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

Abstract

The invention discloses a DC power distribution network load flow calculation method based on a damping factor, and belongs to the technical field of load flow calculation, the initial value of a node voltage is set as a voltage rated value, the active power unbalance of each node is calculated, and a load flow Jacobian matrix and a load flow Hessian matrix of the node power unbalance to the node voltage are calculated; a target function is established with the minimum sum of squares of node power unbalance, and a Hessian matrix is calculated according to a first-order partial derivative and a second-order partial derivative of the target function to node voltage; calculating a voltage correction value according to the Hessian matrix so as to obtain a new voltage iteration value; whether convergence occurs is judged, if yes, the voltage iteration value is the final output node voltage, and the calculation speed is guaranteed while the load flow calculation convergence is improved.

Description

Technical Field

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

[0002] In recent years, distributed generations such as photovoltaic and emerging loads such as electric vehicles have developed rapidly due to their advantages such as flexibility and environmental friendliness. The development of DC-type distributed power sources such as photovoltaic and DC-type loads such as electric vehicle chargers and data centers has made the DC characteristics of the power sources and loads in the distribution system increasingly obvious. Compared with the AC distribution network, the DC distribution network based on the voltage source converter (VSC) can improve the acceptance capacity of distributed power sources and electric vehicles, improve the power quality, reduce the system power loss, and increase the power supply capacity, and has become an important direction for the development of the distribution system.

[0003] Power flow calculation is a basic tool for analyzing the operating state of a power system. The main methods for power flow calculation of a distribution network include the forward-backward substitution power flow calculation method and the Newton-Raphson power flow calculation method. Among them, the forward-backward substitution method is easy to implement and has a fast calculation speed, and is suitable for radial distribution networks. The Newton-Raphson method has a longer calculation time and its convergence is affected by factors such as line parameters. However, the Newton-Raphson method can effectively handle distribution systems containing loop networks and distributed power sources, and its applicable scenarios are more extensive.

[0004] Compared with the traditional AC distribution network, the DC distribution network usually adopts the method of multi-power source power supply and loop network operation, and the node types are affected by various control strategies of VSCs. Referring to the power flow calculation method of the AC distribution network, the power flow calculation methods of the DC distribution network mainly include two categories: the forward-backward substitution method and the Newton-Raphson method. In the power flow calculation of the DC distribution network based on the forward-backward substitution method, Wu Hongbin et al. used the node incidence matrix to determine the power splitting points of the DC distribution network, divided the DC distribution network into several radial networks, and then used the forward-backward substitution method to perform power flow calculation. However, this method is affected by the loop network and the number of power sources in the DC distribution network. Considering that the Newton-Raphson method can effectively handle multi-power source power supply and loop network structure, the power flow calculation method of the DC distribution network based on the Newton-Raphson method has been widely studied. Wang Xiaoxiao et al. established a unified unbalanced equation of converter power and voltage considering various control modes of the converter, and gave the voltage correction equation of the Newton-Raphson method. Wang W et al. aimed at the problem of no voltage-constant slack node in the DC distribution network with full voltage droop control. First, it was assumed that the outlet voltage of the VSC with the largest capacity remained unchanged, and the Newton-Raphson method was used for power flow calculation. According to the power flow calculation results, the outlet voltage of the VSC was corrected, and the above iterative process was repeated until the node voltages of all nodes met the convergence conditions. Liu Qi et al. constructed an equivalent branch model to simulate the droop control, provided a slack node for the power flow calculation of the droop control DC distribution network, and thus proposed a Newton method for the power flow calculation of the DC distribution network based on the equivalent branch model. In the above power flow calculation of the DC distribution network based on the Newton-Raphson method, when the line resistance is large and the load is heavy, the offset of the actual node voltage from the rated value is large, and there may be problems such as an increase in the number of iterations or even the power flow not converging to the accurate value. Summary of the Invention

[0005] Aiming at the above problems existing in the prior art, the present invention proposes a power flow calculation method for a DC distribution network based on a damping factor, which is reasonably designed, solves the deficiencies of the prior art, and has good effects.

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

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

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

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

[0010] Step 4: Establish an objective function with the minimum sum of squares of the node power imbalance, and calculate the improved Hessian matrix according to the first-order partial derivative and the second-order partial derivative of the objective function with respect to the node voltage;

[0011] Step 5: Calculate the voltage correction value based on the improved Hessian matrix, so as to obtain a new voltage iteration value;

[0012] Step 6: Determine whether the power flow calculation converges. If it does not converge, return to Step 2 to recalculate; if it converges, the voltage iteration value in Step 5 is the final output node voltage.

[0013] Further, the specific content of Step 2 is as follows:

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

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

[0016] P i =-P i,load , i ∈ M L (1);

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

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

[0019]

[0020] In the formula: U i,ref and P i,ref are the reference voltage and reference power of the VSC at node i respectively, k i is the droop coefficient of the VSC at node i, and k i takes a positive value; for the VSC adopting voltage level control, its droop coefficient is infinite; for the VSC adopting power grading control, the droop coefficient is 0;

[0021] The unbalance of node active power is:

[0022]

[0023] Further, in Step 3, according to the first-order partial derivative of the node active power unbalance 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] where k represents node k, and k = 1, 2,..., n.

[0028] Furthermore, the specific content of step 4 is as follows:

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

[0030]

[0031] When the convergence condition of the power flow equation is satisfied, 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 of node j is expressed as:

[0033]

[0034] The second-order partial derivative of the objective function with respect to the voltage of node j, that is, 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 of node j are further simplified as:

[0037]

[0038]

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

[0040]

[0041] Furthermore, the specific content of step 5 is as follows:

[0042] The voltage correction amount is:

[0043]

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

[0045] Denote Then the voltage iteration value U (m+1) is:

[0046] U (m+1) = U (m) + ΔU (m) (13);

[0047] where U (m) is the node voltage value in the m-th iteration.

[0048] The beneficial technical effects brought by the present invention:

[0049] The present invention establishes the node power equation of the DC distribution network, derives the Jacobian matrix and Hessian matrix of the node power imbalance with respect to the node voltage; constructs a power flow calculation optimization model with the minimum sum of squares of node power imbalances as the objective, and proposes a Hessian matrix method for power flow calculation based on damping correction factors and acceleration correction factors, which 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 iteration times and better convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flowchart of a DC distribution network power flow calculation method based on a damping factor in the present invention;

[0051] Figure 2 is a schematic diagram of the DC distribution system in Embodiment 1; DETAILED DESCRIPTION OF THE INVENTION

[0052] The following further describes the specific embodiments of the present invention with reference to specific embodiments:

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

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

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

[0056] Regarding the distributed power source as a negative load, the nodes of the DC distribution network 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 the DC distribution network, the active power injection P i at node i is:

[0058]

[0059] Where: G ij is the real part of the element in the \(i\)-th row and \(j\)-th column of the nodal admittance matrix, \(U i and \(U j are the voltages of node \(i\) and node \(j\) respectively, and \(n\) is the number of bus 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\in M L (2);

[0062] Where: \(P i,load is the load power at node \(i\), and the equivalent load power of the distributed power source 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 the VSC at node \(i\) respectively, \(k i is the droop coefficient of the VSC at node \(i\), and \(k i takes a positive value; for the VSC using voltage level control, its droop coefficient is infinite; for the VSC using power grading control, the droop coefficient is 0;

[0066] The unbalance of the nodal active power is:

[0067]

[0068] Step 3: Calculate the Jacobian matrix of the nodal power unbalance with respect to the nodal voltage;

[0069] According to the first-order partial derivative of the nodal active power unbalance with respect to the nodal 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 nodal power deviation with respect to the nodal voltage is obtained, and the power flow Hessian matrix \(H\) is expressed as:

[0072]

[0073] where \(k\) represents node \(k\), \(k = 1,2,\cdots,n\).

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

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

[0076] For the unconstrained optimization problem:

[0077] min f(x) x ∈ R n (7);

[0078] where: x represents the optimization variable.

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

[0080]

[0081]

[0082] x (k+1) = x (k) + Δx (k) (10);

[0083] where: is the first partial derivative of the objective function with respect to the optimization variable; is the second partial derivative of the objective function with respect to the optimization variable, i.e., the Hessian matrix; x (k+1) is the value of the optimization variable at the (k + 1)-th iteration calculation, x (k) is the value of the optimization variable at the k-th iteration calculation, Δx (k) is the correction amount of the optimization variable at the k-th iteration calculation, R is the damping correction factor, the damping factor is a constant, usually taken as 1; g(x (k) ) is the acceleration correction factor.

[0084] At the k-th iteration calculation, g(x (k) ) is iteratively calculated M times, where the first iteration calculation is:

[0085]

[0086] During the iteration process, the expression for the m-th iteration calculation is:

[0087]

[0088] In the DC distribution network power flow calculation, the node voltages are taken as the optimization variables, and the minimum of the sum of squares of all node active power imbalances in formula (4) is used as the optimization objective function:

[0089]

[0090] When the convergence condition of the power flow equation is satisfied, 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 of node j is expressed as:

[0092]

[0093] The second-order partial derivative of the objective function with respect to the voltage of node j, that is, the equation form of the Hessian matrix, is expressed as:

[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 of node j are further simplified as:

[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, so as to obtain the new voltage iteration value;

[0101] The voltage correction amount is:

[0102]

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

[0104] Denote Then the voltage iteration value U (m+1) is:

[0105] U (m+1) = U (m) + ΔU (m) (20);

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

[0107] Step 6: Judge whether the power flow calculation converges. If it does not converge, return to Step 2 to recalculate; if it converges, the voltage iteration value in Step 5 is the final output node voltage.

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

[0109] Example 1

[0110] Taking Figure 2 a DC distribution system as an example for simulation analysis, the system operates in a hand-in-hand ring network, the medium-voltage side voltage level is ±10 kV, the line resistance is 0.3417 Ω / km, and the line lengths and load parameters are as Figure 2 shown, where a negative load point power indicates that the node is a photovoltaic power generation.

[0111] The power flow calculation method proposed in the present invention is used for power flow calculation, and the convergence accuracy of the power imbalance is 10 -10 p.u. The test is carried out on the Matlab 2016b simulation platform, and the computer configuration is Intel(R) Core(TM) i5-8350U CPU. The damping factor in the improved Hessian matrix method is taken as 1. The calculation speeds and iteration numbers of the traditional Newton-Raphson power flow calculation method, the traditional Hessian matrix method, and the improved Hessian matrix method proposed in the present invention are shown in Table 1. Different droop coefficients are selected in different cases. Compared with the Newton-Raphson power flow calculation method and the traditional Hessian matrix method, the proposed improved Hessian matrix method converges stably and evenly under different droop coefficients, and the calculation speed is of the same order of magnitude as that of the Newton-Raphson power flow calculation method, indicating that the proposed improved Hessian matrix method can effectively ensure the calculation speed while improving the convergence of power flow calculations.

[0112] Table 1 Comparison table of calculation speeds and iteration numbers 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 those skilled in the art within the essence of the present invention should also fall within the protection scope 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 with the minimum sum of squares of node power imbalance, and calculate the improved Hessian matrix based on the first-order partial derivative and second-order partial derivative 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.

2. The method for calculating the DC distribution network power flow based on the damping factor according to claim 1, characterized in that: The step 2 is specifically as follows: Distributed 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, k i is the droop coefficient of the 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 of the node is:

3. The method for calculating the DC distribution network power flow based on damping factor according to claim 2 is characterized in that: 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: Here, k represents node k, k=1, 2, ..., n.

4. The method for calculating the DC distribution network power flow based on damping factor according to claim 3 is characterized in that: 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 of 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:

5. A method for calculating the DC distribution network power flow based on damping factor according to claim 4, characterized in that: The step 5 is specifically as follows: The voltage correction 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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