A DC distribution network power flow calculation method based on damping factor

Abstract

The present invention discloses a DC distribution network power flow calculation method based on a damping factor, which belongs to the technical field of power flow calculation. The method comprises the following steps: setting an initial value of a node voltage as a voltage rated value, calculating an active power imbalance of each node, and calculating a power flow Jacobian matrix and a power flow Hessian matrix of the node power imbalance with respect to the node voltage; establishing an objective function by minimizing the sum of squares of the node power imbalance, calculating a Hessian matrix based on first-order partial derivatives and second-order partial derivatives of the objective function with respect to the node voltage; calculating a voltage correction value based on the Hessian matrix, thereby obtaining a new voltage iteration value; and judging whether convergence has occurred. If convergence has occurred, the voltage iteration value is the final output voltage of each node, thereby ensuring the calculation speed while improving the convergence of the power flow calculation.

Description

Technical Field

[0001] The present invention belongs to the technical field of power flow calculation, and in particular relates to a method for calculating power flow in a DC distribution network based on a damping factor. Background Art

[0002] In recent years, distributed generation technologies such as photovoltaics and emerging loads such as electric vehicles have rapidly developed due to their flexibility and environmental friendliness. The growth of DC-based distributed power sources like photovoltaics and DC-based loads such as electric vehicle charging stations and data centers has led to an increasingly pronounced DC characteristic of both sources and loads in distribution systems. Compared to AC distribution networks, DC distribution networks based on voltage source converters (VSCs) offer increased capacity for distributed power sources and electric vehicles, improved power quality, reduced system power losses, and increased power supply capacity, making them a key development direction for distribution systems.

[0003] Power flow calculation is a fundamental tool for analyzing the operating status of power systems. The main methods for calculating power flow in distribution networks include forward-backward substitution and Newton-Raphson. The forward-backward substitution method is easy to implement and fast, making it suitable for radial distribution networks. The Newton-Raphson method takes a long time to calculate, and its convergence is affected by factors such as line parameters. However, the Newton-Raphson method is effective for distribution systems containing ring networks and distributed generation (DGs), making it more applicable in a wider range of scenarios.

[0004] Compared to traditional AC distribution networks, DC distribution networks typically utilize multiple power sources and operate in a ring network, and the node types are affected by various VSC control strategies. Drawing on AC distribution network power flow calculation methods, DC distribution network power flow calculation methods currently primarily include the forward-backward substitution method and the Newton-Raphson method. In a DC distribution network power flow calculation based on the forward-backward substitution method, Wu Hongbin et al. used a node correlation matrix to determine the power distribution points of the DC distribution network, divided the DC distribution network into several radial networks, and then used the forward-backward substitution method to calculate the power flow. However, this method is affected by the number of ring networks and power sources in the DC distribution network. Given its ability to effectively handle multiple power sources and ring network structures, DC distribution network power flow calculation methods based on the Newton-Raphson method have been widely studied. Wang Xiaoxiao et al. established a unified unbalance equation for converter power and voltage, considering various converter control methods, and provided a voltage correction equation for the Newton-Raphson method. To address the problem of no slack nodes with constant voltage in a DC distribution network with full voltage droop control, Wang W et al. first assumed that the outlet voltage of the largest VSC remained constant. They then used the Newton-Raphson method to calculate the power flow. The VSC outlet voltage was then corrected based on the calculated power flow results, and the iterative process was repeated until all node voltages met convergence criteria. Liu Qi et al. constructed an equivalent branch model to simulate droop control, providing slack nodes for the power flow calculation of a droop-controlled DC distribution network. Based on this, they proposed a Newton method for DC distribution network power flow calculation based on the equivalent branch model. In this Newton-Raphson method for DC distribution network power flow calculation, when the line resistance is large and the load is heavy, the actual node voltage deviates significantly from the rated value, potentially leading to an increased number of iterations and even failure of the power flow to converge to an accurate value. Summary of the Invention

[0005] In view of the above problems existing in the prior art, the present invention proposes a DC distribution network power flow calculation method based on damping factor, which has a reasonable design, solves the shortcomings of the prior art and has good effects.

[0006] A method for calculating a DC distribution network power flow based on a damping factor includes the following steps:

[0007] Step 1: Set the initial value of the node voltage to the voltage rating;

[0008] Step 2: Calculate the active power imbalance of each node;

[0009] Step 3: Calculate the power flow Jacobian matrix and power flow Hessian matrix of the node power imbalance to the node voltage;

[0010] Step 4: Establish an objective function based on minimizing the sum of squares of node power imbalances, and calculate the improved Hessian matrix based on the first-order and second-order partial derivatives of the objective function with respect to the node voltage.

[0011] Step 5: Calculate the voltage correction value according to the improved Hessian matrix to obtain a new voltage iteration value;

[0012] Step 6: Determine whether the power flow calculation has converged. If not, return to step 2 and recalculate. If converged, the voltage iteration value in step 5 is the final output voltage of each node.

[0013] Furthermore, the step 2 is specifically as follows:

[0014] Distributed power generation is regarded as a negative load, and the DC distribution network nodes are divided into load nodes and VSC nodes. The load node set is defined as M L =[1, 2, ..., h], the VSC node set is defined as M C =[h+1,h+2,…,n];

[0015] For the load node, the active injection power is:

[0016] P i =-P i,load , i∈M L (1);

[0017] Where: P i,load is the load power at node i, and the equivalent load power of the distributed generation is the negative value of its output power;

[0018] For the VSC node, the active injection power is:

[0019]

[0020] Where: U i,ref and P i,ref are the reference voltage and reference power of VSC at node i, respectively, i is the droop coefficient of VSC at node i, k i Take a positive value; for a VSC using voltage level control, the droop coefficient is infinite; for a VSC using power level control, the droop coefficient is 0;

[0021] The unbalanced amount of active power at the node is:

[0022]

[0023] Furthermore, in step 3, according to the first-order partial derivative of the node active power imbalance with respect to the node voltage in formula (3), the power flow Jacobian matrix J is expressed as:

[0024]

[0025] According to formula (4), the second-order partial derivative of the node power deviation with respect to the node voltage is obtained, and the power flow Hessian matrix is ​​expressed as:

[0026]

[0027] Here, k represents node k, k = 1, 2, ..., n.

[0028] Furthermore, the step 4 is specifically as follows:

[0029] In the DC distribution network power flow calculation, the voltage of each node is used as the optimization variable, and the minimum sum of the squares of the active power imbalance of all nodes in formula (3) is used as the optimization objective function:

[0030]

[0031] When the convergence condition of the power flow equation is met, the objective function value approaches 0;

[0032] According to formula (6), for any node j in the DC distribution network, the first-order partial derivative of the objective function with respect to the voltage at node j is expressed as:

[0033]

[0034] The second-order partial derivative of the objective function with respect to the voltage at node j, i.e., the equation form of the power flow Hessian matrix, is expressed as:

[0035]

[0036] According to the power flow Jacobian matrix (4) and the power flow Hessian matrix (5), the first-order partial derivative and the second-order partial derivative of the objective function with respect to the voltage at node j are further simplified as follows:

[0037]

[0038]

[0039] Therefore, the improved Hessian matrix is ​​specifically expressed as:

[0040]

[0041] Furthermore, the step 5 is specifically as follows:

[0042] The voltage correction amount is:

[0043]

[0044] in, is the voltage correction of the nth node in the mth iteration;

[0045] remember Then the voltage iteration value U (m+1) for:

[0046] U (m+1) =U (m) +ΔU (m) (13);

[0047] Among them, U (m) is the node voltage value in the mth iteration.

[0048] Beneficial technical effects brought about by the present invention:

[0049] The present invention establishes the node power equation of the DC distribution network, and derives the Jacobian matrix and Hessian matrix of the node power imbalance to the node voltage; constructs a power flow calculation optimization model with the goal of minimizing the sum of squares of node power imbalance, and proposes a Hessian matrix method for power flow calculation based on damping correction factor and acceleration correction factor. This method improves the convergence of power flow calculation while ensuring the calculation speed. Compared with the traditional Newton-Raphson power flow calculation method, the proposed power flow calculation method has fewer iterations and better convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a method for calculating DC distribution network power flow based on damping factor in the present invention;

[0051] Figure 2 Schematic diagram of the DC power distribution system in Example 1; DETAILED DESCRIPTION

[0052] The specific implementation of the present invention will be further described below with reference to specific embodiments:

[0053] A DC distribution network power flow calculation method based on damping factor, such as Figure 1 As shown, the following steps are included:

[0054] Step 1: Set the initial value of the node voltage to the voltage rating;

[0055] Step 2: Calculate the active power imbalance of each node;

[0056] Distributed power generation is regarded as a negative load, and the DC distribution network nodes are divided into load nodes and VSC nodes. The load node set is defined as M L =[1, 2, ..., h]. The VSC node set is defined as M C =[h+1,h+2,…,n];

[0057] Theoretically, in a DC distribution network, the active injection power P at node i is i for:

[0058]

[0059] Where: G ij is the real part of the element in the i-th row and j-th column of the node admittance matrix, U i and U j are the voltages of node i and node j respectively, and n is the number of busbar nodes in the DC distribution network;

[0060] In the actual process, for the load node, the active injection power is:

[0061] P i =-P i,load , i∈M L (2);

[0062] Where: P i,load is the load power at node i, and the equivalent load power of the distributed generation is the negative value of its output power;

[0063] For the VSC node, the active injection power is:

[0064]

[0065] Where: U i,ref and P i,ref are the reference voltage and reference power of VSC at node i, respectively, i is the droop coefficient of VSC at node i, k i Take a positive value; for a VSC using voltage level control, the droop coefficient is infinite; for a VSC using power level control, the droop coefficient is 0;

[0066] The unbalanced amount of active power at the node is:

[0067]

[0068] Step 3: Calculate the Jacobian matrix of node power imbalance versus node voltage;

[0069] According to the first-order partial derivative of the node active power imbalance with respect to the node voltage in formula (4), the power flow Jacobian matrix J is expressed as:

[0070]

[0071] According to formula (5), the second-order partial derivative of the node power deviation with respect to the node voltage is obtained, and the power flow Hessian matrix H is expressed as:

[0072]

[0073] Here, k represents node k, k = 1, 2, ..., n.

[0074] Step 4: Establish an objective function based on minimizing the sum of squares of node power imbalances, and calculate the improved Hessian matrix based on the first-order and second-order partial derivatives of the objective function with respect to the node voltage.

[0075] The basic principle of the Hessian matrix method with damping factor is:

[0076] For unconstrained optimization problems:

[0077] minf(x)x∈R n (7);

[0078] Where: x represents the optimization variable.

[0079] The iterative format for solving the problem using the Hessian matrix with damping factor is:

[0080]

[0081]

[0082] x (k+1) =x (k) +Δx (k) (10);

[0083] Where: is the first-order partial derivative of the objective function with respect to the optimization variable; is the second-order partial derivative of the objective function with respect to the optimization variable, i.e., the Hessian matrix; x (k+1) The value of the optimization variable when calculating the k+1th iteration, x (k) is the value of the optimized variable during the k-th iteration calculation, Δx (k) is the correction amount of the optimization variable in the kth iteration calculation, R is the damping correction factor, the damping factor is a constant, usually 1; g(x (k) ) is the acceleration correction factor.

[0084] In the kth iteration calculation, g(x (k) ) performs M iterations, where the first iteration is:

[0085]

[0086] During the iteration process, the calculation expression for the mth iteration is:

[0087]

[0088] In the DC distribution network power flow calculation, the voltage of each node is used as the optimization variable, and the minimum sum of the squares of the active power imbalance of all nodes in formula (4) is used as the optimization objective function:

[0089]

[0090] When the convergence condition of the power flow equation is met, the objective function value approaches 0;

[0091] According to formula (13), for any node j in the DC distribution network, the first-order partial derivative of the objective function with respect to the voltage at node j is expressed as:

[0092]

[0093] The second-order partial derivative of the objective function with respect to the voltage at node j, i.e., the Hessian matrix, is expressed in the form of an equation:

[0094]

[0095] According to the power flow Jacobian matrix (5) and the power flow Hessian matrix (6), the first-order partial derivative and the second-order partial derivative of the objective function with respect to the voltage at node j are further simplified as follows:

[0096]

[0097]

[0098] Therefore, the improved Hessian matrix is ​​specifically expressed as:

[0099]

[0100] Step 5: Calculate the voltage correction value according to the improved Hessian matrix to obtain a new voltage iteration value;

[0101] The voltage correction amount is:

[0102]

[0103] in, is the voltage correction of the nth node in the mth iteration;

[0104] remember Then the voltage iteration value U (m+1) for:

[0105] U (m+1) =U (m) +ΔU (m) (20);

[0106] Among them, U (m) is the node voltage value in the mth iteration.

[0107] Step 6: Determine whether the power flow calculation has converged. If not, return to step 2 and recalculate. If converged, the voltage iteration value in step 5 is the final output voltage of each node.

[0108] Compared to the Newton-Raphson method, the Hessian matrix method requires calculating the first- and second-order partial derivatives of the objective function with respect to the node voltage, resulting in a greater computational effort for each iteration. To improve the convergence of power flow calculations while maintaining computational speed, the traditional Newton-Raphson method is combined with the Hessian matrix method. When the node active power imbalance is greater than 0.001 pu, the Newton-Raphson method is used for power flow calculations. When the node active power imbalance is less than 0.001 pu, the Hessian matrix method is used for power flow calculations.

[0109] Example 1

[0110] by Figure 2 The DC distribution system is used as an example for simulation analysis. The system adopts a hand-in-hand ring network operation. The voltage level on the medium voltage side is ±10kV, the line resistance is 0.3417Ω / km, and the line length and load parameters are as follows: Figure 2 As shown in the figure, a negative value of the load point power indicates that the node is generating power from photovoltaic power.

[0111] The power flow calculation method proposed in this invention is used to calculate the power flow, and the convergence accuracy of power imbalance is 10 -10 pu, tested on a Matlab 2016b simulation platform using an Intel(R) Core(TM) i5-8350U CPU. The damping factor in the improved Hessian matrix method is set to 1. The computational speed and number of iterations for the traditional Newton-Raphson power flow calculation method, the traditional Hessian matrix method, and the improved Hessian matrix method proposed in this invention are shown in Table 1. Different droop coefficients are selected for different scenarios. Compared with the Newton-Raphson power flow calculation method and the traditional Hessian matrix method, the proposed improved Hessian matrix method achieves balanced and stable convergence under different droop coefficients, and its computational speed is on the same order of magnitude as that of the Newton-Raphson power flow calculation method. This demonstrates that the proposed improved Hessian matrix method can effectively guarantee computational speed while improving the convergence of power flow calculations.

[0112] Table 1 Comparison of calculation speed and number of iterations of different methods

[0113]

[0114] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for calculating the power flow of a DC distribution network based on a damping factor, characterized in that: The following steps are involved: Step 1: Set the initial value of the node voltage to the voltage rating; Step 2: Calculate the active power imbalance of each node; Step 3: Calculate the power flow Jacobian matrix and power flow Hessian matrix of node power imbalance to node voltage; Step 4: Establish an objective function based on minimizing the sum of squares of node power imbalances, and calculate the improved Hessian matrix based on the first-order and second-order partial derivatives of the objective function with respect to the node voltage. Step 5: Calculate the voltage correction value according to the improved Hessian matrix to obtain a new voltage iteration value; Step 6: Determine whether the power flow calculation has converged. If not, return to step 2 and recalculate. If converged, the voltage iteration value in step 5 is the final output voltage of each node. The step 2 is specifically as follows: Distributed power generation is regarded as a negative load, and the DC distribution network nodes are divided into load nodes and VSC nodes. The load node set is defined as M L =[1, 2, ..., h], the VSC node set is defined as M C =[h+1,h+2,…,n]; For the load node, the active injection power is: P i =-P i,load ,i∈M L (1); Where: P i,load is the load power at node i, and the equivalent load power of the distributed generation is the negative value of its output power; For the VSC node, the active injection power is: Where: U i,ref and P i,ref are the reference voltage and reference power of VSC at node i, respectively, i is the droop coefficient of VSC at node i, k i Take a positive value; for a VSC using voltage level control, the droop coefficient is infinite; for a VSC using power level control, the droop coefficient is 0; The unbalanced amount of active power at the node is: In step 3, according to the first-order partial derivative of the node active power imbalance with respect to the node voltage in formula (3), the power flow Jacobian matrix J is expressed as: According to formula (4), the second-order partial derivative of the node power deviation with respect to the node voltage is obtained, and the power flow Hessian matrix is ​​expressed as: Wherein, k represents node k, k = 1, 2, ..., n; The step 4 is specifically as follows: In the DC distribution network power flow calculation, the voltage of each node is used as the optimization variable, and the minimum sum of the squares of the active power imbalance of all nodes in formula (3) is used as the optimization objective function: When the convergence condition of the power flow equation is met, the objective function value approaches 0; According to formula (6), for any node j in the DC distribution network, the first-order partial derivative of the objective function with respect to the voltage at node j is expressed as: The second-order partial derivative of the objective function with respect to the voltage at node j, i.e., the equation form of the power flow Hessian matrix, is expressed as: According to the power flow Jacobian matrix (4) and the power flow Hessian matrix (5), the first-order partial derivative and the second-order partial derivative of the objective function with respect to the voltage at node j are further simplified as follows: Therefore, the improved Hessian matrix is ​​specifically expressed as:

2. A DC distribution network power flow calculation method based on damping factor according to claim 1, characterized in that: The step 5 is specifically as follows: The voltage correction amount is: in, is the voltage correction of the nth node in the mth iteration; remember Then the voltage iteration value U (m+1) for: U (m+1) =U (m) +ΔU (m) (13); Among them, U (m) is the node voltage value in the mth iteration.

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