Multi-phase harmonic power flow optimization method considering new energy access

Abstract

The invention discloses a multi-phase harmonic power flow optimization method considering new energy access. The method comprises the following steps: step 1, constructing a target function of a multi-target optimal harmonic power flow model containing new energy; step 2, constructing constraint conditions of the multi-target optimal harmonic power flow model; 3, decoupling the multi-target optimal harmonic power flow model to obtain an optimal fundamental wave power flow sub-model and a quadratic programming sub-model; and 4, carrying out alternate iteration solution on the optimal fundamental wave power flow sub-model and the quadratic programming sub-model to obtain an optimal solution to realize multiphase harmonic power flow optimization. According to the method, the multiphase optimal harmonic power flow model can be quickly solved, the challenge of the non-convex optimal harmonic power flow model in calculation can be effectively handled and solved, and the solving efficiency is remarkably improved. And meanwhile, a good optimization effect is achieved, and network loss, voltage unbalance degree and harmonic distortion degree can be remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimization, and in particular to a multi-phase harmonic power flow optimization method considering the access of new energy sources. Background Art

[0002] The large-scale random access of renewable energy and the uneven distribution of loads have led to increasingly prominent power quality issues, with harmonics being one of the most prominent power quality issues. Harmonics not only cause sensitive equipment to malfunction or refuse to operate, but also cause broadband oscillations, causing renewable energy to disconnect from the grid. Excessive harmonic content has caused accidents such as the combustion of wind turbines in a wind farm and resonance of CRH380 series EMUs. Traditional optimal power flow models do not take harmonics into account, making it difficult to meet the needs of stable operation of renewable energy distribution networks.

[0003] However, the optimal harmonic power flow model that incorporates harmonic variables will lead to problems such as large amount of calculation and difficulty in solving. The current mainstream optimal harmonic power flow solution algorithms are divided into two categories: convex optimization methods and heuristic algorithms. The convex optimization method is to convert the optimal harmonic power flow model into a convex model such as semidefinite programming and second-order cone programming for solution. However, this algorithm solves the fundamental wave and harmonics together. As the number of nodes increases, the computational burden further increases, which may lead to a long solution time or difficulty in solving. This method cannot be applied to all optimal harmonic power flow models. Heuristic algorithms such as the non-dominated sorting genetic algorithm and the gray wolf optimization algorithm lack the guarantee of optimality and feasibility and have high computational requirements. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a multi-phase harmonic power flow optimization method taking into account the access of new energy.

[0005] The technical solution adopted by the present invention is:

[0006] A multiphase harmonic power flow optimization method considering the access of new energy sources comprises the following steps:

[0007] Step 1: Construct the objective function of the multi-objective optimal harmonic power flow model with new energy. The objective function includes the power loss, harmonic distortion and voltage imbalance of the distribution network.

[0008] Step 2: Construct the constraints of the multi-objective optimal harmonic power flow model, which include fundamental power balance constraints, harmonic current balance constraints, and new energy power constraints;

[0009] Step 3: Decouple the multi-objective optimal harmonic power flow model to obtain the optimal fundamental power flow sub-model and the quadratic programming sub-model;

[0010] Step 4: Alternately iterate and solve the optimal fundamental power flow sub-model and the quadratic programming sub-model in step 3 to obtain the optimal solution to achieve multi-phase harmonic power flow optimization.

[0011] Furthermore, the objective function F in step 1 is:

[0012] min F=α1f PL +α2f PVUR +α3f THD

[0013] Where: α1, α2, α3 are weight coefficients, f PL is the power loss of the distribution network, f PVUR is the voltage unbalance, f THD is the harmonic distortion.

[0014] Furthermore, the fundamental power balance constraint includes:

[0015]

[0016] Where: is the i-th node The fundamental node of the phase injects active power, is the i-th node Other fundamental active loads of the phase, is the i-th node Phase of the fundamental wave active power of new energy generation, is the i-th node Phase of the power station fundamental active power; is the i-th node The fundamental node of the phase injects reactive power, is the i-th node Other fundamental reactive loads of the phase, is the i-th node Phase fundamental reactive power of renewable energy generation, is the i-th node Phase of the power station fundamental reactive power;

[0017] Harmonic current balance constraints include:

[0018]

[0019] Where: is the i-th node The real part of the hth harmonic of the current injected into the phase node, is the i-th node The imaginary part of the hth harmonic of the current injected into the phase node, is the i-th node The real part of the hth harmonic of the current injected by the phase new energy, is the i-th node The imaginary part of the hth harmonic of the current injected by the phase new energy, is the i-th node The real part of the hth harmonic of the current injected by other loads in the phase, is the i-th node The imaginary part of the hth harmonic of the current injected by other loads in the phase;

[0020] The constraints of new energy power are:

[0021]

[0022] Where: is the minimum active power of renewable energy generation, is the maximum active power of renewable energy, is the i-th node Phase new energy fundamental wave power generation; N NE A collection of nodes for new energy access;

[0023] The minimum reactive power injected by renewable energy into the system. is the maximum reactive power injected into the system by renewable energy. is the i-th node Phase fundamental reactive power injected into the system by new energy sources;

[0024] H is the maximum harmonic order, h is the harmonic number, is the i-th node The real part of the hth harmonic voltage of phase, is the i-th node The imaginary part of the hth harmonic voltage of the phase, is the i-th node Maximum renewable energy apparent power of the phase.

[0025] Furthermore, the optimal fundamental power flow sub-model in step 3 is:

[0026] min(α1f PL +α2f PVUR )

[0027] It also includes the corresponding constraints;

[0028] The quadratic programming submodel is:

[0029] min f THD

[0030] The corresponding constraints are also included.

[0031] Furthermore, the optimal fundamental power flow sub-model and the quadratic programming sub-model in step 4 are alternately iterated to solve the problem as follows:

[0032] Calculate the fundamental wave and harmonic node admittance matrix according to the distribution network structure, and initialize the apparent power of new energy harmonics;

[0033] Solve the optimal fundamental power flow sub-model and obtain the i-th node The real part of the fundamental voltage of the phase and the i-th node The imaginary part of the fundamental voltage of the phase

[0034] Solve the quadratic programming submodel and get

[0035] According to the calculation results of the optimal fundamental power flow sub-model and the quadratic programming sub-model, the apparent power of the new energy harmonics is calculated.

[0036] Determine whether the convergence conditions are met. If so, the optimal variable is obtained; if not, solve again and iterate repeatedly until the convergence conditions are met.

[0037] Furthermore, in the objective function:

[0038]

[0039]

[0040] Where: is the i-th node The active power of the power station with phase h harmonics, is the i-th node Phase h harmonics of new energy generation active power, is the i-th node Other active loads of phase h harmonics, N is the total number of nodes in the distribution network;

[0041] VX i is the real part of the three-phase fundamental voltage of the ith node, VY i is the imaginary part of the three-phase fundamental voltage of the ith node, α and β are column vectors composed of sine and cosine functions of 0, 4π / 3, and 2π / 3, respectively.

[0042] The beneficial effects of the present invention are:

[0043] (1) The present invention takes reducing network loss, voltage imbalance and harmonic distortion as optimization goals and establishes a multi-objective optimal harmonic power flow model;

[0044] (2) The present invention uses decoupling processing and an alternating iterative algorithm for solving the problem, which can not only significantly improve the solving efficiency but also effectively promote the improvement of the overall performance of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the process of the present invention.

[0046] Figure 2 The figure is a schematic diagram of the flow of alternately iterating and solving the optimal fundamental power flow sub-model and the quadratic programming sub-model in the present invention.

[0047] Figure 3 This is a schematic diagram of an IEEE-123 node in Embodiment 1 of the present invention.

[0048] Figure 4 This is a schematic diagram of an IEEE-34 node in Embodiment 2 of the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0050] like Figure 1 As shown, a multi-phase harmonic power flow optimization method considering the access of new energy sources includes the following steps:

[0051] Step 1: Construct the objective function of the multi-objective optimal harmonic power flow model with new energy. The objective function includes the power loss, harmonic distortion and voltage imbalance of the distribution network.

[0052] The objective function F is:

[0053] min F=α1f PL +α2f PVUR +α3f THD (1)

[0054] Where: α1, α2, α3 are weight coefficients, f PL is the power loss of the distribution network, f PVUR is the voltage unbalance, f THD is the harmonic distortion.

[0055] in:

[0056]

[0057] Where: is the i-th node The active power of the power station with phase h harmonics, is the i-th node Phase h harmonics of new energy generation active power, is the i-th node Other active loads of phase h harmonics, N is the total number of nodes in the distribution network;

[0058] VXi is the real part of the three-phase fundamental voltage of the ith node, VY i is the imaginary part of the three-phase fundamental voltage of the ith node, α and β are column vectors composed of sine and cosine functions of 0, 4π / 3, and 2π / 3, respectively.

[0059]

[0060] α=[sin(0),sin(4π / 3),sin(2π / 3)]′ (7)

[0061] β=[cos(0),cos(4π / 3),cos(2π / 3)]' (8)

[0062] Where: a, b, c are the phases of the three-phase fundamental voltage.

[0063] Step 2: Construct the constraints of the multi-objective optimal harmonic power flow model, which include fundamental power balance constraints, harmonic current balance constraints, and new energy power constraints;

[0064] Fundamental power balance constraints include:

[0065]

[0066] Where: is the i-th node The fundamental node of the phase injects active power, is the i-th node Other fundamental active loads of the phase, is the i-th node Phase of the fundamental wave active power of new energy generation, is the i-th node Phase of the power station fundamental active power; is the i-th node The fundamental node of the phase injects reactive power, is the i-th node Other fundamental reactive loads of the phase, is the i-th node Phase fundamental reactive power of renewable energy generation, is the i-th node Phase fundamental reactive power of the power station.

[0067] in:

[0068]

[0069] Where: is the i-th node The fundamental conductance between the phase and the j-th node ψ phase, is the real part of the fundamental voltage of the jth node ψ phase, is the i-th node The fundamental susceptance between the phase and the j-th node ψ phase, is the imaginary part of the fundamental voltage of the jth node ψ phase, and l is the distribution network line.

[0070] Harmonic current balance constraints include:

[0071]

[0072] Where: is the i-th node The real part of the hth harmonic of the current injected into the phase node, is the i-th node The imaginary part of the hth harmonic of the current injected into the phase node, is the i-th node The real part of the hth harmonic of the current injected by the phase new energy, is the i-th node The imaginary part of the hth harmonic of the current injected by the phase new energy, is the i-th node The real part of the hth harmonic of the current injected by other loads in the phase, is the i-th node The imaginary part of the hth harmonic of the current injected by other loads in the phase.

[0073]

[0074] Where: is the i-th node The conductance of the hth harmonic between the phase and the jth node ψ phase, is the i-th node The susceptance of the hth harmonic between the phase and the jth node ψ phase.

[0075] The constraints of new energy power are:

[0076]

[0077] Where: is the minimum active power of renewable energy generation, is the maximum active power of renewable energy, is the i-th node Phase new energy generation active power; N NE A collection of nodes for new energy access;

[0078] The minimum reactive power injected by renewable energy into the system. is the maximum reactive power injected into the system by renewable energy. is the i-th node Phase fundamental reactive power injected into the system by new energy sources;

[0079] H is the maximum harmonic order, h is the harmonic number, is the i-th node The real part of the hth harmonic voltage of phase, is the i-th node The imaginary part of the hth harmonic voltage of the phase, is the i-th node Maximum renewable energy apparent power of the phase.

[0080] Step 3: Decouple the multi-objective optimal harmonic power flow model to obtain the optimal fundamental power flow sub-model and the quadratic programming sub-model;

[0081] The optimal fundamental power flow sub-model is:

[0082] min(α1f PL +α2f PVUR )(20)

[0083] The corresponding constraints are as follows:

[0084]

[0085] The quadratic programming submodel is:

[0086] min f THD (twenty two)

[0087] The corresponding constraints are as follows:

[0088]

[0089] Step 4: Alternately iterate and solve the optimal fundamental power flow sub-model and the quadratic programming sub-model in step 3. The solution process is as follows: Figure 2 As shown, the optimal solution is obtained to achieve multi-phase harmonic power flow optimization.

[0090] According to the distribution network structure, the fundamental wave and harmonic node admittance matrix are calculated, and the number of initial iterations k = 0. The apparent power of new energy harmonics

[0091] The primal-dual interior point method PDIPM algorithm is used to solve the optimal fundamental power flow submodel and obtain the i-th node The real part of the fundamental voltage of the phase and the i-th node The imaginary part of the fundamental voltage of the phase

[0092] Use Gurobi solver to solve the quadratic programming submodel and get

[0093] According to the calculation results of the optimal fundamental power flow sub-model and the quadratic programming sub-model, the apparent power of the new energy harmonics is calculated.

[0094]

[0095] Determine whether the convergence condition is met. If so, the optimal variable is obtained; if not, the number of iterations is updated k = k + 1; the updated new energy harmonic apparent power Substitute into equation (24) and solve it again, and iterate repeatedly until the convergence condition is met.

[0096] The convergence conditions are as follows:

[0097]

[0098] In order to illustrate the beneficial effects of the method of the present invention, a specific node system is taken as an example for illustration.

[0099] The present invention decouples the optimal harmonic power flow model into an optimal fundamental power flow sub-model and a quadratic programming sub-model, wherein the optimal fundamental power flow sub-model retains fundamental wave related variables and treats harmonic related variables as constants for calculation, and the quadratic programming sub-model retains harmonic related variables and treats fundamental wave variables as constants for calculation. According to the above decoupling, a part of the variables are alternately retained, the other part of the variables are fixed, and the solution is iteratively obtained. The optimal fundamental power flow sub-model obtains the result of the fundamental wave; the quadratic programming model obtains the result of the hth harmonic, where h = 3, 5, 7...H.

[0100] Example 1

[0101] Take the IEEE123 node system as a test example. Figure 3 Assume that there are 30 PVs, 72 EVs, and 122 three-phase branches in the system. Take the reference voltage S B =1MW. The system has 85 loads, with an active load of 2.967MW and a reactive load of 1.632MVar. The maximum active power of PV is 0kW, the minimum and maximum reactive power are -15 and 15kVar respectively, and the maximum apparent power is 15kVA. The maximum active power of EV is 40kW, the minimum and maximum reactive power are -60 and 60kVar respectively, and the maximum apparent power is 60kVA. Objective function f PL With f PVUR The weight coefficients α1 and α2 are (0.3, 0.7) respectively.

[0102] The method of the present invention is used to calculate the nodes of Example 1. The solution time is 16.03s, and the optimized network loss, three-phase unbalance, and harmonic distortion are 0.0062MW, 0.0217%, and 0.0036%, respectively.

[0103] Example 2

[0104] Take the IEEE 34-node system as a test example. Figure 4 shown.

[0105] Assume that 14 PVs are connected to the system and the number of three-phase branches is 33. Take the reference apparent power S B =1MW. The system has 53 loads, with an active load of 1.504MW and a reactive load of 0.887MVar. The maximum active power of PV is 67.54kW, the minimum and maximum reactive power are -120 and 120kVar respectively, and the maximum apparent power is 120kVA.

[0106] The method of the present invention is compared with the existing traditional power flow solution method, and the results are shown in Table 1. The number of iterations of the NSGAⅢ algorithm is 100, the number of partitions is 10, the population size is 200, the crossover ratio is 0.5, the mutation ratio is 0.5, and the mutation probability is 0.06. Since the optimization result of the NSGAⅢ algorithm is not a single value, but a Pareto front composed of a series of values, for the convenience of comparison, the single-objective optimal solution obtained by the two algorithms is compared here.

[0107] Table 1. Comparison of algorithm solution model time cost and optimization effect

[0108]

[0109] It can be seen from the results that the algorithm of the present invention can quickly and efficiently solve the multi-objective optimal harmonic power flow model containing new energy.

[0110] The present invention takes reducing network loss, voltage imbalance and harmonic distortion as optimization goals, and establishes a multi-objective optimal harmonic power flow model. In order to effectively handle this complex model, the present invention further decouples it and innovatively adopts an alternating iterative algorithm as a solution method. This solution strategy can not only significantly improve the solution efficiency, but also effectively promote the improvement of the overall performance of the distribution network, showing good application potential and prospects.

Claims

1. A multiphase harmonic power flow optimization method considering the access of new energy sources, characterized in that: The following steps are involved: Step 1: Construct the objective function of the multi-objective optimal harmonic power flow model with new energy. The objective function includes the power loss, harmonic distortion and voltage imbalance of the distribution network. Step 2: Construct the constraints of the multi-objective optimal harmonic power flow model, which include fundamental power balance constraints, harmonic current balance constraints, and new energy power constraints; Step 3: Decouple the multi-objective optimal harmonic power flow model to obtain the optimal fundamental power flow sub-model and the quadratic programming sub-model; Step 4: Alternately iterate and solve the optimal fundamental power flow sub-model and the quadratic programming sub-model in step 3 to obtain the optimal solution to achieve multi-phase harmonic power flow optimization.

2. A multiphase harmonic power flow optimization method considering the access of new energy sources according to claim 1, characterized in that: The objective function F in step 1 is: min F=α1f PL +α2f PVUR +α3f THD Where: α1, α2, α3 are weight coefficients, f PL is the power loss of the distribution network, f PVUR is the voltage unbalance, f THD is the harmonic distortion.

3. A multiphase harmonic power flow optimization method considering the access of new energy sources according to claim 2, characterized in that: The fundamental power balance constraint includes: Where: is the i-th node The fundamental node of the phase injects active power, is the i-th node Other fundamental active loads of the phase, is the i-th node Phase of the fundamental wave active power of new energy generation, is the i-th node Phase of the power station fundamental active power; is the i-th node The fundamental node of the phase injects reactive power, is the i-th node Other fundamental reactive loads of the phase, is the i-th node Phase fundamental reactive power of renewable energy generation, is the i-th node Phase of the power station fundamental reactive power; Harmonic current balance constraints include: Where: is the i-th node The real part of the hth harmonic of the current injected into the phase node, is the i-th node The imaginary part of the hth harmonic of the current injected into the phase node, is the i-th node The real part of the hth harmonic of the current injected by the phase new energy, is the i-th node The imaginary part of the hth harmonic of the current injected by the phase new energy, is the i-th node The real part of the hth harmonic of the current injected by other loads in the phase, is the i-th node The imaginary part of the hth harmonic of the current injected by other loads in the phase; The constraints of new energy power are: Where: is the minimum active power of renewable energy generation, is the maximum active power of renewable energy, is the i-th node Phase new energy generation fundamental wave active power; N NE A collection of nodes for new energy access; The minimum reactive power injected by renewable energy into the system. is the maximum reactive power injected into the system by renewable energy. is the i-th node Phase fundamental reactive power injected into the system by new energy sources; H is the maximum harmonic order, h is the harmonic number, is the i-th node The real part of the hth harmonic voltage of phase, is the i-th node The imaginary part of the hth harmonic voltage of the phase, is the i-th node Maximum new energy apparent power of the phase.

4. A multiphase harmonic power flow optimization method considering the access of new energy sources according to claim 3, characterized in that: The optimal fundamental power flow sub-model in step 3 is: min(α1f PL +α2f PVUR ) It also includes the corresponding constraints; The quadratic programming submodel is: my name THD The corresponding constraints are also included.

5. A multiphase harmonic power flow optimization method considering the access of new energy sources according to claim 4, characterized in that: The optimal fundamental power flow sub-model and the quadratic programming sub-model in step 4 are alternately iterated to solve the problem as follows: Calculate the fundamental wave and harmonic node admittance matrix according to the distribution network structure, and initialize the apparent power of new energy harmonics; Solve the optimal fundamental power flow sub-model and obtain the i-th node The real part of the fundamental voltage of the phase and the i-th node The imaginary part of the fundamental voltage of the phase Solve the quadratic programming submodel and get According to the calculation results of the optimal fundamental power flow sub-model and the quadratic programming sub-model, the apparent power of the new energy harmonics is calculated. Determine whether the convergence conditions are met. If so, the optimal variable is obtained; if not, solve again and iterate repeatedly until the convergence conditions are met.

6. A multiphase harmonic power flow optimization method considering the access of new energy sources according to claim 5, characterized in that: In the objective function: Where: is the i-th node The active power of the power station with phase h harmonics, is the i-th node Phase h harmonics of new energy generation active power, is the i-th node Other active loads of phase h harmonics, N is the total number of nodes in the distribution network; VX i is the real part of the three-phase fundamental voltage of the ith node, VY i is the imaginary part of the three-phase fundamental voltage of the ith node, α and β are column vectors composed of sine and cosine functions of 0, 4π / 3, and 2π / 3, respectively.

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