Improving the prediction accuracy of wind power is an effective means to reduce the impact of wind power on power grid.Therefore,we proposed an improved African vulture optimization algorithm(AVOA)to realize the predi...Improving the prediction accuracy of wind power is an effective means to reduce the impact of wind power on power grid.Therefore,we proposed an improved African vulture optimization algorithm(AVOA)to realize the prediction model of multi-objective optimization least squares support vector machine(LSSVM).Firstly,the original wind power time series was decomposed into a certain number of intrinsic modal components(IMFs)using variational modal decomposition(VMD).Secondly,random numbers in population initialization were replaced by Tent chaotic mapping,multi-objective LSSVM optimization was introduced by AVOA improved by elitist non-dominated sorting and crowding operator,and then each component was predicted.Finally,Tent multi-objective AVOA-LSSVM(TMOALSSVM)method was used to sum each component to obtain the final prediction result.The simulation results show that the improved AVOA based on Tent chaotic mapping,the improved non-dominated sorting algorithm with elite strategy,and the improved crowding operator are the optimal models for single-objective and multi-objective prediction.Among them,TMOALSSVM model has the smallest average error of stroke power values in four seasons,which are 0.0694,0.0545 and 0.0211,respectively.The average value of DS statistics in the four seasons is 0.9902,and the statistical value is the largest.The proposed model effectively predicts four seasons of wind power values on lateral and longitudinal precision,and faster and more accurately finds the optimal solution on the current solution space sets,which proves that the method has a certain scientific significance in the development of wind power prediction technology.展开更多
The conventional structures in the Switched Reluctance machines are introduced, such as three-phase 12/8 structure Switched Reluctance machine, three-phase 6/4 structure Switched Reluctance machine, four-phase 16/12 s...The conventional structures in the Switched Reluctance machines are introduced, such as three-phase 12/8 structure Switched Reluctance machine, three-phase 6/4 structure Switched Reluctance machine, four-phase 16/12 structure Switched Reluctance machine, and four-phase 8/6 structure Switched Reluctance machine. Three-phase 12/8 structure Switched Reluctance machine is the best choice for the large power Switched Reluctance machine system in coal mines. The asymmetric bridge power converter main circuit and the bifilar winding power converter main circuit are also introduced. Three-phase asymmetric bridge power converter main circuit is the best choice for the large power Switched Reluctance machine system in coal mines. The magnetic paths of the designed large power motor are given with one phase excitation and double phases excitation. The phase current waveforms are also given.展开更多
The validity of electric power system simulation or prediction models depends on static load model. Measurement- based approach is the unique method to identify them adequately. The measured power depends on both load...The validity of electric power system simulation or prediction models depends on static load model. Measurement- based approach is the unique method to identify them adequately. The measured power depends on both load reaction to supply voltage alteration and random process of load alteration Basically, there is no any universal method that can single out the inherent static load model from experimental data. The paper offers a proprietary technique which is the particular solution of the task. The technique considers the selection of neighboring measurement pairs with the supply voltage altering significantly be-tween them, the exclusion of selected pairs by load power factor and subsequent selection of the inherent static load model presented as the polynomial load model. The usage of the technique to identify static load model at “Fenster” industrial enterprise （in Borisov city） is presented. The ideas considered in the paper can be used for future development of static load model identification methods with the data obtained during both active experiment and in other operating models of electric power systems.展开更多
The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using po...The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using power converters they can be strongly non-harmonic, sometimes piecewise constants with zero spaces between them. Then, one deals with power series of time pulses. The impulse switching functions which are orthogonal ones can be derived from these series. The new impulse switching functions are created using Z-transform, inverse Z-transform and numerical series/sequences. The impulse switching functions created this way can be used for both steady- and transient state investigation of converters.展开更多
In the process of oilfield water injection volume of injection allocation often appear with the pump displacement situation does not match, the widespread adoption of stator frequency technology allows the pump displa...In the process of oilfield water injection volume of injection allocation often appear with the pump displacement situation does not match, the widespread adoption of stator frequency technology allows the pump displacement and volume of injection allocation phase matching. But the technology in pump class load application speed range is limited, there is still a reflux valve control blind area,＂ turn off undead＂ problem. ＂ One-for-several＂ rotor frequency Technique in water injection station application, solved the control blind area problem, the full realization of the variable frequency close return voltage injection, at the same time, the successful implementation of the slip power efficient feedback. Stable water injection pressure of the system, and the electric energy is saved, satisfy the oilfield high efficiency, fine water needs, has a high application value.展开更多
In order to ensure power system stability, modern wind turbines are required to be able to endure deep voltage dips. The specifications that determine the voltage dip versus time are called fault r/de-through （FRT） ...In order to ensure power system stability, modern wind turbines are required to be able to endure deep voltage dips. The specifications that determine the voltage dip versus time are called fault r/de-through （FRT） requirements. The purpose of this paper is not only to examine the FRT behavior of a full-power converter wind turbine but also to combine the power system viewpoint to the studies. It is not enough for the turbine to be FRT capable; the loss of mains （LOM） protection of the turbine must also be set to allow the FRT. Enabling FRT, however, means that the LOM protection settings must be loosen, which may sometimes pose a safety hazard. This article introduces unique real-time simulation environment and proposes an FRT method for a wind turbine that also takes the operation of LOM protection relay into account. Simulations are carried out using the simulation environment and results show that wind turbine is able to ride-through a symmetrical power system fault.展开更多
Environmental protection challenges thermal power construction from respects of the reform of investment system, main industrial policies and plant site selection in China. Pollution control of thermal power plants is...Environmental protection challenges thermal power construction from respects of the reform of investment system, main industrial policies and plant site selection in China. Pollution control of thermal power plants is analyzed from the angles of increasingly stringent laws, regulations and standards as well as approval procedures of thermal power projects. The paper points out emphatically that the plant site selection of a thermal power project must satisfy various requirements of rules and regulations, development programme and environmental ftmctions, etc. Different criteria of dust, SO2, NOx and other pollutants control are enumerated speeially.展开更多
The development status of the variable speed system of large power AC(alternating current)motor drive in China is introduced.The large power AC drive fed by AC-AC converters(cycloconverters)has developed greatly,and s...The development status of the variable speed system of large power AC(alternating current)motor drive in China is introduced.The large power AC drive fed by AC-AC converters(cycloconverters)has developed greatly,and some innovations on the theory and engineering technique have been realized.They have been applied to rolling mills,mine hoists,and so on,and remarkable economic and social benefit has been achieved.The development of AC drive fed by large power IGCT(integrated gate commutated thyristors)AC-DC-AC converter is also introduced.It has excellent performance and reliable operation,and has been used in traction.展开更多
This paper presents a new approach to alleviate the harmonics and to enhance the power factor of the ASD （adjustable speed drive）. A conventional ASD with 2-level PWM （pulse width modulation） inverters generate hi...This paper presents a new approach to alleviate the harmonics and to enhance the power factor of the ASD （adjustable speed drive）. A conventional ASD with 2-level PWM （pulse width modulation） inverters generate high dv/dt and high frequency common mode voltages which are harmful for the drive applications. It reduces the motor bearings life and conducted EMI （electro magnetic interference） deteriorates the insulation. In this paper, a diode clamped multilevel （3-level） inverter is used to perform dual task. It generates HF （high frequency） current to be injected at the input of the three-phase front-end rectifier thereby improving the harmonic spectra and the power factor. It also drives the induction motor. The salient feature of this paper is that it does not require separate converters for improving power factor and to drive induction motor. Furthermore, inverter switches operate with ZVS （zero voltage switching）, thus reducing the switching losses substantially, The voltage stress of the switches also has been reduced to half of the conventional 2-level converter. The inverter is operated with SPWM （sinusoidal pulse width modulation） technique. The simulation results for a prototype of 2.2 kW are presented.展开更多
The inter-line dynamic voltage restorer （IDVR） consists of several voltage source inverters connected to different independent distribution feeders with common dc bus. When one of the inverters compensates for volta...The inter-line dynamic voltage restorer （IDVR） consists of several voltage source inverters connected to different independent distribution feeders with common dc bus. When one of the inverters compensates for voltage sag that appears in its feeder （voltage control mode）, the other inverters pump the required power into the dc bus （power control mode）. Each inverter will have both voltage and power controllers; only one controller is in use during the abnormal conditions according to its feeder state. The voltage controller uses one of the dynamic voltage restoration techniques. In this paper, the in-phase technique is applied and two types of loads are considered （constant impedance and three phase induction motor）. Since the voltage restoration process may need real power injection into the distribution system, the power controller injects this power via voltage injection. This voltage injection is simulated by voltage drop across series virtual impedance. A new scheme is proposed to select the impedance value. The impedance value is selected such that the power consumed by this impedance represents the required power to be transferred without perturbing the load voltage. The performance of this system is also studied during voltage swell. A scheme for operation of multi-feeder IDVR system is proposed in this paper. Simulation results substantiate the proposed concept.展开更多
The aim of this paper is to present a new topology of a DC-DC power converter for conditioning the current and voltages behaviors of embarked energy sources used in electrical vehicles. The fuel cells in conjunction w...The aim of this paper is to present a new topology of a DC-DC power converter for conditioning the current and voltages behaviors of embarked energy sources used in electrical vehicles. The fuel cells in conjunction with ultra-capacitors have been chosen as the power supply. The originality of the proposed converter is to use a variable voltage of the DC bus of the vehicle. The goal is to allow a better energy management of the embedded sources onboard the vehicle by improving its energy efficiency. After presenting and explaining the topology of the converter, some simulation and experiments results are shown to highlight its different operation modes.展开更多
This work proposes a 12 kW three-phase grid-connected single stage PWM DC-AC converter destined to process the energy provided by a photovoltaic array composed of 57 KC200GT PV modules with high power factor for any s...This work proposes a 12 kW three-phase grid-connected single stage PWM DC-AC converter destined to process the energy provided by a photovoltaic array composed of 57 KC200GT PV modules with high power factor for any solar radiation. The PWM inverter modeling and the control strategy, using dqO transformation, are proposed in order to also allow the system operation as an active power filter, capable to compensate harmonic components and react power generated by the non-linear loads connected to the mains grid. An input voltage clamping technique is proposed to impose the photovoltaic operation on the maximum power point. Simulation and experimental results are presented to validate the proposed methodology for grid connected photovoltaic generation system.展开更多
The inverter-fed motor is a key component of environmental-friendly hybrid cars, high-speed trains, and other industrial applications. After the widespread use of inverter-fed motors, the repetitive impulse surges fro...The inverter-fed motor is a key component of environmental-friendly hybrid cars, high-speed trains, and other industrial applications. After the widespread use of inverter-fed motors, the repetitive impulse surges from inverters were found to cause new insulation problems in inverter-fed motors that were linked to premature insulation failure. The partial discharge (PD) induced by the overvoltage inner stator windings was found to be the root cause of insulation reliability problems. To mitigate this problem, PD detection and life testing at repetitive square voltages should be performed on new types of insulation models and entire motor insulation systems. The obtained partial discharge inception voltage (PDIV) and lifetime of insulation in the tests can be used to evaluate the insulation status of inverter-fed motor insulation systems and thus to improve the insulation designs. At AC voltage conditions, the voltage frequency can significantly affect PD activity. At repetitive square voltage with rapid rise time, the influence of the square voltage frequency on PD activity should be investigated (1) to suggest values for the repetitive square voltage frequency selection for the PDIV and lifetime tests, and (2) to increase the signal-to-noise ratio when extracting PD pulses from strong disturbances generated by the operating switch of impulse generators. Therefore, the main purpose of this paper was to investigate the effects of repetitive square voltage frequency on PD events. Insulation models of both Type I (low-voltage inverter-fed motor) and Type II (high-voltage inverter-fed motor) were used to obtain single-PD and multi-PD statistical features, respectively. Experimental results indicated that higher frequencies caused less PD events with lower PD magnitudes and shorter delay times in one square voltage cycle. This phenomenon was attributed to the different surface charge decay ratios and the initial electron emission probabilities resulting from different square voltage frequencies. Finally, a number of considerations for PD measurements on inverter-fed motors were provided to improve the sensitivity of the PD test system and to obtain high objective insulation lifetime test results, which are used to assess the insulation status of inverter-fed motors.展开更多
For low power dielectric barrier discharge （DBD） used in small-size material treatment or portable devices, high- step transformer parasitic capacitance greatly influences the performance of the resonant converter a...For low power dielectric barrier discharge （DBD） used in small-size material treatment or portable devices, high- step transformer parasitic capacitance greatly influences the performance of the resonant converter as it is of the same order of magnitude as the equivalent capacitance of DBD load. In this paper, steady-state analysis of the low power DBD is presented, considering the inevitable parasitic capacitance of the high-step transformer. The rectifier-compensated first harmonic approxi- mation （RCFHA） is applied to linearize the equivalent load circuit of DBD at low frequency and the derived expressions are accurate and convenient for the analysis and design of the power supply. Based on the proposed linear equivalent load circuit, the influence of transformer parasitic capacitance on the key parameters, including the frequency range and the applied electrode voltage, is discussed when the power is regulated with pulse frequency modulation （PFM）. Also, a design procedure is presented based on the derived expressions. A prototype is constructed according to the design results and the accuracy of the design is verified by experimental results.展开更多
基金supported by National Natural Science Foundation of China(Nos.61662042,62062049)Science and Technology Plan of Gansu Province(Nos.21JR7RA288,21JR7RE174).
文摘Improving the prediction accuracy of wind power is an effective means to reduce the impact of wind power on power grid.Therefore,we proposed an improved African vulture optimization algorithm(AVOA)to realize the prediction model of multi-objective optimization least squares support vector machine(LSSVM).Firstly,the original wind power time series was decomposed into a certain number of intrinsic modal components(IMFs)using variational modal decomposition(VMD).Secondly,random numbers in population initialization were replaced by Tent chaotic mapping,multi-objective LSSVM optimization was introduced by AVOA improved by elitist non-dominated sorting and crowding operator,and then each component was predicted.Finally,Tent multi-objective AVOA-LSSVM(TMOALSSVM)method was used to sum each component to obtain the final prediction result.The simulation results show that the improved AVOA based on Tent chaotic mapping,the improved non-dominated sorting algorithm with elite strategy,and the improved crowding operator are the optimal models for single-objective and multi-objective prediction.Among them,TMOALSSVM model has the smallest average error of stroke power values in four seasons,which are 0.0694,0.0545 and 0.0211,respectively.The average value of DS statistics in the four seasons is 0.9902,and the statistical value is the largest.The proposed model effectively predicts four seasons of wind power values on lateral and longitudinal precision,and faster and more accurately finds the optimal solution on the current solution space sets,which proves that the method has a certain scientific significance in the development of wind power prediction technology.
基金Project 2008DFA61870 supported by the International S&T Cooperation Program of Chinathe Project [2008]221-12-1 supported by the Chinese-Bulgarian Scientific and Technological Cooperation Project
文摘The conventional structures in the Switched Reluctance machines are introduced, such as three-phase 12/8 structure Switched Reluctance machine, three-phase 6/4 structure Switched Reluctance machine, four-phase 16/12 structure Switched Reluctance machine, and four-phase 8/6 structure Switched Reluctance machine. Three-phase 12/8 structure Switched Reluctance machine is the best choice for the large power Switched Reluctance machine system in coal mines. The asymmetric bridge power converter main circuit and the bifilar winding power converter main circuit are also introduced. Three-phase asymmetric bridge power converter main circuit is the best choice for the large power Switched Reluctance machine system in coal mines. The magnetic paths of the designed large power motor are given with one phase excitation and double phases excitation. The phase current waveforms are also given.
文摘The validity of electric power system simulation or prediction models depends on static load model. Measurement- based approach is the unique method to identify them adequately. The measured power depends on both load reaction to supply voltage alteration and random process of load alteration Basically, there is no any universal method that can single out the inherent static load model from experimental data. The paper offers a proprietary technique which is the particular solution of the task. The technique considers the selection of neighboring measurement pairs with the supply voltage altering significantly be-tween them, the exclusion of selected pairs by load power factor and subsequent selection of the inherent static load model presented as the polynomial load model. The usage of the technique to identify static load model at “Fenster” industrial enterprise （in Borisov city） is presented. The ideas considered in the paper can be used for future development of static load model identification methods with the data obtained during both active experiment and in other operating models of electric power systems.
文摘The paper deals with impulse switching function which are used as exciting functions of one- and multidimensional state-space models of power electronic converters. Obviously, these functions are harmonic but using power converters they can be strongly non-harmonic, sometimes piecewise constants with zero spaces between them. Then, one deals with power series of time pulses. The impulse switching functions which are orthogonal ones can be derived from these series. The new impulse switching functions are created using Z-transform, inverse Z-transform and numerical series/sequences. The impulse switching functions created this way can be used for both steady- and transient state investigation of converters.
文摘In the process of oilfield water injection volume of injection allocation often appear with the pump displacement situation does not match, the widespread adoption of stator frequency technology allows the pump displacement and volume of injection allocation phase matching. But the technology in pump class load application speed range is limited, there is still a reflux valve control blind area,＂ turn off undead＂ problem. ＂ One-for-several＂ rotor frequency Technique in water injection station application, solved the control blind area problem, the full realization of the variable frequency close return voltage injection, at the same time, the successful implementation of the slip power efficient feedback. Stable water injection pressure of the system, and the electric energy is saved, satisfy the oilfield high efficiency, fine water needs, has a high application value.
文摘In order to ensure power system stability, modern wind turbines are required to be able to endure deep voltage dips. The specifications that determine the voltage dip versus time are called fault r/de-through （FRT） requirements. The purpose of this paper is not only to examine the FRT behavior of a full-power converter wind turbine but also to combine the power system viewpoint to the studies. It is not enough for the turbine to be FRT capable; the loss of mains （LOM） protection of the turbine must also be set to allow the FRT. Enabling FRT, however, means that the LOM protection settings must be loosen, which may sometimes pose a safety hazard. This article introduces unique real-time simulation environment and proposes an FRT method for a wind turbine that also takes the operation of LOM protection relay into account. Simulations are carried out using the simulation environment and results show that wind turbine is able to ride-through a symmetrical power system fault.
文摘Environmental protection challenges thermal power construction from respects of the reform of investment system, main industrial policies and plant site selection in China. Pollution control of thermal power plants is analyzed from the angles of increasingly stringent laws, regulations and standards as well as approval procedures of thermal power projects. The paper points out emphatically that the plant site selection of a thermal power project must satisfy various requirements of rules and regulations, development programme and environmental ftmctions, etc. Different criteria of dust, SO2, NOx and other pollutants control are enumerated speeially.
文摘The development status of the variable speed system of large power AC(alternating current)motor drive in China is introduced.The large power AC drive fed by AC-AC converters(cycloconverters)has developed greatly,and some innovations on the theory and engineering technique have been realized.They have been applied to rolling mills,mine hoists,and so on,and remarkable economic and social benefit has been achieved.The development of AC drive fed by large power IGCT(integrated gate commutated thyristors)AC-DC-AC converter is also introduced.It has excellent performance and reliable operation,and has been used in traction.
文摘This paper presents a new approach to alleviate the harmonics and to enhance the power factor of the ASD （adjustable speed drive）. A conventional ASD with 2-level PWM （pulse width modulation） inverters generate high dv/dt and high frequency common mode voltages which are harmful for the drive applications. It reduces the motor bearings life and conducted EMI （electro magnetic interference） deteriorates the insulation. In this paper, a diode clamped multilevel （3-level） inverter is used to perform dual task. It generates HF （high frequency） current to be injected at the input of the three-phase front-end rectifier thereby improving the harmonic spectra and the power factor. It also drives the induction motor. The salient feature of this paper is that it does not require separate converters for improving power factor and to drive induction motor. Furthermore, inverter switches operate with ZVS （zero voltage switching）, thus reducing the switching losses substantially, The voltage stress of the switches also has been reduced to half of the conventional 2-level converter. The inverter is operated with SPWM （sinusoidal pulse width modulation） technique. The simulation results for a prototype of 2.2 kW are presented.
文摘The inter-line dynamic voltage restorer （IDVR） consists of several voltage source inverters connected to different independent distribution feeders with common dc bus. When one of the inverters compensates for voltage sag that appears in its feeder （voltage control mode）, the other inverters pump the required power into the dc bus （power control mode）. Each inverter will have both voltage and power controllers; only one controller is in use during the abnormal conditions according to its feeder state. The voltage controller uses one of the dynamic voltage restoration techniques. In this paper, the in-phase technique is applied and two types of loads are considered （constant impedance and three phase induction motor）. Since the voltage restoration process may need real power injection into the distribution system, the power controller injects this power via voltage injection. This voltage injection is simulated by voltage drop across series virtual impedance. A new scheme is proposed to select the impedance value. The impedance value is selected such that the power consumed by this impedance represents the required power to be transferred without perturbing the load voltage. The performance of this system is also studied during voltage swell. A scheme for operation of multi-feeder IDVR system is proposed in this paper. Simulation results substantiate the proposed concept.
文摘The aim of this paper is to present a new topology of a DC-DC power converter for conditioning the current and voltages behaviors of embarked energy sources used in electrical vehicles. The fuel cells in conjunction with ultra-capacitors have been chosen as the power supply. The originality of the proposed converter is to use a variable voltage of the DC bus of the vehicle. The goal is to allow a better energy management of the embedded sources onboard the vehicle by improving its energy efficiency. After presenting and explaining the topology of the converter, some simulation and experiments results are shown to highlight its different operation modes.
文摘This work proposes a 12 kW three-phase grid-connected single stage PWM DC-AC converter destined to process the energy provided by a photovoltaic array composed of 57 KC200GT PV modules with high power factor for any solar radiation. The PWM inverter modeling and the control strategy, using dqO transformation, are proposed in order to also allow the system operation as an active power filter, capable to compensate harmonic components and react power generated by the non-linear loads connected to the mains grid. An input voltage clamping technique is proposed to impose the photovoltaic operation on the maximum power point. Simulation and experimental results are presented to validate the proposed methodology for grid connected photovoltaic generation system.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51177136, 50377035)the Zhuzhou Electric Motor Company of the South China Locomotive & Rolling Stock Corporation,Limited
文摘The inverter-fed motor is a key component of environmental-friendly hybrid cars, high-speed trains, and other industrial applications. After the widespread use of inverter-fed motors, the repetitive impulse surges from inverters were found to cause new insulation problems in inverter-fed motors that were linked to premature insulation failure. The partial discharge (PD) induced by the overvoltage inner stator windings was found to be the root cause of insulation reliability problems. To mitigate this problem, PD detection and life testing at repetitive square voltages should be performed on new types of insulation models and entire motor insulation systems. The obtained partial discharge inception voltage (PDIV) and lifetime of insulation in the tests can be used to evaluate the insulation status of inverter-fed motor insulation systems and thus to improve the insulation designs. At AC voltage conditions, the voltage frequency can significantly affect PD activity. At repetitive square voltage with rapid rise time, the influence of the square voltage frequency on PD activity should be investigated (1) to suggest values for the repetitive square voltage frequency selection for the PDIV and lifetime tests, and (2) to increase the signal-to-noise ratio when extracting PD pulses from strong disturbances generated by the operating switch of impulse generators. Therefore, the main purpose of this paper was to investigate the effects of repetitive square voltage frequency on PD events. Insulation models of both Type I (low-voltage inverter-fed motor) and Type II (high-voltage inverter-fed motor) were used to obtain single-PD and multi-PD statistical features, respectively. Experimental results indicated that higher frequencies caused less PD events with lower PD magnitudes and shorter delay times in one square voltage cycle. This phenomenon was attributed to the different surface charge decay ratios and the initial electron emission probabilities resulting from different square voltage frequencies. Finally, a number of considerations for PD measurements on inverter-fed motors were provided to improve the sensitivity of the PD test system and to obtain high objective insulation lifetime test results, which are used to assess the insulation status of inverter-fed motors.
基金supported by the National Natural Science Foundation of China(No.51107115)the China Postdoctoral Science Foundation(No.20110491766)
文摘For low power dielectric barrier discharge （DBD） used in small-size material treatment or portable devices, high- step transformer parasitic capacitance greatly influences the performance of the resonant converter as it is of the same order of magnitude as the equivalent capacitance of DBD load. In this paper, steady-state analysis of the low power DBD is presented, considering the inevitable parasitic capacitance of the high-step transformer. The rectifier-compensated first harmonic approxi- mation （RCFHA） is applied to linearize the equivalent load circuit of DBD at low frequency and the derived expressions are accurate and convenient for the analysis and design of the power supply. Based on the proposed linear equivalent load circuit, the influence of transformer parasitic capacitance on the key parameters, including the frequency range and the applied electrode voltage, is discussed when the power is regulated with pulse frequency modulation （PFM）. Also, a design procedure is presented based on the derived expressions. A prototype is constructed according to the design results and the accuracy of the design is verified by experimental results.
