An Optimal Power Flow Calculation Method for Power-Gas Considering the Non-Isothermal Process of Natural Gas

Abstract

The present invention proposes a method for calculating the optimal power - natural gas flow considering the non - isothermal process of natural gas. This method first simplifies the energy conservation equation and proposes a non - isothermal natural gas network model, then couples the power system model with the natural gas system model to establish an optimal power - natural gas flow model, and finally uses the interior - point method based on the starting - point initialization scheme to efficiently calculate the optimal power - natural gas flow and obtain the calculation results of the optimal power - natural gas flow. The method for calculating the optimal power - natural gas flow of the present invention avoids the traditional isothermal assumption of natural gas, can simultaneously evaluate the gas temperature, pressure and flow velocity in the natural gas network, thus greatly improving the accuracy of the optimal power - natural gas flow model.

Description

Technical Field

[0001] The present invention relates to a method for calculating the optimal power flow of electricity-gas considering the non-isothermal process of natural gas, belonging to the field of integrated electricity-gas energy systems. Background Art

[0002] Due to advantages such as environmental friendliness and convenient storage, natural gas has gradually become the main fuel source for power generation. According to the statistical data released by the US Energy Information Administration (EIA), the electricity generated by natural gas accounted for 23% of the global electricity generation in 2019. At the same time, natural gas power generation units have good flexibility and adjustability, and can effectively cope with the randomness and variability of renewable energy power generation. Therefore, the coordinated operation of the integrated electricity-gas energy system is of great significance for improving the efficiency and reliability of the energy system. However, most of the existing integrated electricity-gas energy system models are based on the isothermal assumption of natural gas flow, without considering the impact of temperature changes on the evaluation of gas pressure and flow velocity, which greatly reduces the accuracy of the integrated electricity-gas energy system model. Summary of the Invention

[0003] In order to overcome the deficiencies of the prior art, the purpose of the present invention is to propose a method for calculating the optimal power flow of electricity-gas considering the non-isothermal process of natural gas. The optimal power flow calculation method includes the following steps:

[0004] Step 1: Quantitatively analyze and simplify the partial differential form of the energy conservation equation to establish a non-isothermal natural gas network model. The partial differential form of the energy conservation equation is:

[0005]

[0006] where ν and P are the flow velocity and pressure of the natural gas flow, g is the gravitational constant, θ is the inclination angle of the natural gas pipeline, S is the cross-sectional area of the natural gas pipeline, ε is the friction coefficient of the pipeline, h c is the thermal conductivity, c V is the constant volume heat capacity of the gas, ρ is the gas density, T s and T are the ambient and gas temperatures.

[0007] The quantitative analysis of the energy conservation equation is:

[0008]

[0009]

[0010]

[0011]

[0012]

[0013] Among them, and the weights of these two items in the energy conservation equation are less than 1%, so they can be ignored. Therefore, the energy conservation equation can be simplified to:

[0014]

[0015] Substituting the enthalpy change gives

[0016] mc p dT = -h c (T - T s )dx

[0017] Integrating both sides gives

[0018]

[0019] where i and j represent the inlet and outlet of pipeline p respectively.

[0020] Step 2: Use the fully implicit difference method to transform the partial differential equations in the natural gas network model into algebraic equations, and establish a natural gas network algebraic model considering the non-isothermal process of natural gas. The traditional natural gas momentum equation and continuity equation are:

[0021]

[0022]

[0023] Neglecting the partial differential terms related to time according to the steady-state condition gives

[0024]

[0025]

[0026] where D is the diameter of the natural gas pipeline.

[0027] Neglecting the convection term and assuming the pipeline is horizontally deployed, the momentum equation can be further simplified to

[0028]

[0029] Using the fully implicit difference method, the partial differential equation can be transformed into an algebraic equation, expressed as:

[0030]

[0031] where K represents three variables of gas pressure, temperature and flow rate. Substituting the fully implicit difference method into the momentum equation gives:

[0032]

[0033] Among them, R is the gas constant and Z is the gas compressibility factor.

[0034] Step 3: Couple the DC power flow model of the power system with the established natural gas system model to establish a power-gas optimal power flow model considering the non-isothermal process of natural gas. The objective of the power-gas optimal power flow model is to minimize the operating cost, which is expressed as:

[0035]

[0036] Among them, α i,t and β j,t represent the cost coefficients of natural gas suppliers and coal-fired power units, and represent the outputs of natural gas suppliers and coal-fired power units.

[0037] Power system constraints:

[0038]

[0039]

[0040]

[0041]

[0042] Among them, is the power load, is the output of the gas turbine, B f is the susceptance of the transmission line, and θ i,t is the phase angle of node i.

[0043] Natural gas system constraints:

[0044]

[0045]

[0046]

[0047]

[0048] Among them, is the natural gas load, is the natural gas consumption of the gas turbine, and π i,t is the gas pressure at the node.

[0049] Coupling constraints:

[0050]

[0051]

[0052] Among them, η g is the energy conversion coefficient of the gas turbine, and P i min and P i max are the minimum and maximum outputs of the gas turbine.

[0053] Step 4: Use the starting point initialization scheme to generate a set of feasible solutions, and use this set of feasible solutions as the starting point of the interior point method to solve the power-gas optimal power flow model. The starting point initialization scheme is specifically as follows: 1) Input a decreasing sequence 2) Solve the power-gas optimal power flow model under isothermal conditions and obtain the output of the gas turbine; 3) Update the output of the gas turbine to Solve the power system sub-problem; 5) Solve the natural gas system sub-problem; 6) Check whether all operating constraints are satisfied. If satisfied, output the current initial value. If not satisfied, return to step 3).

[0054] The specific content of step 4) is as follows:

[0055] Use the linear programming method to solve the power system sub-problem. The power system sub-problem is expressed as

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] In step 5), the Newton-Raphson method is used to solve the natural gas system sub-problem, which is expressed as the Newton-Raphson method is used to solve the natural gas system sub-problem, which is expressed as

[0062]

[0063]

[0064] Among them, J is the Jacobian matrix. The Jacobian matrix of the natural gas sub-problem is

[0065]

[0066] Among them, and The expressions of are

[0067]

[0068]

[0069]

[0070]

[0071] Among them, C T and are equivalent matrices. The solution process of C T is as follows: 1) Input the topological matrix A; 2) Determine all the mixing nodes; 3) For pipeline p, if there is no mixing at node j, then C Tii = 1; if there is mixing at node j, then If i is a source node, then , if not, then C Tij = 0; 4) Output the matrix C T .

[0072] Finally, according to the obtained initial points, using the nonlinear solver IPOPT based on the interior point method, the calculation results of the electricity-gas optimal power flow can be obtained.

[0073] The beneficial effects of the present invention are:

[0074] 1) The proposed natural gas network model can accurately evaluate the temperature of the natural gas network, providing a reference for pipeline operators to avoid the formation of hydrates on the inner wall of pipelines.

[0075] 2) The proposed electricity-gas model considering the non-isothermal process of natural gas avoids traditional assumptions, and the obtained system optimal operation strategy has high accuracy.

[0076] 3) The proposed initial point initialization scheme can generate a set of initial points close to the optimal solution and strictly satisfying the operation constraints, thus greatly improving the convergence speed and solution quality of the interior point method. Description of the Drawings

[0077] Figure 1 is the flowchart of the initial point initialization scheme.

[0078] Figure 2 is the flowchart for solving the Jacobian matrix of the natural gas system sub-problem. Detailed Embodiments

[0079] The following is further described with reference to the drawings.

[0080] A method for calculating the electricity-gas optimal power flow considering the non-isothermal process of natural gas includes the following steps:

[0081] Step 1: Conduct a quantitative analysis and simplification of the energy conservation equation in partial differential form to establish a non-isothermal natural gas network model. The energy conservation equation in partial differential form is:

[0082]

[0083]

[0084] where ν and P are the flow velocity and pressure of the natural gas flow, S is the cross-sectional area of the natural gas pipeline, ε is the friction coefficient of the pipeline, h c is the thermal conductivity, c V is the constant volume heat capacity of the gas, ρ is the gas density, T s and T are the ambient and gas temperatures. The quantitative analysis of the energy conservation equation is:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] where and The weights of the two terms account for less than 1% of the energy conservation equation, so they can be neglected. Therefore, the energy conservation equation can be simplified to:

[0091]

[0092] Substituting the enthalpy change gives

[0093] mc p dT = -h c (T - T s )dx

[0094] Integrating both sides gives

[0095]

[0096] where i and j represent the inlet and outlet of pipeline p respectively.

[0097] Step 2: Use the fully implicit difference method to transform the partial differential equation in the natural gas network model into an algebraic equation, and establish an algebraic model of the natural gas network considering the non-isothermal process of natural gas. The traditional natural gas momentum equation and continuity equation are:

[0098]

[0099]

[0100] Ignoring the time - related partial differential terms according to the steady - state conditions, we can obtain

[0101]

[0102]

[0103] Ignoring the convection term and assuming the pipeline is horizontally deployed, the momentum equation can be further simplified to

[0104]

[0105] Using the fully implicit difference method, the partial differential equation can be transformed into an algebraic equation, expressed as:

[0106]

[0107]

[0108] where K represents three variables: gas pressure, temperature, and flow rate. Substituting the fully implicit difference method into the momentum equation, we can get:

[0109]

[0110] where R is the gas constant and Z is the gas compressibility factor.

[0111] Step 3: Coupling the DC power flow model of the power system with the established natural gas system model to establish a power - natural gas optimal power flow model considering the non - isothermal process of natural gas. The objective of the power - natural gas optimal power flow model is to minimize the operating cost, expressed as:

[0112]

[0113] where α i,t and β j,t represent the cost coefficients of natural gas suppliers and coal - fired power plants, and represent the outputs of natural gas suppliers and coal - fired power plants.

[0114] Power system constraints:

[0115]

[0116]

[0117]

[0118]

[0119] Among them, is the electrical load, is the output of the gas turbine, B f is the susceptance of the transmission line, θ i,t is the phase angle of node i.

[0120] Natural gas system constraints:

[0121]

[0122]

[0123]

[0124]

[0125] Among them, is the natural gas load, is the natural gas consumption of the gas turbine, π i,t is the gas pressure of the node.

[0126] Coupling constraints:

[0127]

[0128]

[0129] Among them, η g is the energy conversion coefficient of the gas turbine, P i min and P i max are the minimum and maximum outputs of the gas turbine.

[0130] Step 4: Use the starting point initialization scheme to generate a set of feasible solutions, and use this set of feasible solutions as the starting point of the interior point method to solve the power-gas optimal power flow model. Figure 1 is the flowchart of the starting point initialization scheme, and its main steps are as follows: 1) Input a decreasing sequence 2) Solve the power-gas optimal power flow model under isothermal conditions and obtain the output of the gas turbine; 3) Update the output of the gas turbine to 4) Solve the power system sub-problem; 5) Solve the natural gas system sub-problem; 6) Check whether all operation constraints are satisfied. If satisfied, output the current initial value. If not satisfied, return to step 3).

[0131] The specific content of the said step 4) is:

[0132] Use the linear programming method to solve the power system sub-problem, and the power system sub-problem is expressed as

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] In step 5) above, the Newton-Raphson method is used to solve the natural gas system sub-problem, which is expressed as

[0139]

[0140]

[0141] where J is the Jacobian matrix. The Jacobian matrix of the natural gas sub-problem is

[0142]

[0143] where and The expressions for are

[0144]

[0145]

[0146]

[0147]

[0148] Figure 2 is the Jacobian matrix J of the natural gas system sub-problem 22 The solution flow chart, the main steps of which include the following: 1) Input the topological matrix A; 2) Determine all the mixing nodes; 3) For pipeline p, if there is no mixing at node j, then C Tii = 1; if there is mixing at node j, then If i is a source node, then If not, then C Tij = 0; 4) Output the matrix C T .

Claims

1. An optimal power flow calculation method for electricity-gas considering the non-isothermal process of natural gas, characterized in that: It includes the following steps: Step 1: Quantitatively analyze and simplify the energy conservation equation in partial differential form to obtain a non-isothermal natural gas network model; Step 2: Use the fully implicit difference method to transform the partial differential equation in the natural gas network model obtained in Step 1 into an algebraic equation to obtain a natural gas network algebraic model considering the non-isothermal process of natural gas; Step 3: Couple the DC power flow model of the power system with the natural gas network algebraic model in Step 2 to establish a power-gas optimal power flow model considering the non-isothermal process of natural gas; Step 4: Use the starting point initialization scheme to generate a set of feasible solutions, and use this set of feasible solutions as the starting point of the interior point method to solve the power-gas optimal power flow model; Step 4 specifically includes: 1) Input a decreasing sequence 2) Solve the power-gas optimal power flow model under isothermal conditions and obtain the output of the gas turbine; 3) Update the output of the gas turbine to 4) Solve the power system sub-problem; 5) Solve the natural gas system sub-problem; 6) Check whether all operation constraints are satisfied. If satisfied, output the current initial value; if not, return to step 3); Specifically, Step 4) is as follows: Solve the power system sub-problem using the linear programming method, and the power system sub-problem is expressed as where, β i,t is the cost coefficient of generator i, is the output of generator i, is the output of gas turbine j, is the electricity demand at time t, B f is the electrical susceptance of transmission line f, θ i,t is the phase angle of bus i; in the said step 5), the Newton-Raphson method is used to solve the sub-problem of the natural gas system, expressed as where J is the Jacobian matrix; the Jacobian matrix of the natural gas sub-problem is Among them, and The expression of Among them, C T and are equivalent matrices. The solution process of C T is as follows: 1) Input the topological matrix A; 2. The optimal power flow calculation method for electricity-gas considering the non-isothermal process of natural gas according to claim 1, characterized in that: In Step 1, the energy conservation equation in partial differential form is: where ν and P are the flow velocity and pressure of the natural gas stream, g is the gravitational constant, θ is the inclination angle of the natural gas pipeline, S is the cross-sectional area of the natural gas pipeline, ε is the friction coefficient of the pipeline, h c is the thermal conductivity, c V is the heat capacity at constant volume of the gas, ρ is the gas density, T s and T are the ambient and gas temperatures; The quantitative analysis of the energy conservation equation is: Among them, and The weights of the two items in the energy conservation equation are less than 1% and can be ignored; the energy conservation equation can be simplified to: Substituting the enthalpy change, we can obtain mc p dT = -h c (T - T s )dx Integrating both sides gives where i and j represent the inlet and outlet of the natural gas pipeline p, respectively.

3. The optimal power flow calculation method for electricity-gas considering the non-isothermal process of natural gas according to claim 2, characterized in that: In Step 2, the fully implicit difference method is used to establish a natural gas network algebraic model considering the non-isothermal process of natural gas, specifically as follows: The traditional natural gas momentum equation and continuity equation are: where D is the diameter of the natural gas pipeline; According to the steady state condition, the partial differential terms related to time are ignored, and we can obtain Ignoring the convection term and assuming the pipeline is horizontally deployed, the momentum equation can be simplified to Using the fully implicit difference method, the partial differential equation can be transformed into an algebraic equation to obtain the natural gas network algebraic model equation considering the non-isothermal process of natural gas: where R is the gas constant and Z is the gas compressibility factor.

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