A compensation method for unbalanced three-phase four-wire system under asymmetric voltage distortion

Abstract

The present invention proposes a compensation method for a three-phase four-wire unbalanced system under asymmetric voltage distortion, the method comprising the following steps: (1) estimating the impedance parameters of the load and the neutral line according to the monitoring value; (2) constructing a compensation branch composed of an inductor and a capacitor in series, and establishing a relationship expression between the inductor, the capacitor and the susceptance of the compensation branch; (3) taking the harmonic current on the secondary side of the transformer as the objective function, and minimizing the objective function by calculating the compensation parameters of the compensation branch; (4) taking the resonant frequency of the compensation branch as a constraint condition, connecting the compensation branch formed by the inductor and the capacitor that meet the constraint condition to the three-phase four-wire unbalanced system for compensation. The present invention realizes the compensation of the three-phase four-wire unbalanced system under asymmetric voltage distortion, reduces the harm of the third harmonic to the three-phase four-wire power supply system, and does not cause harmonic amplification and resonance.

Description

Technical Field

[0001] The invention relates to a three-phase four-wire unbalanced system compensation method under asymmetric voltage distortion, belonging to the technical field of passive compensation of power systems. Background Art

[0002] For the current domestic and international power industry, power quality is of great significance for ensuring the normal order of society, the safe and reliable power supply of the people, the safe operation of the power grid, and the stability maintenance of power equipment. The parameters that characterize power quality generally include: three-phase imbalance, voltage fluctuation and flicker, harmonics and interharmonics, voltage deviation, frequency deviation and other important indicators. A large number of experiments have proved that the three-phase imbalance indicator has a close relationship with the quality of power system power, and the three-phase voltage or current imbalance still has an important impact on other indicators. In the actual operation of the power grid, the low-voltage distribution network is directly facing the end user. The quality of its grid operation directly determines the quality of users' electricity consumption, and its importance is self-evident. However, contrary to the important position of the low-voltage distribution network, with the rapid development of modern science and technology, especially in With the widespread popularization of power electronics technology, high-power equipment and nonlinear loads have been widely used, which has greatly improved productivity, but has also led to increasingly serious problems in distribution networks; especially in the problems of current imbalance and harmonic pollution, which have seriously reduced the quality of current; power quality refers to the quality of electric energy transmitted to electric energy users through the power grid. It is an important indicator for measuring the performance of the power system. It is of great significance to ensure the safe operation of the power grid and equipment, the normal progress of industrial production and the normal order of social operation; under the goal of building a global smart grid, improving power quality is an inevitable prerequisite for its construction and development; in addition, with the increasing diversification of load types, the proportion of sensitive loads connected to the power grid has also increased, which has also put forward higher requirements for the improvement of power quality.

[0003] As an important indicator for measuring power quality, three-phase imbalance has a particularly prominent impact in distribution networks and has become a key factor affecting power quality. The proportion of residential electricity consumption in my country's total electricity consumption has increased year by year, and most of the residential electricity consumption is single-phase load supplied by a three-phase four-wire system. Since it is difficult to ensure the balance of loads on each phase during actual operation, the three-phase imbalance caused by this has become increasingly severe. Moreover, after a large number of electric vehicle charging piles have been connected to the power grid, the three-phase imbalance has become increasingly serious. As my country's distributed photovoltaic technology has entered a growth period in recent years, the randomness and volatility of its output have further aggravated the three-phase imbalance of the power grid. The three-phase imbalance of the system has also become a bottleneck for the absorption and access of distributed photovoltaics.

[0004] Therefore, how to compensate for the unbalanced three-phase four-wire system and avoid the harm caused by the third harmonic has become an urgent problem to be solved. Summary of the invention

[0005] The present invention provides a three-phase four-wire unbalanced system compensation method under asymmetric voltage distortion, which aims to reduce the harm of third harmonics to the three-phase four-wire power supply system.

[0006] The technical solution of the present invention is a method for compensating an unbalanced system of a three-phase four-wire system under asymmetric voltage distortion, the method comprising the following steps:

[0007] (1) Estimate the impedance parameters of the load and neutral line based on the monitored values;

[0008] (2) Construct a compensation branch consisting of an inductor and a capacitor connected in series, and establish a relationship expression between the inductor, the capacitor, and the susceptance of the compensation branch;

[0009] (3) Taking the harmonic current on the secondary side of the transformer as the objective function, the objective function is minimized by calculating the compensation parameters of the compensation branch;

[0010] (4) The resonant frequency of the compensation branch is used as a constraint condition, and the compensation branch formed by the inductor and capacitor that meet the constraint condition is connected to the three-phase four-wire unbalanced system for compensation.

[0011] Furthermore, the monitoring values ​​include A-phase fundamental current, B-phase fundamental current, C-phase fundamental current, A-phase fundamental voltage, B-phase fundamental voltage, C-phase fundamental voltage, A-phase third harmonic current, A-phase third harmonic voltage, B-phase third harmonic current, B-phase third harmonic voltage, C-phase third harmonic current, C-phase third harmonic voltage, fundamental zero-sequence current, and third harmonic zero-sequence current.

[0012] Furthermore, the impedance parameters of the load and the neutral line include the conductance of the neutral line, the susceptance of the neutral line, the conductance of the A-phase load, the susceptance of the A-phase load, the conductance of the B-phase load, the susceptance of the B-phase load, the conductance of the C-phase load, and the susceptance of the C-phase load.

[0013] Furthermore, the step (1) estimates the impedance parameters of the load and the neutral line according to the monitoring values, specifically comprising: obtaining a complex equation through the relationship between the fundamental current of phase A, the fundamental current of phase B, the fundamental current of phase C, the fundamental voltage of phase A, the fundamental voltage of phase B, the fundamental voltage of phase C, the third harmonic current of phase A, the third harmonic voltage of phase A, the third harmonic current of phase B, the third harmonic voltage of phase B, the third harmonic current of phase C, the third harmonic voltage of phase C, the fundamental zero-sequence current, and the third harmonic zero-sequence current, and estimating the impedance parameters of the load and the neutral line according to the corresponding monitoring values, and the complex equation is specifically shown in formula (1):

[0014]

[0015] In the formula, is the fundamental current of phase A, is the fundamental current of phase B, is the fundamental current of phase C, is the fundamental voltage of phase A, is the fundamental voltage of phase B, is the fundamental voltage of phase C, is the third harmonic current of phase A, is the third harmonic voltage of phase A, is the third harmonic current of phase B, is the third harmonic voltage of phase B, is the third harmonic current of phase C, is the third harmonic voltage of phase C, G N is the conductivity of the neutral line, B N is the susceptance of the neutral line, is the fundamental zero-sequence current, is the third harmonic zero sequence current, G A is the conductance of phase A load, B A is the susceptance of phase A load; G B is the conductivity of the B phase load, B B is the susceptance of the B phase load; G C is the conductivity of the C phase load, B C is the susceptance of phase C load.

[0016] Furthermore, the step (2) constructs a compensation branch composed of an inductor and a capacitor connected in series, and establishes a relationship expression between the inductor and the capacitor in the compensation branch and the susceptance of the compensation branch, which specifically includes the following steps:

[0017] 1) Establishing a compensation branch under the third harmonic, wherein the compensation branch is composed of an inductor and a capacitor connected in series;

[0018] 2) Taking the inductance and capacitance of the compensation branch as the input quantities to be input, and the susceptance of the compensation branch as the quantity to be calculated, the susceptance of the compensation branch is calculated through the input quantities to be input.

[0019] Furthermore, the compensation branch includes a compensation branch for the third harmonic of phase A, a compensation branch for the third harmonic of phase B, and a compensation branch for the third harmonic of phase C; the inductance and capacitance of the compensation branch include the inductance L of the compensation branch for the third harmonic of phase A A , capacitor C of the compensation branch of the third harmonic of phase A A , the inductance L of the compensation branch of the third harmonic of phase B B , the capacitor C of the compensation branch of the third harmonic of phase B B , the inductance L of the compensation branch of the third harmonic of phase C C, the capacitor C of the compensation branch of the third harmonic of phase C C The susceptance of the compensation branch includes the susceptance B of the compensation branch of the third harmonic of phase A Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 .

[0020] Further, the inductance and capacitance of the compensation branch are the quantities to be input, the susceptance of the compensation branch is the quantity to be calculated, and the susceptance of the compensation branch is calculated through the quantities to be input, specifically including: taking the inductance of the compensation branch of the third harmonic of phase A, the capacitance of the compensation branch of the third harmonic of phase A, the inductance of the compensation branch of the third harmonic of phase B, the capacitance of the compensation branch of the third harmonic of phase B, the inductance of the compensation branch of the third harmonic of phase C, and the capacitance of the compensation branch of the third harmonic of phase C as the quantities to be input; and calculating the susceptance of the compensation branch of the third harmonic of phase A, the susceptance of the compensation branch of the third harmonic of phase B, and the susceptance of the compensation branch of the third harmonic of phase C through formula (2):

[0021]

[0022] Where ω is the angular frequency, L A is the inductance of the compensation branch of the third harmonic of phase A, C A is the capacitance of the compensation branch of the third harmonic of phase A, L B is the inductance of the compensation branch of the third harmonic of phase B, C B is the capacitance of the compensation branch of the third harmonic of phase B, L C is the inductance of the compensation branch of the third harmonic of phase C, C C B is the capacitance of the compensation branch of the third harmonic of phase C; Ak3 is the susceptance of the compensation branch of the third harmonic of phase A; B Bk3 is the susceptance of the compensation branch of the third harmonic of phase B; Ck3 is the susceptance of the compensation branch of the third harmonic of phase C.

[0023] Furthermore, the step (3) takes the harmonic current on the secondary side of the transformer as the objective function, and minimizes the objective function by calculating the compensation parameters of the compensation branch. Specifically, it includes establishing a relationship between the objective function and the network parameters under the third harmonic of each phase under the voltage distortion unbalance system, and inputting the impedance parameters of the load and neutral line estimated in step (1) according to the MATLAB computing platform, and optimizing the inductance and capacitance of the compensation branch to minimize the objective function.

[0024] Furthermore, the step (3) takes the harmonic current on the secondary side of the transformer as the objective function and minimizes the objective function by calculating the compensation parameters of the compensation branch, which specifically includes the following steps:

[0025] 3-1) The harmonic current on the secondary side of the A-phase transformer, the harmonic current on the secondary side of the B-phase transformer, and the harmonic current on the secondary side of the C-phase transformer are taken as the objective function, as shown in the following formula (3):

[0026]

[0027] in, is the harmonic current on the secondary side of the A-phase transformer, is the harmonic current on the secondary side of the B-phase transformer, is the harmonic current on the secondary side of the C-phase transformer;

[0028] 3-2) Establish the calculation formula of harmonic current and network parameters of the secondary side of the transformer in the three-phase four-wire voltage distortion unbalanced system; Among them, the susceptance of the compensation branch of the third harmonic of phase A, the susceptance of the compensation branch of the third harmonic of phase B, and the susceptance of the compensation branch of the third harmonic of phase C are the quantities to be determined, and the third harmonic voltage of phase A, the third harmonic voltage of phase B, the third harmonic voltage of phase C, the susceptance of the load of phase A, the susceptance of the load of phase B, the susceptance of the load of phase C, the conductance of the load of phase A, the conductance of the load of phase B, the conductance of the load of phase C, the conductance of the neutral line, and the susceptance of the neutral line are the known quantities; Specifically, as shown in formula (4) to formula (8):

[0029]

[0030] Wherein, V is the parameter containing the third harmonic voltage; Z1, Z2, and Z3 are the parameters of the three-phase four-wire unbalanced system. Z1, Z2, Z3, and V are as shown in formula (5) to formula (8):

[0031]

[0032]

[0033]

[0034]

[0035] Among them, B Ak3 is the susceptance of the compensation branch of the third harmonic of phase A, B Bk3 is the susceptance of the compensation branch of the third harmonic of phase B, B Ck3 is the susceptance of the compensation branch of the third harmonic of phase C, is the third harmonic voltage of phase A, is the third harmonic voltage of phase B, is the third harmonic voltage of phase C, B A is the susceptance of phase A load, B B is the susceptance of the B phase load, B C is the susceptance of phase C load, GA is the conductance of phase A load, G B is the conductivity of the B phase load, G C is the conductivity of phase C load, G N is the conductivity of the neutral line, B N is the susceptance of the neutral line;

[0036] 3-3) Input the load and neutral line impedance parameters estimated in step (1) into formula (3)-formula (8), and optimize a set of inductors and capacitors to minimize the objective function.

[0037] Furthermore, in step (4), the resonant frequency of the compensation branch is used as a constraint condition, specifically including:

[0038] 4-1) Two constraints for avoiding resonance are used; the two constraints for avoiding resonance are specifically the constraint shown in formula (9) and the constraint shown in formula (10);

[0039] The constraints shown in formula (9) are as follows:

[0040]

[0041] Where ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n1 is the upper limit of harmonic order, and the value of n1 is less than 2;

[0042] The constraints shown in formula (10) are as follows:

[0043]

[0044] ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n2 is the lower limit of harmonic order, and the value of n2 is greater than 1; the values ​​of n1 and n2 can be defined according to engineering requirements;

[0045] 4-2) Substituting the compensation parameters of the corresponding compensation branch calculated in the above step (3) into the two constraints for avoiding resonance in step (4), and performing the operation of step 4-3) according to whether the compensation parameters meet the constraints;

[0046] 4-3) If the inductance and capacitance meet the constraints, the compensation parameters that meet the constraints are connected to the three-phase four-wire unbalanced system for compensation; if the compensation parameters do not meet the constraints, the calculation of step (3) is repeated, and after obtaining the new compensation parameters, they are substituted into the constraints of step (4) until the compensation parameters meet the constraints.

[0047] Beneficial effects of the present invention:

[0048] The present invention considers the influence of the capacitor branch on the harmonic amplification of the system, establishes a compensation branch, and combines it with the equality constraint of its fundamental wave parameter, proposes a calculation method for the capacitance and inductance parameters of each compensation branch, when voltage distortion occurs due to the third harmonic, the established compensation branch is connected to the system, and the inequality constraint is performed in the optimization solution, and finally the compensation of the unbalanced system of the three-phase four-wire system under the asymmetric voltage distortion is realized, the harm of the third harmonic to the three-phase four-wire power supply system is reduced, and harmonic amplification and resonance phenomenon will not be caused. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Attached Figure 1 It is a schematic flow chart of the method of the present invention. DETAILED DESCRIPTION

[0050] A method for compensating an unbalanced system of a three-phase four-wire system under asymmetric voltage distortion, the method comprising the following steps:

[0051] (1) Estimate the impedance parameters of the load and neutral line based on the monitored values;

[0052] (2) Construct a compensation branch consisting of an inductor and a capacitor connected in series, and establish a relationship expression between the inductor, the capacitor, and the susceptance of the compensation branch;

[0053] (3) Taking the harmonic current on the secondary side of the transformer as the objective function, the objective function is minimized by calculating the compensation parameters of the compensation branch;

[0054] (4) The resonant frequency of the compensation branch is used as a constraint condition to ensure that the compensation branch will not have resonance problems. The compensation branch formed by the inductor and capacitor that meet the constraint conditions is connected to the three-phase four-wire unbalanced system for compensation.

[0055] The monitoring value includes the fundamental current of phase A B-phase fundamental current C phase fundamental current A phase fundamental voltage B-phase fundamental voltage C phase fundamental voltage A phase third harmonic current Phase A third harmonic voltage B phase third harmonic current B phase third harmonic voltage C phase third harmonic current Phase C third harmonic voltage Fundamental zero sequence current Third harmonic zero sequence current

[0056] The impedance parameters of the load and the neutral line include the conductance G of the neutral line. N , the neutral line susceptance B N , the conductivity G of phase A load A , the susceptance of phase A load B A , the conductivity G of the B phase load B , the susceptance of phase B load B , the conductivity G of phase C load C , the susceptance of phase C load is B C .

[0057] The step (1) estimates the impedance parameters of the load and the neutral line according to the monitored values, specifically including: B-phase fundamental current C phase fundamental current A phase fundamental voltage B-phase fundamental voltage C phase fundamental voltage A phase third harmonic current Phase A third harmonic voltage B phase third harmonic current B phase third harmonic voltage C phase third harmonic current Phase C third harmonic voltage Fundamental zero sequence current Third harmonic zero sequence current The relationship between is used to obtain a complex equation, and the impedance parameters of the load and the neutral line are estimated by the corresponding monitoring values ​​to reduce the error in the compensation parameter calculation process. The complex equation is specifically shown in formula (1):

[0058]

[0059] In the formula, is the fundamental current of phase A, is the fundamental current of phase B, is the fundamental current of phase C, is the fundamental voltage of phase A, is the fundamental voltage of phase B, is the fundamental voltage of phase C, is the third harmonic current of phase A, is the third harmonic voltage of phase A, is the third harmonic current of phase B, is the third harmonic voltage of phase B, is the third harmonic current of phase C, is the third harmonic voltage of phase C, G N is the conductivity of the neutral line, B N is the susceptance of the neutral line, is the fundamental zero-sequence current, is the third harmonic zero sequence current, G A is the conductance of phase A load, B A is the susceptance of phase A load; G B is the conductivity of the B phase load, B B is the susceptance of the B phase load; G C is the conductivity of the C phase load, B C is the susceptance of phase C load.

[0060] The step (2) constructs a compensation branch composed of an inductor and a capacitor connected in series, and establishes a relationship expression between the inductor, the capacitor in the compensation branch and the susceptance of the compensation branch, which specifically includes the following steps:

[0061] 1) Establishing a compensation branch under the third harmonic, wherein the compensation branch is composed of an inductor and a capacitor connected in series;

[0062] 2) Taking the inductance and capacitance of the compensation branch as the input quantities to be input, and the susceptance of the compensation branch as the quantity to be calculated, the susceptance of the compensation branch is calculated through the input quantities to be input.

[0063] The compensation branch established in step (2) can effectively avoid the problem of harmonic amplification at high frequencies.

[0064] The compensation branch includes a compensation branch for the third harmonic of phase A, a compensation branch for the third harmonic of phase B, and a compensation branch for the third harmonic of phase C; the inductance and capacitance of the compensation branch include an inductance L of the compensation branch for the third harmonic of phase A. A , capacitor C of the compensation branch of the third harmonic of phase A A , the inductance L of the compensation branch of the third harmonic of phase B B , the capacitor C of the compensation branch of the third harmonic of phase B B , the inductance L of the compensation branch of the third harmonic of phase C C , the capacitor C of the compensation branch of the third harmonic of phase C C The susceptance of the compensation branch includes the susceptance B of the compensation branch of the third harmonic of phase A Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 .

[0065] The third harmonic compensation branch of phase A, the third harmonic compensation branch of phase B, and the third harmonic compensation branch of phase C are respectively composed of corresponding inductors and capacitors connected in series.

[0066] The inductance and capacitance of the compensation branch are used as the input quantities to be input, and the susceptance of the compensation branch is used as the quantity to be calculated. The susceptance of the compensation branch is calculated by the input quantities to be input. Specifically, the inductance L of the compensation branch of the third harmonic of phase A is calculated. A , capacitor C of the compensation branch of the third harmonic of phase AA , the inductance L of the compensation branch of the third harmonic of phase B B , the capacitor C of the compensation branch of the third harmonic of phase B B , the inductance L of the compensation branch of the third harmonic of phase C C , the capacitor C of the compensation branch of the third harmonic of phase C C is the input quantity; the susceptance B of the compensation branch of the third harmonic of phase A is calculated by formula (2): Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 :

[0067]

[0068] Where ω is the angular frequency, L A is the inductance of the compensation branch of the third harmonic of phase A, C A is the capacitance of the compensation branch of the third harmonic of phase A, L B is the inductance of the compensation branch of the third harmonic of phase B, C B is the capacitance of the compensation branch of the third harmonic of phase B, L C is the inductance of the compensation branch of the third harmonic of phase C, C C B is the capacitance of the compensation branch of the third harmonic of phase C; Ak3 is the susceptance of the compensation branch of the third harmonic of phase A; B Bk3 is the susceptance of the compensation branch of the third harmonic of phase B; Ck3 is the susceptance of the compensation branch of the third harmonic of phase C.

[0069] The step (3) takes the harmonic current on the secondary side of the transformer as the objective function, and minimizes the objective function by calculating the compensation parameters of the compensation branch. Specifically, it includes establishing a relationship between the objective function and the network parameters under the third harmonic of each phase under the voltage distortion unbalance system, and inputting the impedance parameters of the load and neutral line estimated in step (1) according to the MATLAB computing platform, and optimizing the inductance and capacitance of the compensation branch to minimize the objective function.

[0070] The compensation parameters of the compensation branch include the inductance and capacitance of the compensation branch of the A phase third harmonic connected in series, the inductance and capacitance of the compensation branch of the B phase third harmonic connected in series, and the inductance and capacitance of the compensation branch of the C phase third harmonic connected in series.

[0071] The step (3) takes the harmonic current on the secondary side of the transformer as the objective function and minimizes the objective function by calculating the compensation parameters of the compensation branch, which specifically includes the following steps:

[0072] 3-1) The harmonic current on the secondary side of the A-phase transformer, the harmonic current on the secondary side of the B-phase transformer, and the harmonic current on the secondary side of the C-phase transformer are taken as the objective function, as shown in the following formula (3):

[0073]

[0074] in, is the harmonic current on the secondary side of the A-phase transformer, is the harmonic current on the secondary side of the B-phase transformer, is the harmonic current on the secondary side of the C-phase transformer;

[0075] 3-2) Establish the calculation formula of harmonic current and network parameters on the secondary side of the transformer in the three-phase four-wire voltage distortion unbalanced system; among them, the susceptance B of the compensation branch of the third harmonic of phase A is taken as Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 is the quantity to be determined, and the third harmonic voltage of phase A is B phase third harmonic voltage Phase C third harmonic voltage Susceptance of phase A load B A , Susceptance of phase B load B 、C phase load susceptance B C , Conductivity G of phase A load A , the conductivity G of the B phase load B , the conductivity G of phase C load C , the conductivity of the neutral line G N 、Neutral line susceptance B N is a known quantity; specifically, as shown in formula (4) to formula (8):

[0076]

[0077] Wherein, V is the parameter containing the third harmonic voltage; Z1, Z2, and Z3 are the parameters of the three-phase four-wire unbalanced system. Z1, Z2, Z3, and V are as shown in formula (5) to formula (8):

[0078]

[0079]

[0080]

[0081]

[0082] Among them, B Ak3 is the susceptance of the compensation branch of the third harmonic of phase A, B Bk3is the susceptance of the compensation branch of the third harmonic of phase B, B Ck3 is the susceptance of the compensation branch of the third harmonic of phase C, is the third harmonic voltage of phase A, is the third harmonic voltage of phase B, is the third harmonic voltage of phase C, B A is the susceptance of phase A load, B B is the susceptance of the B phase load, B C is the susceptance of phase C load, G A is the conductance of phase A load, G B is the conductivity of the B phase load, G C is the conductivity of phase C load, G N is the conductivity of the neutral line, B N is the susceptance of the neutral line;

[0083] 3-3) Input the load and neutral line impedance parameters estimated in step (1) into formula (3)-formula (8), and optimize a set of inductors and capacitors to minimize the objective function.

[0084] The network parameters include the susceptance B of the compensation branch of the third harmonic of phase A Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 、A phase load susceptance B A , Susceptance of phase B load B 、C phase load susceptance B C , Conductivity G of phase A load A , the conductivity G of the B phase load B , the conductivity G of phase C load C , the conductivity of the neutral line G N 、Neutral line susceptance B N .

[0085] The susceptance B of the compensation branch of the third harmonic of phase A in the compensation branch Ak3 , the susceptance B of the compensation branch of the third harmonic of phase B Bk3 , the susceptance B of the compensation branch of the third harmonic of phase C Ck3 The inductance and capacitance in each compensation branch vary with each other. Each specific set of inductance and capacitance in each compensation branch determines the harmonic current on the secondary side of a transformer. According to the MATLAB computing platform, the impedance parameters of the load and neutral line estimated in step (1) are input to optimize a set of inductance and capacitance to minimize the objective function.

[0086] In the step (4), the resonant frequency of the compensation branch is used as a constraint condition, which specifically includes:

[0087] 4-1) Two constraints for avoiding resonance are used; the two constraints for avoiding resonance are specifically the constraint shown in formula (9) and the constraint shown in formula (10);

[0088] The constraints shown in formula (9) are as follows:

[0089]

[0090] Where ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n1 is the upper limit of harmonic order, and the value of n1 is less than 2;

[0091] The constraints shown in formula (10) are as follows:

[0092]

[0093] ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n2 is the lower limit of harmonic order, and the value of n2 is greater than 1; the values ​​of n1 and n2 can be defined according to engineering requirements;

[0094] 4-2) Substituting the compensation parameters of the corresponding compensation branch calculated in the above step (3) into the two constraints for avoiding resonance in step (4), and performing the operation of step 4-3) according to whether the compensation parameters inductance and capacitance meet the constraints;

[0095] 4-3) If the inductance and capacitance meet the constraints, the compensation parameters of the inductance and capacitance that meet the constraints are connected to the three-phase four-wire unbalanced system for compensation; if the compensation parameters do not meet the constraints, the calculation of step (3) is repeated, and after obtaining the new compensation parameters, they are substituted into the constraints of step (4) until the compensation parameters of the inductance and capacitance meet the constraints.

[0096] The present invention preferably uses the MATLAB computing platform to input the G estimated in step (1) N , B N , G A , B A , G B , B B , G C , B C , optimize the inductance and capacitance of the third harmonic compensation branch of phase A, phase B, and phase C, substitute the obtained inductance and capacitance into formula (2) to obtain the corresponding susceptance of the third harmonic compensation branch of phase A, phase B, and phase C, and combine formula (3-8) to obtain That is to say, the solution of the objective function is completed.

[0097] The present invention can accurately solve the inductance and capacitance of each compensation branch through optimization, and the calculation result can avoid harmonic amplification caused by the existence of the capacitive compensation branch and avoid the influence of harmonic current on the system; the present invention is suitable for calculating the parameters of the passive compensation network of a three-phase four-wire unbalanced system with asymmetric voltage distortion, and can realize compensation in the case of voltage distortion and asymmetric system without causing harmonic amplification and resonance phenomenon.

Claims

1. A method for compensating an unbalanced three-phase four-wire system under asymmetric voltage distortion, characterized in that The following steps are involved: Step (1) estimating impedance parameters of the load and the neutral line according to the monitored values; Step (2) constructing a compensation branch consisting of an inductor and a capacitor connected in series, and establishing a relationship expression between the inductor, the capacitor and the susceptance of the compensation branch; Step (3) takes the harmonic current on the secondary side of the transformer as the objective function and minimizes the objective function by calculating the compensation parameters of the compensation branch; Step (4) takes the resonant frequency of the compensation branch as a constraint condition, and connects the compensation branch formed by the inductance and capacitance that meet the constraint condition to the three-phase four-wire unbalanced system for compensation; The monitoring values ​​include A-phase fundamental current, B-phase fundamental current, C-phase fundamental current, A-phase fundamental voltage, B-phase fundamental voltage, C-phase fundamental voltage, A-phase third harmonic current, A-phase third harmonic voltage, B-phase third harmonic current, B-phase third harmonic voltage, C-phase third harmonic current, C-phase third harmonic voltage, fundamental zero-sequence current, third harmonic zero-sequence current; The step (1) estimates the impedance parameters of the load and the neutral line according to the monitoring values, specifically comprising: obtaining a complex equation through the relationship between the fundamental wave current of phase A, the fundamental wave current of phase B, the fundamental wave current of phase C, the fundamental wave voltage of phase A, the fundamental wave voltage of phase B, the fundamental wave voltage of phase C, the third harmonic current of phase A, the third harmonic voltage of phase A, the third harmonic current of phase B, the third harmonic voltage of phase B, the third harmonic current of phase C, the third harmonic voltage of phase C, the fundamental zero-sequence current, and the third harmonic zero-sequence current, and estimating the impedance parameters of the load and the neutral line according to the corresponding monitoring values, wherein the complex equation is specifically shown in formula (1): In the formula, is the fundamental current of phase A, is the fundamental current of phase B, is the fundamental current of phase C, is the fundamental voltage of phase A, is the fundamental voltage of phase B, is the fundamental voltage of phase C, is the third harmonic current of phase A, is the third harmonic voltage of phase A, is the third harmonic current of phase B, is the third harmonic voltage of phase B, is the third harmonic current of phase C, is the third harmonic voltage of phase C, G N is the conductivity of the neutral line, B N is the susceptance of the neutral line, is the fundamental zero-sequence current, is the third harmonic zero sequence current, G A is the conductance of phase A load, B A is the susceptance of phase A load; G B is the conductivity of the B phase load, B B is the susceptance of phase B load; G C is the conductivity of phase C load, B C is the susceptance of phase C load; The step (3) takes the harmonic current on the secondary side of the transformer as the objective function and minimizes the objective function by calculating the compensation parameters of the compensation branch, which specifically includes the following steps: 3-1) The harmonic current on the secondary side of the A-phase transformer, the harmonic current on the secondary side of the B-phase transformer, and the harmonic current on the secondary side of the C-phase transformer are taken as the objective function, as shown in the following formula (3): in, is the harmonic current on the secondary side of the A-phase transformer, is the harmonic current on the secondary side of the B-phase transformer, is the harmonic current on the secondary side of the C-phase transformer; 3-2) Establish the calculation formula of harmonic current and network parameters of the secondary side of the transformer in the three-phase four-wire voltage distortion unbalanced system; Among them, the susceptance of the compensation branch of the third harmonic of phase A, the susceptance of the compensation branch of the third harmonic of phase B, and the susceptance of the compensation branch of the third harmonic of phase C are the quantities to be determined, and the third harmonic voltage of phase A, the third harmonic voltage of phase B, the third harmonic voltage of phase C, the susceptance of the load of phase A, the susceptance of the load of phase B, the susceptance of the load of phase C, the conductance of the load of phase A, the conductance of the load of phase B, the conductance of the load of phase C, the conductance of the neutral line, and the susceptance of the neutral line are the known quantities; Specifically, as shown in formula (4) to formula (8): Wherein, V is the parameter containing the third harmonic voltage; Z1, Z2, and Z3 are the parameters of the three-phase four-wire unbalanced system. Z1, Z2, Z3, and V are as shown in formula (5) to formula (8): Among them, B Ak3 is the susceptance of the compensation branch of the third harmonic of phase A, B Bk3 is the susceptance of the compensation branch of the third harmonic of phase B, B Ck3 is the susceptance of the compensation branch of the third harmonic of phase C, is the third harmonic voltage of phase A, is the third harmonic voltage of phase B, is the third harmonic voltage of phase C, B A is the susceptance of phase A load, B B is the susceptance of the B phase load, B C is the susceptance of phase C load, G A is the conductance of phase A load, G B is the conductivity of the B phase load, G C is the conductivity of phase C load, G N is the conductance of the neutral line, B N is the susceptance of the neutral line; 3-3) Input the load and neutral line impedance parameters estimated in step (1) into formula (3)-formula (8), and optimize a set of inductors and capacitors to minimize the objective function.

2. The method for compensating an unbalanced three-phase four-wire system under asymmetric voltage distortion according to claim 1 is characterized in that The impedance parameters of the load and the neutral line include the conductance of the neutral line, the susceptance of the neutral line, the conductance of the A-phase load, the susceptance of the A-phase load, the conductance of the B-phase load, the susceptance of the B-phase load, the conductance of the C-phase load, and the susceptance of the C-phase load.

3. The method for compensating an unbalanced three-phase four-wire system under asymmetric voltage distortion according to claim 1 is characterized in that The step (2) constructs a compensation branch composed of an inductor and a capacitor connected in series, and establishes a relationship expression between the inductor, the capacitor in the compensation branch and the susceptance of the compensation branch, which specifically includes the following steps: 1) Establishing a compensation branch under the third harmonic, wherein the compensation branch is composed of an inductor and a capacitor connected in series; 2) Taking the inductance and capacitance of the compensation branch as the input quantities to be input, and the susceptance of the compensation branch as the quantity to be calculated, the susceptance of the compensation branch is calculated through the input quantities to be input.

4. The method for compensating an unbalanced three-phase four-wire system under asymmetric voltage distortion according to claim 3 is characterized in that The compensation branch includes a compensation branch for the third harmonic of phase A, a compensation branch for the third harmonic of phase B, and a compensation branch for the third harmonic of phase C; the inductance and capacitance of the compensation branch include the inductance of the compensation branch for the third harmonic of phase A, the capacitance of the compensation branch for the third harmonic of phase A, the inductance of the compensation branch for the third harmonic of phase B, the capacitance of the compensation branch for the third harmonic of phase B, the inductance of the compensation branch for the third harmonic of phase C, and the capacitance of the compensation branch for the third harmonic of phase C; the susceptance of the compensation branch includes the susceptance of the compensation branch for the third harmonic of phase A, the susceptance of the compensation branch for the third harmonic of phase B, and the susceptance of the compensation branch for the third harmonic of phase C.

5. The method for compensating an unbalanced three-phase four-wire system under asymmetric voltage distortion according to claim 3, characterized in that The inductance and capacitance of the compensation branch are taken as the input quantities to be input, and the susceptance of the compensation branch is taken as the quantity to be calculated. The susceptance of the compensation branch is calculated through the input quantities. Specifically, the inductance of the compensation branch of the third harmonic of phase A, the capacitance of the compensation branch of the third harmonic of phase A, the inductance of the compensation branch of the third harmonic of phase B, the capacitance of the compensation branch of the third harmonic of phase B, the inductance of the compensation branch of the third harmonic of phase C, and the capacitance of the compensation branch of the third harmonic of phase C are taken as the input quantities to be input; the susceptance of the compensation branch of the third harmonic of phase A, the susceptance of the compensation branch of the third harmonic of phase B, and the susceptance of the compensation branch of the third harmonic of phase C are calculated through formula (2): Where ω is the angular frequency, L A is the inductance of the compensation branch of the third harmonic of phase A, C A is the capacitance of the compensation branch of the third harmonic of phase A, L B is the inductance of the compensation branch of the third harmonic of phase B, C B is the capacitance of the compensation branch of the third harmonic of phase B, L C is the inductance of the compensation branch of the third harmonic of phase C, C C B is the capacitance of the compensation branch of the third harmonic of phase C; Ak3 is the susceptance of the compensation branch of the third harmonic of phase A; B Bk3 is the susceptance of the compensation branch of the third harmonic of phase B; Ck3 is the susceptance of the compensation branch of the third harmonic of phase C.

6. The method for compensating an unbalanced system of a three-phase four-wire system under asymmetric voltage distortion according to claim 1 is characterized in that: In the step (4), the resonant frequency of the compensation branch is used as a constraint condition, which specifically includes: 4-1) Two constraints for avoiding resonance are used; the two constraints for avoiding resonance are specifically the constraint shown in formula (9) and the constraint shown in formula (10); The constraints shown in formula (9) are as follows: Where ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n1 is the upper limit of harmonic order, and the value of n1 is less than 2; The constraints shown in formula (10) are specifically: ω is the angular frequency, L p The inductance that should be substituted into the corresponding compensation branch, C p is the capacitance to be substituted into the corresponding compensation branch, n2 is the lower limit of harmonic order, and the value of n2 is greater than 1; the values ​​of n1 and n2 are defined according to engineering requirements; 4-2) Substituting the compensation parameters of the corresponding compensation branch calculated in the above step (3) into the two constraints for avoiding resonance in step (4), and performing the operation of step 4-3) according to whether the compensation parameters meet the constraints; 4-3) If the inductance and capacitance meet the constraints, the compensation parameters that meet the constraints are connected to the three-phase four-wire unbalanced system for compensation; if the compensation parameters do not meet the constraints, the calculation of step (3) is repeated, and after obtaining the new compensation parameters, they are substituted into the constraints of step (4) until the compensation parameters meet the constraints.

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