controller under the instantaneous temperature change. Therefore, the opening and closing of the refrigerated cabinet is equivalent to the increase or decrease in the number of items in the cabinet, which can highlight the robustness and adaptability of the developed intelligent controller. Figure 36 and Figure 37 show the response of the temperature control of the conventional P-I controller and the proposed extension controller, respectively. It can be found from the figures that with the conventional P-I controller, it takes 191 s to control the temperature to 5 °C. However, only 59 s are required with the proposed extension controller. Therefore, the proposed extension controller can control the temperature inside the cabinet to the temperature set, regardless of the operating environments.

5. Conclusions

The drive of the refrigerated cabinet compressor and the rotational speed control are selected as the topics of this study. The configuration of the drive developed include EMI suppressor, PFC, and inverter. Additionally, the performance of the commercially available drive is compared under the same load conditions. From the results measured, since the drive developed is equipped with an EMI suppression circuit, when the compressor of the refrigerated cabinet is running at 4500 rpm, by using the spectrum analyzer together with the near field probe, the EMI in dB with the maximum magnitude generated at 34.923 MHz is 34.59 dB, complying to the FCC PART 15B regulation stipulated by U.S. Federal Communications Commission. Since the drive developed is equipped with PFC, the input current in the sine wave can be seen from the results measured and is in the same phase as the AC input voltage. Thus, its PF is up to 0.9965 and the THD of the current at AC input side is only 5.905%. However, under the same loads and rotational speed, due to the PFC is not equipped, the PF of the commercially available drive is only 0.5048 and the THD of the current at the AC input side is up to 167.67%. In addition, since the drive developed in this study adopts the SVPWM modulation, there is no low subharmonic component in its output line voltage and phase current. Thus, filtering can be achieved with a lower induction value and a capacitance value, significantly reducing the inverter’s size and cost. Moreover, from the results measured, the output current THD_i of the drive developed is only 5.079%, which is far better than the 19.96% of the commercially available drive. The intelligent variable frequency control approach based on extension theory is adopted for the controller. The results measured show that when the temperature inside the refrigerated cabinet is controlled by the intelligent variable frequency controller proposed, lowering the temperature from 13 °C, 11 °C and 9 °C to 5 °C only takes 367 s, 303 s, and 219 s, respectively. Yet, 434 s, 371 s, and 267 s are taken if controlled by a conventional P-I controller. In conclusion, it is demonstrated that the response of the temperature control of the intelligent variable frequency controller proposed is far better than that of the conventional P-I controller.

This paper focus on using variable frequency drives to drive the compressor of refrigerated cabinets. The variable frequency drive adapted a speed sensorless sine wave inverter. The speed control for the speed sensorless vector controller adapted the extension theory-based intelligent controller to control the speed of the brushless DC motor of the compressor to control the temperature of the refrigerated cabinets. The intelligent controller developed in this paper has the advantages of fast response speed and good steady-state performance. Therefore, it can achieve the refrigerated cabinets’ energy-saving effects, and the control principal architecture is simple and easy to implement. Although the control architecture of the compressor of refrigerated cabinets currently used on the market is not yet fully intelligent, the energy-saving control of the refrigerated cabinets will be part of an international trend in refrigeration equipment in the future, and the international community has also begun to invest in related research. Therefore, the variable frequency drive of the compressor of refrigerated cabinets with energy-saving effects developed in this paper has the technology that is in line with future international standards.