CN108846507A - Electric-gas coupled system based on MIXED INTEGER Second-order cone programming economic load dispatching method a few days ago - Google Patents
Electric-gas coupled system based on MIXED INTEGER Second-order cone programming economic load dispatching method a few days ago Download PDFInfo
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Abstract
The invention discloses a kind of electric-gas coupled system based on MIXED INTEGER Second-order cone programming economic load dispatching methods a few days ago, with whole day energy and the minimum objective function of spare total cost, consider the constraint condition of electric system, the constraint condition of natural gas system and electric-gas coupling and transformational relation, establishes the Optimized model of electric-gas coupled system economic load dispatching a few days ago.On the basis of the model, by carrying out second order cone relaxation to gas pipeline steady-state gas flow equation, the MIXED INTEGER Second-order cone programming model of electric-gas coupled system economic load dispatching a few days ago is established, and solve and obtained initial launch scheme.For the inaccurate problem of natural gas system initial schedule result, the calibration model based on natural gas system steady parameter method is established, to be corrected to initial launch scheme.The present invention realizes the accurate solution of non-convex nonlinear optimal problem, dispatched a few days ago for electric-gas coupled system provide it is feasible, economical, accurately optimize operating scheme.
Description
Technical Field
The invention relates to a day-ahead economic dispatching method for an electric-gas coupling system, in particular to a day-ahead economic dispatching method for the electric-gas coupling system based on mixed integer second-order cone programming.
Background
In recent years, the construction and development of gas generator sets (gas turbine sets) using clean energy as fuel have been accelerated due to serious environmental pollution problems. Meanwhile, the breakthrough of the American shale gas technology greatly reduces the cost of natural gas and provides a new opportunity for the development of gas turbine units. Compared with the traditional coal-fired unit, the gas-fired unit has the advantages of rapid climbing, flexible control and the like in performance, so that the gas-fired unit is commonly used for balancing real-time load fluctuation and relieving peak shaving pressure of the system in an electric power system. With the rapid development of gas turbine units, an electric-gas coupling system using the gas turbine units as links and using a power network and a natural gas network as main transmission channels draws wide attention, and becomes an important technical means for improving the comprehensive utilization efficiency of energy and realizing multi-energy coordination and complementation.
The related research of the electric-gas coupling system is mainly developed from three levels of planning, operation and transaction, wherein the day-ahead economic dispatching of the electric-gas coupling system is a basic problem of the operation level, and aims to provide a day-ahead dispatching plan which meets the operation requirement of the system and realizes the optimal economy for a dispatcher. Compared with the day-ahead economic dispatching of a traditional power system, the electricity-gas coupling system needs to increase the related constraint of a natural gas network, wherein a steady-state gas flow equation of a gas transmission pipeline is expressed as a complex quadratic equation about pressure drop at two ends, so that the day-ahead economic dispatching optimization model of the electricity-gas coupling system is a non-convex non-linear mixed integer programming problem and is difficult to directly solve. Currently, to solve the above problems, three methods are generally adopted: the first is an intelligent algorithm, namely, a non-convex nonlinear optimization model is directly solved by utilizing traditional or improved intelligent algorithms such as a genetic algorithm, a particle swarm algorithm and the like; the second is a numerical iteration method, such as a Newton-Raphson method, a Newton trust domain method and other iteration methods, which can solve the non-linear problem of the steady-state air flow equation; the third method is a piecewise linearization method, which approximates the original non-convex nonlinear optimization model to a mixed integer linear programming problem by piecewise linearization of a steady-state gas flow equation of a gas transmission pipeline, thereby realizing solution.
At present, the piecewise linearization method has the advantages of simple algorithm, high stability, strong universality and the like, so that the piecewise linearization method is widely applied to solving the optimization problem of the electric-gas coupling system. However, the piecewise linearization method is an approximate method, and is difficult to obtain an accurate result of the day-ahead economic dispatching of the electric-gas coupling system, and the node air pressure of the natural gas network and the transmission flow of the gas transmission pipeline obtained by solving the method have large errors, so that the network operation requirement of the natural gas system cannot be met, and reasonable guidance and suggestion cannot be provided for the operation dispatching of the electric-gas coupling system. In order to improve the calculation accuracy, the piecewise linearization method needs to increase the number of segments, thereby greatly reducing the solution efficiency. Therefore, how to simultaneously ensure the calculation accuracy and the solution efficiency is a great challenge faced by the current day-ahead economic dispatch of the electric-gas coupling system.
Disclosure of Invention
The invention aims to provide a day-ahead economic dispatching method of an electric-gas coupling system based on mixed integer second-order cone programming.
In order to achieve the purpose, the invention adopts the following technical scheme:
1) taking the minimum total cost of the all-day energy and the reserve as an objective function, and considering the constraint condition of the power system, the constraint condition of the natural gas system and the relation between the electricity-gas coupling and the conversion, establishing an optimization model of the day-ahead economic dispatching of the electricity-gas coupling system; the constraint conditions of the natural gas system comprise a steady-state gas flow equation of the gas transmission pipeline;
2) performing second-order cone relaxation on a steady-state gas flow equation of a gas transmission pipeline in the optimization model to obtain a mixed integer second-order cone planning model of the day-ahead economic dispatching of the electric-gas coupling system;
3) solving the mixed integer second-order cone programming model to obtain an initial operation scheme of the day-ahead economic dispatch of the electric-gas coupling system;
4) establishing a correction model of the day-ahead economic dispatch of the electric-gas coupling system based on a natural gas system steady-state load flow calculation method;
5) and correcting the operation scheme part aiming at the natural gas system in the initial operation scheme by solving the correction model to obtain the optimal operation scheme of the day-ahead economic dispatching of the electric-gas coupling system. The optimal operation scheme comprises two parts: the first part is an operation scheme part (an accurate scheduling result of the power system) aiming at the power system in the initial operation scheme; the second part is the corrected operation scheme part for the natural gas system (the accurate scheduling result of the natural gas system).
Preferably, the power system comprises a power load, a coal-fired unit, a gas-fired unit and a power transmission line; the natural gas system comprises a natural gas load, a gas unit equivalent load, a gas well, a compressor and a gas transmission pipeline, wherein the compressor is driven by a gas turbine; the power system is coupled with the natural gas system through a gas turbine set.
Preferably, the objective function is expressed as:
wherein,representing the gas output, alpha, of the gas well u during the scheduling period tu,tRepresenting the gas purchase cost of the gas well u for the scheduled time period t,andrespectively representing the output power, the load standby and the accident standby of the coal-fired unit j in the scheduling time t,andrespectively representing the electric energy purchase cost, the load reserve purchase cost and the accident reserve purchase cost of the coal-fired unit j in a scheduling time interval T, wherein T represents a scheduling time interval, Nt、NspAnd NcAnd respectively representing the total number of the scheduling time intervals, the total number of the gas wells and the total number of the coal-fired units.
Preferably, the constraint conditions of the power system comprise a power balance equation, output power constraint of a coal-fired unit, output power constraint of a gas unit, climbing rate constraint of the coal-fired unit, climbing rate constraint of the gas unit, response time constraint of load standby, response time constraint of accident standby, system minimum capacity requirement of load standby, system minimum capacity requirement of accident standby and transmission power constraint of a power transmission line;
preferably, the constraint conditions of the natural gas system further include an airflow balance equation of a gas network node, a gas output constraint of a gas well, a gas pressure constraint of the gas network node, a transmission flow limit of a gas transmission pipeline, a gas consumption constraint of a compressor, a compression ratio constraint of the compressor, and a transmission flow constraint of the compressor;
the electric-gas coupling and conversion relation comprises the relation among the output power, the load reserve, the accident reserve and the gas consumption of the gas turbine, and the relation between the actual natural gas load of the gas network node and the equivalent load of the gas turbine.
Preferably, the step 2) specifically comprises the following steps:
2.1) carrying out equivalent transformation on a steady-state air flow equation of the gas transmission pipeline by using a large M method and a variable of 0-1;
2.2) performing second-order cone relaxation on the secondary equation obtained after transformation to obtain an inequality form and a segmented inequality form of the steady-state gas flow equation, and further equating the segmented inequality form of the steady-state gas flow equation to a segmented second-order cone form;
2.3) introducing two continuous variables according to the segmented second-order cone form, converting the segmented constraints of the two continuous variables into two groups of continuous linear constraints by using a large M method, and substituting the two continuous variables into the segmented second-order cone form of the steady-state airflow equation to obtain the second-order cone constraint of the steady-state airflow equation of the gas transmission pipeline.
Preferably, in the optimization model of the day-ahead economic dispatch of the electric-gas coupling system, the steady-state gas flow equation of the gas transmission pipeline is as follows:
wherein, cpDenotes the transmission constant, Fl, of the gas transmission line p connecting the nodes n 'and n' of the gas networkp,tRepresenting the delivery flow of the gas pipeline p during the scheduling period t, sgn (n ', n')p,tIs a symbolic function and represents the transmission direction, pi, of the gas transmission pipeline p in the scheduling time period tn′,tRepresenting the pressure value, pi, of the air network node n' during the scheduling period tn″,tIndicating the pressure value of the air network node n "during the scheduled time period t.
Preferably, in the mixed integer second-order cone planning model for the day-ahead economic dispatch of the electric-gas coupling system, the steady-state gas flow equation of the gas transmission pipeline is expressed as:
wherein u isp,tAnd vp,tRepresenting two successive variables, x, introduced for the gas pipeline p during the scheduling period tp,tIs a variable from 0 to 1 when xp,tWhen the value is 0, the transmission direction of the gas pipeline p in the scheduling period t is from the gas network node n' to the gas network node n ″, and when x isp,tWhen 1, it means that the transmission direction of the gas pipeline p in the scheduling period t is from the gas network node n ″ to the gas network node n', and M is an arbitrarily large positive number, not infinite.
Preferably, the correction model of the day-ahead economic dispatch of the electric-gas coupling system is represented as:
wherein, YtVector, Δ L, representing all unbalance quantities of the scheduling period ttVector, Δ Fl, representing the amount of flow imbalance of all the nodes of the air network during the scheduling period ttIndicating the transmission of all gas pipelines during the scheduled time period tA vector of flow unbalance quantities, delta tau represents a vector of air consumption unbalance quantities of all compressors in a scheduling period t, and delta pitVector, X, representing the amount of pressure imbalance of all compressors during the scheduled time period ttVector of all state variables, π, representing the scheduling period ttVector, Fl, representing the pressure values of all the nodes of the air network except the reference node of the air pressure during the scheduled time period ttVector representing the transmission flow composition of all gas transmission pipelines in a scheduling period t, Ft comA vector consisting of the delivery flows of all the compressors during the scheduling period t,vector, Δ G, representing the consumption composition of all compressors during the scheduled period ttAnd the total regulating quantity of the gas well gas output quantity in the scheduling period t is represented, and J represents a Jacobian matrix.
Preferably, the correction model is solved by a newton-raphson iteration method, including the following steps:
5.1) making the iteration number z equal to 0, and taking the operation scheme part aiming at the natural gas system in the initial operation scheme as XtInitial operating point of
5.2) calculating Y according to the calculation equation of the steady-state power flow of the natural gas system and the regulation equation of the gas well gas outputt zIf max (Y)t z) If the precision of epsilon is less than or equal to epsilon, the epsilon is convergence precision, then outputAs part of the operating scheme for the natural gas system in the optimal operating scheme, otherwise, go to 5.3);
5.3) calculating the Jacobian matrixThen correcting XtIs composed ofGo to 5.2).
The invention has the beneficial effects that:
the method takes the minimum total daily energy and standby cost as an objective function, comprehensively considers the constraint conditions of the power system, the constraint conditions of the natural gas system and the electric-gas coupling and conversion relation, and establishes an optimization model of the day-ahead economic dispatching of the electric-gas coupling system; the solution of the non-convex nonlinear optimization problem is realized by performing second-order cone relaxation on a steady-state air flow equation of the gas transmission pipeline; meanwhile, aiming at the problem that the initial scheduling result of the natural gas system is inaccurate, a correction model based on the steady-state load flow calculation of the natural gas system is established, and finally, a feasible, economic and accurate optimized operation scheme is provided for the day-ahead scheduling of the electricity-gas coupling system.
Drawings
Fig. 1 is a flowchart of a day-ahead economic dispatching method of an electric-gas coupling system based on mixed integer second-order cone programming.
FIG. 2 is a schematic diagram of an electro-pneumatic coupling test system according to an embodiment of the present invention; wherein, B1-B39 are power grid node numbers, and N1-N15 are air grid node numbers.
FIG. 3 is a graph of power and gas pre-day load predictions for an electro-pneumatic coupling test system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only for the purpose of illustrating the present invention and are not to be construed as limiting the present invention.
Referring to fig. 1, the day-ahead economic scheduling method of the electric-gas coupling system based on the mixed integer second-order cone programming, provided by the invention, comprises the following steps:
step 1, obtaining basic parameters and operation requirements needed by the day-ahead economic dispatching of the electric-gas coupling system.
The basic parameters include those of the power system as well as the natural gas system, as shown in table 1, where the compressor only considers the type of gas turbine drive; the operational requirements include scheduling intervals, response times for load and incident backups, and system minimum requirements for load and incident backups.
TABLE 1 basic parameters required for day-ahead economic dispatch of an electric-pneumatic coupled system
And 2, taking the minimum total daily energy and reserve cost as an objective function, considering the constraint condition of the power system, the constraint condition of the natural gas system and the electric-gas coupling and conversion relation, and establishing an optimization model of the day-ahead economic dispatching of the electric-gas coupling system.
The objective function of the optimization model is represented as:
wherein,representing the gas output, alpha, of the gas well u during the scheduling period tu,tRepresenting the gas purchase cost of the gas well u for the scheduled time period t,andrespectively representing the output power, the load standby and the accident standby of the coal-fired unit j in the scheduling time t,andrespectively representing the electric energy purchase cost, the load reserve purchase cost and the accident reserve purchase cost of the coal-fired unit j in a scheduling time interval T, wherein T represents a scheduling time interval, Nt、NspAnd NcAnd respectively representing the total number of the scheduling time intervals, the total number of the gas wells and the total number of the coal-fired units.
The constraint conditions of the optimization model comprise:
1) constraints of an electric power system
The power balance equation is shown in formula (2), the output power constraints of the coal-fired unit and the gas-fired unit are respectively shown in formulas (3) and (4), the climbing rate constraints of the coal-fired unit and the gas-fired unit are shown in formula (5), the response time constraints of the load reserve and the accident reserve are respectively shown in formulas (6) and (7), the minimum capacity requirements of the system of the load reserve and the accident reserve are shown in formula (8), and the transmission power constraint of the power transmission line is shown in formula (9);
wherein,andrespectively representing the output power, the load standby and the accident standby of the gas unit i in the scheduling time t,representing the predicted value of the power load of the grid node b in the scheduling period t, Ng、NbRespectively represents the total number of the gas turbine units and the total number of the power grid nodes,and ri gRespectively representing the maximum output power, the minimum output power and the climbing rate of the gas turbine set i,andrespectively representing the most important of coal-fired units jHigh output power, minimum output power and ramp rate, T-1 represents the last scheduling period, Ta、TrRespectively representing the response time of the load backup regulation and the response time of the accident backup regulation,minimum system demand for load reserve, minimum system demand for emergency reserve, Plk,tRepresents the transmission power, Pl, of the transmission line k during the scheduling period tkmax、PlkminRespectively represents the maximum transmission power and the minimum transmission power of the transmission line k, HkbIs a power transmission distribution factor, represents the influence of the injected power of the grid node b on the transmission power of the transmission line k,the element of the row b and the column i of the gas turbine group-power grid node incidence matrix is represented,and (3) elements of a b-th row and a j-th column of the coal-fired unit-grid node incidence matrix are represented.
2) Constraints of natural gas system
The gas flow balance equation of the gas network nodes is shown in a formula (10), the gas output constraint of the gas well is shown in a formula (11), the gas pressure constraint of each gas network node is shown in a formula (12), the steady-state gas flow equation of the gas transmission pipeline is shown in formulas (13) and (14), the transmission flow limit of the gas transmission pipeline is shown in a formula (15), and the gas consumption constraint, the compression ratio constraint and the transmission flow constraint of the compressor are respectively shown in formulas (16), (17) and (18);
wherein,representing the actual value of the natural gas load of the gas network node n during the scheduling period t, cpRepresenting the transmission constant, Fl, of the gas transmission line p (connecting gas network nodes n' and n ″)p,tRepresenting the transmission flow of the gas transmission pipeline p in the scheduling period t,representing the transmission flow of compressor q (connecting gas network nodes l and l') during the scheduled time period t,representing the air consumption of the compressor q during the scheduled time period t,the element of the nth row and the u th column of the gas well-gas network node incidence matrix is represented,the element of the nth row and the pth column of the gas transmission pipeline-gas network node incidence matrix is represented,the element representing the nth row and the qth column of the compressor-grid node correlation matrix,element representing the nth row and the qth column of the compressor drive-gas network node association matrix, Nf、NcomRespectively representing the total number of gas transmission pipelines and the total number of compressors,respectively represents the maximum gas output and the minimum gas output of the gas well u, and pin,tRepresenting the pressure value, pi, of the air network node n during the scheduling period tnmax、πnminRespectively representing the maximum air pressure value, the minimum air pressure value, sgn (n ', n')p,tIs a symbolic function and represents the transmission direction, pi, of the gas transmission pipeline p in the scheduling time period tn′,tRepresenting the pressure value, pi, of the air network node n' during the scheduling period tn″,tIndicating the pressure value, Fl, of the air network node n' during the scheduled time period tpmax、FlpminRespectively represents the maximum transmission flow and the minimum transmission flow of the gas transmission pipeline p,the air consumption coefficient of the compressor q is generally 3-5%,representing the compression ratio of the compressor q during the scheduled period t,respectively representing the minimum compression ratio and the maximum compression ratio of the compressor q,respectively representing the maximum transmission flow, the minimum transmission flow, pi, of the compressor ql',tRepresenting the air pressure value, pi, of the air network node l' during the scheduling period tl,tRepresenting the air pressure value of the air network node l during the scheduled time period t.
3) Electric-to-gas coupling and conversion relation
The natural gas consumed by the gas turbine unit when providing output power, load standby and accident standby is respectively shown as formulas (19), (20) and (21), and the actual natural gas load of each gas network node is the sum of the initial predicted value and the equivalent load of the gas turbine unit, as shown as a formula (22);
wherein,andrespectively representing that the gas turbine set i provides output power, load standby and accident in the scheduling time tSpare gas consumption, GHV denotes a fixed high heating value,represents the heat consumption coefficient of the gas turbine set i,representing the predicted value of the natural gas load of the gas network node n in the scheduling period t,representing the equivalent load of the gas turbine set i during the scheduling period t,and elements of the nth row and the ith column of the gas turbine set-gas network node incidence matrix are represented.
And 3, performing second-order cone relaxation on the steady-state air flow equation of the gas transmission pipeline on the basis of the optimization model established in the step 2, and establishing a mixed integer second-order cone planning model for the day-ahead economic dispatching of the electric-gas coupling system.
The second-order cone relaxation is carried out on the steady-state gas flow equation of the gas transmission pipeline, and the specific process is as follows:
1) equations (13) and (14) are equivalently transformed using the large M method and the 0-1 variable, as shown in equations (23) - (25):
wherein x isp,tIs a variable from 0 to 1 when xp,tWhen it is 0, it indicates transmissionThe transmission direction of the air pipeline p in the scheduling period t is from the air network node n 'to the air network node n', when x isp,tWhen 1, the transmission direction of the gas transmission pipeline p in the scheduling period t is from the gas network node n ″ to the gas network node n', and M is a positive number which is arbitrarily large (but not infinite);
2) the second order cone relaxation is directly performed on the quadratic equation in equation (25), resulting in the inequality form shown in equation (26), and the piecewise inequality form shown in equation (27), where equation (27) is further equivalent to a piecewise second order cone, as shown in equation (28):
3) to obtain the standard form of the second-order cone constraint, two continuous variables u are introducedp,tAnd vp,tUsing the large M method to transform up,tAnd vp,tThe piecewise constraint (equation (29)) is rewritten into two continuous linear constraints as shown in equations (30) - (31), and finally the two continuous variables are substituted into equation (28) to obtain the standard second-order cone constraint of the steady-state gas flow equation of the gas transmission pipeline as shown in equation (32):
wherein u isp,tAnd vp,tTwo continuous variables are shown that are newly introduced for the gas pipeline p at the scheduled time period t.
The established mixed integer second-order cone programming model of the day-ahead economic dispatch of the electric-gas coupling system is as follows:
an objective function: formula (1)
And 4, solving the mixed integer second-order cone programming model established in the step 3 to obtain an initial operation scheme of the day-ahead economic dispatch of the electric-gas coupling system.
The initial operating scheme comprises two parts: the first part is the accurate scheduling result of the power system, including the output power of the coal-fired unit in each scheduling periodLoad reserveRotate for standbyAnd the output power of the gas turbineLoad reserveRotate for standbyAnd transmission power Pl of the transmission linek,t(ii) a The second part is the initial scheduling result of the natural gas system, including the equivalent load of the gas turbine set in each scheduling periodCompression ratio of compressorAnd gas well gas outputAir pressure value pi of air network noden,tFlow Fl of gas pipelinep,tDelivery flow of compressorAnd the gas consumption of the compressorSubsequent correction consisting only of pit、Flt、And Δ Gt。
And 5, establishing a correction model of the day-ahead economic dispatch of the electric-gas coupling system based on the natural gas system steady-state load flow calculation method.
The correction model is only used for correcting the initial scheduling result of the natural gas system, and the specific establishment process is as follows:
1) the gas flow distribution of the natural gas system is calculated by adopting a multi-balance node model, namely the gas flow unbalance can be maintained to be balanced by adjusting the gas well gas output quantities, and the steady-state power flow calculation equation of the natural gas system is shown as an equation (33) according to equation equations (10), (13), (16) and (17), wherein the gas well gas output quantities are adjusted according to the equation (34):
wherein, Δ Ln,tRepresenting the amount of flow imbalance, Δ Fl, of the air network node n during the scheduling period tp,tRepresenting the amount of transmission flow imbalance of the gas transmission pipeline p in the scheduling period t,represents the amount of unbalance of the air consumption of the compressor q in the scheduling period t, delta piq,tRepresenting the amount of pressure unbalance, Δ G, of the compressor q during the scheduled time period ttThe total regulating quantity (the initial value is 0) of gas well gas output quantity representing the scheduling time period t is deltau,tRepresenting the unbalance apportionment coefficient of the gas well u in the scheduling time period t,representing the initial gas output of the gas well u in the scheduling time period t;
2) as shown in equation (35), all the unbalance amounts of the scheduling period t constitute a vector YtAll state variables except the pressure variable of the gas pressure reference node constitute a vector Xt(ii) a And (3) performing Taylor expansion on the formula (33) at a given initial operating point, and obtaining a modified formula of the steady-state power flow calculation formula of the natural gas system after only a first-order term is reserved, wherein the modified formula is shown in formulas (36) to (37):
wherein, Δ Lt＝[ΔL1,t；…；ΔLn,t；…],ΔFlt＝[ΔFl1,t；…；ΔFlp,t；…],Δπt＝[Δπ1,t；…；Δπq,t；…],πt＝[π1,t；…；πq,t；…](degassing pressure reference node), Flt＝[Fl1,t；…；Flp,t；…], Representing the initial operating point given by the scheduling period t, and J represents the jacobian matrix of the correction equation.
And 6, solving the correction model established in the step 5, correcting the initial operation scheme obtained in the step 4, and finally outputting the optimal operation scheme of the day-ahead economic dispatching of the electric-gas coupling system.
The solution of the correction model can adopt a Newton-Raphson iteration method, and the specific process is as follows:
substep-1: let the iteration number z be 0 and the convergence accuracy epsilon be 10-6The initial scheduling result of the natural gas system is used as a state variable XtThe initial operating point of (a);
substep-2: calculating the unbalance amount Y according to the equations (33) - (34)t zIf max (Y)t z) Not more than epsilon (taking the maximum value of the iteration values of all the unbalance quantities at this time), and outputting the state variableAs a result of the accurate scheduling of the natural gas system, otherwise, going to substep-3;
substep-3: calculating the Jacobian matrix according to equation (37)The state variable is then modified according to equation (36) toReturn to substep-2.
The optimal operation scheme output in the step 6 comprises two parts: the first part is an accurate scheduling result of the power system in the initial operation scheme; and the second part is a corrected accurate scheduling result of the natural gas system.
Simulation example
Referring to fig. 1, the day ahead economic dispatch scheme for an electro-pneumatic coupling test system is as follows:
the first step is as follows: obtaining basic parameters and operation requirements required by day-ahead economic dispatching of the electricity-gas coupling test system. The electricity-gas coupling test system (figure 2) consists of an IEEE 39 node power system and a 15 node natural gas system, and comprises 8 coal-fired units, 5 gas-fired units, 2 gas wells, 46 power transmission lines, 12 transmission pipelines and 4 compressors. The detailed data of the coal-fired unit and the gas-fired unit are shown in tables 2 and 3, and the day-ahead prediction curves of the power load and the natural gas load are shown in fig. 3. The scheduled scheduling time interval is 1 hour, the load standby response time is 5 minutes, the accident standby response time is 10 minutes, the minimum demand of the system of the load standby is 2% of the total power load, the minimum demand of the system of the accident standby is 8% of the total power load, and the maximum single unit capacity is larger.
TABLE 2 detailed data of coal-fired units in the electric-gas coupling test System
TABLE 3 detailed data of gas turbine units in the electric-gas coupling test System
The second step is that: the method comprises the steps of taking the minimum total daily energy and reserve cost as an objective function, considering the constraint condition of a power system, the constraint condition of a natural gas system and the relation between electric-gas coupling and conversion, and establishing an optimization model of the day-ahead economic dispatching of an electric-gas coupling system, wherein the electricity purchasing cost is shown in table 2, the gas purchasing cost is 190$/MMSCF (1# gas well) and 210$/MMSCF (2# gas well), and the gas consumption coefficient of a compressor is 3%.
The third step: performing second-order cone relaxation on the steady-state gas flow equation of the gas transmission pipeline on the basis of the optimization model established in the second step, wherein the value of M is 106And establishing a mixed integer second-order cone programming model of the day-ahead economic dispatch of the electric-gas coupling system in the Matlab platform.
The fourth step: and solving the mixed integer second-order cone planning model established in the third step by using Gurobi optimization software to obtain an initial operation scheme of the day-ahead economic dispatching of the electric-gas coupling system, wherein the accurate dispatching result of the electric power system is shown in Table 4.
The fifth step: and establishing a correction model of the day-ahead economic dispatching of the electric-gas coupling system based on the natural gas system steady-state load flow calculation method. Wherein the unbalance apportionment coefficient of each gas well is deltau,t＝1/Nsp。
And a sixth step: solving the correction model established in the fifth step by using a Newton-Raphson iterative method, correcting the initial operation scheme (specifically, correcting the initial scheduling result of the natural gas system) obtained in the fourth step, and finally outputting the optimal operation scheme (consisting of the accurate scheduling result of the power system obtained in the fourth step and the accurate scheduling result of the natural gas system obtained by correcting the initial scheduling result of the natural gas system) of the day-ahead economic scheduling of the electric-gas coupling system, wherein the minimum cost of the energy and the reserve in the whole day is 2.1578 multiplied by 106$ natural gas $The system fine scheduling results are shown in table 5.
TABLE 4 accurate scheduling result statistics for power systems in electro-pneumatic coupling test systems
TABLE 5 accurate scheduling results for natural gas systems in electro-pneumatic coupling test systems
In addition, the scheduling result is compared with the scheduling result obtained by the conventional piecewise linearization method in terms of five aspects, i.e., the objective function value, the second-order cone constraint number, the integer variable number, the calculation time and the maximum error, as shown in table 6, where the number of segments in the piecewise linearization method is 10.
TABLE 6 comparison of the method of the invention with conventional piecewise linearization
Taking the day-ahead economic dispatch of the electric-gas coupling test system shown in fig. 2 as an example, as can be seen from the dispatch results of the simulation examples, the invention realizes the solution of the non-convex nonlinear day-ahead economic dispatch optimization problem of the electric-gas coupling test system by performing second-order cone relaxation on the steady-state gas flow equation of the gas transmission pipeline, and obtains an accurate dispatch result by using the correction model. Compared with a common piecewise linearization method, the method provided by the invention has the advantages that the objective function value obtained by solving is obviously reduced, the calculation time is effectively shortened, and the maximum error is greatly reduced. Therefore, the method can obtain a scheduling result with better economical efficiency on the basis of ensuring the calculation precision and the solving efficiency.
In a word, the method aims at minimizing the total daily energy and the standby total cost, obtains the final optimized operation scheme of the day-ahead economic dispatching of the electric-gas coupling system by solving the mixed integer second-order cone planning model and the correction model based on the steady-state load flow calculation of the natural gas system, and is suitable for various electric-gas coupling systems to carry out feasible, economic and accurate day-ahead economic dispatching.
Claims (10)
1. The day-ahead economic dispatching method of the electric-gas coupling system based on mixed integer second-order cone programming is characterized by comprising the following steps of: the method comprises the following steps:
1) taking the minimum total cost of the all-day energy and the reserve as an objective function, and considering the constraint condition of the power system, the constraint condition of the natural gas system and the relation between the electricity-gas coupling and the conversion, establishing an optimization model of the day-ahead economic dispatching of the electricity-gas coupling system; the constraint conditions of the natural gas system comprise a steady-state gas flow equation of the gas transmission pipeline;
2) performing second-order cone relaxation on a steady-state gas flow equation of a gas transmission pipeline in the optimization model to obtain a mixed integer second-order cone planning model of the day-ahead economic dispatching of the electric-gas coupling system;
3) solving the mixed integer second-order cone programming model to obtain an initial operation scheme of the day-ahead economic dispatch of the electric-gas coupling system;
4) establishing a correction model of the day-ahead economic dispatch of the electric-gas coupling system based on a natural gas system steady-state load flow calculation method;
5) and correcting the operation scheme part aiming at the natural gas system in the initial operation scheme by solving the correction model to obtain the optimal operation scheme of the day-ahead economic dispatching of the electric-gas coupling system.
2. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the power system is coupled with the natural gas system through a gas turbine set.
3. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the objective function is represented as:
wherein,representing the gas output, alpha, of the gas well u during the scheduling period tu,tRepresenting the gas purchase cost of the gas well u for the scheduled time period t,andrespectively representing the output power, the load standby and the accident standby of the coal-fired unit j in the scheduling time t,andrespectively representing the electric energy purchase cost, the load reserve purchase cost and the accident reserve purchase cost of the coal-fired unit j in a scheduling time interval T, wherein T represents a scheduling time interval, Nt、NspAnd NcAnd respectively representing the total number of the scheduling time intervals, the total number of the gas wells and the total number of the coal-fired units.
4. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the constraint conditions of the power system comprise a power balance equation, output power constraint of a coal-fired unit, output power constraint of a gas unit, climbing rate constraint of the coal-fired unit, climbing rate constraint of the gas unit, response time constraint of load standby, response time constraint of accident standby, system minimum capacity requirement of load standby, system minimum capacity requirement of accident standby and transmission power constraint of a power transmission line;
the constraint conditions of the natural gas system further comprise an airflow balance equation of the gas network node, gas output constraint of the gas well, air pressure constraint of the gas network node, transmission flow limit of a gas transmission pipeline, gas consumption constraint of the compressor, compression ratio constraint of the compressor and transmission flow constraint of the compressor;
the electric-gas coupling and conversion relation comprises the relation among the output power, the load reserve, the accident reserve and the gas consumption of the gas turbine, and the relation between the actual natural gas load of the gas network node and the equivalent load of the gas turbine.
5. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the step 2) specifically comprises the following steps:
2.1) carrying out equivalent transformation on a steady-state air flow equation of the gas transmission pipeline by using a large M method and a variable of 0-1;
2.2) performing second-order cone relaxation on the secondary equation obtained after transformation to obtain an inequality form and a segmented inequality form of the steady-state gas flow equation, and further equating the segmented inequality form of the steady-state gas flow equation to a segmented second-order cone form;
2.3) introducing two continuous variables according to the segmented second-order cone form, converting the segmented constraints of the two continuous variables into two groups of continuous linear constraints by using a large M method, and substituting the two continuous variables into the segmented second-order cone form of the steady-state airflow equation to obtain the second-order cone constraint of the steady-state airflow equation of the gas transmission pipeline.
6. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: in the optimization model of the day-ahead economic dispatch of the electric-gas coupling system, a steady-state gas flow equation of a gas transmission pipeline is as follows:
wherein, cpDenotes the transmission constant, Fl, of the gas transmission line p connecting the nodes n 'and n' of the gas networkp,tRepresenting the delivery flow of the gas pipeline p during the scheduling period t, sgn (n ', n')p,tIs a symbolic function and represents the transmission direction, pi, of the gas transmission pipeline p in the scheduling time period tn′,tRepresenting the pressure value, pi, of the air network node n' during the scheduling period tn″,tIndicating the pressure value of the air network node n "during the scheduled time period t.
7. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: in the mixed integer second-order cone planning model for the day-ahead economic dispatch of the electric-gas coupling system, the steady-state gas flow equation of the gas transmission pipeline is expressed as follows:
wherein, cpDenotes the transmission constant, u, of the gas transmission line p connecting the nodes n 'and n' of the gas networkp,tAnd vp,tRepresenting two successive variables, x, introduced for the gas pipeline p during the scheduling period tp,tIs a variable from 0 to 1 when xp,tWhen the value is 0, the transmission direction of the gas pipeline p in the scheduling period t is from the gas network node n' to the gas network node n ″, and when x isp,tWhen 1, the transmission direction of the gas pipeline p in the scheduling period t is from the gas network node n 'to the gas network node n', M is an arbitrarily large but not infinite positive number, and pin′,tRepresenting the pressure value, pi, of the air network node n' during the scheduling period tn″,tIndicating the pressure value, Fl, of the air network node n' during the scheduled time period tp,tWhich represents the transmission flow of the gas transmission pipeline p during the scheduled time period t.
8. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the correction model of the day-ahead economic dispatch of the electric-gas coupling system is expressed as follows:
wherein, YtVector, Δ L, representing all unbalance quantities of the scheduling period ttVector, Δ Fl, representing the amount of flow imbalance of all the nodes of the air network during the scheduling period ttExpressing the vector formed by the unbalance amount of the transmission flow of all the gas transmission pipelines in the scheduling time t, delta tau expressing the vector formed by the unbalance amount of the gas consumption of all the compressors in the scheduling time t, and delta pitVector, X, representing the amount of pressure imbalance of all compressors during the scheduled time period ttVector of all state variables, π, representing the scheduling period ttVector, Fl, representing the pressure values of all the nodes of the air network except the reference node of the air pressure during the scheduled time period ttVector representing the transmission flow composition of all gas transmission pipelines in a scheduling period t, Ft comA vector consisting of the delivery flows of all the compressors during the scheduling period t,vector, Δ G, representing the consumption composition of all compressors during the scheduled period ttAnd the total regulating quantity of the gas well gas output quantity in the scheduling period t is represented, and J represents a Jacobian matrix.
9. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system of claim 8, wherein: the correction model is solved by adopting a Newton-Raphson iteration method, and the method comprises the following steps:
5.1) making the iteration number z equal to 0,taking the operation scheme part aiming at the natural gas system in the initial operation scheme as XtInitial operating point of
5.2) calculating Y according to the calculation equation of the steady-state power flow of the natural gas system and the regulation equation of the gas well gas outputt zIf max (Y)t z) If the precision of epsilon is less than or equal to epsilon, the epsilon is convergence precision, then outputAs part of the operating scheme for the natural gas system in the optimal operating scheme, otherwise, go to 5.3);
5.3) calculating the Jacobian matrixThen correcting XtIs composed ofGo to 5.2).
10. The hybrid integer second-order cone programming-based day-ahead economic scheduling method of the electric-gas coupling system according to claim 1, characterized in that: the optimal operation scheme comprises two parts: the first part is an operation scheme part aiming at the power system in the initial operation scheme; the second section is a modified portion of the operating scheme for the natural gas system.
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