Enhancing Power Quality in Distributed Energy Resource Systems Through Permanent Magnet Retrofitting of Single-Phase Induction Motors

Abstract

Distributed energy resource systems offer improved energy utilization and reduced transmission losses by decentralizing power generation and load management. However, the power quality is often compromised by inefficient customer-side equipment, such as single-phase induction motors, which suffer from low efficiency and poor power factor. To address this issue, this paper proposes a permanent magnet retrofitting method for single-phase induction motors, which replaces the squirrel-cage rotor with a permanent magnet rotor while preserving the original stator and winding structure. The proposed method aims to enhance motor performance without significant structural changes. A single-phase induction motor was retrofitted using the proposed method, and its performance was evaluated through finite element simulations to verify the effectiveness of the design approach. This study also investigated the key factors influencing motor starting performance after the introduction of permanent magnets. This study presents a practical and effective method for the permanent magnet retrofitting of single-phase induction motors, which contributes to improving motor efficiency and enhancing power quality in distributed energy resource systems.

1. Introduction

With the advancement of energy transition, the distributed energy resource system installing power generation and energy storage equipment near users is increasingly expanding. This approach allows for greater flexibility in electricity usage while enhancing energy utilization efficiency and reducing transmission losses [1]. However, these systems exhibit lower overall stability, and their power quality remains susceptible to fluctuations in user-side loads. Single-phase induction motors are widely used in agricultural equipment (irrigation pumps, grain processing machinery) and household appliances (air conditioners, washing machines, refrigerators) due to their structural simplicity, low cost, and easy maintenance [2,3,4]. However, constrained by high copper losses and low power factor in traditional designs, single-phase induction motors generally operate at low efficiencies (typically below 60%), resulting in significant energy waste [5,6]. Consequently, the research on enhancing the efficiency of these motors is critically important for reducing electrical energy losses and improving power quality in distributed energy resource systems.

Currently, several researchers have studied approaches to improve the efficiency of single-phase induction motors. In terms of structural optimization, several studies have investigated the impact of rotor bar geometry on the efficiency of single-phase induction motors, demonstrating that motor performance can be improved by optimizing the rotor configuration [7,8]. Reference [9] optimized motor parameters using the magnetic equivalent circuit method to approximate a circular rotating field, thereby reducing copper losses. In addition, the adoption of novel materials or advanced manufacturing processes has also been shown to enhance motor efficiency. For example, in [10], the use of grain-oriented electrical steel for the rotor core and copper bars in place of traditional materials led to a 1.6% improvement in the efficiency of a single-phase induction motor. Reference [11] proposed a rotor aluminum die-casting method to improve slot fill factor, with experimental verification showing a 2% efficiency gain over conventional techniques. While these studies effectively enhance single-phase induction motor efficiency, the improvements achieved are limited, particularly when the motor operates under light load conditions. Consequently, it is imperative to replace single-phase induction motors with single-phase permanent magnet motors, which offer higher efficiency and power density. Research concerning the design of single-phase permanent magnet motors primarily references methodologies developed for three-phase line-start permanent magnet synchronous motors. This involves selecting appropriate air-gap flux density and electric loading based on rated data to determine the fundamental motor dimensions. However, this design approach necessitates the complete redesign of the stator core and winding structure, thereby increasing both design and manufacturing costs.

In this context, this paper aims to develop a permanent magnet retrofit method for existing single-phase induction motors, in which the rotor is redesigned while the stator structure remains unchanged. The objectives of this study are as follows: (1) to propose a rotor design approach that incorporates permanent magnets to improve efficiency while ensuring compatibility with existing stator configurations; (2) to analyze the electromagnetic performance of the redesigned motor using finite element simulations; (3) to investigate the influence of key parameters, including back electromotive force and auxiliary winding capacitance, on the starting performance of the single-phase permanent magnet motor.

2. A Permanent Magnetization Design Method for the Single-Phase Induction Motor

2.1. The Principle of the Single-Phase Permanent Magnet Motor

The single-phase permanent magnet motor can be regarded as a hybrid of a permanent magnet synchronous motor and a single-phase induction motor, and its structure is shown in Figure 1. The stator structure is identical to that of a single-phase induction motor. The rotor incorporates both permanent magnets and a squirrel-cage winding. The squirrel-cage winding generates asynchronous torque, akin to an induction motor, enabling the motor to start and pull into synchronism. Meanwhile, the permanent magnets primarily govern the steady-state performance.

Single-phase motors are primarily classified into four basic types based on their winding configurations: capacitor-start, resistance-start, capacitor-operated and dual-value capacitor. Among these, the capacitor-operated single-phase motors are the most widely used. Its stator slots contain two sets of windings: a main winding and an auxiliary winding. The axes of the main winding and auxiliary winding are spaced 90 electrical degrees apart in space. The auxiliary winding is connected in series with a capacitor that participates in both the motor starting and running processes. Its winding configuration is shown in Figure 2.

2.2. The Permanent Magnetization Design Process of the Single-Phase Induction Motor

During the permanent magnet retrofit design process for the single-phase induction motor, both the stator structure and winding configuration remain unchanged. Consequently, the primary focus is on designing the rotor structure including the dimensions of the permanent magnets and the squirrel-cage based on the requirements for motor efficiency and starting performance.

In the design process of the single-phase permanent magnet motor, the motor’s efficiency is directly dependent on the design of the permanent magnet rotor. For a permanent magnet motor operating steadily, its efficiency (η) can be expressed as:

$$\eta ={\displaystyle \frac{P_{\mathrm{em}}-P_{\mathrm{Fe}}-P_{\mathrm{mec}}}{P_{\mathrm{em}}+P_{\mathrm{Cu}}}}$$

(1)

where P_em is the electromagnetic power, P_Fe is the core loss, P_Cu is the copper loss, and P_mec is the mechanical loss.

$$P_{\mathrm{em}}={\omega }_{\mathrm{r}}p[{\psi }_{\mathrm{f}}{i}_{\mathrm{q}}+(L_{\mathrm{d}}-L_{\mathrm{q}})i_{\mathrm{d}}{i}_{\mathrm{q}}]$$

(2)

where ω_r is the angular velocity of the fundamental magnetic field, p is the number of pole pairs, ${\psi }_{\mathrm{f}}$ is the permanent magnet flux linkage, L_d is the d-axis inductance, L_q is the q-axis inductance, i_d is the d-axis current, and i_q is the q-axis current.

Given that the winding configuration remains unchanged, the electromagnetic power is predominantly influenced by the dimensions of the permanent magnets. The key dimensions of the permanent magnets primarily include the magnet width (W_m) and the magnet length in the magnetization direction (h_m). The axial length of the permanent magnet (L_m) is typically set equal to or slightly less than the axial length of the stator core. Consequently, in practical design, only two magnet dimensions require determination: W_m and h_m. The general design procedure for the permanent magnets in a single-phase permanent magnet synchronous motor is illustrated in Figure 3 below.

Based on the RMS value of the no-load phase back-EMF determined by the efficiency requirements, the permanent magnet width can be subsequently calculated. The method is as follows:

The formula for the no-load air-gap flux per pole is:

$${\Phi }_{\mathsf{\delta }0}={\displaystyle \frac{b_{\mathrm{m}0}}{{\sigma }_0}}{B}_{\mathrm{r}}{W}_{\mathrm{m}}{l}_{\mathrm{ef}}$$

(3)

where Φ_δ0 is the no-load air-gap flux per pole, Wm is the permanent magnet width, b_m0 is the no-load operating point flux density of the permanent magnet, σ₀ is the no-load leakage coefficient, l_ef is the effective core length, and B_r is the residual magnetic flux density. According to the above formula, it can be obtained:

$$W_{\mathrm{m}}={\Phi }_{\mathsf{\delta }0}\cdot {\displaystyle \frac{{\sigma }_0}{b_{\mathrm{m}0}{B}_{\mathrm{r}}{l}_{\mathrm{ef}}}}$$

(4)

$$b_{\mathrm{m}0}={\displaystyle \frac{{\lambda }_{\mathrm{n}}}{{\lambda }_{\mathrm{n}}+1}}$$

(5)

$${\lambda }_{\mathrm{n}}={\sigma }_0{\lambda }_{\mathsf{\delta }}$$

(6)

$${\lambda }_{\mathsf{\delta }}={\displaystyle \frac{{\mathsf{\Lambda }}_{\mathsf{\delta }}}{{\mathsf{\Lambda }}_0}}={\displaystyle \frac{h_{\mathrm{m}}{\alpha }_{\mathrm{i}}\tau }{2{\mu }_{\mathrm{r}}{w}_{\mathrm{m}}\delta k_{\mathsf{\delta }}{k}_{\mathrm{s}}}}$$

(7)

where λ_n is the per-unit value of the permeance of total external magnetic circuit, λ_δ is the per-unit value of the permeance of direct-axis magnetic circuit, α_i is the calculated pole arc coefficient, δ is the air-gap length, τ is the pole pitch, k_δ is the air-gap coefficient, and k_s is the magnetic circuit saturation coefficient. Based on (3)–(7), the following can be obtained:

$${\displaystyle \frac{{\sigma }_0}{b_{\mathrm{m}0}}}={\sigma }_0+{\displaystyle \frac{2{\mu }_{\mathrm{r}}{w}_{\mathrm{m}}\delta k_{\mathsf{\delta }}{k}_{\mathrm{s}}}{h_{\mathrm{m}}{\alpha }_{\mathrm{i}}\tau }}$$

(8)

Therefore, the expression for the permanent magnet width can be derived as:

$$W_{\mathrm{m}}={\displaystyle \frac{{\sigma }_0}{\frac{B_{\mathrm{r}}{l}_{\mathrm{ef}}}{{\Phi }_{\mathsf{\delta }0}}-\frac{{\mu }_{\mathrm{r}}\delta }{{\alpha }_{\mathrm{i}}\tau h_{\mathrm{m}}}}}$$

(9)

Furthermore, the no-load air-gap flux per pole (Φ_δ0) can be determined from the value of the no-load back-EMF using the formula:

$${\Phi }_{\mathsf{\delta }0}={\displaystyle \frac{E_0}{4.44fN{K}_{\mathrm{dp}1}}}$$

(10)

where E₀ is the RMS no-load back-EMF, K_dq1 is the fundamental winding factor of the armature winding. Therefore, the final expression for determining the permanent magnet width is:

$$W_{\mathrm{m}}={\displaystyle \frac{{\sigma }_0}{\frac{4.44B_{\mathrm{r}}{l}_{\mathrm{ef}}fN{K}_{\mathrm{dp}1}}{E_0}-\frac{{\mu }_{\mathrm{r}}\delta }{{\alpha }_{\mathrm{i}}\tau h_{\mathrm{m}}}}}$$

(11)

3. Finite Element Simulation of the Single-Phase Permanent Magnet Motor

Based on the methodology described previously, a YY7114 single-phase induction motor is redesigned into a single-phase permanent magnet synchronous motor. Its key specifications are presented in

Table 1. The basic size of the motor.

Parameter	Value
rated voltage (V)	220
rated power (W)	300
rated speed (rpm)	1500
stator outer diameter (mm)	110
width of PM (mm)	28
thickness of PM (mm)	3

.

The model of the single-phase permanent magnet motor and its corresponding external circuit, constructed within the finite element software Maxwell 2D are shown in Figure 4.

A no-load finite element simulation was performed on the single-phase permanent magnet motor. The resulting no-load back-EMF waveform is presented in Figure 5. The RMS value of the no-load back-EMF in the main winding is 179 V, while that in the auxiliary winding is 228 V. The ratio of the main-to-auxiliary winding no-load back-EMF magnitudes essentially equals the ratio of their respective coil turns. Furthermore, the back-EMF in the main winding is 0.81 times the supply voltage.

A simulation at the rated output power condition was performed. The resulting motor output torque waveform is shown in Figure 6. The average value of the output torque for the single-phase permanent magnet motor is 1.95 N·m. The output power, calculated using the standard power formula is 306 W. This meets the design requirement of 300 W.

The corresponding main and auxiliary winding currents are presented in Figure 7. As can be seen from the figure, when the motor output power is at the rated value of 300 W, the RMS currents in the main and auxiliary windings are 1.41 A and 0.67 A, respectively. The capacitor-induced phase difference between the main and auxiliary winding currents is approximately 90 electrical degrees. Based on these current values, the copper loss (P_Cu) can be calculated using the expression:

$$P_{\mathrm{Cu}}=I_{\mathrm{m}}^2{R}_{\mathrm{m}}+I_{\mathrm{a}}^2{R}_{\mathrm{a}}$$

(12)

where I_m is the current of main winding, I_a is the current of auxiliary winding, R_m is the resistance of main winding, and R_a is the resistance of auxiliary winding.

Motor losses were calculated using finite element software. The curves for the core loss and solid loss are presented in Figure 8 and Figure 9, respectively. In addition to the losses mentioned above, the motor also experiences losses during steady-state operation due to currents induced in the squirrel cage by the negative-sequence magnetic field, as well as mechanical losses. Stray losses (including those from the negative-sequence field) and mechanical losses are influenced by numerous factors such as stator/rotor structure, manufacturing processes, and operating environment, making them difficult to calculate accurately. Based on empirical data, these combined losses are typically estimated at approximately 2% of the input power. According to (1), when the motor output power is at the rated 300 W, the efficiency of single-phase permanent magnet motor is approximately 72.9%. In comparison, the efficiency of the reference YY7114 single-phase induction motor at its rated power is 60%.

Using the method proposed in this paper, manufacturing a single-phase permanent magnet (PM) motor only requires embedding permanent magnets into the original rotor. For factories that already possess the capability to produce single-phase induction motors, modifying the rotor lamination to accommodate permanent magnets introduces negligible additional manufacturing cost. Therefore, the primary increase in cost stems from the magnets themselves. Based on market research, the production cost of a single-phase PM motor using this method is approximately 9% higher than that of the original induction motor. However, the market price of a single-phase PM motor with the same power rating is roughly 1.8 times that of its induction counterpart. These findings indicate that the proposed rotor retrofitting method for single-phase induction motors offers significant economic value.

4. Research on the Starting Performance of the Single-Phase Permanent Magnet Motors

4.1. Analysis of Torque Characteristics During the Starting Process of Single-Phase Permanent Magnet Motors

Compared to single-phase induction motors, single-phase permanent magnet motors exhibit significant advantages in terms of efficiency, power factor, and power density. However, due to the incorporation of permanent magnets on the rotor, the single-phase permanent magnet motor experiences a substantial generative braking torque during the starting process. This severely compromises the motor’s starting performance, preventing it from starting under relatively high loads. Therefore, this chapter primarily focuses on the research and analysis of the torque performance during the motor starting process.

Based on electric machine field theory, when the stator and rotor rotating magnetic fields rotate in the same direction and at the same speed, they produce a constant torque. Otherwise, a pulsating torque is generated. During the starting process, the stator windings are energized with current at frequency f₁. However, due to the inherent asymmetry between the main and auxiliary phase winding currents, an elliptical rotating magnetic field is produced. This elliptical field can be resolved into two counter-rotating magnetic fields: one rotating at speed +n₁ and the other at speed −n₁. At a motor slip s, these two counter-rotating fields induce alternating currents in the rotor squirrel cage at frequencies s·f₁ and (2 − s)·f₁, respectively. Because the rotor magnetic circuit is asymmetric, the rotor currents at each frequency generate two magnetic fields rotating in opposite directions. Simultaneously, the permanent magnets rotate with the rotor at speed (1 − s)·n₁. They induce a generative current in the stator windings at frequency (1 − s)·f₁. This generative current, in turn, produces a rotating magnetic field at speed (1 − s)·n₁. The rotational speeds of the various stator and rotor magnetic fields during the motor starting process, along with the electromagnetic torques they produce, are summarized in

Table 2. Magnetic field speed and corresponding torque of stator and rotor.

Speed of Rotor Field	Speed of Stator Field
	n1	−n1	(1 − 2 s)n1	(3 − 2 s)n1	(1 − s)n1
n1	positive sequence asynchronous torque	torque ripple	torque ripple	torque ripple	torque ripple
-n1	torque ripple	negative sequence asynchronous torque	torque ripple	torque ripple	torque ripple
(1 − 2 s)n1	torque ripple	torque ripple	positive sequence reluctance torque	torque ripple	torque ripple
(3 − 2 s)n1	torque ripple	torque ripple	torque ripple	negative sequence reluctance torque	torque ripple
(1 − s)n1	torque ripple	torque ripple	torque ripple	torque ripple	generative braking torque

.

The positive-sequence asynchronous torque plays the dominant role during the starting process and is crucial for successful motor starting. The positive-sequence reluctance torque acts as a positive torque for slips s > 0.5 but becomes a negative torque for slips s < 0.5. In contrast, the negative-sequence asynchronous torque, negative-sequence reluctance torque, and the generative braking torque consistently act as braking torques throughout the entire starting process. Consequently, how to suppress these braking torques becomes key to improving starting performance. Furthermore, the interaction between rotating magnetic fields of different frequencies produces pulsating torque. While this pulsating torque does not contribute directly to the acceleration during starting, it plays a critical role in enabling the motor to pull into synchronism. The ideal torque–slip (T–s) curve for the motor starting process is illustrated in Figure 10.

In the figure: T_av is the total torque, T_a1 is the positive-sequence asynchronous torque, T_a2 is the negative-sequence asynchronous torque, T_b1 is the positive-sequence reluctance torque, T_b2 is the negative-sequence reluctance torque, and T_g is the generative braking torque.

4.2. Starting Performance Factors in Single-Phase Permanent Magnet Motors

4.2.1. Effect of Back-EMF on Starting Performance

Based on preceding analysis, a primary contributor to the inferior starting performance of single-phase permanent magnet synchronous motors compared to single-phase induction motors is the generative braking torque induced during startup by rotor permanent magnets. The magnitude of this braking torque is directly proportional to the motor’s back electromotive force. Consequently, reducing back-EMF diminishes generative braking torque and enhances starting capability. During the design phase, back-EMF adjustment is typically achieved by modifying permanent magnet width or thickness. Starting simulations were conducted for motors with varying back-EMF configurations, evaluated from two critical perspectives maximum load starting torque and no-load starting time. The resultant data are presented in Figure 11.

As evidenced by Figure 11, reducing back-EMF while maintaining other motor parameters enhances starting performance. However, this reduction concurrently increases stator current, elevating copper losses and diminishing efficiency. Consequently, quantifying the efficiency–back-EMF relationship becomes essential. In this study, the back electromotive force (EMF) corresponding to different rotor designs are obtained by performing parametric simulations with varying permanent magnet thickness. The efficiency of each design is then calculated, resulting in the efficiency–EMF relationship curve shown in Figure 12. As observed, the efficiency reaches its peak near EMF = 0.9 per unit. Because at this point, the magnetic flux provided by the permanent magnets is sufficient to minimize copper losses while avoiding excessive magnetic saturation or core losses. Increasing EMF beyond this point leads to reduced efficiency due to elevated iron losses and current harmonics. Therefore, in the design process of single-phase permanent magnet synchronous motors, engineers must strike a balance between motor efficiency and starting performance.

4.2.2. Influence of Auxiliary Winding Series Capacitance on Starting Performance

When a capacitor is connected in series with the auxiliary phase winding of a single-phase permanent magnet synchronous motor, the circuit impedance can become capacitive. As a result, the phase difference between the main and auxiliary winding currents can approach 90 electrical degrees. The equivalent circuit of the auxiliary phase is shown in Figure 13. Based on the previous analysis, the closer the phase difference between the main and auxiliary winding currents is to 90 electrical degrees during startup, the smaller the negative-sequence asynchronous torque of the motor becomes. Therefore, the motor’s starting performance improves accordingly.

Based on the parameters of a single-phase induction motor, the auxiliary winding series capacitance value for the motor model designed in this paper is determined as C_st = 20 μF. However, the starting capability of a single-phase permanent magnet synchronous motor is significantly inferior to that of a single-phase induction motor, indicating that this capacitance value is not optimal. Therefore, it is necessary to analyze the relationship between the auxiliary winding series capacitance value and starting performance using finite element software. Keeping other motor parameters unchanged and varying only the auxiliary winding series capacitance, simulations were conducted for four capacitance values: 15 μF, 20 μF, 25 μF, and 35 μF. The resulting speed–time curves during no-load starting are shown in Figure 14. The speed–time curve during motor startup under a 1 Nm load is shown in Figure 15. The locked-rotor torque of the motor is shown in Figure 16.

Compared to the starting process of single-phase induction motors, single-phase permanent magnet synchronous motors exhibit higher stator current values. The presence of rotor permanent magnets increases core saturation, elevates magnetic circuit reluctance, and reduces the motor’s magnetizing reactance. Consequently, the auxiliary winding requires a smaller capacitive reactance value, meaning a larger series capacitance value is needed. The series capacitance value of the auxiliary winding not only affects the motor’s starting time but also influences its load starting capability. Simulations were conducted on the maximum load starting capability under four capacitance values, and the resulting maximum load starting torques for different auxiliary winding series capacitances are presented in

Table 3. Maximum load starting torque of the motor under the condition of each matching capacitor.

Capacitor Values	Maximum Load Starting Torque
15 μF	0.8 Nm
20 μF	1.2 Nm
25 μF	1.3 Nm
35 μF	1.5 Nm

.

In summary, appropriately increasing the series capacitance value of the auxiliary winding can enhance the starting torque, reduce starting time, and improve load starting capability. However, increasing this capacitance value also enlarges the phase angle between the main and auxiliary winding currents during steady-state operation, thereby increasing magnetic field asymmetry. Figure 17 illustrates the speed fluctuations during stable operation after the motor has pulled into synchronous speed. The speed fluctuation measures 5.3% when the auxiliary winding series capacitance is 15 μF, but escalates to 13.3% at 35 μF. Increasing the series capacitance amplifies speed fluctuations during stable operation, which not only intensifies vibration and noise in practical operation but also induces currents in the rotor squirrel cage, thereby elevating motor losses. Concurrently, the heightened current in the auxiliary winding reduces motor efficiency. Consequently, selecting the series capacitance for auxiliary windings in single-phase permanent magnet synchronous motors necessitates a careful trade-off among starting capability, operational efficiency, and running stability.

5. Conclusions

To promote energy conservation and enhance power quality in distributed energy resource systems, this paper proposes a permanent magnet retrofit design method for single-phase induction motors. The method focuses on redesigning the rotor by incorporating permanent magnets, while comprehensively considering both efficiency and starting performance. Using this approach, a conventional single-phase induction motor was successfully converted into a single-phase permanent magnet motor, and its electromagnetic performance was evaluated through finite element simulations. The simulation results demonstrate a 12.9% improvement in efficiency compared to the original motor. In addition, a detailed analysis was conducted on the electromagnetic torque components during the starting process. The effects of back electromotive force and the auxiliary winding series capacitance on starting capability were also investigated. This paper provides valuable insights and a theoretical foundation for enhancing the starting performance and overall viability of single-phase permanent magnet motors in practical distributed energy resource system applications.