Load flow calculation method based on quantum PQ decomposition algorithm

Abstract

The invention relates to the field of quantum calculation and power load flow calculation, and discloses a load flow calculation method based on a quantum PQ decomposition algorithm, which comprises the following steps of: establishing a node admittance matrix according to a power grid topological structure and parameter data, and constructing complex representation of node power; constructing polar coordinate representation forms of active power and reactive power of the nodes based on an admittance matrix; secondly, constructing an error nonlinear equation of active power and reactive power of the node, and forming two constant coefficient matrixes according to the nonlinear equation; thirdly, constructing a quantum linear correction equation by combining a classical linear equation and a quantum algorithm on the basis of equation characteristics realized by the constant coefficient matrix; and finally, carrying out iteration on the active power error, the reactive power error, and the corresponding voltage phase angle and voltage amplitude needing to be corrected until a convergence condition is met. According to the quantum load flow calculation method, the iteration convergence speed can be increased, and the operation efficiency and precision of load flow calculation are achieved.

Description

Technical Field

[0001] The present invention relates to the fields of quantum computing and power flow computing, and in particular to a power flow computing method based on a quantum PQ decomposition algorithm. Background Art

[0002] Quantum computing has the characteristics of quantum state superposition and quantum entanglement. Quantum bits can be in a superposition state of 0 and 1 at the same time, allowing quantum computing to break through the computing power limits of classical computing and realize high-speed parallel computing, providing efficient and high-quality solutions for optimization, modeling, machine learning and other fields.

[0003] The power flow calculation problem is one of the core issues in the power system. By solving the node voltage equation, it makes important contributions to the reasonable planning of power capacity, the discovery of potential problems in the power grid, and the safe and stable operation of the power grid. However, due to the large number of nonlinear elements in the power system, such as loads and power sources, the power flow calculation involves a large number of high-dimensional nonlinear equations. Traditional calculation methods require multiple iterations to solve these nonlinear equations. For large-scale power systems, the computing power and efficiency of classical algorithms are great challenges.

[0004] At present, the mainstream classical algorithms used in power flow calculation include PQ decomposition algorithm, Newton-Raphson algorithm and Gauss-Seidel algorithm. Compared with other algorithms, the PQ decomposition algorithm simplifies the polar coordinate equation of the Newton-Raphson algorithm, and its coefficient matrix is ​​a constant matrix, which reduces the required memory and improves the calculation speed, and is widely used. However, for today's power system, the development tends to be towards large-scale, energy integration and other fields. The scale and complexity of the system lead to the restriction of calculation efficiency and accuracy by simply using classical algorithms to calculate power flow problems. The parallelism of quantum computing can process large-scale power system data. Introducing quantum computing into classical computing algorithms can effectively and quickly help solve the solution of nonlinear equations in power flow calculation. For this reason, the present invention proposes a power flow calculation method based on quantum PQ decomposition algorithm. Summary of the invention

[0005] The purpose of the present invention is to propose a power flow calculation method based on a quantum PQ decomposition algorithm, which can realize power flow calculation to improve the iterative convergence speed and realize the computational efficiency and accuracy of power flow analysis.

[0006] The technical solution of the present invention is: To achieve the above object, the technical solution provided by the power flow calculation method based on the quantum PQ decomposition algorithm of the present invention includes the following steps: S1. Based on the power grid topology structure and parameter data, establish the nodal admittance matrix, construct the complex power flow equation of nodal power, and construct the polar coordinate representation forms of nodal active power and reactive power based on the admittance matrix; Y ki is the admittance matrix: The diagonal Y ki (k = i) is the self-admittance, Y ki (k ≠ i) is the mutual admittance.

[0007] The complex representation of nodal power including the admittance matrix is: Nodal power can be decomposed into nodal active power P k and nodal reactive power Q k : Among them, the real part of nodal power is active power, and the imaginary part is reactive power.

[0008] S2. Construct the error nonlinear equations of nodal active power and reactive power, and form two constant coefficient matrices B′ and B″ according to the nonlinear equations; For the nonlinear equations of active power error ΔP and reactive power error ΔQ containing trigonometric functions, use Taylor series expansion: Among them, ΔP is the difference between the specified active power and the calculated power, ΔP k =[ΔP 1 , ΔP 2 ,…ΔP N T ; ΔQ is the difference between the specified reactive power and the calculated power, ΔQ k =[ΔQ 1 , ΔQ 2 ,...ΔQ N T , and U is the diagonal matrix composed of the voltages of each node.

[0009] The basic representation of the parameterized PQ decomposition method can be deduced from the admittance matrix as follows: Among them, B′ and B″ are coefficient symmetric matrices. B′ is the susceptance matrix for PQ and PV nodes under the premise of neglecting conductance, and B″ is the susceptance matrix for PQ nodes under the premise of neglecting conductance; Δθ and ΔU are the changes in voltage phase angle and voltage amplitude respectively; ΔP is the order of the sum of PQ nodes and PV nodes, and ΔQ is the order of PQ nodes; ​​S3. Based on the equation characteristics realized by the constant coefficient matrix, the quantum linear correction equation is constructed by combining the classical linear equation and the quantum algorithm; the classical linear equation is expressed as: Ax = b Where A is a Hermitian conjugate matrix, which is equal to its conjugate transpose.

[0010] Using the HHL algorithm, the above classical linear equation is expressed in quantum state form as: A|x>=|b> quantum correction equation: Among them, γ i and η i It is the characteristic value of the unbalanced amount of active power and reactive power.

[0011] S4. Iterate the active power error, reactive power error, and the corresponding voltage phase angle and voltage amplitude that need to be corrected until the convergence condition is met.

[0012] The iterative formula of Δθ, ΔU is: Δθ K =B′ -1 (U K+1 ) -1 ΔP(θ K ,U K+1 ) Δθ K+1 =θ K +Δθ K ΔU K =B″ -1 (U K ) -1 ΔQ(θ K ,U K ) ΔU K+1 =U K +ΔU K Where K is the number of iterations.

[0013] The advantages of the present invention are: Compared with the classical traditional PQ decomposition method, the power flow calculation method based on the quantum PQ decomposition algorithm proposes a method for calculating the power flow based on the quantum PQ decomposition algorithm on the basis of fully considering the limited computing power of the classical algorithm for large and complex power network systems. The method converts the mathematical model of the classical algorithm into a quantum form and utilizes the high efficiency of quantum computing parallel computing, thereby realizing efficient analysis and calculation of the power flow of large and complex power network systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The figure is an overall flow chart of the power flow calculation method based on the quantum PQ decomposition method of the present invention. DETAILED DESCRIPTION

[0015] The method of the present invention is described in detail below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention and are not intended to limit the scope and application of the present invention. Figure 1 Shown is a flow chart of the method of the present invention, and the method of the present invention is specifically described below.

[0016] In this embodiment, the present invention Figure 1 The implementation steps of the power flow calculation method flow based on the quantum PQ decomposition method include S1a-S4d.

[0017] S1a. According to the grid topology and parameter data, the number of PQ nodes in the power system network is N. Q , the number of PV nodes is N U , the number of balanced nodes is 1, and the node admittance matrix is ​​established; In the power system network, k represents the kth node, k∈[1,N], and N is the total number of nodes; according to Kirchhoff's law, the voltage equation represented by the node admittance matrix is: Among them, Y ki is the admittance matrix, Diagonal Y ki (k=i) is the self-admittance, Y ki (k≠i) is the mutual admittance.

[0018] The complex number representation of the node power including the admittance matrix is: The admittance matrix can be expressed as: ki =G ki +jB ki (3) Among them, the real part G ki is the conductance between nodes k and i, Y ki (k=i) is the self-admittance, Y ki (k≠i) is the mutual admittance; the imaginary part B ki is the susceptance between nodes k and i, B ki (k=i) is the self-susceptance, B ki (k≠i) is the mutual admittance.

[0019] The complex representation of the node voltage is constructed as: U k =|U k |(cosθ k +jsinθ k ) (4) The polar coordinates of node power are expressed as: The node power can be decomposed into the node active power P k and the node reactive power Q k : Among them, the real part of the node power is the active power, and the imaginary part is the reactive power.

[0020] S2b. For the nonlinear equations of active power error ΔP and reactive power error ΔQ containing trigonometric functions, use Taylor series expansion: Where ΔP is the difference between the specified active power and the calculated power, ΔP k =[ΔP 1 ,ΔP 2 ,...ΔP N ] T ; ΔQ is the difference between the specified reactive power and the calculated power, ΔQ k =[ΔQ 1 ,ΔQ 2 ,...ΔQ N ] T , U is the diagonal matrix composed of the voltages of each node.

[0021] In order to avoid a pathological network, the reactance value is made much larger than the resistance value, the phases between nodes are approximately equal, and the mutual conductance is much smaller than the mutual susceptance.

[0022] Preferably, the continuous PQ decomposition method is used here, and the basic expression of the parameterized PQ decomposition method can be deduced from the admittance matrix as follows: Among them, B′, B″ are coefficient symmetric matrices, B′ is the susceptance matrix under the premise of ignoring the conductance of PQ and PV nodes, and B″ is the susceptance matrix under the premise of ignoring the conductance of PQ nodes; Δθ, ΔU are the changes in voltage phase angle and voltage amplitude respectively; ΔP is the order of the sum of PQ nodes and PV nodes, and ΔQ is the order of PQ nodes; S3c. Based on the PQ decomposition method, find the iterative matrix [ΔθΔU] T ; Because B′, B″ are constant coefficient matrices, essentially we need to find the iterative matrix [ΔθΔU] T A linear equation needs to be solved; The classic linear equation is expressed as: Ax = b Find the iterative matrix [ΔθΔU] T That is, solving the classic linear equation for x.

[0023] Using the HHL algorithm, the above classical linear equation is expressed in quantum state form as: A|x>=|b> Where A is a Hermitian conjugate matrix, which is equal to its conjugate transpose.

[0024] Preferably, the coefficient matrix here is a Hermitian conjugate matrix, so the quantum state representation of the coefficient matrix B′, B″ is: Among them, λ′ and λ″ are eigenvalues, |b i ′> and |b i ″> is the feature vector.

[0025] According to the quantum state representation of the coefficient matrix B′, B″, the inverse of the quantum state of the coefficient matrix B′, B″ is solved as follows: Preferably, the quantum state of the active power and reactive power imbalance is expressed as: Among them, γ i and η i It is the characteristic value of the unbalanced amount of active power and reactive power.

[0026] S4d. The iterative formula of Δθ, ΔU is: Δθ K =B′ -1 (U K+1 ) -1 ΔP(θ K ,U K+1 ) (17) Δθ K+1 =θ K +Δθ K (18) ΔU K =B″ -1 (U K ) -1 ΔQ(θ K ,U K ) (19) ΔU K+1 =U K +ΔU K (20) Among them, the quantum state of Δθ, ΔU is expressed as:

[0027] Compared with the classical traditional PQ decomposition method, the power flow calculation method based on the quantum PQ decomposition algorithm proposes a method for calculating the power flow based on the quantum PQ decomposition algorithm on the basis of fully considering the limited computing power of the classical algorithm for large and complex power network systems. The method converts the mathematical model of the classical algorithm into a quantum form and utilizes the high efficiency of quantum computing parallel computing, thereby realizing efficient analysis and calculation of the power flow of large and complex power network systems.

Claims

1. A power flow calculation method based on quantum PQ decomposition algorithm, the method comprising the following steps: S1. According to the grid topology and parameter data, a node admittance matrix is ​​established, a complex number representation power flow equation of the node power is constructed, and a polar coordinate representation of the node active power and reactive power is constructed based on the admittance matrix; S2. Construct the error nonlinear equation of node active power and reactive power, and form two constant coefficient matrices B′ and B″ according to the nonlinear equation; S3. Based on the equation characteristics realized by the constant coefficient matrix, the quantum linear correction equation is constructed by combining the classical linear equation and the quantum algorithm; S4. Iterate the active power error, reactive power error, and the corresponding voltage phase angle and voltage amplitude that need to be corrected until the convergence condition is met.

2. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S1, a node admittance matrix is ​​constructed, Y ki is the admittance matrix: Diagonal Y ki (k=i) is the self-admittance, Y ki (k≠i) is the mutual admittance.

3. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S1, a complex representation of node power is constructed:

4. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S1, a polar coordinate representation of the active power and reactive power of the node is constructed:

5. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S2, the error nonlinear equation of the node active power and reactive power is constructed: Where ΔP is the difference between the specified active power and the calculated power, ΔP k =[ΔP1, ΔP2, … ΔP N ] T ; ΔQ is the difference between the specified reactive power and the calculated power, ΔQ k =[ΔQ1, ΔQ2, ... ΔQ N ] T , U is the diagonal matrix composed of the voltages of each node.

6. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S2, two constant coefficient matrices B′ and B″ are formed: Among them, B′ and B″ are coefficient symmetric matrices, B′ is the susceptance matrix under the premise that the conductance of the PQ and PV nodes is ignored, and B″ is the susceptance matrix under the premise that the conductance of the PQ node is ignored; Δθ and ΔU are the changes in the voltage phase angle and voltage amplitude respectively; ΔP is the order of the sum of the PQ node and the PV node, and ΔQ is the order of the PQ node.

7. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S3, the classical linear equation and the quantum algorithm are combined to construct a quantum linear correction equation: Classic linear equation: Ax = b Quantum linear equation: A|x>=|b> Quantum correction equation: Among them, γ i and η i It is the characteristic value of the unbalanced amount of active power and reactive power.

8. The power flow calculation method based on the quantum PQ decomposition algorithm according to claim 1 is characterized in that: In step S4, the active power error, the reactive power error, and the corresponding voltage phase angle and voltage amplitude that need to be corrected are iterated; the iterative equation is: Dth K =B′ -1 (U K+1 ) -1 ΔP(θ K ,U K+1 ) Dth K+1 =θ K +Δθ K D.U. K =B″ -1 (U K ) -1 ΔQ(θ K ,U K ) ΔU K+1 =U K +ΔU K Where K is the number of iterations.

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