Research on the Transient Characteristics of Microgrid with Pulsed Load

Unlike traditional load, pulsed load typically features small average power and large peak power. In this paper, the mathematic models of microgrid consisting of synchronous generator and pulsed load are established. Average Magnitude Difference Compensate Function (AMDCF) is proposed to calculate the frequency of synchronous generator, and, based on AMDCF, relative deviation rate (RDR) which characterizes the impact of pulsed load on the AC side of grid is firstly defined and this paper describes calculation process in detail. Insulated Gate Bipolar Transistor (IGBT) is used as DC switch to control the on/off state of resistive load for simulating pulsed load, the period and duty-cycle of the pulsed load are simulated by setting the gate signal of IGBT, and the peak power of the pulsed load is simulated by setting the resistance. The system dynamic characteristics under pulsed load are analyzed in detail, and the influence of duty-cycle, period, peak power, and filter capacitance of the pulsed load on system dynamic indicators is studied and validated experimentally.


Introduction
Microgrid combines distributed power supply, energy storage devices, load and control devices, and so forth as a controlled small-capacity power supply system to supply electricity and heat to the user.Microgrid could not only operate with the traditional power grid network but also operate as island by disconnecting with grid network in case of failures in grid network, thus providing support for grid network and improving the reliability of electricity supply units [1][2][3].In recent years, the development of microgrid attracts attention of many countries worldwide.EU, the United States, and Japan have pilot projects under construction to promote the study on the concept verification, control testing, and operating characteristics of microgrid.
From a structural point of view, there are two kinds of microgrid: AC microgrid [4] and DC microgrid [5].Currently, AC microgrid is still the main form of microgrid, while in DC microgrid distributed power, energy storage devices, and load are connected to DC bus, which is connected to the AC network via power electronic inverters.Due to the robustness and consistency of modern DC devices and the increase of DC output power supply, DC microgrid has become the rapid development direction of distributed generation systems.With respect to AC microgrid, DC microgrid has the following advantages [6][7][8][9][10][11][12][13][14]: (1) Hybrid systems can be easily constructed among different power supplies to deliver energy into microgrid, and the system can be expanded according to the load ratio.
(2) DC microgrids reduce the energy conversion and filter, allowing higher efficiency.
(3) They make it easier to integrate renewable energy sources, especially DC source, such as photovoltaic cells, fuel cells, super capacitors, flow cell, and the like.
(4) They directly supply DC load, such as electric vehicles, communications equipment, LED lighting, and the like, to avoid additional power conversion.
(5) The problems of frequency synchronization and reactive power flow do not exist and the system control and operation are more simple and reliable.
Overall, DC microgrid has better compatibility, higher efficiency, and easier operability.In the conventional power system, since AC grid is still dominant, DC microgrid system mainly based on renewable energy power generation has been gradually showing its great potential for development and the future prospects for broad application.DC microgrid is more consistent with the demand of the establishment of environment-friendly and resource-saving society, and it will become an increasingly important form of energy supply.
Due to the limitation of natural conditions, distributed power supplies in microgrid such as solar power and wind power cannot generate constant output power, especially in remote areas without connection to the utility grid.Since new energy generation is severely restricted to natural conditions, diesel generator as a relatively mature power supply plays a supporting role in microgrid.In case new energy cannot continuously provide electricity, diesel generator will operate according to a certain control strategy to improve power grid reliability.As a typical structure of microgird, diesel generator connects the DC bus through rectifier and the energy storage system accesses the grid via a bidirectional DC-DC converter to stabilize the DC voltage.
With the development of information technology, in order to meet the demand of high-power signal transmission devices or energy conversion, a large number of power electronics switching devices are used in Switching Mode Power Supply (SMPS) of digital devices, such as communication stations, radar, advanced mobile equipment, electromagnetic rail weapon launch systems, and free electron lasers.Those particular loads draw very high short time current in an intermittent fashion [15]; the power consumption of such electrical equipment during normal operation is not uniform, showing pulse characteristics, featuring with low average power, but large peak power.Henceforth, they will be referred to collectively as pulsed loads.Different from traditional linear load, not only does pulsed load impact the power supply during starting and stopping, but also the power mutation under normal operation leads to repeated loading and unloading on the power supply, which causes sharp and frequent current variation in transmission lines, thus affecting the power output characteristics of the power supply.Therefore, the dynamic characteristics of DC microgrid with pulse load are very different from those of common grid.
Mohamed et al. [15][16][17] proposed some algorithms or schemes for mitigation of pulsed load.The impact of changes in the power of the inverter load on output characteristics of diesel generator set was analyzed in [18].But it did not discuss the influence extent of various elements of the system on the output voltage and speed.With ignoring the factor of magnetic saturation, in [19,20], as to the issue of synchronous generator capacity with nonlinear load, the effect of line harmonic current on the output voltage and torque of synchronous generator was qualitatively analyzed.References [21][22][23][24] analyzed the possible electromagnetic saturation and eddy current effects in synchronous generator under load disturbances, but the variation of the frequency was not taken into account.Besides, the transient electromotive force of synchronous generator is generally assumed to be constant in literatures; however, this assumption is only true for analysis under linear load condition.While in the case of pulsed load, though equipped with automatic adjustment excitation device, the output voltage is in the state of dynamical adjustment instead of constant value due to the fact that synchronous generator frequently suffers from pulsed load.Considering the transient process of the excitation regulation system and generator rotor circuit, even if transient electromotive force does not mutate at the moment of a sudden disturbance, it could not remain constant.Therefore, the impact from the variation of transient electromotive force should be carefully considered to analyze the output power of synchronous generator under pulsed load.
A method for enhancing the immunity of diesel generator against pulsed load disturbances was proposed [25], which reduces the unit speed regulation ratio.And the dynamic behavior in the pulsed load connected generator via rectifier which is widely used in the aircraft application was discussed [26].Through the analysis of the distortion impact of pulsed load on the generator output power fluctuation, a method to improve the generator excitation regulation device according to current variation was proposed; due to the existence of isolated transformer, the impact of harmonic current injected into the generator was not taken into account, as well as the frequency fluctuation.
The shock impact on system from the power variation of pulsed load in ship power system under different converter configurations was studied in [27] and it proposed the suggestion that the shock impact from the pulsed load can be reduced by structural optimization in power converters.The operating mechanism of pulsed load was studied and three kinds of pulsed load structure were designed for test analysis and the foundation was provided for carrying out pulsed load test and theoretical research [28].Reference [29], the operating mechanism of pulsed load, studied the effects of large-capacity pulsed power load on power quality and designed the filter device to improve power quality, but the application was for infinite system, for example, public grid.
In summary, the impact mechanism of pulsed load on power supply is not clear, and the existing evaluation indices of electrical parameters, such as RMS and THD, which do not accurately reflect the operating characteristics of pulsed load, for example, the operation of pulsed load, will lead to frequent fluctuations, and with large amplitude, but existing evaluation indices are usually defined based on constant frequency (50 Hz), so the operating characteristics of the microgrid AC power supply cannot be reflected.Therefore, the paper uses synchronous generator as the microgrid power supply, establishes the model of microgrid, and proposes the evaluation indices to reflect the operating characteristics of pulsed load in order to find the law between power generator and pulsed load.Moreover, the influence of different operating parameters in pulsed load on power supply is studied in detail to improve the microgrid operation reliability.

Generator Model with Varying Transient Electromotive.
With ignoring the electromagnetic transient of stator windings and friction losses, while considering the electromagnetic transient of damper winding ,  and excitation winding, and the mechanical dynamic of stator, in synchronous rotating coordinate system 0, the mathematic model of synchronous generator can be expressed as follows.
Stator voltage equation is Rotor winding voltage equation is Damper winding voltage equation is Rotor motion equation is where As described in Section 1, the transient electromotive could not remain constant in pulsed load, so the relationship between power and transient electromotive is deduced as follows.
Voltage equation of generator excitation circuit is Multiplying both sides with   /  , In (7), the left side (  /  )  corresponding to no-load EMF caused by forced component   /  of excitation current under excitation voltage   is generally referred to as forced no-load EMF   .That is,   = (  /  )  , where   is field winding and   is the direct axis reactance of armature reaction.Consider Equation ( 10) describes the process of variation in the transient electromotive force, it shows that   ,    are controlled by   , that is, the excitation voltage   .
In case transient force and transient reactance are used to express generator, the output current can be expressed as Active power is By inserting ( 11) into (12), Equation ( 13) is the expression of synchronous generator output power, which reflects the relationship among synchronous generator output power, transient force    , power angle , and output voltage .

Pulsed Load Model.
The DC pulsed load is supplied by three-phase AC voltage from synchronous generator via controllable rectifier and the output voltage of rectifier can be adjusted by setting the trigger angle of rectifier controller.The circuit diagram of rectifier and pulsed load is shown in Figure 1.
The controllable rectifier shown in Figure 1 consists of six thyristors with the same specifications.Inductor  and capacitor  are filter elements,  0 is the rectifier output voltage, and  dc is the load current.Various operating modes of the pulsed load can be simulated by setting the DC switch  and resistor   .
In order to keep it consistent with the output expression of synchronous generator,  coordinate system is applied in the rectifier.By introducing the "equal power" coordinate rotation transformation, the symmetrical three-phase stationary coordinate system (, , ) is converted into the synchronous rotation coordinate system (, , 0).Assuming that  is the initial angle between -axis of the rotating coordinate system and -axis of the stationary coordinate system, the orthogonal rotation transformation matrix C  can be expressed as follows: The switching functions   ,   , and   are used in this paper and   and   are behind Sa 120 ∘ and 240 ∘ , respectively.In case of ignoring the stator winding resistance, while considering the commutation process, the Fourier series expansion of the switching function   can be expressed as where , and  is the initial phase angle of phase (a) current.
and  1 are the commutation reactance and EMF amplitude, respectively, the expression is shown in [30].
where  1 is the initial phase angle of the fundamental component of switching function.
From the PWM modulation principle, After the introduction of the rotating coordinate transformation, where By inserting ( 14) and ( 17) into (19), The pulsed power load is simulated by controlling the on/off state of resistive load via DC switch; the circuit with combination of LC filter is shown in Figure 2.
When the DC switch is turned on, the current is shown in Figure 3(a), according to the circuit KVL and KCL theorems: With inductor current and the capacitor voltage as state variables, the appropriate state-space equation is derived as follows: where When the DC switch is turned off, the current is shown in Figure 3(b), according to the circuit KVL and KCL theorems: The appropriate state-space equation is derived as follows: where , and   2 = [0 0].These two different equations can be weighted averagely by the duty-cycle ; two state equations can be merged into a unified state equation; that is, where and 25) describes the operating characteristics of pulsed load.

Transient Performance Indices
3.1.Frequency Calculation Method.Due to the repeated action of pulsed load, the electromagnetic torque of synchronous generator is not constant, but periodically changing.According to (5), the rotor mechanical speed will change and the variation rate relates to the change rate of electromagnetic torque.In particular when diesel engine is used to drive the synchronous generator as power supply, the obvious characteristics of this power source are small capacity, small mechanical inertia, and large inner resistance which will result in substantial fluctuations on the engine speed.Consequently, the frequency of generator will change and the change rate is related to the working mode of pulsed load.Before defining the evaluation indices of system operation, the frequency calculation methods under pulsed load are studied.
The method of Autocorrelation Function (ACF), which is an approach to measure the similarity between signal and its own translated waveform, is mainly used to study the periodicity of signal waveform.By setting the   (), part of the AC side voltage signal (), as the study object, the shortterm ACF can be defined as where  is the delay time, () is autocorrelative function,  is signal length, and  is sampling point.It can be seen from the definition that ACF is periodical with the same period as the periodical signal and if the amount of translation is an integer multiple of the period, ACF will generate peak values; thus the period of signal can be obtained by detecting the time interval between two sequential ACF peaks.
From (26), with increasing the translation , the summation term of correlation coefficient decreases dramatically, which leads to sharp decrease on the peak magnitude of ACF (), thus making it more difficult to detect the time interval between peaks; meanwhile, a large number of internal multiplication is present in ACF, so the calculation will take more time for longer intercepted signal   ().Therefore, in order to overcome the drawback of large amount of computation, Average Magnitude Difference Function (AMDF) is defined as Further, in order to effectively correct the shortcoming that ACF peak increases with decrease in the lag time, based on AMDF, Average Magnitude Difference Compensate Function (AMDCF) was proposed, which is defined as The voltage   () is periodical when the amount of translation is an integer multiple of the period and the theoretical result of AMDCF is zero; that is, valley appears in AMDCF.The voltage period, which is the time interval of contiguous valleys, can be obtained by determining the location of valleys.Moreover, this function only contains simple addition, compared to the ACF method, subtraction, and absolute operation; the amount of computation is significantly reduced.Compared to the AMDF method, the amplitude adjustment item 1/( − ) is added to compensate the amplitude and suppress the attenuation of peak amplitude.It is ensured that the peak amplitude of voltage signal at integer multiples frequency is held at a certain height to make it easy to find the corresponding time coordinates of peaks, thus improving the accuracy of frequency detection.Taking a pulsed load operating model, for example, programming (26), (27), and ( 28) by MATLAB M file, the results of system frequency calculation are shown as Figure 4.
In Figure 4, The horizontal axis represents time and the unit is second and the vertical axis is () calculated by (10)∼ (11).In order to be consistent, normalization processing had been done with vertical axis.
The calculated result with ACF method is shown in Figure 4(a); the amplitude decreases gradually, the computation time is long, and the frequency is calculated via detecting peak points; Figures 4(b) and 4(c) show the calculated results with AMDF method and AMDCF method, respectively, the valleys are detected for frequency calculation in both of them.From Figure 4 AMDCF, while the waveform amplitude is the same and the positions of valleys are clear, which is in favor of frequency detection, as shown in Figure 4(c).

Frequency Fluctuation Rate.
The output frequency of synchronous generator fluctuates with the power variation of pulsed load; AMDCF is used to calculate the frequency of electrical signals during the sampling time; the frequency fluctuation rate is defined as where  max ,  min , and  av are the maximum value, minimum value, and average value of frequency during the sampling time.
Frequency fluctuation rate reflects the degree of pulsed load influence on the system frequency.Under the same conditions of the speed governor of prime mover, the greater the fluctuation rate is, the stronger the impact of pulsed load on synchronous generator is.Therefore, the prime mover speed fluctuates greater.

Relative Deviation Rate.
The notable features of pulsed load are large peak power and small average power, and the DC side load current is in interrupted state and closely related to the duty-cycle, so distortion occurs intermittently on the AC side current.Moreover, the AC current suffers serious distortion and shows intermittent characteristics under the operation with pulsed load.
For example, the period of pulsed load is 56 ms, the dutycycle is 0.4, and the influence of pulsed load on supply lasts 22.4 ms within one cycle.The influence of pulsed load on supply is intermittent.The waveforms of AC current and DC current within one pulse period are shown in Figure 5.
In Figure 5,  0 - 5 and  0 - 2 are the pulse period and the AC period, respectively.The working interval of pulsed load is  0 - 3 .Considering the effects of filter capacitor and system inertia, generator starts to work after a delay and the working interval is  1 - 4 ; that is, the pulsed load affects the supply only during  1 - 4 within one period, while in  0 - 1 and  4 - 6 , pulsed load has almost no influence on the generator.In order to characterize the impact of pulsed load on the AC side signal, this paper defines the concept of relative deviation rate (RDR).
Definition 1. Relative deviation rate means the degree of the signal deviates from a sinusoidal signal within one pulsed load period; the RMS and frequency of this sinusoidal signal are the same as those of AC signal at that moment.The calculation steps are as follows.
First, calculate the frequency of AC signal with AMDCF: where   ,  +1 are the time corresponding to two contiguous valleys in the AMDCF waveform and  is the th period of sampling signal.Second, calculate the RMS of AC signal: where  is the number of sampling points during   ∼  +1 .Third, construct the sine function where  0 is the phase angle of the AC signal   () at the time   .Fourth, calculate RDR during one period: Fifth, calculate the average RDR: Equation ( 34) is the average RDR of AC signal; the higher the value is, the greater the impact of pulsed load on the AC side is.

Fluctuation Rate of DC Voltage. The average voltage at DC side load is
The pulsed load will lead to frequent fluctuation of DC side voltage; the fluctuation rate during the sampling time is where  = Δ/  and  av ,  max ,  min are the average value, maximum value, and minimum value of DC voltage during the th switching period, respectively.The average power of DC pulsed load is

Experimental Results and Analysis
4.1.System Dynamic Characteristics of Pulsed Load.The typical feature of pulsed power is that power changes frequently and dramatically, which is equivalent to the repeated sudden increase and decrease of load on the diesel generator.Therefore, the impact of pulsed load on the generator is much greater than that of normal load.When the pulsed load operates in a fixed mode, system variables will reach a dynamic equilibrium after a moment of adjustment; that is, the RMS of output voltage, the frequency oscillation amplitude, and the frequency of synchronous generator are kept in a certain range.
The circuit configuration of the experiment is shown in Figure 6.Diesel engine is used as the prime mover and conventional diesel generator units with the nominal power of 30 kW are selected.The diesel engine model is Cummins 4BT3.9-G2, the rated power is 36 kW, and the rated speed is 1500 r/min, and electronic governor is used.The synchronous generator is YTM Salient Brushless Excitation Generator produced by Jiangsu YINGTAI Ltd.; the number of pole pairs is 2, the rated capacity is 37.5 kVA, the power factor is 0.8 (i.e., the rated power is 30 kW), excitation regulator adopts excitation type SE353 AVR, the units output line voltage is 400 V, and the frequency is 50 Hz.The output voltage of controllable rectifier is set to 500 V, the rectifier filter capacitor value is adjusted according to the test content, and the smoothing inductor is 0.125 mH.The pulsed load is simulated via controlling the switching state of IGBT remarked as FF300R12KE3, produced by Infineon Company.
In the simulation device of pulsed load, three sets of resistors are connected, as shown in Figure 6, and the IGBT trigger pulse is set as the square wave with the period of 56 ms and duty-cycle of 0.4.The operating mode of pulsed mode can be set as peak power 30 kW, switching period 56 ms, dutycycle 0.4, filter capacitor 4000 uF, and smoothing inductor 0.125 mH.The experimental results are shown in Figure 7.
Figures 7(a) and 7(b) show the voltage and current waveforms of pulsed load during five switching periods; it can be seen that the pulsed load current under normal operation shows pulsed variation, while DC load voltage fluctuates slightly with the current variation.Figures 7(c) and 7(d) show the diesel generator unit output voltage and current waveforms; the AC voltage suffers periodical distortion following the pulsed variation of load current; meanwhile, the AC current amplitude changes dramatically following the load variation.power, the mechanical power of diesel generator is smaller than the electromagnetic power, while the throttle regulator still does not response; therefore, the speed is slowed down to maintain constant mechanical torque; then the oil into cylinder increases and diesel generator output power increases gradually and the mechanical torque increases, so the speed is restored to the rated speed as shown in (5).However, due to the periodical power fluctuation of pulsed load, the diesel generator unit output frequency fluctuates around a fixed value periodically with the period of   .Other electromagnetic indices under this operation mode are shown in Figure 7.
Figures 8(a) and 8(b) compare the varying trend of electromagnetic torque excitation current with the actual load power consumption.It can be found that all waveforms fluctuate at the period of   .By observing the time of varying waveforms, the internal electromagnetic calorimeter variation of synchronous generator lags behind the changes in actual load power consumption; this shows that the equivalent response time of the diesel generator unit is larger than that of the filter capacitor.That is, when  is closed, load current increases sharply, DC side voltage decreases, and the capacitor discharges rapidly; then stator current increases, so does the electromagnetic torque of synchronous generator, the diesel engine speed decreases, and field winding of generator and diesel generator governor is adjusted accordingly.In case of no-load power consumption, the speed and output voltage of diesel generator are restored to the rated value.
Figure 8(c) shows the current variation in LC filter branch at DC side under operation with pulsed load and Figure 8(d) shows the zoom-out of current variation within one switching period.It can be seen that before closing the switch , no current is conducting on each branch at DC side.When  is closed, the step signal of load current immediately appears and capacitor current changes simultaneously with the same amplitude of load current variation, but in opposite direction.It shows that the diesel generator unit and rectifier do not respond to the variation of load current yet; instead, load is only supplied via the capacitor for several milliseconds.In case the capacitor voltage is lower than the rectifier output voltage, the inductor current starts to rise to supply power to load.Because of the limited capacitor capacity, the capacitor current begins to decrease.The load is supplied by both the diesel generator unit and the storage capacitor during this process until the load is completely supplied by the diesel generator via rectifier.When  is open, the load current disappears immediately and the inductor current is equal to the capacitor charging current; this is the charging process of filter capacitor.In case the capacitor voltage equals the rectifier output voltage, the charging process ends and DC side current goes to zero.Once  starts to act again, the above process is repeated.

Influence of System Parameters on Transient Characteristics.
In order to analyze the influence of different operation modes under pulsed load on various dynamic characteristic indices, different system operation modes are obtained by altering peak power   , switching period   , duty-cycle , and filter capacitor .And system characteristic indices are analyzed under various operating modes; the impact of the above-mentioned variants on the system dynamic characteristics can be studied by comparative analysis.

Change the Duty-Cycle 𝐷.
The switching period   and duty-cycle  can be adjusted by setting the period and dutycycle.Filter capacitor  is 4 mF, peak power   is 30 kW, and switching period   is 56 ms; all performance indices are listed in Table 1 with changing the duty-cycle; the varying trends of load power  dc , relative deviation rate of voltage RDR  , frequency fluctuation rate   , and fluctuation rate of DC voltage   are shown in Figure 9, where the curve is obtained from calculation in the statistical software SPSS.
As can be seen from Figure 9, the load power consumption and the voltage relative deviation increase monotonically with the increase of duty-cycle , while the frequency fluctuation rate and the voltage fluctuation firstly increase and then decrease.The reason is that when the load power is low, the generator output power increases with the increase of duty-cycle, and the impact of the switching transition of load on the generator soars gradually.The fluctuations of voltage and frequency are relatively large as well.In case the duty-cycle reaches a certain level, the pulse effects generated by the change in load power will be weakened; that is, the adjustment time of unit responding to sudden load change will be longer.Therefore, the fluctuation within each pulse period turns to be smaller.

4.2.2.
Change the Switching Period   .The switching period   of pulsed load power can be adjusted by setting the time in the "period" column, while holding the filtering    10.
It can be seen from Table 2 that the RMS output voltage and the frequency of diesel generator unit do not change dramatically with the periodic variation of pulsed load, while the voltage and the frequency fluctuation vary significantly.
As shown in Figure 9, the voltage relative deviation rate and the frequency change monotonically along with the increase of switching period.As can be found from Table 3 and Figure 11, with the increase of the peak power   , the indices of voltage relative deviation, frequency fluctuation rate, and fluctuation rate of DC voltage increase gradually.But the DC voltage and power transmission ratio decrease monotonically.In addition, the output current of diesel generator unit increases accordingly with the increase of load power consumption, which will lead to significant armature reaction.The high peak current resulting from high pulsed load power will lead to magnetic potential saturation in the air gap.

Change the Filtering
Capacitor .In order to evaluate the impact of the filtering capacitor  on system dynamic performance, the values of the peak power at pulsed load   (30 kW), switching period   (56 ms), and duty-cycle  (0.4) are kept constant; each index is measured by adjusting the capacitance gradually; the measured results are shown in  As can be seen from Table 4 and Figure 12, increasing the filter capacitor can improve the actual power of load and reduce the fluctuation of voltage and frequency, since the filter capacitor can effectively suppress the voltage fluctuation at DC side and increase the flat component of AC voltage; the relative deviation rate of AC voltage changes monotonously with the capacitance.

Conclusions
This paper constructs a microgrid operating platform and simulates multiple operating modes of the DRP system by setting the trigger pulse of IGBT or changing the equivalent resistance of load.The influence of various factors, such as filter capacitor , the peak power of pulsed load   , switching period   , and duty-cycle , on the dynamic characteristics is investigated according to experimental results.
Based on the frequency calculated by AMDCF proposed in this paper, the relative deviation rate is defined.The voltage relative deviation rate increases monotonously with the increase of load power and decreases monotonously with the increase of filtering capacitor.The frequency fluctuation rate increases monotonously with the increase of load peak power, switching period, and duty-cycle.Great correlation exists among the DC voltage fluctuation rate and various system factors.The increasing peak power of pulsed load   and switching period   will result in higher DC voltage fluctuation rate, which decreases with the increase of filter capacitor . in addition, the DC voltage fluctuation rate shows nonlinear relationship with duty-cycle.
It is generally accepted that the energy storage devices play more and more important role in microgrid.In order to suppress the effect of pulsed load on voltage and frequency, hybrid energy storage systems will be adopted in the future work.And this paper mainly researched the relationship

Figure 1 :
Figure 1: Equivalent circuit of rectifier and pulsed load.

Figure 2 :
Figure 2: Schematic of pulsed load model with LC filter.

Figure 4 :
Figure 4: The results of frequency calculation with different methods. t Figure 7(e)  shows the variation of frequency with pulsed load under normal operation.At the time 2 s, the switch  controls resistive load periodically under the pulsed triggering; due to the dramatic increase of load

Figure 6 :
Figure 6: The circuit configuration of the experiment.

Figure 7 :
Figure 7: Measured voltage and current waveforms at AC side and DC side.

Figure 8 :
Figure 8: Dynamical processes of other electromagnetic variants under pulsed load.

4. 2 . 3 .
Change the Peak Power   .The adjustment in peak power   can be realized by changing the equivalent resistance of pulsed load.The values of filtering capacitor  (4 mF), switching period   (56 ms), and duty-cycle  (0.4) are kept constant; the system dynamic performance indices under various peak power are shown in Table3and the change trends of  dc , RDR  ,   , and   are shown in Figure11.
is the angle between -axis and the reference axis,  is rotor speed,   is inertia time constant,   is mechanical torque, and   is electromagnetic torque.

Table 1 :
System performance indices under different duty-cycle of pulsed load./VRDR  /%   /%  dc /V   /%  ac /kW    are shown in Table2, and the change trends of RDR  and   are shown in Figure capacitor  (4 mF), peak power   (30 kW), and duty-cycle  (0.4) unchanged.Corresponding system performance indices under different

Table 2 :
System performance indices under different switching period   .Table 4 and the corresponding change trends of each index are shown in Figure 12.

Table 4 :
System performance indices under different capacitor .