Single-segment linear modeling method for energy flow in electric-gas interconnected system

Abstract

The present invention discloses a single-segment linearization modeling method for energy flow of an electric-gas interconnected system, which relates to the technical field of power system optimization, and includes the following steps: constructing a single-segment linearization energy flow model based on the state space transformation theory according to the correlation between the linearization error of the energy flow model and the variable state space; constructing a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system with the gas pressure amplitude power function as the state space variable; constructing a state space variable optimization selection model with the goal of minimizing the global maximum error, and proposing a split solution strategy for the state space variable optimization selection model; establishing a system optimal energy flow model for the electric-gas interconnected system; and simulating and verifying the system optimal energy flow model. The present invention provides a basic model with high accuracy and low representation complexity for the optimization decision of the electric-gas interconnected system through transformation state space selection and single-segment linear processing of nonlinear natural gas model, thereby improving the calculation efficiency of optimization decision.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimization, and in particular to a single-segment linearization modeling method for energy flow of an electricity-gas interconnected system, and in particular to transformation state space selection, single-segment linear processing of a nonlinear natural gas model, and optimal energy flow modeling of an electricity-gas interconnected system. Background Art

[0002] The energy flow model is the model basis for the optimization decision and state analysis of the electric-gas interconnected system, and is of great significance to the decision and analysis results. Errors in the energy flow modeling of the electric-gas interconnected system will have serious consequences, ranging from reducing energy utilization efficiency to violating the system operation safety constraints and causing operation risks. The widespread nonlinear characteristics in the energy flow model make the optimization decision problem of the electric-gas interconnected system constrained by it non-convex, which leads to problems such as poor convergence of the optimization calculation, low robustness of the calculation results, and non-zero dual gap of the optimization problem.

[0003] To solve the above problems, the energy flow model of the natural gas system is generally approximated by piecewise linear technology. The reason for this treatment is that the accuracy of the linearized model based on Taylor series expansion technology depends on the deviation between the actual operating point and the initial operating point. If the value range of each state variable in the system is wide, for example, the node gas pressure of the natural gas system can vary from hundreds of psi to thousands of psi, the model error is large when the actual operating point deviates far from the initial operating point. By comparing the effects of several piecewise linear methods on the Weymouth equation in the natural gas system, it is pointed out that the incremental piecewise linear approximation method is the best.

[0004] However, no matter which piecewise linear method is used, integer variables need to be introduced to indicate whether each segment is selected, and the number of integer variables increases with the number of segments. At this time, the optimization scheduling problem is modeled as a mixed integer linear programming problem. This problem is generally solved based on a branch-and-bound process, and its computational burden increases exponentially with the number of integer variables. In order to ensure a high linear model accuracy, the number of segments is generally large, and the computational burden is unbearable. On this basis, an improved two-stage piecewise linear method is proposed. In the first stage, this method sets a small number of segments to roughly predict the linearization interval where the optimal solution is located. In the second stage, only the linearization processing with a limited number of segments is further performed within the interval determined in the first stage, thereby greatly reducing the number of integer variables. In addition, there is a method that uses an envelope composed of two sets of piecewise linear functions to approximate the Weymouth equation. But in any case, as long as the piecewise linear technology is used, the enumeration computational burden brought by the integer variables needs to be solved. Summary of the invention

[0005] In order to solve the deficiencies in the above-mentioned prior art, the present invention provides a single-segment linearization modeling method for energy flow in an electric-gas interconnected system, which provides an accurate basic model with low representation complexity for optimization decision-making of the electric-gas interconnected system and improves the calculation efficiency of the optimization decision-making.

[0006] The technical solution proposed by the present invention is:

[0007] The single-segment linear modeling method of energy flow in an electric-gas interconnected system includes the following steps:

[0008] According to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed;

[0009] A single-segment linear model of pipeline flow and pipeline storage in a natural gas system is constructed with the gas pressure amplitude power function as the state space variable;

[0010] Construct a state space variable optimization selection model with the goal of minimizing the global maximum error, and propose a split solution strategy for the state space variable optimization selection model;

[0011] Establish the optimal energy flow model of the electric-gas interconnected system;

[0012] The optimal energy flow model of the system is simulated and verified.

[0013] As a further technical solution of the present invention, according to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed; specifically including:

[0014] For a nonlinear function F(x 1 ,x 2 ,…,x N )=0, in the original variable state space (x 1 ,x 2 ,…,x N ) is converted into a linear approximate expression: where b i (i=0,1,…,N) is the linear approximation model coefficient;

[0015] Introducing variable state space (ψ(x 1 ),ψ(x 2 ),ψ(x 3 )) makes the original equation transformed into this space and the corresponding expression F'(ψ(x 1 ),ψ(x 2 ),ψ(x 3 ))=0;

[0016] The linearization process is used to obtain the approximate model:

[0017] As a further technical solution of the present invention, the construction of a single-segment linearized model of pipeline flow and pipeline storage of a natural gas system with a gas pressure amplitude power function as a state space variable specifically includes:

[0018] The pipeline flow and storage model of the natural gas system is:

[0019]

[0020]

[0021]

[0022]

[0023] in, is the average gas flow through the pipe mn; K R,mn is the pipeline flow model coefficient; π m,t is the pressure of gas node m; and are the gas flow rates flowing into and out of the pipe mn respectively; L mn,t M is the pipe stock; mn is the pipeline storage model coefficient; N p is the number of pipelines in the natural gas system; (m,n)∈N p Indicates that nodes m and n are located at the beginning and end of a pipeline respectively;

[0024] The above nonlinear characteristics are mainly present in the Weymouth equation (1), which is approximated as a A linear plane in the variable state space, namely:

[0025] Select an initial operating point Here with L mn,t , and The first-order Taylor series expansion of equations (1) and (3) is performed for independent variables; the linear convex model expression obtained is as follows:

[0026]

[0027]

[0028] As a further technical solution of the present invention, the state space variable optimization selection model with the goal of minimizing the global maximum error is constructed; specifically comprising:

[0029] To construct a state space variable optimization selection model with the goal of minimizing the global maximum error, two key features must be determined:

[0030] 1) The optimal target state space, i.e. the value of k;

[0031] 2) Optimal change position, i.e. initial operating point

[0032] The maximum flow / pipe storage error between the linear convex model and the original model in the feasible domain of variables is used as the judgment index;

[0033] Let the flow and storage variables in the original nonlinear model (1) and (3) be and L mn,t , the flow and pipe storage variables in the linear convexification model (5) and (6) are and L L,mn,t , then the linear convexification model error is defined as:

[0034]

[0035]

[0036] In the formula, the square operation (·) 2 The error is guaranteed to be positive;

[0037] In formula (7)-(8) L mn,0 ,π m,0 ,π n,0 ,k is a variable parameter, π m,t ,π n,t is an independent variable, then the optimal value of the variable parameter is determined by the two-level robust optimization problem of formula (9):

[0038]

[0039] Where:

[0040]

[0041] in, L is the upper and lower limits of pipeline flow; mn,min , L mn,max is the upper and lower limits of the storage; π min , π max k is the upper and lower limits of node pressure; min , k max The upper and lower limits of k.

[0042] As a further technical solution of the present invention, the proposed split solution strategy for the state space variable optimization selection model is as follows: solving the double-layer robust optimization problem of formula (9);

[0043] When the parameter L mn,0 ,π m,0 ,π n,0 That is, when the transformation position is given, determine the optimal k value:

[0044]

[0045] Where D 1 :={k min ≤k≤k max};

[0046] make Different k values ​​correspond to different optimal points There are two situations at this time:

[0047] Scenario 1: If The corresponding maximum value is an extreme point, then π m,t and π n,t The first derivative of is 0:

[0048]

[0049]

[0050] The functional relationship between the optimal point and the value of k is obtained by combining equations (11) and (12): and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k;

[0051] Scenario 2: If When the maximum value is taken, the upper and lower limits of a variable are bounded. Since the pipeline flow and storage variables can be explicitly represented by the pressure variable, the upper and lower limits of the bounded variables can be constrained by the equation G(π m,t ,π n,t )=0 means;

[0052] Constructing Lagrangian functions At the optimal point of the conditional extreme value problem, the Lagrangian function is π m,t and π n,t The first derivative of is 0:

[0053]

[0054]

[0055] The combined equations (13)-(14) and G(π m,t ,π n,t )=0, and the functional relationship between the optimal value point and the value of k is obtained. and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k;

[0056] When the parameter k, i.e. the target state space, is given, the optimal transformation position is determined:

[0057]

[0058] Where:

[0059]

[0060] As a further technical solution of the present invention, the establishment of the optimal energy flow model of the electric-gas interconnected system specifically includes:

[0061] The single-segment linear model of natural gas pipeline flow and pipeline storage is used as an equality constraint to establish the optimal energy flow model of the electricity-gas interconnection system:

[0062] The objective function includes the power generation cost of coal-fired units and the gas supply cost:

[0063]

[0064] Operation constraints include power system-related constraints, natural gas system-related constraints, and coupled equipment-related constraints;

[0065] The power system-related constraints adopt the DC optimal power flow model in the form of transfer distribution factors, including the overall active power balance constraint of the system (17), the upper and lower limit constraints of the coal-fired unit power generation capacity (18), and the upper and lower limit constraints of the branch power transmission capacity (19):

[0066]

[0067]

[0068]

[0069] The constraints related to the natural gas system include: node flow balance equation, pipeline flow model, pipeline flow upper and lower limits, pipeline storage model pipeline storage upper and lower limits, compressor flow model, compressor flow upper and lower limits, compression ratio upper and lower limits, gas source gas production upper and lower limits, gas pressure upper and lower limits; among them,

[0070] The node flow balance equation is:

[0071]

[0072] in,

[0073]

[0074] The pipeline flow model is:

[0075]

[0076]

[0077] in,

[0078]

[0079]

[0080]

[0081] The upper and lower limits of pipeline flow are:

[0082]

[0083] The storage model is:

[0084]

[0085]

[0086] in,

[0087]

[0088]

[0089] The upper and lower limits of the storage are:

[0090]

[0091] The compressor flow model is:

[0092]

[0093] The upper and lower limits of the compressor flow are:

[0094]

[0095] The upper and lower limits of compression ratio are:

[0096] Pipeline flow model and pipeline storage model and As an independent variable, the upper and lower limits of the compression ratio of the compressor are:

[0097]

[0098]

[0099] The upper and lower limits of gas source gas production are:

[0100]

[0101] The upper and lower limits of air pressure are:

[0102] Similarly, the upper and lower limits of air pressure are For the independent variable it is written as:

[0103]

[0104] The constraints related to the coupled equipment include: the electricity-gas energy conversion model, the upper limit of gas consumption of the gas generator set, and the upper and lower limits of the power generation of the gas generator set;

[0105] Among them, the electricity-gas energy conversion model is:

[0106]

[0107] The upper limit of gas consumption of gas generator sets is:

[0108]

[0109] The upper and lower limits of gas generator set power generation are:

[0110]

[0111] Among them, N s 、N c 、N g 、N e 、N l 、N m 、N p 、N b are the number of gas sources, coal-fired units, gas-fired generators, power system nodes, power system branches, natural gas nodes, natural gas pipelines and compressors in the system; T is the total number of dispatching periods; is the gas production of the gas source; is the power generation cost coefficient of coal-fired units; is the gas production cost of gas source; P i,t Inject active power into the node; The upper and lower limits of the power allowed to flow through the branch; and are the active outputs of coal-fired units and gas-fired generating units respectively; The upper and lower limits of the permitted output of coal-fired units; is the node normal load; PTDF h-i is the corresponding element in the hth row and ith column of the transfer distribution factor matrix; is the upper limit of pipeline flow; L mn,max and L mn,min The upper and lower limits of the storage; is the upper limit of the compressor flow rate; and The kth power of the upper and lower limits of the compression ratio of the compressor; and It is the upper and lower limits of gas source output; and is the kth power of the upper and lower limits of the node pressure; and It is the upper and lower limits of gas generator set output.

[0112] The beneficial effects of the present invention are:

[0113] The present invention proposes a single-segment linearization modeling method for energy flow of an electric-gas interconnected system based on state space transformation theory. According to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearization of the energy flow model based on state space transformation theory is proposed; a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system with a gas pressure amplitude power function as a state space variable is established; a state space variable optimization selection model with the goal of minimizing the global maximum error is proposed, and a splitting solution strategy for the preferred model is proposed; an optimal energy flow modeling of an electric-gas interconnected system without integer variables is established, and simulation analysis and verification are performed; the present invention provides a basic model with high accuracy and low representation complexity for the optimization decision of the electric-gas interconnected system through transformation state space selection, single-segment linear processing of nonlinear natural gas models and optimal energy flow modeling of the electric-gas interconnected system, thereby improving the calculation efficiency of the optimization decision. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 This is a flow chart of the single-segment linear modeling method for energy flow of an electric-gas interconnected system proposed by the present invention;

[0115] Figure 2a This is a schematic diagram of the linear approximation of the original state space of the linear convexification method based on state space transformation proposed in the present invention;

[0116] Figure 2b This is a schematic diagram of linear approximation of the state space after the transformation of the linear convexification method based on state space transformation proposed in the present invention;

[0117] Figure 3 Schematic diagram of the Weymouth equation proposed by the present invention;

[0118] Figure 4aIt is a linear expansion diagram of the Weymouth equation proposed by the present invention with different k values ​​at the same initial operating point;

[0119] Figure 4b It is a linear expansion diagram of the Weymouth equation proposed by the present invention with different k values ​​at the same initial operating point;

[0120] Figure 5 This is a schematic diagram of a linearization model based on Taylor series expansion proposed by the present invention;

[0121] Figure 6a This is a schematic diagram of the maximum error of the flow model alone under different k values ​​of M2 proposed by the present invention;

[0122] Figure 6b This is a schematic diagram of the maximum error of the single pipe storage model under different k values ​​of M2 proposed in the present invention;

[0123] Figure 6c It is a schematic diagram of the comprehensive maximum error of the pipeline flow model and the pipeline storage model under different k values ​​of M2 proposed by the present invention;

[0124] Figure 7 This is a schematic diagram of the maximum error of the pipeline flow model of M1 proposed in the present invention under different numbers of segments;

[0125] Figure 8 This is a schematic diagram of the calculation error of the optimal energy flow model under different objective function coefficients proposed in the present invention. DETAILED DESCRIPTION

[0126] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention, so as to fully understand the purpose, characteristics and effects of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative work are all within the scope of protection of the present invention.

[0127] like Figure 1 As shown, it shows a specific embodiment of the present invention,

[0128] The single-segment linear modeling method of energy flow in an electric-gas interconnected system includes the following steps:

[0129] According to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed;

[0130] A single-segment linear model of pipeline flow and pipeline storage in a natural gas system is constructed with the gas pressure amplitude power function as the state space variable;

[0131] Construct a state space variable optimization selection model with the goal of minimizing the global maximum error, and propose a split solution strategy for the state space variable optimization selection model;

[0132] Establish the optimal energy flow model of the electric-gas interconnected system;

[0133] The optimal energy flow model of the system is simulated and verified.

[0134] The present invention proposes a single-segment linearization modeling method for energy flow of an electric-gas interconnected system based on state space transformation theory. First, the correlation between the linearization error of the energy flow model and the variable state space is revealed, and the single-segment linearization idea of ​​the energy flow model based on the state space transformation theory is proposed; then, a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system with the gas pressure amplitude power function as the state space variable is established; then, a state space variable optimization selection model with the goal of minimizing the global maximum error is proposed, and a split solution strategy for the preferred model is proposed; finally, the optimal energy flow modeling of an electric-gas interconnected system without integer variables is established. A simulation analysis of an electric-gas interconnected system consisting of an IEEE 14-node power system and a 10-node natural gas system is used to verify the effectiveness of the present invention. A basic model with high accuracy and low representation complexity is provided for the optimization decision of the electric-gas interconnected system, thereby improving the calculation efficiency of the optimization decision.

[0135] In the embodiment of the present invention, according to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed;

[0136] The three-dimensional schematic diagram given in Figure 2 is used to briefly introduce the linear convexification method of the energy flow model based on the state space transformation theory.

[0137] For a nonlinear function F(x 1 ,x 2 ,…,x N )=0, it can be found in the original variable state space (x 1 ,x 2 ,…,x N ) to convert it into a linear approximate expression where b i (i=0,1,…,N) are the linear approximation model coefficients. However, the error of the approximation model is directly related to the nonlinearity of the original equation. As shown in Figure 2(a), when F(x 1 ,x 2 ,…,x N )=0When the nonlinearity is high, no matter what method is used, it is impossible to obtain a linear approximation model with ideal accuracy. 1 ),ψ(x2 ),ψ(x 3 )) makes the original equation transformed into this space and the corresponding expression F'(ψ(x 1 ),ψ(x 2 ),ψ(x 3 ))=0 The nonlinearity is low, as shown in Figure 2(b). On this basis, further linearization can obtain an approximate model with better accuracy.

[0138] In the embodiment of the present invention, a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system is constructed with a gas pressure amplitude power function as a state space variable; specifically, it includes:

[0139] The pipeline flow and storage model of the natural gas system is:

[0140]

[0141]

[0142]

[0143]

[0144] in, is the average gas flow through the pipe mn; K R,mn is the pipeline flow model coefficient; π m,t is the pressure of gas node m; and are the gas flow rates flowing into and out of the pipe mn respectively; L mn,t M is the pipe stock; mn is the pipeline storage model coefficient; N p is the number of pipelines in the natural gas system; (m,n)∈N p Indicates that nodes m and n are located at the beginning and end of a pipeline respectively.

[0145] The above nonlinear characteristics are mainly presented in the Weymouth equation (1), Figure 3 A schematic diagram of the variable values ​​of the Weymouth equation for a certain pipeline at a certain moment is given.

[0146] like Figure 3 As shown in Figure 2, the quadratic coupling relationship between variables makes It is difficult to find a linear plane that can effectively approximate the Weymouth equation in the state space with as the independent variable. Therefore, based on the state space transformation theory, this paper proposes to approximate the Weymouth equation as a linear plane in The linear plane in the variable state space, that is: take In order to ensure the consistency of the model expression for energy flow calculation, the pipe storage model (3) ismn,t ,π m,t ,π n,t ) is a linear plane in the variable state space, but it still needs to be approximated as A linear plane in the variable state space.

[0147] To achieve this goal, an initial operating point is selected Here with L mn,t , and The first-order Taylor series expansion of equations (1) and (3) is performed on the independent variables. The obtained linear convex model expression is as follows:

[0148]

[0149]

[0150] Figure 4 shows a schematic diagram of different linear expansion forms of the Weymouth equation. The yellow surface in the figure corresponds to the original nonlinear Weymouth equation, the surfaces of other colors in Figure 4(a) correspond to linear models with the same initial operating point but different k values, and the surfaces of other colors in Figure 4(b) correspond to linear models with the same k value but different initial operating points. Therefore, in order to improve the accuracy of models (5)-(6), two key features need to be determined:

[0151] ① The optimal target state space, i.e. the value of k. This feature determines the surface shape characteristics of the linear convex model in the original state space, and thus determines the degree of similarity between the approximate model and the original model surface;

[0152] ②The best change position, i.e. the initial operating point Since the feasible range of state variables in the natural gas system is relatively wide, different initial operating points selected during Taylor series expansion will affect the tangent position between the plane of the linear convex model obtained by equations (5)-(6) and the surface of the original model, thereby affecting the similarity between the linear convex model and the original model.

[0153] In order to select the optimal target state space and transformation position, it is necessary to define the accuracy judgment index of the linear convexification model. The linear convexification method based on Taylor series expansion generally ensures that the approximate model has high accuracy near the selected initial operating point. When the model operation state deviates far from the initial point, the accuracy of the approximate model decreases accordingly.

[0154] For example Figure 5 For x 0 To expand the points to obtain a linear model, run the points x 2 The error at the operating point x is much larger than 1On the other hand, the purpose of linear convexification of the multi-energy model in this paper is to apply it to the characterization of the boundary of flexible adjustment capacity, so it is necessary to ensure the accuracy of the obtained linear convexification model in the entire feasible domain of its variables. Based on this, this chapter takes the maximum flow / pipeline storage error between the linear convexification model and the original model in the feasible domain of variables as the judgment indicator, and proposes an optimal selection strategy for the state space and transformation position of the target variable.

[0155] Let the flow and storage variables in the original nonlinear model (1) and (3) be and L mn,t , the flow and pipe storage variables in the linear convexification model (5) and (6) are and L L,mn,t , then the linear convexification model error is defined as:

[0156]

[0157]

[0158] Here, the square operation (·)2 ensures that the error is positive;

[0159] The formulas (7) and (8) are L mn,0 ,π m,0 ,π n,0 ,k is a variable parameter, π m,t ,π n,t is an independent variable, then the optimal value of the variable parameter is determined by the two-level robust optimization problem of formula (9):

[0160]

[0161] Where:

[0162]

[0163] in, L is the upper and lower limits of pipeline flow; mn,min , L mn,max is the upper and lower limits of the storage; π min , π max k is the upper and lower limits of node pressure; min , k max The upper and lower limits of k.

[0164] However, the complex nonlinear characteristics of the constraints in (9) make this optimization problem difficult to solve, so it is transformed into two aspects for discussion:

[0165] ① When the parameter L mn,0 ,π m,0 ,π n,0That is, when the transformation position is given, determine the optimal k value:

[0166]

[0167] Where D 1 :={k min ≤k≤k max};

[0168] make Different k values ​​correspond to different optimal points There are two situations at this time:

[0169] Scenario 1: If The corresponding maximum value is an extreme point, then π m,t and π n,t The first derivative of is 0:

[0170]

[0171]

[0172] The functional relationship between the optimal point and the value of k is obtained by combining equations (11) and (12): and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k;

[0173] Scenario 2: If When the maximum value is taken, the upper and lower limits of a variable are bounded. Since the pipeline flow and storage variables can be explicitly represented by the pressure variable, the upper and lower limits of the bounded variables can be constrained by the equation G(π m,t ,π n,t )=0 means;

[0174] Constructing Lagrangian functions At the optimal point of the conditional extreme value problem, the Lagrangian function is π m,t and π n,t The first derivative of is 0:

[0175]

[0176]

[0177] The combined equations (13)-(14) and G(π m,t ,π n,t )=0, and the functional relationship between the optimal value point and the value of k is obtained. and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k;

[0178] In either case, equation (10) is equivalent to the problem of finding the minimum value of the single variable function H'(k).

[0179] ② When the parameter k, i.e. the target state space, is given, determine the optimal transformation position:

[0180]

[0181] Where:

[0182]

[0183] In the embodiment of the present invention, a system optimal energy flow model of an electric-gas interconnected system is established; specifically, it includes:

[0184] The single-segment linear model of natural gas pipeline flow and pipeline storage is used as an equality constraint to establish the optimal energy flow model of the electricity-gas interconnection system:

[0185] The objective function includes the power generation cost of coal-fired units and the gas supply cost:

[0186]

[0187] Operation constraints include power system-related constraints, natural gas system-related constraints, and coupled equipment-related constraints;

[0188] The power system-related constraints adopt the DC optimal power flow model in the form of transfer distribution factors, including the overall active power balance constraint of the system (17), the upper and lower limit constraints of the coal-fired unit power generation capacity (18), and the upper and lower limit constraints of the branch power transmission capacity (19):

[0189]

[0190]

[0191]

[0192] The constraints related to the natural gas system include: node flow balance equation, pipeline flow model, pipeline flow upper and lower limits, pipeline storage model pipeline storage upper and lower limits, compressor flow model, compressor flow upper and lower limits, compression ratio upper and lower limits, gas source gas production upper and lower limits, gas pressure upper and lower limits; among them,

[0193] The node flow balance equation is:

[0194]

[0195] in,

[0196]

[0197] The pipeline flow model is:

[0198]

[0199]

[0200] in,

[0201]

[0202]

[0203]

[0204] The upper and lower limits of pipeline flow are:

[0205]

[0206] The storage model is:

[0207]

[0208]

[0209] in,

[0210]

[0211]

[0212] The upper and lower limits of the storage are:

[0213]

[0214] The compressor flow model is:

[0215]

[0216] The upper and lower limits of the compressor flow are:

[0217]

[0218] The upper and lower limits of compression ratio are:

[0219] Pipeline flow model and pipeline storage model and As an independent variable, the upper and lower limits of the compression ratio of the compressor are:

[0220]

[0221]

[0222] The upper and lower limits of gas source gas production are:

[0223]

[0224] The upper and lower limits of air pressure are:

[0225] Similarly, the upper and lower limits of air pressure are For the independent variable it is written as:

[0226]

[0227] The constraints related to the coupled equipment include: the electricity-gas energy conversion model, the upper limit of gas consumption of the gas generator set, and the upper and lower limits of the power generation of the gas generator set;

[0228] Among them, the electricity-gas energy conversion model is:

[0229]

[0230] The upper limit of gas consumption of gas generator sets is:

[0231]

[0232] The upper and lower limits of gas generator set power generation are:

[0233]

[0234] Among them, N s 、N c 、N g 、N e 、N l 、N m 、N p 、N b are the number of gas sources, coal-fired units, gas-fired generators, power system nodes, power system branches, natural gas nodes, natural gas pipelines and compressors in the system; T is the total number of dispatching periods; is the gas production of the gas source; is the power generation cost coefficient of coal-fired units; is the gas production cost of gas source; P i,t Inject active power into the node; The upper and lower limits of the power allowed to flow through the branch; and are the active outputs of coal-fired units and gas-fired generating units respectively; The upper and lower limits of the permitted output of coal-fired units; is the node normal load; PTDF h-i is the corresponding element in the hth row and ith column of the transfer distribution factor matrix; is the upper limit of pipeline flow; L mn,max and L mn,min The upper and lower limits of the storage; is the upper limit of the compressor flow rate; and The kth power of the upper and lower limits of the compression ratio of the compressor; and It is the upper and lower limits of gas source output; and is the kth power of the upper and lower limits of the node pressure; and It is the upper and lower limits of gas generator set output.

[0235] The effectiveness of the proposed method is verified in an IEEE 14-node power system and a 10-node natural gas system. The following models are compared:

[0236] M0: The natural gas pipeline model in the optimal energy flow is an accurate nonlinear model;

[0237] M1: Replace the Weymouth equation of the pipeline flow model with a piecewise linear model;

[0238] M2: Replace the pipeline flow model and pipeline storage model with the proposed linear model.

[0239] Model accuracy verification for a single pipeline:

[0240] When the initial operation is selected L mn,0 =80.0994MMCFD,π m,0 =583.2889psi,π n,0 =512.5284psi, as the value of the target state space indicator variable k changes from 0.1 to 3, the maximum error of the pipeline flow model and the maximum error of the pipe storage model of M0 and M2 within the feasible range change trend as shown in Figure 2. Taking the maximum error of the flow model as the goal, that is, the objective function in formula (1.9) only takes the first term The maximum error corresponding to different k values ​​is shown in Figure 6(a). It can be seen from the figure that when k is 0.95, the maximum error is the smallest, which is 6.7588psi. For the nonlinear coupling form in the Weymouth equation Flow variables and the pressure variable π m,t , π n,t It still shows an approximate linear correlation, so it is reasonable for the optimal value of k to be around 1. The goal is to minimize the maximum error of the pipe storage model, that is, the objective function in equation (1.9) only takes the second term minmaxΔL mn,tThe maximum error corresponding to different k values ​​is shown in Figure 6(b). mn,t and the pressure variable π m,t , π n,t There is a strict linear correlation, so the optimal value of k is 1, at which time the maximum value of the tube storage error is 0, that is, there is no error.

[0241] In order to ensure the consistency of the variables of each constraint in the optimal energy flow problem, the optimal k value determined when the pipeline flow model and the pipeline storage model are linearly convexed should minimize the maximum comprehensive error of the two models in this variable state space, that is, the objective function in equation (1.9) takes the complete two terms As shown in Figure 6(c), when k is 0.95, the comprehensive maximum error is the smallest. At this time, the maximum error of flow is 3.0429psi, and the maximum error of pipe storage is 4.4410psi. The optimal value of k is 0.95 when considering the maximum error of flow-pipe storage and the maximum error of flow alone. However, due to the solution characteristics of nonlinear optimization problems, the maximum error of flow in the two cases is different in value.

[0242] When the piecewise linear model M1 is used, since the selection of state variables does not change, only the pipeline flow model (1.1) is approximated. Figure 7 The changing trend of the maximum error of the pipeline flow model under different numbers of segments is given. It can be seen that the maximum error shows an L-shaped downward trend with the increase of the number of segments. When the number of segments is already large, the marginal effect of continuing to increase the number of segments on reducing the maximum error is negligible. When the number of segments is 40, the maximum error of the pipeline flow is 6.3567psi, which is close to the optimal result of 6.7588psi when M2 is used and only the maximum error of the pipeline flow is minimized; when the number of segments is 80, the maximum error of the pipeline flow is 3.153psi, which is close to the optimal result of 3.0429psi when M2 is used and the comprehensive minimization of the maximum error of the pipeline flow and the maximum error of the pipe storage is considered. Therefore, it is concluded that the method proposed in this paper achieves a model calculation accuracy similar to that of the existing piecewise linear method while avoiding the introduction of integer variables.

[0243] Model accuracy verification for electrical-gas interconnected systems:

[0244] The model of each pipeline in the system in each optimization period is linearized using M1 and M2. In this section, 1000 different sets of objective function coefficients are obtained through Monte Carlo sampling, and M0 to M2 are used to optimize the calculation for each set of samples. The purpose is to compare the errors caused by each energy flow model when the optimal value point of the optimal power flow is different. Among them, M0 has a high degree of nonlinearity and is only successfully solved under 305 sets of samples. The calculation result of M0 is used as the benchmark value for comparison.

[0245] Table 1 shows the single optimal energy flow calculation time under different methods. Among them, M2 has the fastest calculation speed of 1.1124 seconds / time because the constraints are linear and do not contain integer variables. Figure 7 It shows that the calculation accuracy is improved with the increase of the number of segments, but when applying the solution method of mixed integer linear programming such as branch and bound, the calculation burden will increase exponentially with the increase of the number of integer variables. When 10-segment linear processing is used for each pipeline model, the optimal energy flow calculation time is 6.1456 seconds / time, the calculation time of the 40-segment linear model is 17608.2579 seconds / time, and the 80-segment linear model is not successfully solved within an acceptable time. In general, when the model accuracy is similar, the calculation efficiency of M2 is much higher than that of M1. In addition, considering the calculation efficiency and calculation accuracy, this paper uses a 10-segment linear model for M1 when performing calculation error verification.

[0246] Figure 8 The optimal value error distribution of 305 groups of M0 feasible samples successfully solved is given, where M2 is calculated according to Figure 8 Select k as 0.95. At this time, the maximum error of the optimal value of M1 is $1.1560 and the average error is $0.3690, and the maximum error of the optimal value of M2 is $0.8868 and the average error is $0.3319. It can be seen that all kinds of error indicators of M1 are higher than those of M2, which verifies the effectiveness of the proposed model in terms of accuracy.

[0247] Table 1 Optimal energy flow calculation time under different methods

[0248] Table 2.10 Calculation time of economic dispatch with different methods

[0249]

[0250] The present invention is described in detail above, but the present invention is not limited to the above-mentioned embodiments. Various changes can be made within the knowledge of ordinary technicians in the field without departing from the purpose of the present invention. Many other changes and modifications can be made without departing from the concept and scope of the present invention. It should be understood that the present invention is not limited to specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A single-segment linear modeling method for energy flow in an electric-gas interconnected system, characterized in that: The following steps are involved: According to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed; A single-segment linear model of pipeline flow and pipeline storage in a natural gas system is constructed with the gas pressure amplitude power function as the state space variable; Construct a state space variable optimization selection model with the goal of minimizing the global maximum error, and propose a split solution strategy for the state space variable optimization selection model; Establish the optimal energy flow model of the electric-gas interconnected system; Simulate and verify the optimal energy flow model of the system; The construction of a single-segment linearization model of pipeline flow and pipeline storage of a natural gas system with a gas pressure amplitude power function as a state space variable specifically includes: The pipeline flow and storage model of the natural gas system is: in, is the average gas flow through the pipe mn; K R,mn is the pipeline flow model coefficient; π m,t is the pressure of gas node m; and are the gas flow rates flowing into and out of the pipe mn respectively; L mn,t M is the pipe stock; mn is the pipeline storage model coefficient; N p is the number of pipelines in the natural gas system; (m,n)∈N p Indicates that nodes m and n are located at the beginning and end of a pipeline respectively; The nonlinear characteristics are present in the Weymouth equation (1), which can be approximated as a A linear plane in the variable state space, namely: Select an initial operating point ( L mn,0 ,π m,0 ,π n,0 ), here L mn,t , and The first-order Taylor series expansion of equations (1) and (3) is performed for independent variables; the linear convex model expression obtained is as follows: The construction of a state space variable optimization selection model with the goal of minimizing the global maximum error specifically includes: To construct a state space variable optimization selection model with the goal of minimizing the global maximum error, two key features must be determined: 1) The optimal target state space, i.e. the value of k; 2) The best change position, that is, the initial operating point ( L mn,0 ,π m,0 ,π n,0 ); The maximum flow / pipe storage error between the linear convex model and the original model in the feasible domain of variables is used as the judgment index; Let the flow and storage variables in the original nonlinear model (1) and (3) be and L mn,t , the flow and pipe storage variables in the linear convexification model (5) and (6) are and L L,mn,t , then the linear convexification model error is defined as: In the formula, the square operation (·) 2 The error is guaranteed to be positive; In formula (7)-(8) L mn,0 ,π m,0 ,π n,0 ,k is a variable parameter, π m,t ,π n,t is an independent variable, then the optimal value of the variable parameter is determined by the two-level robust optimization problem of formula (9): Where: in, L is the upper and lower limits of pipeline flow; mn,min , L mn,max is the upper and lower limits of the storage; π min , π max k is the upper and lower limits of node pressure; min , k max The upper and lower limits of k; The proposed split solution strategy for the state space variable optimization selection model is as follows: solving the double-layer robust optimization problem of formula (9); When the parameter L mn,0 ,π m,0 ,π n,0 That is, when the transformation position is given, determine the optimal k value: In the formula, D1:={k min ≤k≤k max }; make Different k values ​​correspond to different optimal points There are two situations at this time: Scenario 1: If The corresponding maximum value is an extreme point, then π m,t and π n,t The first derivative of is 0: The functional relationship between the optimal point and the value of k is obtained by combining equations (11) and (12): and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k; Scenario 2: If When the maximum value is taken, the upper and lower limits of a variable are bounded. Since the pipeline flow and storage variables can be explicitly represented by the pressure variable, the upper and lower limits of the bounded variables can be constrained by the equation G(π m,t ,π n,t )=0 means; Constructing Lagrangian functions At the optimal point of the conditional extreme value problem, the Lagrangian function is π m,t and π n,t The first derivative of is 0: The combined equations (13)-(14) and G(π m,t ,π n,t )=0, and the functional relationship between the optimal value point and the value of k is obtained. and Substitute it into So that H(π m,t ,π n,t ,k) is transformed into a function H'(k) that is only related to the variable k; When the parameter k, i.e. the target state space, is given, the optimal transformation position is determined: Where: The establishment of the optimal energy flow model of the electric-gas interconnected system specifically includes: The single-segment linear model of natural gas pipeline flow and pipeline storage is used as an equality constraint to establish the optimal energy flow model of the electricity-gas interconnection system: The objective function includes the power generation cost of coal-fired units and the gas supply cost: Operation constraints include power system-related constraints, natural gas system-related constraints, and coupled equipment-related constraints; The power system-related constraints adopt the DC optimal power flow model in the form of transfer distribution factors, including the overall active power balance constraint of the system (17), the upper and lower limit constraints of the coal-fired unit power generation capacity (18), and the upper and lower limit constraints of the branch power transmission capacity (19): The constraints related to the natural gas system include: node flow balance equation, pipeline flow model, pipeline flow upper and lower limits, pipeline storage model pipeline storage upper and lower limits, compressor flow model, compressor flow upper and lower limits, compression ratio upper and lower limits, gas source gas production upper and lower limits, gas pressure upper and lower limits; among them, The node flow balance equation is: in, The pipeline flow model is: in, The upper and lower limits of pipeline flow are: The storage model is: in, The upper and lower limits of the storage are: The compressor flow model is: The upper and lower limits of the compressor flow are: The upper and lower limits of compression ratio are: Pipeline flow model and pipeline storage model and As an independent variable, the upper and lower limits of the compression ratio of the compressor are: The upper and lower limits of gas source gas production are: The upper and lower limits of air pressure are: Similarly, the upper and lower limits of air pressure are For the independent variable it is written as: The constraints related to the coupled equipment include: the electricity-gas energy conversion model, the upper limit of gas consumption of the gas generator set, and the upper and lower limits of the power generation of the gas generator set; Among them, the electricity-gas energy conversion model is: The upper limit of gas consumption of gas generator sets is: The upper and lower limits of gas generator set power generation are: Among them, N s 、N c 、N g 、N e 、N l 、N m 、N p 、N b are the number of gas sources, coal-fired units, gas-fired generators, power system nodes, power system branches, natural gas nodes, natural gas pipelines and compressors in the system; T is the total number of dispatching periods; is the gas production of the gas source; is the power generation cost coefficient of coal-fired units; is the gas production cost of gas source; P i,t Inject active power into the node; The upper and lower limits of the power allowed to flow through the branch; and are the active outputs of coal-fired units and gas-fired generating units respectively; The upper and lower limits of the permitted output of coal-fired units; is the normal load of the node; PTDF h-i is the corresponding element in the hth row and ith column of the transfer distribution factor matrix; is the upper limit of pipeline flow; L mn,max and L mn,min The upper and lower limits of the storage; is the upper limit of the compressor flow rate; and The kth power of the upper and lower limits of the compression ratio of the compressor; and It is the upper and lower limits of gas source output; and is the kth power of the upper and lower limits of the node pressure; and It is the upper and lower limits of gas generator set output.

2. The single-segment linear modeling method for energy flow of an electric-gas interconnected system according to claim 1 is characterized in that: According to the correlation between the linearization error of the energy flow model and the variable state space, a single-segment linearized energy flow model based on the state space transformation theory is constructed; specifically including: For a nonlinear function F(x1,x2,…,x N )=0, in the original variable state space (x1,x2,…,x N ) is converted into a linear approximate expression: where b i , i=0,1,…,N; are the linear approximate model coefficients; Introduce variable state space (ψ(x1), ψ(x2), ψ(x3)) so that the original equation is transformed into this space and the corresponding expression F'(ψ(x1), ψ(x2), ψ(x3)) = 0; The linearization process is used to obtain the approximate model:

Images