Day-ahead unit commitment optimization method for gas-fired power system considering pipeline ramping

Abstract

A method for optimizing the day-ahead unit combination of a gas-electricity system taking into account pipeline ramping includes the following steps: S1, establishing a natural gas dynamic process pipeline transmission model taking into account pipeline ramping; S2, establishing a natural gas pipeline compressor power consumption model; S3, taking minimizing the operating cost of the gas-electricity system as the objective function, establishing a day-ahead unit combination model of the gas-electricity system taking into account pipeline ramping; S4, using the C&CG algorithm to solve the day-ahead robust scheduling problem of the gas-electricity system. This design fully considers the fluid mechanics characteristics of natural gas in the pipeline, and at the same time accurately models the compressor to deal with the gas pressure limit problem that may occur due to pipeline ramping, solving the problem of inaccurate modeling of the existing model; at the same time, the optimization method can make full use of gas units, power-to-gas units and compressors to exchange energy between the natural gas system and the power system, improving the flexibility of the gas-electricity system and effectively promoting wind power consumption.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering, and in particular to a method for optimizing the day-ahead unit combination of a gas-electricity combined system taking pipeline climbing into account. Background Art

[0002] In order to solve energy problems such as energy crisis and global warming, renewable energy represented by wind power has been developed on a large scale across the country. At the same time, due to the intermittent and volatile nature of renewable energy, higher requirements are placed on the flexibility of the power system. The integrated energy system based on natural gas-electricity interconnection can effectively solve the problem of large-scale wind power access: on the one hand, both gas units and P2G units have the ability to quickly adjust output, which can effectively smooth out the output fluctuations of wind power; on the other hand, natural gas pipelines have extremely excellent energy storage potential, and can be used with P2G units to absorb more wind power during peak hours.

[0003] Unlike the power system, where energy can be transmitted at the speed of light, the carrier of material energy transmission in the natural gas system is fluid, and its transmission speed in the natural gas pipeline is far less than the speed of light. It often takes several hours for the natural gas system to reach a steady state from the initial response, while in the power system this process can be completed in milliseconds. Therefore, in the study of the gas-electricity combined system, the results obtained by using the natural gas steady-state model are not of practical significance, and the dynamic process of natural gas must be considered. At the same time, natural gas may pass through long pipelines with high drop heights during transmission, so the influence of pipeline slope must also be taken into account while considering the dynamic process. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects and problems of low modeling accuracy in the prior art and to provide a method for optimizing the day-ahead unit combination of a gas-electricity combined system with high modeling accuracy and taking pipeline ramping into account.

[0005] To achieve the above objectives, the technical solution of the present invention is: a method for optimizing the day-ahead unit combination of a gas-electricity combined system taking into account pipeline ramping, the method comprising the following steps:

[0006] S1. Establish a natural gas dynamic process pipeline transmission model taking into account pipeline ramp;

[0007] S2. Establish a natural gas pipeline compressor power consumption model;

[0008] S3. Taking minimizing the operating cost of the gas-electricity combined system as the objective function, a day-ahead unit combination model of the gas-electricity combined system taking into account pipeline ramping is established;

[0009] S4. The C&CG algorithm is used to solve the day-ahead robust dispatch problem of the gas-fired power system.

[0010] In step S1, the natural gas dynamic process is described by the following three equations:

[0011] Natural gas momentum equation:

[0012]

[0013] In the formula, A ij is the cross-sectional area of ​​the pipe ij, M Fij，t+1 is the natural gas material flow rate at the front end of pipeline ij at time t+1, M Eij，t+1 is the natural gas material flow at the end of pipeline ij at time t+1, M Fij，t is the natural gas material flow rate at the front end of pipeline ij at time t, M Eij，t is the natural gas material flow rate at the end of pipeline ij at time t, Δt is the time step, L ij is the length of the pipe ij, p j，t+1 is the natural gas pressure at the end node j of pipeline ij at time t+1, p i，t+1 is the natural gas pressure at the front node i of pipeline ij at time t+1, p j，t is the natural gas pressure at the end node j of pipeline ij at time t, p i，t is the natural gas pressure at the front node i of the pipeline ij at time t, g is the gravity acceleration, α is the angle between the pipeline ij and the horizontal plane, c is the speed of sound, λ is the friction coefficient, is the average flow rate of natural gas in pipeline ij, d ij is the diameter of the pipe ij;

[0014] Pipeline material balance equation:

[0015]

[0016] Gas state equation:

[0017] p=c 2 ρ

[0018] Where p is the natural gas pressure and ρ is the natural gas density.

[0019] The boundary condition constraints of the nodes in the natural gas system are:

[0020] Node material balance constraints:

[0021]

[0022] Where M Dk，t is the natural gas load of node k at time t, including the gas consumption of the gas unit and the gas production of the power-to-gas unit; (·)k is the set of natural gas pipelines with the front node k, and k(·) is the set of natural gas pipelines with the end node k;

[0023] For the source node in the natural gas system, the gas pressure is stable at a certain value:

[0024]

[0025] In the formula, K s is the source node set, p si，0 is the constant value of the air pressure at the source node;

[0026] The upper and lower limit constraints of pipeline material flow and node pressure:

[0027]

[0028] In step S2, a compressor is set at the natural gas pipeline node to adjust the node gas pressure. The compressor power consumption model is as follows:

[0029]

[0030] Where, M is the compressor power consumption constant, R is the molar gas constant, T is the gas temperature; n is the compression ratio, p j is the natural gas pressure at the end node j of pipeline ij, p i is the natural gas pressure at the front node i of pipeline ij;

[0031] Assuming that a compressor has m gears that can be adjusted, the compression ratio n is:

[0032]

[0033] In the formula, α i is the decision variable, representing that the compressor is running at the i-th gear; n i is the compression ratio of the compressor running in the i-th gear;

[0034] The compressor power consumption model can be transformed into:

[0035]

[0036] In step S3, the objective function of the day-ahead unit combination model of the gas-electricity combined system is:

[0037]

[0038] Where N g is the number of traditional thermal power units, N gas is the number of gas units, N ACU is the number of compressors, N p2g is the number of power-to-gas units, is the coal consumption cost of thermal power unit i at time t, C sui，tis the startup cost of thermal power unit i at time t, C sdi，t is the shutdown cost of thermal power unit i at time t, is the power generation of gas unit i at time t, is the gas consumption of gas generator set i at time t, is the gas price corresponding to gas generator set i at time t, is the quadratic cost coefficient of gas unit i at time t, is the power consumption of power-to-gas unit i at time t, is the gas production of power-to-gas unit i at time t, is the gas price corresponding to the power-to-gas unit i at time t, is the quadratic cost coefficient of power-to-gas unit i at time t, c coal is the real-time price of standard coal in that month, c ACU is the power cost coefficient of the compressor, is the power consumption of compressor i at time t.

[0039] The constraints of the day-ahead unit combination model of the gas-electricity combined system are:

[0040] (1) Electric power balance constraints:

[0041]

[0042] In the formula, is the wind power of wind farm i at time t, is the load power of load j at time t, is the operating power of compressor j at time t;

[0043] (2) Power system branch capacity constraints:

[0044]

[0045] In the formula, C mn is the upper limit of the transmission power between node m and node n, The relationship matrix between the node injection power and branch power flow power of the thermal power unit in the power system is obtained. The relationship matrix between the injected power and branch power flow of the gas generator node in the power system is obtained. The relationship matrix between the power injection power and branch power flow power of the power system power-to-gas unit node is calculated. The relationship matrix between the power injection into wind farm nodes and the branch power flow is Develop a power-to-branch power flow relationship matrix for power system load nodes;

[0046] (3) Operation constraints of thermal power units:

[0047]

[0048] In the formula, u i，t is the start and stop status of thermal power unit i at time t, is the maximum ramp-up power of thermal power unit i, is the maximum down-slope power of thermal power unit i, is the maximum startup power of thermal power unit i, is the maximum shutdown power of thermal power unit i;

[0049] (4) Minimum start and stop time constraints:

[0050]

[0051] Where, T i U is the minimum startup time that unit i needs to maintain, T i D is the minimum downtime that unit i needs to maintain;

[0052] The minimum start-stop time constraint at the beginning of the simulation period needs to be constrained in combination with the initial start-stop state of the unit. If the unit is in the start-up state at the initial time t=0, the minimum start-stop constraint is:

[0053]

[0054] In the formula, is the time that unit i has been started before the simulation period;

[0055] The minimum downtime constraint after degradation is as follows, ensuring that i D The internal unit cannot be restarted:

[0056] u i，t ≤u i，t-1 ≤T i D

[0057] If the unit is in shutdown state at the initial time t=0, the minimum start-stop constraint is:

[0058]

[0059] Where, T i D0 is the length of time that unit i has been shut down before the simulation period;

[0060] The minimum startup time constraint after degradation is as follows, ensuring that i U The internal unit cannot be shut down again:

[0061] ui，t-1 ≤u i，t t≤T i D

[0062] (5) Gas unit operation constraints:

[0063]

[0064] In the formula, is the upper limit of the output of gas generator set i, is the gas-to-electricity conversion efficiency of gas generator set i, is the gas consumption of gas generator set i at time t;

[0065] (6) Power-to-gas unit operation constraints:

[0066]

[0067] Where P i p2g，max is the upper limit of the power of the power-to-gas unit i, is the conversion efficiency of power-to-gas unit i, is the gas production of power-to-gas unit i at time t;

[0068] (7) Relaxation of coal consumption in thermal power generation:

[0069]

[0070] In the formula, a i，k 、b i，k are the first-order coefficient and the vertical axis intercept coefficient of the kth segment of the coal consumption curve of thermal power unit i after piecewise linearization, k max is the number of segments of the coal consumption curve of thermal power units;

[0071] (8) Relaxation of thermal power start-up and shutdown costs:

[0072]

[0073] In the formula, is the single startup cost of thermal power unit i, is the single shutdown cost of thermal power unit i.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] In the method for optimizing the day-ahead unit combination of a gas-electricity combined system taking into account pipeline climbing of the present invention, a natural gas system model taking into account the dynamic process of pipeline climbing is proposed. The model fully considers the fluid mechanics characteristics of natural gas in the pipeline, and at the same time accurately models the compressor to deal with the problem of gas pressure exceeding the limit that may occur due to pipeline climbing, thereby solving the problem of inaccurate modeling of the existing model. At the same time, the proposed method for optimizing the day-ahead unit combination of a gas-electricity combined system can make full use of gas units, power-to-gas units and compressors to exchange energy between the natural gas system and the power system, thereby improving the flexibility of the gas-electricity combined system and effectively promoting the consumption of wind power. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the method for optimizing the day-ahead unit combination of a gas-electricity combined system taking pipeline ramping into account according to the present invention.

[0077] Figure 2 It is a flow chart of using the C&CG algorithm in the present invention to solve the day-ahead robust scheduling problem of the gas-electricity combined system.

[0078] Figure 3 It is a schematic diagram of the topology of a 39-node power system in an embodiment of the present invention.

[0079] Figure 4 27-node natural gas system topology diagram in an embodiment of the present invention.

[0080] Figure 5 It is a schematic diagram of electric power load, wind power forecast value and natural gas load in an embodiment of the present invention.

[0081] Figure 6 It is a schematic diagram of a startup mode of a thermal power unit in an embodiment of the present invention.

[0082] Figure 7 Schematic diagram of the air pressure exceeding limit in each calculation example in the embodiment of the present invention. DETAILED DESCRIPTION

[0083] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0084] See also Figure 1 , Figure 2 , a method for optimizing the day-ahead unit commitment of a gas-fired power system taking pipeline ramping into account, the method comprising the following steps:

[0085] S1. Establish a natural gas dynamic process pipeline transmission model taking into account pipeline ramp;

[0086] For natural gas in the pipeline, its transmission process is driven by the pressure at both ends of the pipeline and is related to its own temperature, density and other factors; the natural gas flow process in the pipeline can be regarded as a one-dimensional fluid motion process with state variables of velocity, density and pressure; this design considers the slow dynamic process caused by the change of natural gas node load, so it is assumed that this process is a constant temperature process, that is, the influence of temperature change is ignored. The natural gas dynamic process is described by the following three equations: pipeline momentum equation, pipeline material balance equation and gas state equation.

[0087] The pipeline momentum equation, namely the Navier-Stokes equation, is used to describe the momentum transfer of pipeline natural gas:

[0088]

[0089] Where t is time; x is spatial distance; p is natural gas pressure, in Pa; ω is natural gas flow rate, in m / s; ρ is natural gas density parallel to the horizontal plane, in kg / m 3 ρ a is the density of natural gas at an angle α with the horizontal plane, in kg / m 3 ; d is the pipe diameter, in m; g is the acceleration due to gravity, in m / s 2 ;λ is the friction coefficient;

[0090] In the formula, Describes the acceleration effect of natural gas in the pipeline. describes the convection effect of natural gas, Describes the static effect of natural gas, g(ρ-ρ a )sinɑ describes the effect of horizontal height on the momentum equation, represents the second-order deviatoric stress tensor component;

[0091] The material balance equation in a natural gas pipeline describes the flow of materials in the pipeline:

[0092]

[0093] Through the speed of sound c, the gas state equation is constructed between the pressure and density of natural gas:

[0094] p=c 2 ρ

[0095] Where p is the natural gas pressure and ρ is the natural gas density;

[0096] The momentum transfer equation of natural gas in pipelines based on fluid mechanics is very complex. Both the natural gas momentum equation and the pipeline material balance equation are complex partial differential equations. This design simplifies these two equations through certain assumptions.

[0097] Since the convection term only exists when the fluid velocity is close to the speed of sound, this term can be ignored for the natural gas flow process in the pipeline. Under the above assumptions, the natural gas momentum equation can be simplified to:

[0098]

[0099] Since the deviator stress tensor in the momentum equation is a nonlinear term containing the product of the gas flow rate ω and the quadratic term and the gas density ρ, in order to linearize the equation, the average gas flow rate is used. To approximate the quadratic term in the simplified form:

[0100]

[0101] At the same time, the natural gas material flow rate M, in kg / s, is used to represent the flow of natural gas in the pipeline. It has the following relationship with the natural gas density ρ, the natural gas flow velocity ω and the pipeline cross-sectional area A:

[0102] M=ρωA

[0103] The natural gas mass flow rate M is used to replace the natural gas flow rate ω in the simplified natural gas momentum equation and pipeline material balance equation. At the same time, the natural gas density ρ in the equation is expressed by pressure p using the state equation, which can be further simplified:

[0104]

[0105] After a certain simplification, the natural gas momentum equation and pipeline material balance equation are still partial differential equations and cannot be directly applied in the field of optimization. Therefore, the Lax-Wendroff difference method is used to differentiate the above partial differentials in two steps. The general form of the Lax-Wendroff difference method is as follows:

[0106]

[0107] Where Δt and Δx are the differential steps of time and space distance, respectively.

[0108] The finite difference element of the Lax-Wendroff difference method has second-order accuracy and a truncation error of O(Δt 2 +Δx 2 ).

[0109] right The Lax-Wendroff difference approximation is performed, in which a variable step size is used for the spatial distance x, that is, for the dynamic equation and material balance equation of each pipeline ij, Δx is equal to the pipeline length L ij, and the pipeline node subscript i+1 also corresponds to the pipeline end node j; for any pipeline ij, there are linearized natural gas momentum equations and pipeline material balance equations:

[0110] Natural gas momentum equation:

[0111]

[0112] In the formula, A ij is the cross-sectional area of ​​the pipe ij, M Fij，t+1 is the natural gas material flow rate at the front end of pipeline ij at time t+1, M Eij，t+1 is the natural gas material flow at the end of pipeline ij at time t+1, M Fij，t is the natural gas material flow rate at the front end of pipeline ij at time t, M Eij，t is the natural gas material flow rate at the end of pipeline ij at time t, Δt is the time step, L ij is the length of the pipe ij, p j，t+1 is the natural gas pressure at the end node j of pipeline ij at time t+1, p i，t+1 is the natural gas pressure at the front node i of pipeline ij at time t+1, p j，t is the natural gas pressure at the end node j of pipeline ij at time t, p i，j is the natural gas pressure at the front node i of the pipeline ij at time t, g is the gravity acceleration, α is the angle between the pipeline ij and the horizontal plane, c is the speed of sound, λ is the friction coefficient, is the average flow rate of natural gas in pipeline ij, d ij is the diameter of the pipe ij;

[0113] Pipeline material balance equation:

[0114]

[0115] The boundary condition constraints of the nodes in the natural gas system are:

[0116] For each natural gas node, the node inlet gas is equal to the node outlet gas, that is, the node material balance constraint:

[0117]

[0118] Where, MD k，t is the natural gas load of node k at time t, including the gas consumption of the gas unit and the gas production of the power-to-gas unit; (·)k is the set of natural gas pipelines with the front node k, and k(·) is the set of natural gas pipelines with the end node k;

[0119] For the source node in the natural gas system, the gas pressure is stable at a certain value:

[0120]

[0121] In the formula, K s is the source node set, p si，0 is the constant value of the air pressure at the source node;

[0122] The upper and lower limit constraints of pipeline material flow and node pressure:

[0123]

[0124] When the natural gas pipeline becomes longer and the pipeline slope becomes larger (i.e., a long pipeline with a high drop height occurs), the node gas pressure drops or rises significantly, causing the natural gas pressure to fail to meet the constraint conditions, resulting in the natural gas system experiencing a pressure over-limit situation. In addition, large-scale natural gas systems require the addition of compressors and other pressurizing equipment to ensure that natural gas operates under safety constraints. Therefore, it is very necessary to consider the natural gas pipeline climbing according to the dynamic process in the integrated energy system.

[0125] S2. Establish a natural gas pipeline compressor power consumption model;

[0126] In order to solve the problem of gas pressure exceeding the limit caused by the natural gas pipeline climbing, a compressor is set at the key nodes of the natural gas pipeline to adjust the node gas pressure. The compressor power consumption model is as follows:

[0127]

[0128] Where, M is the compressor power consumption constant, R is the molar gas constant, T is the gas temperature; n is the compression ratio, p j is the natural gas pressure at the end node j of pipeline ij, p i is the natural gas pressure at the front node i of pipeline ij;

[0129] Because the compressor power consumption model is a nonlinear model, in order to embed the compressor model in the natural gas system, the compressor model must be linearized; and because the compressor regulates the gas pressure by multiple compression pumps working at the same time, the compressor regulates the node gas pressure discretely;

[0130] Assuming that a compressor has m gears that can be adjusted, the compression ratio n is:

[0131]

[0132] In the formula, α i is the decision variable, representing that the compressor is running at the i-th gear; n i is the compression ratio of the compressor running in the i-th gear;

[0133] The compressor power consumption model can be transformed into:

[0134]

[0135] S3. Taking minimizing the operating cost of the gas-electricity combined system as the objective function, a day-ahead unit combination model of the gas-electricity combined system taking into account pipeline ramping is established;

[0136] Based on the proposed linearized model of natural gas dynamic process considering pipeline ramping, and further considering the uncertainty brought by large-scale wind power access, a robust day-ahead unit combination scheduling model for gas-power combined system is established. Through the feasibility sub-problem test, the day-ahead unit combination results can adapt to all day-ahead wind power scenarios without exceeding the system constraints.

[0137] The objective function of the day-ahead unit combination model of the gas-electricity combined system is the operating cost of the gas-electricity combined system, including the operating cost of traditional thermal power units, gas units and power-to-gas units, and the power-to-gas revenue is deducted. The above costs are all unit operating costs under the expected wind power scenario. The cost of the thermal power unit is linearized using a piecewise linear function to obtain the following objective function:

[0138]

[0139] Where N g is the number of traditional thermal power units, N gas is the number of gas units, N ACU is the number of compressors, N p2g is the number of power-to-gas units, is the coal consumption cost of thermal power unit i at time t, C sui，t is the startup cost of thermal power unit i at time t, C sdi，t is the shutdown cost of thermal power unit i at time t, is the power generation of gas unit i at time t, is the gas consumption of gas generator set i at time t, is the gas price corresponding to gas generator set i at time t, is the quadratic cost coefficient of gas unit i at time t, is the power consumption of power-to-gas unit i at time t, is the gas production of power-to-gas unit i at time t, is the gas price corresponding to the power-to-gas unit i at time t, is the quadratic cost coefficient of power-to-gas unit i at time t, c coal is the real-time price of standard coal in that month, c ACU is the power cost coefficient of the compressor, is the power consumption of compressor i at time t;

[0140] The constraints of the day-ahead unit combination model of the gas-electricity combined system are:

[0141] (1) Electric power balance constraints:

[0142]

[0143] In the formula, is the wind power of wind farm i at time t, is the load power of load j at time t, is the operating power of compressor j at time t;

[0144] (2) Power system branch capacity constraints:

[0145]

[0146] Where D mn is the upper limit of the transmission power between node m and node n, The relationship matrix between the node injection power and branch power flow power of the thermal power unit in the power system is obtained. The relationship matrix between the injected power and branch power flow of the gas generator node in the power system is obtained. The relationship matrix between the power injection power and branch power flow power of the power system power-to-gas unit node is calculated. The relationship matrix between the power injection into wind farm nodes and the branch power flow is Develop a power-to-branch power flow relationship matrix for power system load nodes;

[0147] (3) Operation constraints of thermal power units:

[0148]

[0149] In the formula, u i，t is the start and stop status of thermal power unit i at time t, is the maximum ramp-up power of thermal power unit i, is the maximum down-slope power of thermal power unit i, is the maximum startup power of thermal power unit i, is the maximum shutdown power of thermal power unit i;

[0150] The above five formulas are respectively the upper and lower limit constraints of the output of thermal power unit i, the upward climbing constraint of unit i, the downward climbing constraint of unit i, the maximum power constraint of thermal power unit i at the start-up time, and the maximum power constraint of thermal power unit i at the shutdown time; M is a large constant, which is used to ensure that the unit climbing constraint involving the unit shutdown time is always established, and the maximum start-stop power constraint of the unit is always established when the thermal power unit is in the start-up state;

[0151] (4) Minimum start and stop time constraints:

[0152]

[0153] In the formula, is the minimum startup time that unit i needs to maintain, is the minimum downtime that unit i needs to maintain;

[0154] The minimum start-stop time constraint at the beginning of the simulation period needs to be constrained in combination with the initial start-stop state of the unit. If the unit is in the start-up state at the initial time t=0, the minimum start-stop constraint is:

[0155]

[0156] Where, T i U0 is the time that unit i has been started before the simulation period;

[0157] The minimum downtime constraint after degradation is as follows, ensuring that i D The internal unit cannot be restarted:

[0158] u i，t ≤u i，t-1 t≤T i D

[0159] If the unit is in shutdown state at the initial time t=0, the minimum start-stop constraint is:

[0160]

[0161] Where, T i D0 is the length of time that unit i has been shut down before the simulation period;

[0162] The minimum startup time constraint after degradation is as follows, ensuring that i U The internal unit cannot be shut down again:

[0163] u i，t-1 ≤u i，t ≤T i D

[0164] (5) Gas unit operation constraints:

[0165]

[0166] Where P i gas，max is the upper limit of the output of gas generator set i, is the gas-to-electricity conversion efficiency of gas generator set i, is the gas consumption of gas generator set i at time t; the above two equations are the upper and lower limit constraints of the output of gas generator set i and the corresponding relationship constraint of gas consumption-power generation of gas generator set i respectively;

[0167] (6) Power-to-gas unit operation constraints:

[0168]

[0169] Where P i p2g，max is the upper limit of the power of the power-to-gas unit i, is the conversion efficiency of power-to-gas unit i, is the gas production of the power-to-gas unit i at time t; the above two equations are respectively the upper and lower limit constraints of the power of the power-to-gas unit i and the corresponding relationship constraint between the power consumption and gas production of the power-to-gas unit i;

[0170] (7) Relaxation of coal consumption in thermal power generation:

[0171]

[0172] In the formula, a i，k 、b i，k are the first-order coefficient and the vertical axis intercept coefficient of the kth segment of the coal consumption curve of thermal power unit i after piecewise linearization, k max is the number of segments of the coal consumption curve of thermal power units;

[0173] (8) Relaxation of thermal power start-up and shutdown costs:

[0174]

[0175] In the formula, is the single startup cost of thermal power unit i, is the single shutdown cost of thermal power unit i;

[0176] S4. Use C&CG algorithm to solve the day-ahead robust dispatch problem of gas-electricity combined system;

[0177] The day-ahead unit combination problem is the main problem, which is used to solve the decision-making day-ahead startup method, while the feasibility sub-problem is used to verify whether the obtained startup method meets all wind power scenarios. If not, the wind power scenario is returned to generate new related constraints. Finally, the startup method that can meet the unit startup constraints in all wind power scenarios is obtained by iteration.

[0178] When the slack variable When both are 0, it means that under the obtained startup mode, all wind power scenarios can meet the constraints of the gas-power combined system.

[0179] If the feasibility subproblem optimization objective function is not 0, there is a slack variable If it is not 0, it means that there are wind power scenarios that do not meet the system constraints.

[0180] In order to ensure that the operation constraints of the gas-electricity combined system are met in all wind power scenarios, it is necessary to perform a feasibility check on the unit combination (start-up mode) obtained by solving the main problem. The feasibility sub-problem can be simplified as follows:

[0181]

[0182] In the formula, x is the optimization variable of the feasibility sub-problem, including thermal power output, gas unit output, power-to-gas unit output and auxiliary variable s; w is a random variable, that is, wind power random output; b is the objective function coefficient column vector, the coefficient corresponding to the auxiliary variable s is 1, and the rest are 0. The constraints are consistent with the main problem constraints, including power balance constraints, power system branch flow constraints, unit operation constraints, natural gas state variable constraints, etc. Among them, the constraints that need to add slack variables are the optimal thermal power startup mode obtained by solving the main problem. Constraints, namely thermal power operation constraints:

[0183]

[0184] In the formula, is the slack variable, It corresponds to the output of thermal power units in random wind power scenarios.

[0185] If the feasibility subproblem optimization objective function is 0, that is, all slack variables is 0, indicating that under the obtained startup mode, all wind power scenarios can meet the constraints of the gas-power combined system; if the feasibility sub-problem optimization objective function is not 0, there is a slack variable If it is not 0, it means that there are wind power scenarios that do not meet the system constraints.

[0186] The feasibility subproblem is a max-min problem, which is a two-level optimization problem with the same inner and outer optimization objective functions. The duality theory can be used to transform the min problem in the feasibility subproblem into its dual form. For the min problem, the random variable w is a known parameter (non-optimization variable), so the problem can be transformed into the following form:

[0187]

[0188] Where π is the constraint Gx+Mw+Eu in the original problem * ≤h dual variable. Nonlinear terms (Mw) appear in the objective function of the dual variable. T π, this embodiment uses binary representation and big-M method to simplify the nonlinear term.

[0189] In the robust algorithm, as long as the wind power extreme scenario meets the constraints, all wind power scenarios can meet the constraints. Substituting for the random variable w, the limiting scenario is expressed as follows:

[0190]

[0191] In the formula, Δ w is the interval of wind power random variables, v is a 0 / 1 integer variable, representing whether the wind power limit scenario takes the upper bound or the lower bound, so the nonlinear term (Mw) T π is converted to:

[0192] (Mw) T π=(M w +MΔ w v) T π

[0193] =(M w ) T π++(MΔ w v) T π

[0194] In the formula, (MΔ w v) T π is a bilinear term of multiplication of an integer variable and a continuous variable, which can be linearized using the Big M method. Let x tem is the intermediate variable (MΔ w v) T π, which satisfies the following constraints:

[0195] 0-N c v≤x em ≤0+N c v

[0196] (MΔ w ) T π-N c (1-v)≤x tem ≤(MΔ w ) T π+N c (1-v)

[0197] Where N c is a sufficiently large constant, when v=0, (MΔ w v) T π=x tem =0; when v = 1, (MΔ w v) T π=x tem =(MΔ w ) T π. At this point, the original feasibility subproblem is transformed into a mixed integer optimization problem that can be solved directly:

[0198]

[0199] sG T π≤b

[0200] π≤0

[0201] 0-N c v≤x tem ≤0+N c v

[0202] (MΔ w ) T π-N c (1-v)≤x tem ≤(MΔ w ) T π+N c (1-v)

[0203] The C&CG algorithm obtains a wind power scenario that does not meet the system operation constraints by solving the feasibility sub-problem, and then substitutes the wind power scenario into the main problem to solve the startup method that satisfies both the wind power scenario and the predicted wind power scenario.

[0204] This example analyzes a gas-electricity combined system consisting of a 39-node power system and a 27-node natural gas system. Figure 3 , Figure 4 As shown; the gas-electricity combined system has a total of 6 coal-fired units, 2 gas-fired units, 2 wind turbines, and 2 power-to-gas (P2G) units; the power system nodes 32 and 33 are connected to the natural gas system nodes 13 and 22 through the gas units, and the power system nodes 17 and 22 are connected to the natural gas system nodes 27 and 8 through the P2G units. The unit parameters are shown in Table 1.

[0205] Table 1 Parameters of gas-electricity combined system units

[0206]

[0207] The power load of the gas-electricity combined system, the predicted value of wind power, and the natural gas load are Figure 5 As shown;

[0208] This embodiment designs the following four examples for comparison:

[0209] Example 1: Deterministic optimal scheduling of a gas-electricity system without considering the dynamic process of natural gas pipeline ramping;

[0210] Example 2: Deterministic optimal scheduling of a gas-electricity system taking into account the dynamic process of natural gas pipeline ramping;

[0211] Example 3: Unit Commitment Optimization Method for Gas-Power Combined System Considering Natural Gas Dynamic Process State Constraints with Pipeline Ramp;

[0212] Example 4: The unit combination optimization method of the gas-fired power system taking into account the uncertainty of wind power and the natural gas dynamic process constraints of pipeline ramping, that is, the algorithm proposed in this design;

[0213] The startup modes of thermal power units in each case are as follows: Figure 6 As shown;

[0214] Compared with the basic example 1, the example 2 which takes into account the pipeline climbing and the example 3 which takes into account the natural gas state constraint, the output of the gas unit and the P2G are inconsistent, but their size only changes the output distribution of the traditional unit, which is not serious enough to adjust the startup mode. The gas pressure conditions of nodes 15 and 16 in each example are as follows: Figure 7 As shown in the figure, it can be seen that the pressure of nodes 15 and 16 exceeds the limit in Example 1 and Example 2. In Example 3, the compressor is enabled to make the node pressure within the safe range of the upper and lower limits of the pressure. In Example 4, the uncertainty of wind power ±20% is considered in the example, and the startup mode is changed, such as Figure 6 (d) As shown; Example 4 adds the shutdown of unit 3 (200MW) at time t = 1 to 15h on the basis of Example 3. This is because the node air pressure peak and wind power peak overlap at about t = 14h. In order to ensure that the air pressure of nodes 15 and 16 does not exceed the limit, the gas unit must ensure a certain output. Therefore, compared with Example 3, the downward adjustment space of the generator set in Example 4 is reduced. In order to have a solution under +20% wind power, Example 4 shuts down one more thermal power unit 3.

[0215] In the wind power forecasting scenario, the total system cost of each case is shown in Table 2. Case 1, which does not consider the dynamic constraints of natural gas and the uncertainty of wind power, has the lowest total system cost, while the system costs of cases 2 and 3 are higher than those of case 1. Case 4, which takes into account the dynamic constraints of natural gas and the uncertainty of wind power, has the highest cost. This is because: considering the dynamic constraints of natural gas will reduce the output adjustment space of gas units and P2G units. In order to ensure that the gas pressure at the natural gas node does not exceed the limit, the gas units with higher costs need to maintain a certain output value, resulting in an increase in the total system cost; and considering the uncertainty of wind power requires the startup mode to simultaneously meet the ±20% wind power deviation so that the system can operate stably, resulting in an increase in cost.

[0216] Table 2 Total system cost of each example

[0217]

[0218] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing the unit commitment of a gas-fired power system taking into account pipeline ramping, characterized in that: The method comprises the following steps: S1. Establish a natural gas dynamic process pipeline transmission model taking into account pipeline ramp; The natural gas dynamics are described by the following three equations: Natural gas momentum equation: In the formula, A ij is the cross-sectional area of ​​the pipe ij, M Fij，t+1 is the natural gas material flow rate at the front end of pipeline ij at time t+1, M Eij，t+1 is the natural gas mass flow rate at the end of pipeline ij at time t+1, MF ij，t is the natural gas material flow rate at the front end of pipeline ij at time t, M Eij，t is the natural gas material flow rate at the end of pipeline ij at time t, Δt is the time step, L ij is the length of the pipe ij, p j，t+1 is the natural gas pressure at the end node j of pipeline ij at time t+1, p i，t+1 is the natural gas pressure at the front node i of pipeline ij at time t+1, p j，t is the natural gas pressure at the end node j of pipeline ij at time t, p i，t is the natural gas pressure at the front node i of the pipeline ij at time t, g is the gravity acceleration, α is the angle between the pipeline ij and the horizontal plane, c is the speed of sound, λ is the friction coefficient, is the average flow rate of natural gas in pipeline ij, d ij is the diameter of the pipe ij; Pipeline material balance equation: Gas state equation: p=c 2 ρIn the formula, p is the natural gas pressure and ρ is the natural gas density; S2. Establish a natural gas pipeline compressor power consumption model; A compressor is set at the natural gas pipeline node to adjust the node gas pressure. The compressor power consumption model is as follows: Where, M is the compressor power consumption constant, R is the molar gas constant, T is the gas temperature; n is the compression ratio, p j is the natural gas pressure at the end node j of pipeline ij, p i is the natural gas pressure at the front node i of pipeline ij; Assuming that a compressor has m gears that can be adjusted, the compression ratio n is: In the formula, α i is the decision variable, representing that the compressor is running at the i-th gear; n i is the compression ratio of the compressor running in the i-th gear; The compressor power consumption model can be transformed into: S3. Taking minimizing the operating cost of the gas-electricity combined system as the objective function, a day-ahead unit combination model of the gas-electricity combined system taking into account pipeline ramping is established; S4. The C&CG algorithm is used to solve the day-ahead robust dispatch problem of the gas-fired power system.

2. The method for optimizing the day-ahead unit commitment of a gas-electricity combined system taking pipeline ramping into account according to claim 1, characterized in that: The boundary condition constraints of the nodes in the natural gas system are: Node material balance constraints: Where M Dk，t is the natural gas load of node k at time t, including gas consumption of gas units and gas production of power-to-gas units; (.)k is the set of natural gas pipelines with front-end node k, and k(.) is the set of natural gas pipelines with end node k; For the source node in the natural gas system, the gas pressure is stable at a certain value: In the formula, K s is the source node set, p si，0 is the constant value of the air pressure at the source node; The upper and lower limit constraints of pipeline material flow and node pressure:

3. The method for optimizing the day-ahead unit commitment of a gas-electricity combined system taking pipeline ramping into account according to claim 1, characterized in that: In step S3, the objective function of the day-ahead unit combination model of the gas-electricity combined system is: Where N g is the number of traditional thermal power units, N gas is the number of gas units, N ACU is the number of compressors, N p2g is the number of power-to-gas units, is the coal consumption cost of thermal power unit i at time t, C sui，t is the startup cost of thermal power unit i at time t, C sdi，t is the shutdown cost of thermal power unit i at time t, is the power generation of gas unit i at time t, is the gas consumption of gas generator set i at time t, is the gas price corresponding to gas generator set i at time t, is the quadratic cost coefficient of gas unit i at time t, is the power consumption of power-to-gas unit i at time t, is the gas production of power-to-gas unit i at time t, is the gas price corresponding to the power-to-gas unit i at time t, is the quadratic cost coefficient of power-to-gas unit i at time t, c coal is the real-time price of standard coal in that month, c ACU is the power cost coefficient of the compressor, is the power consumption of compressor i at time t.

4. The method for optimizing the day-ahead unit commitment of a gas-electricity combined system taking pipeline ramping into account according to claim 3, characterized in that: The constraints of the day-ahead unit combination model of the gas-electricity combined system are: (1) Electric power balance constraints: In the formula, is the wind power of wind farm i at time t, is the load power of load j at time t, is the operating power of compressor j at time t; (2) Power system branch capacity constraints: In the formula, C mn is the upper limit of the transmission power between node m and node n, The relationship matrix between the node injection power and branch power flow power of the thermal power unit in the power system is obtained. The relationship matrix between the injected power and branch power flow of the gas generator node in the power system is obtained. The relationship matrix between the power injection power and branch power flow power of the power system power-to-gas unit node is calculated. The relationship matrix between the power injection into wind farm nodes and the branch power flow is Develop a power-to-branch power flow relationship matrix for power system load nodes; (3) Operation constraints of thermal power units: In the formula, u i，t is the start and stop status of thermal power unit i at time t, is the maximum ramp-up power of thermal power unit i, is the maximum down-slope power of thermal power unit i, is the maximum startup power of thermal power unit i, is the maximum shutdown power of thermal power unit i; (4) Minimum start and stop time constraints: Where, T i U is the minimum startup time that unit i needs to maintain, T i D is the minimum downtime that unit i needs to maintain; The minimum start-stop time constraint at the beginning of the simulation period needs to be constrained in combination with the initial start-stop state of the unit. If the unit is in the start-up state at the initial time t=0, the minimum start-stop constraint is: Where, T i U0 is the time that unit i has been started before the simulation period; The minimum downtime constraint after degradation is as follows, ensuring that i D The internal unit cannot be restarted: in i，t in i，t-1 t≤T i D If the unit is in shutdown state at the initial time t=0, the minimum start-stop constraint is: Where, T i D0 is the length of time that unit i has been shut down before the simulation period; The minimum startup time constraint after degradation is as follows, ensuring that i U The internal unit cannot be shut down again: in i，t-1 in i，t t≤T i D (5) Gas unit operation constraints: Where P i gas，max is the upper limit of the output of gas generator set i, is the gas-to-electricity conversion efficiency of gas generator set i, is the gas consumption of gas generator set i at time t; (6) Power-to-gas unit operation constraints: Where P i p2g，max is the upper limit of the power-to-gas unit i, is the conversion efficiency of the power-to-gas unit i, is the gas production of power-to-gas unit i at time t; (7) Relaxation of coal consumption constraints for thermal power generation: In the formula, a i，k 、b i，k are the first-order coefficient and the vertical axis intercept coefficient of the kth segment of the coal consumption curve of thermal power unit i after piecewise linearization, k max is the number of segments of the coal consumption curve of thermal power units; (8) Relaxation of thermal power start-up and shutdown costs: In the formula, is the single startup cost of thermal power unit i, is the single shutdown cost of thermal power unit i.

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