CN102445612B - Load characteristic analysis method for rectifier bridge of AC parallel capacitor type - Google Patents

Abstract

The invention provides a load characteristic analysis method for a rectifier bridge of AC parallel capacitor type. The conduction order of diodes is determined according to the relation of each phase of an AC power supply, each phase is divided into four stages of phase change, conduction, phase change and cut off, corresponding circuit equations are listed for each stage, and then, based on the principle that the phase voltage before and after the conduction and cut off points cannot mutate and the current can mutate, corresponding circuit equations are supplemented according to characteristics of periodicity and the like in the phase change process, and the voltage, the current wave form and corresponding load characteristic of the rectifier bridge can be obtained by simultaneously solving the equation set. The method can effectively obtain the corresponding fundamental voltage and current characteristic for describing the rectifier load, and also describes the harmonic characteristic more accurately, so that the method can lay a base for optimized design of two sets of winding capacities of an induction generator.

Description

Method for analyzing load characteristics of alternating current parallel capacitor rectifier bridge

Technical Field

The invention belongs to the technical field of performance analysis of induction generators, and particularly relates to a method for analyzing load characteristics of an alternating current shunt capacitor rectifier bridge.

Background

In independent systems such as ships, airplanes, vehicles, oil drilling platforms and the like, the demand for electric energy is larger and larger, and the volume and the weight of a power supply system are also larger and larger along with the increase of capacity, so that the power density and the efficiency of the power generation and supply system must be improved, and the volume and the weight of the power generation and supply system must be reduced.

One effective way to increase the power density of a power generation and supply system is to increase the rotational speed of the generator. The induction generator (asynchronous generator) has simple rotor structure, high mechanical strength, high speed operation and much higher power density than that of synchronous generator and DC generator with the same capacity. When the traditional induction generator is connected with a large power grid in parallel, although an excitation adjusting device is not needed, the efficiency is low because the power factor is very low; the induction generator in the independent system can only adopt the parallel capacitor to realize the excitation regulation voltage stabilization function when the load changes, the excitation system has large volume and complex control, and the capacitor can not be continuously regulated, so the voltage stabilization control effect is poor. With the development of power electronic technology, the bottleneck problem restricting the excitation control of the induction generator in an independent system can be solved by adopting the power electronic technology, for example, the multiphase rectification/three-phase auxiliary excitation control high-speed induction generator (patent number: ZL 200410055584.9) invented by the applicant can better solve the problem of voltage regulation by combining the characteristics of an alternating-current capacitor and an auxiliary excitation device.

The alternating current side of a traditional rectifier bridge load system is generally a first-order system, and is mostly analyzed by adopting a switching function method, and the method is characterized in that the conduction time of each diode is determined. Once the ac side of the rectifier bridge is connected in parallel with the self-excited capacitor, even if an approximation method of neglecting the resistance of the ac side is adopted for simplification, the ac side model of the system cannot be equivalent to a first-order system, the simplified ac side model is at least a second-order system, and considering the nonlinearity of the load of the rectifier bridge, the determined diode conduction time cannot be obtained through simple analysis at this time, so that the characteristic analysis of the rectifier bridge cannot be performed by adopting a switching function method.

Disclosure of Invention

The invention aims to provide a rectifier bridge load characteristic analysis method of an alternating current shunt capacitor for a high-speed induction generator controlled by multiphase rectification/three-phase auxiliary excitation.

A load characteristic analysis method for an alternating current shunt capacitor rectifier bridge is characterized in that A, B, C phases are analyzed according to the following modes:

power supply electromotive force phase omega_sthe results of t analysis during the period from 0 to π are the same as those during the period from π to 2 π, and the analysis during the period from 0 to π is as follows:

and (3) constructing an equation system:

wherein,

A'₃＝A'₁， ${B^{\′}}_3={B^{\′}}_1-\frac{\frac{2\mathrm{\π}}{3}{\mathrm{\ω}}_0}{{\mathrm{\ω}}_s},$ ${\mathrm{\ω}}_0=\frac{1}{\sqrt{\mathrm{LC}}},$ I_dl1＝I_dl2＝I_dl；

i represents A or B or C phase, E is i-phase electromotive force fundamental wave, omega_sIs the angular frequency of the electromotive force of the power supply, C is the parallel connection capacitance of i phase, L is the equivalent leakage inductance of i phase, t is time, e_iIs the power supply electromotive force of I phase, I_dIs a direct side current, I_dlThe critical current is provided for the sudden change of the self-excited capacitance current in the phase change process,

representing a derivation over time; u. of_i(w_st)₊Indicates that i phase is in phase w_sVoltage u after sudden change at time t_i(w_st)_-Indicates that i phase is in phase w_sVoltage before sudden change at time t;

solving the equation set to determine a parameter A'₁、B'₁、A'₂、B'₂、A'₃、B'₃、A'₄、B'₄Initial phase of electromotive force of power supply

Change of overlap angle gamma, current break I at the moment of starting conduction_dl1And the current break I at the moment of starting to turn off_dl2Thereby obtaining i-phase voltage u_i(w_st), and determining the current expression of the i phase according to the relation between the voltage and the current.

The technical effects of the invention are as follows:

the method provided by the invention analyzes the load characteristic of the rectifier bridge with the AC self-excited capacitor by utilizing the characteristic that the voltage of the AC capacitor can not change suddenly and the current can not change suddenly according to two conditions of considering a commutation overlap angle and not considering the commutation overlap angle, writes corresponding equation sets by utilizing the characteristics of the voltage and current change characteristic of the capacitor at the moment of commutation, the conduction and cut-off characteristic of the rectifier bridge, the half-period symmetry and the like, analyzes and analyzes the condition (corresponding to most of operation conditions) of not considering the commutation overlap angle, finds that the characteristic that the load of the rectifier bridge always presents the capacitance from no load to full load can be met as long as the equivalent inductance of the self-excited capacitor and the motor meets certain conditions, and not only can improve the power factor of a power winding by utilizing the characteristic, but also can greatly reduce the compensation capacity of the SAVR. The invention comprises the following steps:

(1) an equivalent circuit model of an induction generator system with a rectified load is derived. Considering that the impedance of the rotor loop to the higher harmonic current is far larger than the fundamental wave impedance, the high-frequency component of the rotor loop flux linkage can be ignored, and simultaneously, because the time constant of the squirrel-cage winding is very small, the low-frequency component in the rotor loop is quickly attenuated, so the potential of the transformer in the rotor loop can be ignored in the quasi-steady state analysis of the rectifier bridge load, and accordingly, the induction generator can be simplified into an equivalent circuit in the form that a sinusoidal voltage source and the impedance are connected in series according to a basic motor equation.

(2) And analyzing the load characteristic of a rectifier bridge externally connected with an alternating current capacitor by the alternating current power supply. Firstly, determining the conduction sequence of a diode according to the phase relation of each phase of an alternating current power supply, dividing each phase into four stages of phase change, conduction, phase change and cut-off, writing a corresponding loop equation for each stage, supplementing a corresponding circuit equation according to the principle that phase voltage can not change suddenly and current can change suddenly before and after the conduction and cut-off points and considering the characteristics of periodicity and the like in the phase change process, and simultaneously solving the equation set to obtain the voltage and current waveforms and the corresponding load characteristics of a rectifier bridge.

The method for analyzing the load characteristics of the rectifier bridge of the alternating current parallel capacitor of the induction generator can obtain fundamental wave voltage and current characteristics corresponding to the rectifier bridge load, accurately describe harmonic wave characteristics and lay a foundation for the optimization design of the capacity of two sets of windings of the induction generator.

In order to verify the analysis method, the voltage and the current are measured through experiments and compared with the calculated value, and the calculation result is consistent with the actual measurement result, so that the effectiveness and the accuracy of the method for analyzing the load characteristics of the rectifier bridge of the alternating current shunt capacitor are explained.

Drawings

Fig. 1 is an equivalent circuit of an induction generator rectification system.

FIG. 2 is a waveform diagram showing a power supply voltage, a winding voltage and a rectifier bridge AC side current, and FIG. 2(a) shows an a-phase voltage u_aAnd an internal potential e_aWaveform, FIG. 2(b) is rectifier bridge ACSide a phase current i_aAnd (4) waveform.

FIG. 3 is a graph of voltage versus current for a power winding at 20% load, and FIG. 3(a) is a graph of power winding current i_aWaveform, FIG. 3(b) is power winding current i_aFIG. 3(c) shows the power winding voltage u_aWaveform, FIG. 3(d) is power winding voltage u_aHarmonic analysis of (4).

FIG. 4 is a graph of voltage versus current for a power winding at 60% load, and FIG. 4(a) is a graph of power winding current i_aWaveform, FIG. 4(b) is power winding current i_aFIG. 4(c) shows the power winding voltage u_aWaveform, FIG. 4(d) is power winding voltage u_aHarmonic analysis of (4).

FIG. 5 is a graph of voltage versus current for a power winding at 100% load, and FIG. 5(a) is a graph of power winding current i_aWaveform, FIG. 5(b) is power winding current i_aFIG. 5(c) shows the power winding voltage u_aWaveform, FIG. 5(d) is power winding voltage u_aHarmonic analysis of (4).

Detailed Description

The method for analyzing the load characteristics of the rectifier bridge of the invention is specifically described by taking a three/three-phase double-winding induction motor as an example. For the rectifier bridge load with the self-excited capacitor on the ac side, although the phase commutation process is not required to be considered under most load conditions, the current sudden change capability of the self-excited capacitor cannot complete the current instantaneous phase commutation process as the load increases, and at this time, the influence of the rectifier bridge phase commutation process must be considered, and the phase commutation process is considered as the load characteristic when the phase commutation overlap angle is considered in detail below.

The critical current provided by the sudden change of the self-excited capacitor current in the phase change process is set to be I_dlWhen the load current is larger than I_dlIn time, the current sudden change capability of the capacitor cannot complete the current instantaneous phase change process, and due to the existence of the alternating current inductance, the capacitor cannot complete the current instantaneous phase change processA ignored commutation period; when the load current is less than I_dlThe current sudden change capability of the capacitor can complete the phase change process instantly, and the phase change time period caused by the existence of the inductor can be not considered.

Because the alternating-current side voltage and current waveforms in the analyzed circuit meet the positive and negative half-wave symmetry, the circuit analysis only needs to be carried out in a half alternating-current period. Taking phase a as an example (the analysis process of phase b and phase c is completely consistent with the result and phase a, and the phases are sequentially different by 120 degrees and 240 degrees), as shown in fig. 1 and fig. 2, when the phase overlap angle γ is considered, i.e. γ >0, the conduction sequence of the diode is

①0～γ

Column write circuit loop equation

$u_a=e_a-L\frac{{\mathrm{di}}_a}{\mathrm{dt}}---\left(1a\right)$

$i_a-C\frac{{\mathrm{du}}_a}{\mathrm{dt}}+i_c-C\frac{{\mathrm{du}}_c}{\mathrm{dt}}=I_d---\left(1b\right)$

$u_c=e_c-L\frac{{\mathrm{di}}_c}{\mathrm{dt}}---\left(1c\right)$

In formulae (1a) to (1c), e_a，e_cA, c phase of supply electromotive force, u_a，u_cA, C phase voltage waveform, C parallel connection capacitance, t time, L equal effective leakage inductance, i_a，i_cIs a, c phase current waveform, I_dIs a direct side current.

The a-phase voltage u can be obtained from the expressions (1a) to (1c)_aSatisfied differential equation

In the formula (2), E is the fundamental wave of each phase electromotive force, omega_sFor the angular frequency of the electromotive force of the power supply,

for the initial phase of electromotive force of power supply

The general solution of formula (2) is

Wherein A'₁，B'₁In order to determine the coefficient to be determined,

②γ～2π/3

column write circuit loop equation

$u_a=e_a-L\frac{{\mathrm{di}}_a}{\mathrm{dt}}---\left(4a\right)$

$i_a=C\frac{{\mathrm{du}}_a}{\mathrm{dt}}+I_d---\left(4b\right)$

From the equations (4a), (4b) the equations can be derived

$\mathrm{LC}\frac{d^2{u}_a}{{\mathrm{dt}}^2}+u_a=e_a---\left(5\right)$

The general solution of equation (5) is

Wherein A'₂，B'₂Is the undetermined coefficient.

③2π/3～2π/3+γ

Column write circuit loop equation

$u_a=e_a-L\frac{{\mathrm{di}}_a}{\mathrm{dt}}---\left(7a\right)$

$i_a-C\frac{{\mathrm{du}}_a}{\mathrm{dt}}+i_b-C\frac{{\mathrm{du}}_b}{\mathrm{dt}}=I_d---\left(7b\right)$

$u_b=e_b-L\frac{{\mathrm{di}}_b}{\mathrm{dt}}---\left(7c\right)$

i_bFor phase b current, u_bIs the b-phase voltage, e_bB-phase power supply electromotive force

Obtained from the formulae (7a) to (7c)

The general solution of formula (8) is

Wherein A'₃，B'₃Is the undetermined coefficient.

④2π/3+γ～π

Column write circuit loop equation

$u_a=e_a-L\frac{{\mathrm{di}}_a}{\mathrm{dt}}---\left(10a\right)$

$i_a=C\frac{{\mathrm{du}}_a}{\mathrm{dt}}---\left(10a\right)$

Obtained from the formulae (10a) to (10b)

$\mathrm{LC}\frac{d^2{u}_a}{{\mathrm{dt}}^2}+u_a=e_a---\left(11\right)$

General solution of formula (11) is

Wherein A'₄，B'₄Is the undetermined coefficient.

Considering the periodicity of the conduction or the cut-off of the three-phase rectifier bridge interval 2 pi/3, the principle that the interval between 0 and beta and the interval between 2 pi/3 and 2 pi/3 + beta are completely equal is A'₃＝A′₁ (13)

${B^{\′}}_3={B^{\′}}_1-\frac{\frac{2\mathrm{\π}}{3}{\mathrm{\ω}}_0}{{\mathrm{\ω}}_s}---\left(14\right)$

When formula (13) and formula (14) are substituted into formula (9), then A 'will be present at that time'₁、B'₁、A'₂、B'₂、A'₄、B'₄、

γ、I_dl1(the amount of current surge representing the time of starting conduction) and I_dl2Ten variables (representing the amount of current inrush at the moment of starting to turn off) and thus ten equations have to be written.

And (5) writing equation sets (15a) to (15j) according to equations (3), (6), (9) and (12) and the principle that the phase voltage cannot change suddenly and the current can change suddenly before and after the conduction and cut-off points, and the periodic conditions in the phase commutation process.

u_a(γ)_-＝u_a(γ)₊(the phase voltage cannot be abruptly changed due to the presence of a capacitor) (15a)

(the phase voltage cannot be abruptly changed due to the presence of a capacitor) (15 b)

(the phase voltage cannot be abruptly changed due to the presence of a capacitor) (15 c)

u_a(0)₊＝-u_a(π)_-(using half-periodicity odd symmetry) (15 d)

(using semi-periodic odd symmetry and the jump characteristic of the commutation moment current) (15 e)

$C\frac{{\mathrm{du}}_a{\left(\frac{2}{3}\mathrm{\π}\right)}_{-}}{\mathrm{dt}}-C\frac{{\mathrm{du}}_a{\left(\frac{2}{3}\mathrm{\π}\right)}_{+}}{\mathrm{dt}}=-I_{\mathrm{dl}2}$ (utilizing the jump characteristic of the commutation moment current) (15 f)

${\∫}_0^{\mathrm{\γ}}\frac{1}{L}(e_a-u_a)\mathrm{d\θ}-C(\frac{{\mathrm{du}}_a{\left(\mathrm{\γ}\right)}_{-}}{\mathrm{dt}}-\frac{{\mathrm{du}}_a{\left(0\right)}_{+}}{\mathrm{dt}})=I_d-I_{\mathrm{dl}1}$ (utilizing commutation process ending characteristics) (15 g)

${\∫}_{\frac{2}{3}\mathrm{\π}}^{\frac{2}{3}\mathrm{\π}+\mathrm{\γ}}\frac{1}{L}(e_a-u_a)\mathrm{d\θ}-C(\frac{{\mathrm{du}}_a{(\frac{2}{3}\mathrm{\π}+\mathrm{\γ})}_{-}}{\mathrm{dt}}-\frac{{\mathrm{du}}_a{\left(\frac{2}{3}\mathrm{\π}\right)}_{+}}{\mathrm{dt}})=-(I_d-I_{\mathrm{dl}2})$ (utilizing commutation process ending characteristics) (15 h)

(by using the current continuity characteristic at the end of the commutation process) (15 i)

(by using the current continuity characteristic at the end of the commutation process) (15j)

According to symmetry, has I_dl1＝I_dl2＝I_dl(I_dlThe magnitude of the critical current that can be provided by the abrupt change of the self-excited capacitor current during the phase change process is a known value, as mentioned above), so that any one of the equations (15 e) to (15 h) can be eliminated.

After solving the equations (15a) - (15j), the a-phase voltage waveform u under consideration of the commutation overlap angle can be obtained according to the equations (3), (6), (9) and (12)_aThe corresponding current waveform can be obtained from the relationships between the voltage waveform and the current, that is, the expressions (1a), (4a), (7a) and (10 a).

Finally, the 3/3 phase induction generator is calculated under the working conditions of 20%, 60% and 100% of load by adopting the method, and only compared with the actual measurement, the detailed results are shown in fig. 3-5 and table 1, the coincidence of the two results is better, and the correctness and the accuracy of the invention are verified.

The method is also suitable for analyzing the load characteristic of the rectifier bridge of the multiphase induction generator.

The invention has been described with reference to the detailed drawings of the preferred embodiments. Those skilled in the art can derive numerous variations from the preferred embodiments without departing from the scope of the invention. Accordingly, the preferred embodiments should not limit the scope of the invention. The scope of the invention is defined in the claims.

TABLE 1 comparison of different load tests and analytical analysis results

(motor speed n =1500r/min, shunt capacitance C =100 μ F, rectified voltage U_dc=510V)

In Table 1I_dFor a direct side current of a rectifier bridge, U_pIs the effective value of a, b, c phase voltage, U_p1Is the fundamental effective value of a, b, c phase voltage_pEffective value of a, b, c phase current, I_p1Is the effective value of the fundamental wave of the phase current of a, b and c, and is angle U_p1I_p1The phase difference between the phase voltage a, b and c and the phase current, f is the electromotive force frequency of the motor, and s is the slip of the motor.

Claims (1)

1. A load characteristic analysis method for an alternating current shunt capacitor rectifier bridge is characterized in that A, B, C phases are analyzed according to the following modes:

power supply electromotive force phase omega_sthe results of t analysis during the period from 0 to π are the same as those during the period from π to 2 π, and the analysis during the period from 0 to π is as follows:

and (3) constructing an equation system:

wherein,

A'₃＝A'₁， ${B^{\′}}_3={B^{\′}}_1-\frac{\frac{2\mathrm{\π}}{3}{\mathrm{\ω}}_0}{{\mathrm{\ω}}_s},$ ${\mathrm{\ω}}_0=\frac{1}{\sqrt{\mathrm{LC}}},$ I_dl1＝I_dl2＝I_dl；

i represents A or B or C phase, E is i-phase electromotive force fundamental wave, omega_sIs the angular frequency of the electromotive force of the power supply, C is the parallel connection capacitance of i phase, L is the equivalent leakage inductance of i phase, t is time, e_iIs the power supply electromotive force of I phase, I_dIs a direct side current, I_dlThe critical current is provided for the sudden change of the self-excited capacitance current in the phase change process,

representing a derivation over time; u. of_i(w_st)₊Indicates that i phase is in phase w_sVoltage u after sudden change at time t_i(w_st)_-Indicates that i phase is in phase w_sVoltage before sudden change at time t;

solving the equation set to determine a parameter A'₁、B'₁、A'₂、B'₂、A'₃、B'₃、A'₄、B'₄Initial phase of electromotive force of power supply

Current transient I at the moment of starting conduction of commutation overlap angle gamma_dl1And the current break I at the moment of starting to turn off_dl2Thereby obtaining i-phase voltage u_i(w_st), and determining the current expression of the i phase according to the relation between the voltage and the current.

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