A method for calculating zero positive and negative sequence coupling impedance of three-phase unbalanced RLC load

Abstract

The present invention discloses a method for calculating the zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load, which relates to the field of distribution network, and includes the following steps: 1. Listing the node impedance matrix of the three-phase unbalanced RLC load; 2. Setting six groups of three-phase asymmetric voltages, and obtaining the six groups of three-phase currents corresponding to the six groups of voltages added to the unbalanced RLC load; performing symmetrical component decomposition on the three-phase asymmetric voltages and currents corresponding to the above six groups, and then converting these symmetrical components into components under a synchronous rotating coordinate system; 3. Based on the relationship between the zero positive and negative sequence components of the above voltage and current dq, writing equations through Ohm's law, and obtaining the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load. The present invention fully considers the coupling impedance effect that is prevalent between different symmetrical components of the three-phase unbalanced RLC load, and avoids the error caused by the traditional method of only measuring the self-coupling impedance under a certain sequence component and ignoring the mutual coupling impedance effect.

Description

Technical Field

[0001] The invention relates to the field of power distribution networks, and in particular to a method for calculating zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load. Background Art

[0002] Power systems, especially distribution networks, often operate in a three-phase unbalanced state due to the uneven distribution of loads, causing imbalance in network current and voltage. For such systems, it is necessary to decompose the symmetrical components and then control the three components separately, which is the mainstream control solution at present. However, at present, there is a lack of a universal method to evaluate the impedance effect of RLC series or parallel loads in a symmetrical component system; common algorithms generally only use the voltage component divided by the current component under zero positive and negative three sequences, which only considers the self-impedance under each sequence and ignores the mutual impedance effect between sequences. A large amount of field measurement data indirectly confirms the existence of mutual impedance, and there is no effective quantitative method for this, which is related to the accuracy of control based on the symmetrical component method. Summary of the invention

[0003] The object of the present invention is to provide a method for calculating the zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A method for calculating zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load comprises the following steps:

[0006] 1. Write the node impedance matrix of the three-phase unbalanced RLC load;

[0007] Second, set six groups of three-phase asymmetric voltages, whose phase sequence remains unchanged (phase A leads phase B, phase B leads phase C), and these six groups of voltages should avoid linear correlation; calculate the six groups of three-phase currents corresponding to these six groups of voltages added to the unbalanced RLC load through the impedance matrix;

[0008] The above six groups of corresponding three-phase asymmetric voltages and currents are decomposed into symmetrical components respectively, and then these symmetrical components are further converted into components in a synchronous rotating coordinate system. After decomposition, a group of voltage or current will obtain six components, namely, zero-sequence d-axis component, zero-sequence q-axis component, positive-sequence d-axis component, positive-sequence q-axis component, negative-sequence d-axis component, and negative-sequence q-axis component;

[0009] 3. Assume that the RLC load is still an RLC load under the symmetrical component system, and therefore set the self-coupling resistance matrix and mutual coupling reactance matrix between the dq axes under this system, a total of four 3*3 matrices, involving 36 variables; based on the self-coupling resistance matrix and the mutual coupling reactance matrix, according to Ohm's law, write the relationship between the above voltage and current dq zero positive and negative sequence components, solve the equations, obtain the values ​​of 36 variables, and summarize the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load.

[0010] As a further solution of the present invention, the step 1 is specifically:

[0011] Step 1.1: Write the node impedance matrix of the three-phase unbalanced RLC load Z abc :

[0012]

[0013] In formula (1), Z mn ( m = a , b , c ; n = a , b , c ) is the self / mutual impedance of the three-phase circuit (self-impedance when m=n, mutual impedance when m≠n).

[0014] As a further solution of the present invention, the step 2 is specifically:

[0015] Step 2.1: Set 6 sets of linearly unrelated voltage vectors:

[0016]

[0017] The phase sequence of each set of voltage vectors should maintain the relationship that phase A leads phase B, and phase B leads phase C. Then, using Ohm's law, based on the impedance matrix, the six sets of three-phase current vectors generated by the six sets of voltage vectors added to the unbalanced RLC load are obtained:

[0018]

[0019] Where k is an integer ranging from 1 to 6;

[0020] Step 2.2: Transform the zero, positive and negative components of phase A:

[0021]

[0022] in, ， ， They are the zero-sequence, positive-sequence, and negative-sequence components of the A-phase voltage or current of the power grid, for The inverse matrix of is the transformation matrix for symmetrical decomposition of voltage or current:

[0023]

[0024] in, , j represents an imaginary unit;

[0025] Step 2.3: Transform the zero, positive and negative components of phase B of the three-phase unbalanced electrical quantity:

[0026]

[0027] in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the B-phase voltage or current of the power grid respectively;

[0028] Step 2.4: Transform the zero, positive and negative components of the C phase of the three-phase unbalanced electrical quantity:

[0029]

[0030] in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the C-phase voltage or current of the power grid respectively;

[0031] Step 2.5: Convert the symmetrical component expression of the three-phase electrical signal into a trigonometric function form. The converted trigonometric function form is as follows:

[0032]

[0033] in, is the voltage or current component in the form of trigonometric functions, , for The main angle at time 0 is calculated as follows: ;

[0034] Step 2.6: Convert the voltage or current zero-sequence component of phase A to The angle is reduced ,get , the dq component of the zero-sequence component of the electrical signal in the synchronous rotating coordinate system is obtained using the following formula:

[0035]

[0036] in, (t) is the d-axis component of the voltage or current zero-sequence component, (t) is the q-axis component of the voltage or current zero-sequence component, oh is the angular frequency, ω=2πf ,in, f is the AC power grid frequency, i for t=0 The angle at which the d-axis in the dq coordinate axis leads the a-axis in the three-phase stationary coordinate system at the moment, that is, the angle that the a-axis rotates counterclockwise to the d-axis position;

[0037] Step 2.7: Use the following formula to obtain the dq component of the positive sequence component of the electrical signal in the synchronous rotating coordinate system:

[0038]

[0039] in, (t) is the d-axis component of the voltage or current positive sequence component, (t) is the q-axis component of the voltage or current positive sequence component, (t) is the zero-axis component of the voltage or current positive sequence component;

[0040] Step 2.8: Use the following formula to obtain the dq component of the negative sequence component of the electrical signal in the synchronous rotating coordinate system:

[0041]

[0042] in, (t) is the d-axis component of the negative sequence component of voltage or current, (t) is the q-axis component of the negative sequence component of voltage or current, (t) is the zero-axis component of the negative-sequence component of voltage or current.

[0043] As a further solution of the present invention, the step three is specifically as follows: assuming that the RLC load is still an RLC load in a symmetrical component system, and therefore setting the self-coupling resistance matrix and the mutual coupling reactance matrix between the dq axes in this system (a total of four 3*3 matrices, involving 36 variables); based on the self-coupling resistance matrix and the mutual coupling reactance matrix, write the relationship between each group of voltage and current dq zero positive and negative sequence components according to Ohm's law:

[0044]

[0045] Among them, the above group , , , There are 6 equations provided, and a total of 36 variables need to be solved, so 6 sets of data are needed;

[0046] The above formula: Represents the coupling resistance between the zero and positive sequences of the d-axis, It represents the negative-sequence and zero-sequence coupling reactance of the q-axis to the d-axis. The meanings of other symbols are similar.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1) Set the self-coupling resistance matrix and the mutual coupling reactance matrix, write the correlation equations of multiple sets of voltages and currents on the three-phase asymmetric RLC load according to Ohm's law, and obtain the coupling impedance matrix under zero positive and negative sequence by solving it, which has high accuracy and simple calculation;

[0049] 2) Fully consider the mutual impedance effect of the RLC load to avoid the accuracy problem caused by the traditional method that only considers the self-impedance effect of each sequence. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] In an embodiment of the present invention, a method for calculating zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load includes the following steps:

[0052] 1. Write the node impedance matrix of the three-phase unbalanced RLC load;

[0053] Second, set six groups of three-phase asymmetric voltages, whose phase sequence remains unchanged (phase A leads phase B, phase B leads phase C), and these six groups of voltages should avoid linear correlation; calculate the six groups of three-phase currents corresponding to these six groups of voltages added to the unbalanced RLC load through the impedance matrix;

[0054] The above six groups of corresponding three-phase asymmetric voltages and currents are decomposed into symmetrical components respectively, and then these symmetrical components are further converted into components in a synchronous rotating coordinate system. After decomposition, a group of voltage or current will obtain six components, namely, zero-sequence d-axis component, zero-sequence q-axis component, positive-sequence d-axis component, positive-sequence q-axis component, negative-sequence d-axis component, and negative-sequence q-axis component;

[0055] 3. Assume that the RLC load is still an RLC load under the symmetrical component system, and therefore set the self-coupling resistance matrix and mutual coupling reactance matrix between the dq axes under this system, a total of four 3*3 matrices, involving 36 variables; based on the self-coupling resistance matrix and the mutual coupling reactance matrix, according to Ohm's law, write the relationship between the above voltage and current dq zero positive and negative sequence components, solve the equations, obtain the values ​​of 36 variables, and summarize the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load.

[0056] The step 1 is specifically as follows:

[0057] Step 1.1: Write the node impedance matrix of the three-phase unbalanced RLC load Z abc :

[0058]

[0059] In formula (1), Z mn ( m = a , b , c ; n = a , b , c ) is the self / mutual impedance of the three-phase circuit (self-impedance when m=n, mutual impedance when m≠n).

[0060] The step 2 is specifically as follows:

[0061] Step 2.1: Set 6 sets of linearly unrelated voltage vectors:

[0062]

[0063] The phase sequence of each set of voltage vectors should maintain the relationship that phase A leads phase B, and phase B leads phase C. Then, using Ohm's law, based on the impedance matrix, the six sets of three-phase current vectors generated by the six sets of voltage vectors added to the unbalanced RLC load are obtained:

[0064]

[0065] The value of k is an integer ranging from 1 to 6.

[0066] Step 2.2: Transform the zero, positive and negative components of phase A:

[0067]

[0068] in, ， ， They are the zero-sequence, positive-sequence, and negative-sequence components of the A-phase voltage or current of the power grid, for The inverse matrix of is the transformation matrix for symmetrical decomposition of voltage or current:

[0069]

[0070] in, , j represents an imaginary unit;

[0071] Step 2.3: Transform the zero, positive and negative components of phase B of the three-phase unbalanced electrical quantity:

[0072]

[0073] in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the B-phase voltage or current of the power grid respectively;

[0074] Step 2.4: Transform the zero, positive and negative components of the C phase of the three-phase unbalanced electrical quantity:

[0075]

[0076] in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the C-phase voltage or current of the power grid respectively;

[0077] Step 2.4: Convert the symmetrical component expression of the three-phase electrical signal into a trigonometric function form. The converted trigonometric function form is as follows:

[0078]

[0079] in, is the voltage or current component in the form of trigonometric functions, , for The main angle at time 0 is calculated as follows: ;

[0080] Step 2.6: Convert the voltage or current zero-sequence component of phase A to The angle is reduced ,get , the dq component of the zero-sequence component of the electrical signal in the synchronous rotating coordinate system is obtained using the following formula:

[0081]

[0082] in, (t) is the d-axis component of the voltage or current zero-sequence component, (t) is the q-axis component of the voltage or current zero-sequence component, oh is the angular frequency, ω=2πf ,in, f is the AC power grid frequency, i for t=0 The angle at which the d-axis in the dq coordinate axis leads the a-axis in the three-phase stationary coordinate system at the moment, that is, the angle that the a-axis rotates counterclockwise to the d-axis position;

[0083] Step 2.7: Use the following formula to obtain the dq component of the positive sequence component of the electrical signal in the synchronous rotating coordinate system:

[0084]

[0085] in, (t) is the d-axis component of the voltage or current positive sequence component, (t) is the q-axis component of the voltage or current positive sequence component, (t) is the zero-axis component of the voltage or current positive sequence component;

[0086] Step 2.8: Use the following formula to obtain the dq component of the negative sequence component of the electrical signal in the synchronous rotating coordinate system:

[0087]

[0088] in, (t) is the d-axis component of the negative sequence component of voltage or current, (t) is the q-axis component of the negative sequence component of voltage or current, (t) It is the zero-axis component of the negative-sequence component of voltage or current.

[0089] The step three is specifically as follows: assuming that the RLC load is still an RLC load in a symmetrical component system, and therefore setting the self-coupling resistance matrix and mutual coupling reactance matrix between the dq axes in this system (a total of four 3*3 matrices, involving 36 variables); based on the self-coupling resistance matrix and the mutual coupling reactance matrix, write the relationship between each group of voltage and current dq zero positive and negative sequence components according to Ohm's law:

[0090]

[0091] Among them, the above group , , , There are 6 equations provided, and a total of 36 variables need to be solved, so 6 sets of data are needed;

[0092] The above formula: Represents the coupling resistance between the zero and positive sequences of the d-axis, It represents the negative-sequence and zero-sequence coupling reactance of the q-axis to the d-axis. The meanings of other symbols are similar.

[0093] In summary, the present invention fully considers the coupling impedance effect commonly existing between different symmetrical components of the three-phase unbalanced RLC load, and avoids the error caused by the traditional method of only measuring the self-coupling impedance under a certain sequence component and ignoring the mutual coupling impedance effect.

[0094] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered exemplary and non-restrictive in all respects, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present invention.

[0095] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for calculating the zero positive and negative sequence coupling impedance of a three-phase unbalanced RLC load. It is characterized in that The steps include:

1. Write the node impedance matrix of the three-phase unbalanced RLC load; Second, set six groups of three-phase asymmetric voltages, whose phase sequence remains unchanged, that is, phase A leads phase B, and phase B leads phase C. These six groups of voltages should avoid linear correlation; calculate the six groups of three-phase currents corresponding to these six groups of voltages added to the unbalanced RLC load through the impedance matrix; The above six groups of corresponding three-phase asymmetric voltages and currents are decomposed into symmetrical components respectively, and then these symmetrical components are further converted into components in a synchronous rotating coordinate system. After decomposition, a group of voltage or current will obtain six components, namely, zero-sequence d-axis component, zero-sequence q-axis component, positive-sequence d-axis component, positive-sequence q-axis component, negative-sequence d-axis component, and negative-sequence q-axis component; 3. Assume that the RLC load is still an RLC load under the symmetrical component system, and therefore set the self-coupling resistance matrix and mutual coupling reactance matrix between the dq axes under this system, a total of four 3*3 matrices, involving 36 variables; based on the self-coupling resistance matrix and the mutual coupling reactance matrix, write the relationship between the above voltage and current dq zero positive and negative sequence components according to Ohm's law, solve the equation, obtain the values ​​of 36 variables, and summarize the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load; The step three is specifically as follows: assuming that the RLC load is still an RLC load in a symmetrical component system, and therefore setting the self-coupling resistance matrix and mutual coupling reactance matrix between the dq axes in this system, a total of four 3*3 matrices, involving 36 variables; based on the self-coupling resistance matrix and the mutual coupling reactance matrix, write the relationship between each group of voltage and current dq zero positive and negative sequence components according to Ohm's law: Among them, the above group , , , There are 6 equations provided, and a total of 36 variables need to be solved, so 6 sets of data are needed; The above formula: Represents the coupling resistance between the zero and positive sequences of the d-axis, It represents the negative-sequence and zero-sequence coupling reactance of the q-axis to the d-axis. The meanings of other symbols are similar.

2. The method for calculating the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load according to claim 1, It is characterized in that The step 1 is specifically as follows: Step 1.1: Write the node impedance matrix of the three-phase unbalanced RLC load Z abc : In formula (1), Z mn ( m = a , b , c ; n = a , b , c ) is the self / mutual impedance of the three-phase circuit. When m=n, it is self-impedance; when m≠n, it is mutual impedance.

3. The method for calculating the zero positive and negative sequence coupling impedance of the three-phase unbalanced RLC load according to claim 1, It is characterized in that The step 2 is specifically as follows: Step 2.1: Set 6 sets of linearly unrelated voltage vectors: The phase sequence of each set of voltage vectors should maintain the relationship that phase A leads phase B, and phase B leads phase C. Then, using Ohm's law, based on the impedance matrix, the six sets of three-phase current vectors generated by the six sets of voltage vectors added to the unbalanced RLC load are obtained: Where k is an integer ranging from 1 to 6; Step 2.2: Transform the zero, positive and negative components of phase A: in, ， ， They are the zero-sequence, positive-sequence, and negative-sequence components of the A-phase voltage or current of the power grid, for The inverse matrix of is the transformation matrix for symmetrical decomposition of voltage or current: in, , j represents an imaginary unit; Step 2.3: Transform the zero, positive and negative components of phase B of the three-phase unbalanced electrical quantity: in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the B-phase voltage or current of the power grid respectively; Step 2.4: Transform the zero, positive and negative components of the C phase of the three-phase unbalanced electrical quantity: in, ， ， They are the zero-sequence, positive-sequence and negative-sequence components of the C-phase voltage or current of the power grid respectively; Step 2.5: Convert the symmetrical component expression of the three-phase electrical signal into a trigonometric function form. The converted trigonometric function form is as follows: in, is the voltage or current component in the form of trigonometric functions, , for The main angle at time 0 is calculated as follows: ; Step 2.6: Convert the voltage or current zero-sequence component of phase A to The angle is reduced ,get , the dq component of the zero-sequence component of the electrical signal in the synchronous rotating coordinate system is obtained using the following formula: in, is the d-axis component of the voltage or current zero-sequence component, is the q-axis component of the voltage or current zero-sequence component, ω is the angular frequency, ω=2πf ,in, f is the AC power grid frequency, θ for t=0 The angle at which the d-axis in the dq coordinate axis leads the a-axis in the three-phase stationary coordinate system at the moment, that is, the angle that the a-axis rotates counterclockwise to the d-axis position; Step 2.7: Use the following formula to obtain the dq component of the positive sequence component of the electrical signal in the synchronous rotating coordinate system: in, (t) is the d-axis component of the voltage or current positive sequence component, (t) is the q-axis component of the voltage or current positive sequence component, (t) is the zero-axis component of the voltage or current positive sequence component; Step 2.8: Use the following formula to obtain the dq component of the negative sequence component of the electrical signal in the synchronous rotating coordinate system: in, (t) is the d-axis component of the negative sequence component of voltage or current, (t) is the q-axis component of the negative sequence component of voltage or current, (t) It is the zero-axis component of the negative-sequence component of voltage or current.

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