A method for calculating voltage sensitivity considering the coupling characteristics of load voltage and power

Abstract

The present invention discloses a method for calculating voltage sensitivity considering the coupling characteristics of load voltage and power, which comprises the following steps: S1: Start the node voltage sensitivity calculation program; S2: Construct a linearized power flow model based on fixed-point iteration to obtain an analytical expression of the node voltage with respect to the node load injection power and the slack node voltage; S3: Consider the voltage-power coupling characteristics to obtain an analytical expression of the node voltage considering the voltage-power coupling characteristics; S4: Calculate the voltage sensitivity of the PQ nodes; S5: Calculate the voltage sensitivity of the slack node. The voltage sensitivity calculation method provided by the present invention can calculate the voltage sensitivity in real time when the system operating state or parameters change, and considers the load voltage-power coupling characteristics. At the same time, the voltage sensitivity can also be extended from the PQ nodes to the slack node.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system voltage sensitivity calculation, and particularly relates to a voltage sensitivity calculation method considering the load voltage-power coupling characteristic. Background Art

[0002] Voltage sensitivity describes the influence of node injection power on node voltage, establishes a linear relationship between node voltage and node power change, can greatly reduce the computational complexity of advanced applications, and is widely used in power system applications such as real-time voltage optimization. Traditionally, voltage sensitivity is obtained by inverting the Jacobian matrix of the system power flow equation. However, whenever the system operating state changes, it is necessary to re-establish the Jacobian matrix, resulting in a large computational burden; at the same time, this method is only applicable to PQ type nodes and cannot obtain the voltage sensitivity of slack nodes. On the other hand, existing voltage sensitivity calculation methods only consider the characteristics of the power network, assume that loads are all constant power loads, and ignore the influence of the load voltage-power coupling characteristic. The load voltage-power coupling characteristic enables the load power to respond to the node voltage change, and this change interacts with the influence of the load power on the node voltage, which will affect the voltage sensitivity calculation.

[0003] With the gradual development of power system advanced applications towards real-time and refined, and considering the increasingly complex load characteristics, there is an urgent need for a method that can consider the influence of the load voltage-power coupling characteristic and achieve high-precision analytical calculation of voltage sensitivity to help improve the calculation efficiency of power system advanced applications. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide a voltage sensitivity calculation method considering the load voltage-power coupling characteristic. When the system operating state or parameters change, the voltage sensitivity can be calculated in real time, and the load voltage-power coupling characteristic is considered. At the same time, the voltage sensitivity can also be extended from PQ nodes to slack nodes.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A voltage sensitivity calculation method considering the load voltage-power coupling characteristic includes the following steps:

[0007] S1: Start the node voltage sensitivity calculation program;

[0008] S2: Construct a linearized power flow model based on fixed-point iteration to obtain an analytical expression of node voltage with respect to node load injection power and slack node voltage;

[0009] S3: Considering the voltage-power coupling characteristic, divide the node load power into a constant-power component and a constant-impedance component, represent the constant-impedance component of the power with the node equivalent impedance, modify the node admittance matrix and the node injection power matrix of the system, and combine with the node voltage analytical expression obtained in step S2 to obtain the node voltage analytical expression considering the voltage-power coupling characteristic;

[0010] S4: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the PQ node voltage sensitivity;

[0011] S5: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the voltage sensitivity of the slack node.

[0012] Further, in step S2, the following steps are included:

[0013] S2.1: For a typical distribution network with 1 slack node and N PQ nodes, according to the relationship between current, voltage, and power, the system power flow is shown in equations (1) and (2):

[0014]

[0015] Where, represents the conjugate matrix of x; diag(x) represents a diagonal matrix with the elements of matrix x as its diagonal elements; x T represents the transpose matrix of x; S0 is the node injection power of the slack node; S is the node injection power of the PQ nodes, S = (S1, S2, S3, ···, S N ) T ; V0 is the voltage phasor of the slack node; V is the voltage phasor of the PQ nodes, V = (V1, V2, V3, ···, V N ) T ; I0 is the node injection current of the slack node; I is the node injection current of the PQ nodes, I = (I1, I2, I3, ···, I N ) T ; Y is the node admittance matrix of the system;

[0016] S2.2: Further divide the Y matrix according to whether it is the root node:

[0017]

[0018] In the formula, Y 00 is the self-admittance of the root node;

[0019] S2.3: Use equations (1)-(3) to organize and obtain the distribution network node voltage calculation model, as shown in equation (4):

[0020]

[0021] wherein,

[0022] S2.4: For any operating state S° that satisfies the power flow, use Equation (5) to iteratively calculate the voltage,

[0023]

[0024] S2.5: Adopt a linear approximation method based on a single fixed-point iteration. Through a single-step iteration, construct a linearized model of the node voltage nonlinear model with respect to the reference power flow point: Select the latest operating point V° of the system as the reference power flow point. When the operating state changes, the node power is updated to S, and use Equation (6) to obtain the node voltage V through a single-step iteration:

[0025]

[0026] wherein, A is jointly determined by the line parameters and the reference power flow point; W is jointly determined by the line parameters and the slack node voltage;

[0027] Further, step S3 includes the following steps:

[0028] S3.1: According to the load voltage-power coupling characteristic coefficient, divide the node load power into a constant power component and a constant impedance component, as shown in Equations (7) and (8);

[0029] P L,P = P L,0 (1 - CVRfac / 2) (7)

[0030] P L,Z = P L,0 (CVRfac / 2) (8)

[0031] wherein, P L,P and P L,Z are respectively the constant power component and the constant impedance component of the node active power, and CVRfac is the load voltage-power coupling characteristic coefficient;

[0032] S3.2: For the constant power component of the load, the original linearized power flow method can be used for processing; for the power of the constant impedance component of the load, it is represented by the node equivalent impedance, as shown in Equation (9):

[0033] Z L = (V 0 ) 2 / (P L,Z + jQ L,Z ) (9)

[0034] In the formula, Z L is the equivalent impedance of the constant impedance component, and P L,Z and Q L,Z are respectively the constant impedance components of the active and reactive powers of the nodes;

[0035] S3.3: Use Equations (10) and (11) to correct the node admittance matrix and the node injection power matrix of the system, and combine with the node voltage analytical expression obtained in Step S2 to obtain the node voltage analytical expression considering the voltage-power coupling characteristic.

[0036]

[0037] Further, Step S4 is specifically: Calculate the voltage sensitivity of the PQ nodes by using the node voltage analytical expression considering the voltage-power coupling characteristic obtained in Step S3. The voltage sensitivity of the PQ nodes is the partial derivative of the node voltage with respect to the node injection power, as shown in Equations (12) and (13);

[0038]

[0039] In the formula, V is the node voltage matrix without the slack node, V = (V1, V2, V3, ···, V N ) T ; P and Q are respectively the active and reactive power matrices of the nodes without the slack node, P = (P1, P2, P3, ···, P N ) T , Q = (Q1, Q2, Q3, ···, Q N ) T .

[0040] Further, Step S5 is specifically: Calculate the voltage sensitivity of the slack node by using the node voltage analytical expression considering the voltage-power coupling characteristic obtained in Step S3. The voltage sensitivity of the slack node is:

[0041]

[0042] In the formula, V0 is the voltage of the slack node.

[0043] Compared with the prior art, the voltage sensitivity calculation method considering the load voltage-power coupling characteristic provided by the present invention has the following beneficial effects:

[0044] The voltage sensitivity calculation method considering the load voltage-power coupling characteristic provided by the present invention constructs a linearized power flow model based on fixed-point iteration, obtains an analytical expression of the nodal voltage with respect to the nodal load injection power and the slack nodal voltage, and can analytically calculate the voltage sensitivities of PQ nodes and slack nodes. Compared with the existing voltage sensitivity calculation methods, the present invention firstly realizes the analytical calculation of voltage sensitivity, improves the calculation speed of voltage sensitivity; meanwhile, the present invention considers the load voltage-power characteristic, and the calculated voltage sensitivity takes into account the influence of nodal injection power on nodal voltage and the influence of nodal voltage on nodal injection power, which is more in line with the actual operation conditions of the power system; in addition, the present invention extends the voltage sensitivity from PQ nodes to slack nodes, realizing the full-coverage calculation of nodal voltage sensitivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The present invention will be further described in detail below with reference to the drawings.

[0046] Figure 1 is a flowchart of the voltage sensitivity calculation method considering the load voltage-power coupling characteristic provided by the present invention;

[0047] Figure 2 is a comparison schematic diagram of the linearized power flow model based on single fixed-point iteration and other models in the present invention;

[0048] Figure 3 is a schematic diagram of equivalent modeling of the constant impedance component of the load. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The present invention will be further described below with reference to the embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0050] Please refer to Figure 1 , Figure 1 is a flowchart of the voltage sensitivity calculation method considering the load voltage-power coupling characteristic provided by the present invention.

[0051] The voltage sensitivity calculation method considering the load voltage-power coupling characteristic provided by the present invention includes the following steps:

[0052] S1: Start the nodal voltage sensitivity calculation program;

[0053] S2: Construct a linearized power flow model based on fixed-point iteration, and obtain an analytical expression of the nodal voltage with respect to the nodal load injection power and the slack nodal voltage;

[0054] S3: Considering the voltage-power coupling characteristic, divide the node load power into a constant-power component and a constant-impedance component, represent the constant-impedance component of the power with the node equivalent impedance, modify the node admittance matrix and the node injection power matrix of the system, and combine with the node voltage analytical expression obtained in step S2 to obtain the node voltage analytical expression considering the voltage-power coupling characteristic;

[0055] S4: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the PQ node voltage sensitivity;

[0056] S5: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the voltage sensitivity of the slack node.

[0057] Among them, in step S1, when the operator needs to update the node voltage sensitivity, start the calculation of the node voltage sensitivity.

[0058] In step S2, construct a linearized power flow model based on fixed-point iteration to obtain the analytical expression of the node voltage with respect to the node load injection power and the slack node voltage, which specifically includes the following steps:

[0059] For a typical distribution network with 1 slack node (usually the root node, i.e., node 0) and N PQ nodes, according to the relationship between current, voltage, and power, the system power flow is shown in equations (1) and (2):

[0060]

[0061] Among them, represents the conjugate matrix of x; diag(x) represents a diagonal matrix with the elements of matrix x as the diagonal elements; x T represents the transpose matrix of x; S0 is the node injection power of the slack node; S is the node injection power of the PQ nodes, S = (S1, S2, S3, ···, S N ) T ; V0 is the voltage phasor of the slack node; V is the voltage phasor of the PQ nodes, V = (V1, V2, V3, ···, V N ) T ; I0 is the node injection current of the slack node; I is the node injection current of the PQ nodes, I = (I1, I2, I3, ···, I N ) T ; Y is the node admittance matrix of the system;

[0062] S2.2: Further divide the Y matrix according to whether it is the root node:

[0063]

[0064] In the formula, Y00 is the self - admittance of the root node;

[0065] S2.3: Using equations (1) - (3), the node voltage calculation model of the distribution network is sorted out and shown in equation (4):

[0066]

[0067] In the formula,

[0068] S2.4: The node voltage calculation model shown in equation (4) has an obvious iterative function property. For any operating state S° that satisfies the power flow, using equation (5) to iteratively calculate the voltage, the voltage will converge to a unique solution.

[0069]

[0070] S2.5: To reduce the number of iterative steps, a linear approximation method based on single - step fixed - point iteration is adopted. Through single - step iteration, a linearized model of the node voltage nonlinear model with respect to the reference power flow point is constructed: Select the latest operating point V° of the system as the reference power flow point. When the operating state changes, the node power is updated to S, and the node voltage V is obtained by single - step iteration using equation (6):

[0071]

[0072] In the formula, A is jointly determined by the line parameters and the reference power flow point; is jointly determined by the line parameters and the slack node voltage.

[0073] The power flow model shown in equation (6) considers that the node voltage is composed of a current - source part (i.e., ) and a voltage - source part (i.e., W).

[0074] The loads, capacitors, and new energy in the PQ nodes can be modeled as equivalent current sources with respect to the nodes they are connected to, and the slack node can be modeled as an equivalent voltage source. The power flow model shown in equation (6) uses the superposition principle to calculate the node voltage. When considering the influence of the current source, the voltage source of the slack node is short - circuited to the ground, and the node voltage is affected by each equivalent current source, showing as the current - source part; while when considering the influence of the voltage source, all node equivalent current sources are removed, and the node voltage is only determined by the voltage source of the slack node.

[0075] When the line topology, network parameters, and reference power flow point are determined, A and W can be calculated offline. A and W construct a linearized relationship between the node voltage and the node injection power. Equation (6) is essentially a relationship between two power flow points of the system (0, W) and (S o , V oThe linear interpolation between them is essentially different from the standardized linearization method of the tangent plane at a certain feasible solution, such as the first-order Taylor expansion, which enables a single fixed-point iteration to maintain a high accuracy in a larger interval, as Figure 2 shown Figure 2 is a schematic diagram comparing the linearized power flow model based on a single fixed-point iteration with other models in the present invention.

[0076] The above power flow model is based on the constant power load assumption. In fact, different loads all have a certain voltage-power coupling characteristic, and the load power is closely related to the node voltage amplitude.

[0077] In step S3, considering the voltage-power coupling characteristic, the node load power is divided into a constant power component and a constant impedance component. The constant impedance component of the power is represented by the node equivalent impedance, and the node admittance matrix and the node injection power matrix of the system are corrected. Combining with the node voltage analytical expression obtained in step S2, the node voltage analytical expression considering the voltage-power coupling characteristic is obtained, specifically as follows:

[0078] S3.1: According to the load voltage-power coupling characteristic coefficient, the node load power is divided into a constant power component and a constant impedance component, as shown in formulas (7) and (8);

[0079] P L,P = P L,0 (1 - CVRfac / 2) (7)

[0080] P L,Z = P L,0 (CVRfac / 2) (8)

[0081] In the formula, P L,P and P L,Z are respectively the constant power component and the constant impedance component of the node active power, and CVRfac is the load voltage-power coupling characteristic coefficient;

[0082] S3.2: For the constant power component of the load, the original linearized power flow method can be used for processing; for the power of the constant impedance component of the load, since its power is proportional to the square of the voltage, it is represented by the node equivalent impedance, as shown in formula (9):

[0083] Z L = (V 0 ) 2 / (P L,Z + jQ L,Z ) (9)

[0084] In the formula, Z L is the equivalent impedance of the constant impedance component, and P L,Z and Q L,Z are respectively the constant impedance components of the node active and reactive powers;

[0085] S3.3: Modify the nodal admittance matrix and nodal injection power matrix of the system using Equations (10) and (11), as Figure 3 shown Figure 3 is the schematic diagram of the equivalent modeling of the constant impedance component of the load. Combining the nodal voltage analytical expression obtained in Step S2, the nodal voltage analytical expression considering the voltage-power coupling characteristic is obtained, and thus the nodal voltage can be calculated considering the load voltage-power coupling characteristic.

[0086]

[0087] In Step S4, use the nodal voltage analytical expression considering the voltage-power coupling characteristic obtained in Step S3 to calculate the voltage sensitivity of the PQ nodes.

[0088] PQ nodes are common node types in the distribution network, such as constant power loads. When the load power changes, the equivalent injected current of its node changes, affecting the voltages of other nodes through the line voltage drop. The power flow model shown in Equation (6) considers that the nodal voltage is composed of both a current source part and a voltage source part. After the voltage source is grounded and short-circuited, the current source part is the effect of the equivalent current of each node on the system voltage, which has the same physical meaning as the voltage sensitivity of the PQ node type. Therefore, for a distribution network with 1 slack node and N PQ nodes, using the linearized voltage model as shown in Equation (6), the voltage sensitivity of the PQ node is the partial derivative of the nodal voltage with respect to the nodal injection power, as shown in Equations (12) and (13);

[0089]

[0090] where V is the nodal voltage matrix without the slack node, V = (V1, V2, V3, ···, V N ) T ; P and Q are the nodal active and reactive power matrices without the slack node, P = (P1, P2, P3, ···, P N ) T , Q = (Q1, Q2, Q3, ···, Q N ) T .

[0091] Obtain system parameters and the latest power flow operating point V°, and then the voltage sensitivity of each nodal voltage with respect to the nodal injection power can be analytically calculated through Equations (12) and (13).

[0092] In Step S5, use the nodal voltage analytical expression considering the voltage-power coupling characteristic obtained in Step S3 to calculate the voltage sensitivity of the slack node.

[0093] The voltage of the slack node determines the system reference voltage. When the voltage of the slack node changes, the voltages of the entire system will change accordingly. In the power flow model shown in Equation (6), the voltage source part describes the influence of the equivalent voltage source of the slack node on the voltages of each node and can be used to calculate the voltage sensitivity of the slack node. Using the linearized voltage model shown in Equation (6) and combining with real-time measurement data, the voltage sensitivities of other nodes with respect to the slack node are shown in Equation (14).

[0094]

[0095] In the formula, V0 is the voltage of the slack node.

[0096] The present invention provides a method for calculating voltage sensitivity considering the load voltage-power coupling characteristic. When the system operation state or parameters change, the voltage sensitivity can be calculated in real time, and the load voltage-power coupling characteristic is considered. At the same time, the voltage sensitivity can also be extended from the PQ node to the slack node.

[0097] At this point, those skilled in the art should recognize that although multiple exemplary embodiments of the present invention have been shown and described in detail herein, many other variations or modifications that conform to the principles of the present invention can still be directly determined or derived from the content disclosed in the present invention without departing from the spirit and scope of the present invention. Therefore, the scope of the present invention should be understood and determined to cover all these other variations or modifications.

Claims

1. A method for calculating voltage sensitivity considering the coupling characteristics of load voltage and power, characterized in that The method includes the following steps: S1: Start the node voltage sensitivity calculation program; S2: Construct a linearized power flow model based on fixed-point iteration to obtain an analytical expression of the node voltage with respect to the node load injection power and the slack node voltage; S3: Considering the voltage-power coupling characteristic, divide the node load power into a constant power component and a constant impedance component, represent the constant impedance component of the power with the node equivalent impedance, correct the node admittance matrix and the node injection power matrix of the system, and combine the node voltage analytical expression obtained in step S2 to obtain a node voltage analytical expression considering the voltage-power coupling characteristic; S4: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the PQ node voltage sensitivity; S5: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the voltage sensitivity of the slack node; In the said step S2, it includes the following steps: S2.1: For a typical distribution network with 1 slack node and N PQ nodes, according to the relationship between current, voltage and power, the system power flow is shown in formulas (1) and (2): Among them, represents the conjugate matrix of x; diag(x) represents the diagonal matrix with the elements of matrix x as its diagonal elements; x T represents the transpose matrix of x; S0 is the nodal injection power of the slack node; S is the nodal injection power of the PQ node, S = (S1, S2, S3, ···, S N ) T ; V0 is the voltage phasor of the slack node; V is the voltage phasor of the PQ node, V = (V1, V2, V3, ···, V N ) T ; I0 is the nodal injection current of the slack node; I is the nodal injection current of the PQ node, I = (I1, I2, I3, ···, I N ) T ; Y is the nodal admittance matrix of the system; S2.2: Further divide the Y matrix according to whether it is a root node: where Y 00 is the self-admittance of the root node; S2.3: Use formulas (1)-(3) to organize and obtain a distribution network node voltage calculation model, as shown in formula (4): In the formula, S2.4: For any operating state S° that satisfies the power flow, use formula (5) to iteratively calculate the voltage; S2.5: Adopt a linear approximation method based on single fixed-point iteration. Through single-step iteration, construct a linearized model of the node voltage nonlinear model with respect to the reference power flow point: Select the latest operating point V° of the system as the reference power flow point. When the operating state changes, the node power is updated to S, and the node voltage V is obtained by single-step iteration using formula (6); In the formula, A is jointly determined by the line parameters and the reference power flow point; W is jointly determined by the line parameters and the slack bus voltage.

2. The voltage sensitivity calculation method considering the load voltage power coupling characteristic according to claim 1, wherein Step S3 includes the following steps: S3.1: According to the load voltage-power coupling characteristic coefficient, divide the node load power into a constant power component and a constant impedance component, as shown in formulas (7) and (8); P L,P = P L,0 (1 - CVRfac / 2)(7) P L,Z = P L,0 (CVRfac / 2) (8) where P L,P and P L,Z are the constant power component and the constant impedance component of the active power of the node respectively, and CVRfac is the load voltage power coupling characteristic coefficient; S3.2: For the constant power component of the load, the original linearized power flow method can be used for processing; for the power of the constant impedance component of the load, it is represented by the node equivalent impedance, as shown in formula (9); Z L = (V 0 ) 2 / (P L,Z + jQ L,Z ) (9) Where, Z L is the equivalent impedance of the constant impedance component, P L,Z and Q L,Z are the constant impedance components of the active and reactive powers of the node respectively; S3.3: Use formulas (10) and (11) to correct the node admittance matrix and the node injection power matrix of the system, and combine the node voltage analytical expression obtained in step S2 to obtain a node voltage analytical expression considering the voltage-power coupling characteristic:

3. A method for calculating voltage sensitivity considering the load voltage power coupling characteristic according to claim 2, characterized in that Step S4 is specifically: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the PQ node voltage sensitivity. The PQ node voltage sensitivity is the partial derivative of the node voltage with respect to the node injection power, as shown in formulas (12) and (13); wherein, V is the node voltage matrix without slack nodes, V = (V1, V2, V3, ···, V N ) T ; P and Q are the node active power and reactive power matrices without slack nodes respectively, P = (P1, P2, P3, ···, P N ) T , Q = (Q1, Q2, Q3, ···, Q N ) T .

4. A method for calculating voltage sensitivity considering the load voltage power coupling characteristic according to claim 3, characterized in that Step S5 is specifically: Use the node voltage analytical expression considering the voltage-power coupling characteristic obtained in step S3 to calculate the voltage sensitivity of the slack node. The voltage sensitivity of the slack node is: wherein, V0 is the voltage of the slack node.

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