CN109241652B - Single-phase PAPF circuit modeling method considering coupling relation - Google Patents

Single-phase PAPF circuit modeling method considering coupling relation Download PDF

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CN109241652B
CN109241652B CN201811118122.5A CN201811118122A CN109241652B CN 109241652 B CN109241652 B CN 109241652B CN 201811118122 A CN201811118122 A CN 201811118122A CN 109241652 B CN109241652 B CN 109241652B
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孙立军
田铭兴
徐金阳
张子麒
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Lanzhou Jiaotong University
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    • Y02E40/20—Active power filtering [APF]
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Abstract

The invention discloses a single-phase PAPF circuit modeling method considering a coupling relation, which comprises the following steps: acquiring the value of the direct-current side voltage of the single-phase PAPF circuit; obtaining the value of an alternating current side inductor of the single-phase PAPF circuit; acquiring the value of a direct current side capacitor of the single-phase PAPF circuit; modeling is performed based on the value of the dc-side voltage, the value of the ac-side inductance, and the value of the dc-side capacitance. The compensation requirements under all working conditions of a specific load can be met by reasonably selecting the parameters of the single-phase PAPF circuit, the form is simple, the calculation is convenient, the universality is strong, the equipment cost can be reduced, the compensation effect is improved, and the stability of the whole system can be improved. Meanwhile, starting from actual working conditions, a definite parameter selection method is obtained through MATLAB three-dimensional modeling and data optimization processing aiming at the coupling relation among the main circuit parameters, and both simulation and experiment results verify the correctness and feasibility of the method.

Description

Single-phase PAPF circuit modeling method considering coupling relation
Technical Field
The invention relates to the technical field of power electronics, in particular to a single-phase PAPF circuit modeling method considering a coupling relation.
Background
In recent years, a large number of single-phase nonlinear power electronic devices are used in large-scale industrial power utilization occasions such as electrified railways and arc furnaces, and the pollution to a power grid is more serious. The single-phase Parallel Active Power Filter (PAPF) can effectively inhibit power grid harmonics and compensate reactive power, so that the filter is widely concerned by people.
At present, researches on PAPF are mainly focused on three-phase PAPF equipment, single-phase PAPF researches are few, and researches focus on a topological structure, a detection method and a control strategy. However, reasonable selection of key parameters of the main circuit of the PAPF is also an indispensable loop in the whole compensation system, and proper parameter selection can reduce equipment cost, improve compensation effect and improve system performance.
For the problem of parameter selection of the main circuit of the PAPF, the traditional research mainly focuses on selecting a certain specific parameter to perform theoretical analysis and solving an analytic formula of the specific parameter, which is convenient for calculation, and does not consider the coupling relationship among the parameters. In addition, although the scholars mention that the parameters of the main circuit of the PAPF have a coupling relationship, no single-phase PAPF main circuit parameter selection method considering the coupling relationship of the parameters is provided, so that accurate modeling cannot be performed.
Disclosure of Invention
The present invention aims to solve the above problems, and to provide a method for modeling a single-phase PAPF circuit by considering a coupling relationship, so as to solve at least part of the problems of the prior art.
In order to achieve the above object, the technical solution of the present invention provides a single-phase PAPF circuit modeling method considering a coupling relationship, including:
acquiring the value of the direct-current side voltage of the single-phase PAPF circuit;
obtaining the value of an alternating current side inductor of the single-phase PAPF circuit;
acquiring the value of a direct current side capacitor of the single-phase PAPF circuit;
modeling is performed based on the value of the dc side voltage, the value of the ac side inductance, and the value of the dc side capacitance.
Preferably, before the step of obtaining the value of the dc-side voltage of the single-phase PAPF circuit, the method further includes: determining factors influencing the inductance of the alternating current side of the single-phase PAPF circuit;
factors affecting the dc side capacitance of the single phase PAPF circuit are determined.
Preferably, the factors affecting the dc side capacitance of the single-phase PAPF circuit include:
the sum of the amplitudes of the harmonics of each order of the compensation current, the voltage fluctuation rate and the direct-current side voltage.
Preferably, the determining factors affecting the inductance of the ac side of the single-phase PAPF circuit includes:
and obtaining a value formula of the alternating current side inductor.
Preferably, the value formula of the alternating-current side inductance is as follows:
Figure BDA0001810958020000021
in the formula: l is the inductance on the AC side, delta is the DC voltage fluctuation ratio, U d Is a DC side voltage, I pm∑ For compensating the sum of the amplitudes of the harmonics of the current, U sm The amplitude of the supply voltage, ω is the supply angular frequency.
Preferably, the value range of the delta is 0-5%.
Preferably, the sum I of the amplitudes of the harmonics of the compensation current pm∑ The phase shift range of alpha is 0-90 degrees in relation to the trigger angle alpha of the thyristor.
Preferably, the sum I of the amplitudes of the harmonics of the compensation current pm∑ The relationship with the firing angle α of the thyristor is:
Figure BDA0001810958020000022
in the formula: u. of s Is the supply voltage, R d Is the equivalent resistance of the load>
Figure BDA0001810958020000023
And N is the harmonic order.
Preferably, the factors affecting the dc side capacitance of the single-phase PAPF circuit include:
the voltage at the direct current side, the fluctuation rate of the direct current voltage and the equivalent resistance value of the load;
the determining of the factors influencing the direct-current side capacitance of the single-phase PAPF circuit specifically comprises the following steps:
and obtaining a value formula of the direct current side capacitor according to the direct current side voltage, the direct current voltage fluctuation rate and the equivalent resistance value of the load.
Preferably, the value of the dc side capacitance of the single-phase PAPF circuit is related to the firing angle a of the thyristor, when a =41.08,
the value formula of the direct current side capacitor is as follows:
Figure BDA0001810958020000031
in the formula: c is a DC side capacitor, u s Is a supply voltage, U d Is a DC side voltage, R d Is the equivalent resistance of the load, δ is the direct voltage fluctuation ratio, and f is the frequency.
According to a specific implementation of an embodiment of the invention,
the technical scheme of the invention has the following beneficial effects:
according to the technical scheme, modeling is carried out based on the value of the direct-current side voltage, the value of the alternating-current side inductor and the value of the direct-current side capacitor, the compensation requirement under all working conditions of a specific load can be met, the method is simple in form, convenient to calculate and high in universality, the equipment cost can be reduced, and the compensation effect can be improved.
According to the technical scheme, by combining the harmonic characteristics of a specific load and analyzing the parameters of the single-phase PAPF main circuit, analytical expressions of an alternating current side inductor, a direct current side capacitor and a direct current side voltage are obtained, then the coupling relation among the parameters is considered, an optimization model is established, the compensated harmonic content is lower than 2% and serves as a comprehensive optimization target, and finally a set of complete parameter selection method is obtained. The single-phase PAPF main circuit obtained by the invention has reasonable parameter selection, can meet the compensation requirements of specific loads under all working conditions, has simple form, convenient calculation and strong universality, can reduce the equipment cost, improves the compensation effect and can improve the stability of the whole system. Meanwhile, aiming at the coupling relation among the main circuit parameters, the method starts from the actual working condition, obtains a clear parameter selection method through MATLAB three-dimensional modeling and data optimization processing, and verifies the correctness and feasibility of the method through simulation and experiment results. In addition, the invention overcomes the defects of the existing theory on the parameter calculation of the single-phase PAPF circuit, and the scheme provided systematically realizes the parameter design requirement on the whole circuit, thereby increasing the practical value of the single-phase PAPF to a certain extent.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
Fig. 1 is a flowchart of a single-phase PAPF circuit modeling method considering a coupling relationship according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the structure and power flow of a single-phase PAPF compensation system according to an embodiment of the present invention;
FIG. 3 is a L, C variation three-dimensional parametric model according to an embodiment of the present invention;
fig. 4 is a diagram illustrating a variation of the ac side inductor L according to the trigger angle α and the dc voltage fluctuation ratio δ in the embodiment of the present invention;
FIG. 5 illustrates a load current waveform according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a compensation current waveform according to an embodiment of the present invention;
FIG. 7 is a compensated power supply current waveform according to an embodiment of the present invention;
FIG. 8 is a graph of the harmonic content before compensation (THD) according to an embodiment of the present invention;
fig. 9 is a graph of the compensated harmonic content (THD) according to an embodiment of the present invention.
Detailed Description
It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The parallel active power filter is abbreviated as PAPF.
As shown in fig. 1, a single-phase PAPF circuit modeling method considering a coupling relationship includes:
step S101: acquiring the value of the direct-current side voltage of the single-phase PAPF circuit;
step S102: obtaining the value of an alternating current side inductor of the single-phase PAPF circuit;
step S103: acquiring the value of a direct current side capacitor of the single-phase PAPF circuit;
step S104: modeling is performed based on the value of the dc side voltage, the value of the ac side inductance, and the value of the dc side capacitance.
Preferably, before the step of obtaining the value of the dc-side voltage of the single-phase PAPF circuit, the method further includes: determining factors influencing the inductance of the alternating current side of the single-phase PAPF circuit;
factors that affect the dc side capacitance of a single phase PAPF circuit are determined.
Preferably, the factors affecting the dc side capacitance of the single-phase PAPF circuit include:
the sum of the amplitudes of the harmonics of the compensation current, the voltage fluctuation rate and the direct-current side voltage.
Preferably, the determining factors affecting the inductance of the ac side of the single-phase PAPF circuit includes:
and obtaining a value formula of the alternating current side inductor.
Preferably, the factors affecting the dc side capacitance of the single-phase PAPF circuit include:
the voltage at the direct current side, the fluctuation rate of the direct current voltage and the equivalent resistance value of the load;
the determining of the factors influencing the direct-current side capacitance of the single-phase PAPF circuit specifically comprises the following steps:
and obtaining a value formula of the direct current side capacitor according to the direct current side voltage, the direct current voltage fluctuation rate and the equivalent resistance value of the load.
The specific implementation mode is as follows:
step 1, determining influence factors of an inductance L at an alternating current side:
as shown in fig. 2, the voltage constraint equation satisfying the real-time tracking capability of the single-phase PAPF is obtained as shown in equation (1) while ignoring the influence of the line impedance:
Figure BDA0001810958020000051
assuming that the power supply voltage of the single-phase PAPF circuit is an ideal sine wave, the number of compensated highest harmonics N =49, there are:
u s ＝U sm sinωt (2)，
Figure BDA0001810958020000052
wherein, U sm And I pmn Amplitude, alpha, of the respective harmonics of the supply voltage and the compensating current, respectively n The initial phase angle of the n-th harmonic wave is shown, and omega is the angular frequency of the power supply. At the same time, set the DC side voltage u dc The maximum and minimum values of the fluctuation are respectively Delta U 1 And Δ U 2 The following can be obtained:
δ＝(ΔU 1 +ΔU 2 )/U d (4)，
u dc ＝U d [1+δsin(2ωt+θ d )] (5)，
where, δ is the DC voltage fluctuation ratio, θ d Is u dc 2 harmonic phase angle, U d Is straight u dc The flow voltage. And because:
Figure BDA0001810958020000061
I pmn to compensate for the amplitude of the harmonics of the current, I pm∑ Is the sum of the amplitudes of the harmonics of the compensation current. Therefore, the following formula (1) shows that:
Figure BDA0001810958020000062
when u is dc Taking the minimum value, i.e. u dc ＝U d (1- δ), the inductance upper limit formula can be obtained:
Figure BDA0001810958020000063
for a single-phase fully-controlled bridge load type rectifying circuit with resistance and inductance, neglecting the phase change process and current pulsation, carrying out Fourier decomposition on load current, and obtaining an expression as follows:
Figure BDA0001810958020000064
wherein alpha is the trigger angle of the thyristor, the phase shift range is 0-90 DEG, the harmonic frequency is N =2N' -1, then
Figure BDA0001810958020000065
And N is the harmonic order. . The AC side inductor L has a smoothing effect on the load current, and if the value of L is large, the load current i can be obtained d Continuous and with a waveform approximating a straight line with the average value I of the DC current delivered to the load d 。
And enabling the PAPF to simultaneously compensate the harmonic waves and the reactive power of the load, wherein the compensated power supply current is the fundamental wave active component of the load current. Therefore, the compensated power supply current and the actual compensation current expression can be obtained:
Figure BDA0001810958020000071
Figure BDA0001810958020000072
by combining the above formulae (6) and (11) to obtain I pm∑ Expression:
Figure BDA0001810958020000073
neglecting the effect of sin α on the overall result when N' is large, an approximate expression of equation (12) can be obtained:
Figure BDA0001810958020000074
substituting the formula (13) into the formula (8) can obtain a value formula of the single-phase PAPF alternating-current side inductance, wherein the value formula is as follows:
Figure BDA0001810958020000075
the above formula is a selected expression of the inductance L parameter at the alternating current side of the single-phase PAPF circuit, wherein delta is used as a variable for describing the voltage fluctuation at the direct current side, and the size of delta is controlled within the range of 0-5% under the conditions of comprehensively considering the limitation of capacitance ripple, cost, field application and the like. Therefore, the selection of the inductance L on the AC side is mainly influenced by the fluctuation ratio delta of the DC voltage and the voltage U on the DC side d And the sum I of amplitudes of harmonics of the compensation current pm∑ And compensating for the sum I of the amplitudes of the harmonics of the current pm∑ Influenced by the firing angle alpha of the thyristor.
Step 2, determining influence factors of the direct current side capacitor C:
as shown in FIG. 2, u s Is the supply voltage i s Is the supply current i p To compensate for the current, i L Is the load current u dc The instantaneous value of the PAPF dc side capacitor voltage,
Figure BDA0001810958020000081
based on the average power required by the load output by the power supply>
Figure BDA0001810958020000082
To require power buffered on the DC side, p L The power required by the load.
Instantaneous power p required by load L By
Figure BDA0001810958020000083
And &>
Figure BDA0001810958020000084
Two parts are formed. When the PAPF is compensated, the power supply need only output the average power->
Figure BDA0001810958020000085
And/or>
Figure BDA0001810958020000086
Its presence results in a PAPF dc side voltage u in order to require a dc side buffered power dc Is fluctuating. Combine single-phase full accuse bridge to have the working condition of inductance load circuit, under the condition of ignoring rectifier bridge and line loss, obtain the expression:
Figure BDA0001810958020000087
Figure BDA0001810958020000088
Figure BDA0001810958020000089
wherein, α is not less than ω t not more than π + α,0 is not less than α not more than π/2, and the solution continues to solve the above formula power fluctuation amount, which can be known as: when sin ω t =2cos α/pi,
Figure BDA00018109580200000810
and obtaining the specific value of the ω t at the extreme point. Order:
Figure BDA0001810958020000091
and (3) obtaining an energy expression of the capacitance charging and discharging process in a fluctuation period according to the result obtained by the formula (18) and a capacitance energy calculation formula:
Figure BDA0001810958020000092
the value of the direct current side capacitor C is influenced by the trigger angle alpha of the thyristor, and the programming calculation in MATLAB shows that when the trigger angle alpha of the thyristor is =41.08 degrees, the obtained capacitance parameter expression meeting the design requirement is as follows:
Figure BDA0001810958020000093
according to the above formula, the DC-side capacitor C is selected in consideration of the DC-side voltage U d D, the D.C. voltage fluctuation factor delta and the equivalent resistance R of the load d The variation of the three parameters, f is the frequency, and in a specific implementation scenario f is 50Hz. Wherein the equivalent resistance R of the load d In actual conditions, variations may occur, but nominal values are generally taken as design criteria in the design process.
Step 3, determining the voltage U of the direct current side d Taking values:
as shown in the formulas (14) and (20), the single-phase PAPF main circuitDC side voltage U d The three parameters of the direct current side capacitor C and the alternating current side inductor L have a certain coupling relation with each other. From the main circuit DC side voltage U d And starting with the direct-current voltage fluctuation rate delta, and selecting and analyzing specific circuit parameters by combining the actual change condition of the trigger angle alpha of the thyristor.
Furthermore, the selection of the AC side inductor L, the DC side capacitor C and the DC side voltage U can be obtained from the formulas (14) and (20) d It is relevant. In actual calculation, a DC side voltage U needs to be preliminarily determined d Value, DC side voltage U d Should be greater than the peak value of the alternating current mains phase voltage, otherwise the situation that the compensating current does not change according to the requirement may occur, on this basis, the direct current side voltage U d The larger the compensation current tracking speed, the higher the voltage requirement of the switching device for too high a voltage. Therefore, by combining with practical engineering experience, 1.2-1.5 times of allowance is taken on the basis of phase voltage peak value, and finally, the direct-current side voltage U is obtained d The more reasonable calculation formula is:
Figure BDA0001810958020000101
therefore, the DC side voltage U d Is taken from the value of
Figure BDA0001810958020000102
Within the range, an initial value is selected within the range.
Step 4, determining the value of the inductance L at the AC side:
from the step 1, it can be known that the value of the inductance L on the AC side is influenced by the fluctuation rate delta of the DC voltage and the trigger angle alpha of the thyristor. The value range of the direct current voltage fluctuation ratio delta is 0-5%, and the phase shift range of the trigger angle alpha of the thyristor is 0-90 degrees. Determining the DC side voltage U d Then, a three-dimensional parameter model of L, C is established in MATLAB according to the relational expressions obtained in step 1 and step 2, as shown in FIG. 3. And a simulation result is shown in fig. 4, and a simulation graph of the value of the inductance L on the alternating current side with alpha and delta as independent variables is obtained through simulation. So as to be within the range of the alpha and delta transformations,and the value of the inductance L at the alternating current side is superposed with the simulation curve as much as possible, and the minimum value is the constraint condition, so that the value of the inductance L at the alternating current side and the corresponding alpha and delta values are obtained.
And 5, substituting the result obtained in the step 4 into the direct current side capacitor C value relation in the step 2 to obtain the specific value of the direct current side capacitor C.
Step 6, effect verification: using the DC side voltage U obtained in step 3, step 4 and step 5 d And the parameters of the inductor L at the alternating current side and the capacitor C at the direct current side are used for building a simulation model for the circuit shown in the figure 2 in Matlab/Simulink software and verifying the filtering effect of the system. The simulated load current waveform is shown in fig. 5, and it can be seen from fig. 5 that the current waveform of the load is similar to a square wave, and at this time, the load current waveform is the power supply current waveform before compensation. The compensation current waveform is shown in fig. 6, which is the current waveform provided by PAPF in order to improve the power supply current waveform. The compensated power supply current waveform is shown in fig. 7, and it can be seen from fig. 7 that the power supply current waveform after PAPF compensation is a sine wave. According to the oscillogram, the compensation effect is good.
The pre-compensation harmonic content (THD) values are shown in fig. 8, and the post-compensation harmonic content (THD) values are shown in fig. 9. Comparing fig. 8 and fig. 9, it can be seen that the current THD value in the grid before compensation is 34.74%, and is reduced to 1.23% after compensation is applied, which is better than the comprehensive optimization target that the harmonic content is lower than 2% after compensation.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A single-phase PAPF circuit modeling method considering a coupling relation is characterized by comprising the following steps:
acquiring the value of the direct-current side voltage of the single-phase PAPF circuit;
obtaining the value of an alternating current side inductor of the single-phase PAPF circuit;
acquiring the value of a direct current side capacitor of the single-phase PAPF circuit;
modeling based on the value of the direct-current side voltage, the value of the alternating-current side inductor and the value of the direct-current side capacitor;
before the step of obtaining the value of the direct-current side voltage of the single-phase PAPF circuit, the method further comprises the following steps: determining factors influencing the inductance of the alternating current side of the single-phase PAPF circuit;
the factors influencing the direct-current side capacitance of the single-phase PAPF circuit comprise:
compensating the sum of the amplitudes of the harmonics of each time, the voltage fluctuation rate and the direct-current side voltage of the current;
the factors for determining the inductance of the alternating current side of the single-phase PAPF circuit are specifically as follows:
obtaining a value formula of the alternating current side inductor;
the value formula of the alternating current side inductance is as follows:
Figure FDA0004044042870000011
in the formula: l is the inductance on the AC side, delta is the ripple ratio of the DC voltage, U d Is a DC side voltage, I pm∑ For compensating the sum of the amplitudes of the harmonics of the current, U sm Is the amplitude of the power supply voltage, and omega is the power supply angular frequency;
the value range of delta is 0-5%;
sum of amplitudes of harmonics of compensating current I pm∑ Is associated with the trigger angle alpha of the thyristor, and the phase shift range of the alpha is 0-90 degrees;
sum of amplitudes of harmonics I of compensating current pm∑ The relationship with the firing angle α of the thyristor is:
Figure FDA0004044042870000021
in the formula: u. of s Is the supply voltage, R d Is the equivalent resistance of the load>
Figure FDA0004044042870000022
And N is the harmonic order.
2. The coupling-relationship-considered single-phase PAPF circuit modeling method according to claim 1,
the factors influencing the direct-current side capacitance of the single-phase PAPF circuit comprise:
the voltage at the direct current side, the fluctuation rate of the direct current voltage and the equivalent resistance value of the load;
the determining of the factors influencing the direct-current side capacitance of the single-phase PAPF circuit specifically comprises the following steps:
and obtaining a value formula of the direct current side capacitor according to the direct current side voltage, the direct current voltage fluctuation rate and the equivalent resistance value of the load.
3. The method for modeling a single-phase PAPF circuit considering a coupling relationship according to claim 1, wherein a value of a direct-current side capacitance of the single-phase PAPF circuit is related to a firing angle α of a thyristor;
when the α =41.08,
the value formula of the direct current side capacitor is as follows:
Figure FDA0004044042870000023
in the formula: c is a DC side capacitance u s Is a supply voltage, U d Is a DC side voltage, R d Is the equivalent resistance of the load, δ is the direct voltage fluctuation ratio, and f is the frequency. />
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