CN113988453A - Method, device and equipment for accelerating convex dispersion optimization of data of electric-gas interconnection system - Google Patents
Method, device and equipment for accelerating convex dispersion optimization of data of electric-gas interconnection system Download PDFInfo
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Abstract
The invention relates to an accelerated convex dispersion optimization method, device and equipment for data of an electric-gas interconnection system, wherein the method comprises the following steps: acquiring first parameter data, second parameter data and energy coupling data; performing nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network; performing iteration processing on the first parameter data, the second parameter data and the energy coupling data for n times by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor; and if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result. According to the method, the first parameter data, the second parameter data and the energy coupling data are subjected to alternative iterative processing through the combination of nonlinear non-convex constraint and Benders decomposition algorithm, so that the optimized calculation of the data of the electric-gas interconnection system is completed, the data calculation efficiency of the electric-gas interconnection system is improved, and the data transmission quantity is also reduced.
Description
Technical Field
The invention relates to the technical field of electrical data processing, in particular to a method, a device and equipment for accelerating the convex dispersion optimization of data of an electrical-gas interconnection system.
Background
The comprehensive energy system is a new-form system derived from a traditional power system, and the scheduling data of the existing electric-gas interconnected comprehensive energy system is generally subjected to centralized optimization solution. Under a centralized optimization framework, all data information of a power grid and a gas grid needs to be uploaded to an upper-layer center for unified calculation, and the data transmission quantity is large; in addition, the natural gas pipeline airflow equation is non-convex constraint, and has certain influence on the convergence of data dispersion solution in the electric-gas interconnection system.
With the continuous increase of the scale of the power grid and the gas grid, the problems of insufficient memory of a computer, data transmission bottleneck, information privacy and the like are gradually generated, the power network and the natural gas network belong to two departments, and the parameters of the grid frame and private information cannot be completely shared. Therefore, it is necessary to develop a dispersion optimization method for an electrical-pneumatic interconnection system.
Disclosure of Invention
The embodiment of the invention provides an accelerated convex dispersion optimization method, device and equipment for data of an electric-gas interconnection system, which are used for solving the technical problems of low calculation efficiency and large data transmission quantity in the existing processing of data of a power grid and data of a gas grid.
In order to achieve the above object, the embodiments of the present invention provide the following technical solutions:
a test platform is connected with a converter valve to be tested, the converter valve to be tested comprises a power module and a bypass switch connected with the power module, and the accelerated convex dispersion optimization method comprises the following steps:
s1, acquiring first parameter data of a power network, second parameter data of a natural gas network and energy coupling data of the power network and the natural gas network;
s2, performing nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network;
s3, carrying out n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor;
s4, if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result; wherein the convergence condition is:
in the formula, epsilon1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1Is a penalty function for k-1 iterations.
Preferably, the method for accelerating the convex dispersion optimization of the data of the electric-gas interconnection system comprises the following steps: and S5, if the relaxation variable and/or the penalty function do not meet the convergence condition, updating the penalty factor, and executing the step S3 again.
Preferably, the applying a nonlinear non-convex constraint process to the second parameter data to obtain the relaxation variable of the natural gas network includes:
processing the second parameter data by adopting a natural gas pipeline gas flow formula to obtain a transmission characteristic constant of the natural gas pipeline;
processing the second parameter data and the transmission characteristic constant by adopting non-convex constraint to obtain a constraint inequality of the natural gas;
performing reduced term linearization processing on the constraint inequality in a first-order Taylor expansion mode to obtain a linearization constraint inequality;
and performing multiple iteration processing on the second parameter data and the transmission characteristic constant to obtain a relaxation variable meeting the linearization constraint inequality.
Preferably, the natural gas pipeline gas flow formula is:
the constraint inequality is:
the linearization constraint inequality is:
in the formula,. DELTA.xijIs the space step length between the natural gas pipeline node i and the node j, M2In order to be a constant of the transfer characteristic,
for the gas pressure at location d between natural gas pipeline node i and node j at time t,
for the gas pressure at position d +1 between natural gas pipeline node i and node j at time t,
for the amount of gas flow between natural gas pipeline node i and node j at position d at time t,
the gas pressure after k-1 iterations at the position d between the natural gas pipeline node i and the node j at the time t,
for the gas flow after k-1 iterations at position d between natural gas pipeline node i and node j at time t,
and k is a natural number greater than zero, and is a relaxation variable at a position d between the natural gas pipeline node i and the node j at the time t, namely the relaxation variable of the natural gas network.
Preferably, the obtaining a penalty function and a penalty factor by performing n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data according to the relaxation variables and by using a Benders decomposition algorithm includes:
performing relaxation treatment on the first parameter data and the energy coupling data by adopting a convex quadratic constraint inequality to obtain a natural gas network variable and a natural gas flow;
if the target function of the natural gas network has a solution, obtaining a solution vector, and processing the natural gas network variable and the natural gas flow by adopting a coupling constraint formula to obtain a Benders cut constraint inequality;
if the objective function of the natural gas network has no solution, increasing the fuel gas relaxation variable of the coupling constraint, and processing the natural gas network variable, the natural gas flow and the energy coupling data by adopting the natural gas network constraint of the Benders decomposition algorithm to obtain a feasible Benders cut constraint inequality;
carrying out iteration processing on the Benders cut constraint inequality and the feasibility Benders cut constraint inequality for n times by adopting the power network constraint of the Benders decomposition algorithm to obtain an upper boundary and a lower boundary of the target function;
if the upper boundary and the lower boundary meet the optimal solution condition, obtaining a penalty factor;
and constituting a penalty function by the penalty factor, the optimization target of the energy coupling data and the relaxation variable.
Preferably, the convex quadratic constraint inequality is: f. ofGT,a,t≥h2，a(PGT,a,t)2+h1,aPGT,a,t+h0,a，a∈ΩGT，
a∈ΩGT(ii) a In the formula (f)GT，a，tThe natural gas flow h consumed by the gas turbine set a at the moment t0，aIs the first consumption characteristic coefficient h of the gas turbine set a1，aIs the second consumption characteristic coefficient, h, of the gas turbine unit a2，aIs the third consumption characteristic coefficient of the gas unit a, a is the serial number of the gas unit, omegaGTAs a gasSet of units, PGT，a，tThe active power of the gas turbine set a at the moment t,
is a natural gas network variable.
Preferably, the objective function is:
the coupling constraint is as follows:
s.t.
the Benders cuts the inequality of constraint as: fgas(gn)+Fpower(p)+(λn)TE(p-pn)≤μ；
In the formula, FgasFor the purpose of a natural gas network,
is the relaxation variable between natural gas pipeline node i and node j at time t at position d, omegadFor a collection of natural gas pipeline locations, ΩpipeIs a set between different nodes i and j, T is a set of moments, pkA is a penalty factor after the kth iteration, a is the number of the gas turbine set, omegaGTIs the set of gas units, b is the number of the electric-to-gas units, omegaP2GIs a collection of electric gas-converting machine sets,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
as a natural gas network variable, hP2GIs the conversion coefficient of electricity to gas,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tMu is real variable, g is active power consumed by the electric gas conversion unit b after the nth iteration at the moment tnIs the solution vector of the nth iteration, E is the coefficient matrix of coupling constraint, FpowerFor a power network objective, p is a decision vector for the power network objective,
as a result of the nth iteration, lambdanCoupled to the contracted multiplier vector in the nth iteration.
Preferably, the natural gas network constraints are:
min v
s.t. natural gas network constraints
The feasible Benders cuts the inequality of constraint as:
the power network constraints are:
minμ
s.t. power network constraints
Fgas(gn)+Fpower(p)+(λn)TE(p-pn)≤μ
The optimal solution conditions are as follows: i UB-LB|≤ε|LB|；
In the formula etacFor the c-th coupled constraint, v is the sum of the individual gas relaxation variables, UBIs the upper boundary of the objective function, LBIs the lower boundary of the objective function, epsilon is the convergence parameter of the optimal solution,
as a function of the natural gas network variables,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
the gas relaxation variable for the c-th coupling constraint of gas train a,
the gas relaxation variable of the coupling constraint of the c-th of the electric gas conversion unit b,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tActive power h consumed by the electric gas-converting unit b after the nth iteration at the moment tP2GIs the conversion coefficient of electricity to gas,
coupling a constrained multiplier vector under the constraint of a natural gas network in the nth iteration, E is a coefficient matrix of the coupling constraint, p is a decision vector of a power network target,
as a result of the nth iteration, mu is a real variable, lambdanFor multiplying coupling constraints in the nth iterationSubvector, FpowerFor the purpose of the power network, FgasFor natural gas network purposes, gnIs the solution vector of the nth iteration.
The invention also provides an accelerating convex dispersion optimizing device of the data of the electric-gas interconnection system, which comprises a data processing module, a constraint processing module, a decomposition processing module and an optimizing output module;
the data processing module is used for acquiring first parameter data of the power network, second parameter data of the natural gas network and energy coupling data of the power network and the natural gas network;
the constraint processing module is used for carrying out nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network;
the decomposition processing module is used for carrying out n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor;
the optimization output module is used for outputting an optimization result if the relaxation variable and the penalty function both meet a convergence condition;
wherein the convergence condition is:
in the formula, epsilon1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1Is a penalty function for k-1 iterations.
The invention also provides an accelerating convex dispersion optimization device of the data of the electric-gas interconnection system, which comprises a processor and a memory;
the memory is used for storing program codes and transmitting the program codes to the processor;
the processor is configured to execute the method for accelerated convex-concave optimization of electrical-electrical interconnection system data according to instructions in the program code.
According to the technical scheme, the embodiment of the invention has the following advantages: the method, the device and the equipment for accelerating the convex dispersion optimization of the data of the electric-gas interconnection system comprise the following steps: acquiring first parameter data of a power network, second parameter data of a natural gas network and energy coupling data of the power network and the natural gas network; performing nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network; performing iteration processing on the first parameter data, the second parameter data and the energy coupling data for n times by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor; and if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result. The accelerated convex dispersion optimization method carries out alternate iterative processing on first parameter data, second parameter data and energy coupling data through the combination of nonlinear non-convex constraint and Benders decomposition algorithm, realizes the dispersion solution of the centralized optimization objective function and constraint of the power network and the natural gas network, thereby completing the optimization calculation of the data of the electric-gas interconnection system, improving the data calculation efficiency of the electric-gas interconnection system, reducing the data transmission quantity and solving the technical problems of low calculation efficiency and large data transmission quantity in the existing processing of the data of the power network and the gas network.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a flowchart illustrating steps of a method for accelerated convex-concave optimization of electrical-to-electrical interconnection system data according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for accelerated convex-concave optimization of electrical-to-electrical interconnect system data according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of gas relaxation variables and iteration times of an accelerated convex dispersion optimization method for data of an electrical-gas interconnection system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of gas relaxation variables and iteration times of an accelerated convex dispersion optimization method for data of an electrical-gas interconnection system according to an embodiment of the present invention;
fig. 5 is a block diagram of an apparatus for accelerated convex distribution optimization of electrical-to-electrical interconnection system data according to an embodiment of the present invention.
Detailed Description
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the embodiments described below are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the application provides an accelerated convex dispersion optimization method, device and equipment for data of an electric-gas interconnection system, and is used for solving the technical problems of low calculation efficiency and large data transmission quantity in the existing processing of data of a power grid and data of a gas grid.
The first embodiment is as follows:
fig. 1 is a flowchart illustrating steps of a method for optimizing data of an electrical-to-electrical interconnection system according to an embodiment of the present invention, and fig. 2 is a flowchart illustrating a method for optimizing data of an electrical-to-electrical interconnection system according to an embodiment of the present invention.
As shown in fig. 1 and fig. 2, an embodiment of the present invention provides a method for accelerating the convex dispersion optimization of data of an electrical-electrical interconnection system, including the following steps:
s1, acquiring first parameter data of a power network, second parameter data of a natural gas network and energy coupling data of the power network and the natural gas network.
It should be noted that the parameter data and the energy coupling data of the initialized power network and the initialized natural gas network are mainly acquired. The first parameter data of the power network comprises power network topological relation, transmission line resistance, reactance, power network node load, generator set output limit value, generator set power generation cost coefficient, generator set climbing speed, power and the like. The second parameter data of the natural gas network comprises a natural gas network topological relation, a natural gas network node air pressure limit value, a natural gas pipeline flow limit value, a natural gas network node air load, an air source output limit value, an air source supply cost, an air storage tank capacity and the like. In this embodiment, the first parameter data mainly includes a power network target, a decision vector of the power network target, and the like; the second parameter data mainly comprises natural gas network targets, pipeline positions, nodes, natural gas flow, consumed power, gas turbine units and the like.
In the embodiment of the invention, the interconversion of two energy sources is realized by a power to gas (P2G) through a gas turbine and an electricity-to-gas (P2 to gas) technology, the two energy flows of the power network and the natural gas network are coupled and constrained to be realized through a consumption characteristic equation of the gas turbine and a P2G electricity-to-gas conversion equation, and the consumption characteristic equation of the gas turbine is as follows: f. ofGT,a,t＝h2,a(PGT,a,t)2+h1,aPGT,a,t+h0,a a∈ΩGT(ii) a The P2G electro-pneumatic conversion equation is: f. ofP2G,b,t＝hP2GPP2G,b,t b∈ΩP2GIn the formula: omegaGTIs a collection of gas units, omegaP2GAs a collection of electric gas-converting units, fGT，a，tNatural gas flow rate, P, consumed by gas turbine set a at time tGT，a，tIs the active power of the gas turbine set a at the moment t, h0，aIs the first consumption characteristic coefficient h of the gas turbine set a1，aIs the second consumption characteristic coefficient, h, of the gas turbine unit a2，aIs the third consumption characteristic coefficient f of the gas unit aP2G，b，tThe active power consumed by the electric gas-converting unit b after the nth iteration at the time t,
for the natural gas converted by the electric gas-converting unit b after the nth iteration at the time tFlow rate, a is the number of the gas turbine set, b is the number of the electric gas turbine set, hP2GIs the conversion coefficient of electricity to gas.
It should be noted that the energy coupling data includes a consumption characteristic equation coefficient of the gas turbine, an electric-to-gas conversion coefficient, an electric-to-gas turbine, power consumption, a conversion coefficient, and the like.
And S2, carrying out nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network.
In step S2, the nonlinear non-convex constraint processing is mainly performed on the second parameter data of the natural gas network, such as gas pressure, gas flow, time step, space step, and the like, to obtain the relaxation variable of the natural gas network. The nonlinear non-convex constraint in step S2 is an outer layer processing method.
And S3, carrying out n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor.
It should be noted that, in step S3, the target functions in the electrical network and the natural gas network are alternately and iteratively processed by a Benders decomposition algorithm, and data conversion between the electrical network and the natural gas network is converted into an iterative process that gradually tightens the constraint relaxation domain, so as to obtain an optimal penalty function and penalty factor. Wherein, the Benders decomposition algorithm of the step S3 is an inner layer processing mode.
In the embodiment of the present application, the penalty function is:
wherein F is the electric gas-transfer target, WkFor the penalty function of the k-th iteration,
is the relaxation variable between natural gas pipeline node i and node j at position d at time t, rhokIs the penalty factor, Ω, after the kth iterationdFor a collection of natural gas pipeline locations, ΩpipeIs the set between different nodes i and j, and T is the set of time.
And S4, if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result.
In the embodiment of the present invention, the convergence condition is:
in the formula, epsilon1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1And k belongs to n, and n is a natural number greater than 0.
It should be noted that, in step S4, the relaxation variable obtained in step S2 and the penalty function in step S3 are mainly determined according to the convergence condition, and the natural gas flow and the active power required for the gas turbine unit to be converted between the natural gas network and the electrical network are output only when the convergence condition is satisfied; in the case where the convergence condition is not satisfied, step S5 is executed.
And S5, if the relaxation variable and/or the penalty function do not meet the convergence condition, updating the penalty factor, and executing the step S3 again.
It should be noted that, the slack variable obtained in step S2 and the penalty function in step S3 are mainly determined according to the convergence condition, and if one of the slack variable and the penalty function does not meet the convergence condition, the penalty factor needs to be updated, and the process is executed again according to step S3.
In the embodiment of the present invention, the rule for updating the penalty factor is: rhok+1＝min(vcρk,ρmax) In the formula, vcA coefficient is dynamically adjusted for a penalty factor, and vc>1，ρmaxIs the penalty factor maximum.
It should be noted that the maximum value of the dynamic adjustment coefficient and the penalty factor may be set according to the requirement, and is not limited herein.
The invention provides an accelerated convex dispersion optimization method of electric-gas interconnection system data, which comprises the following steps: acquiring first parameter data of a power network, second parameter data of a natural gas network and energy coupling data of the power network and the natural gas network; performing nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network; performing iteration processing on the first parameter data, the second parameter data and the energy coupling data for n times by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor; and if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result. The accelerated convex dispersion optimization method carries out alternate iterative processing on first parameter data, second parameter data and energy coupling data through the combination of nonlinear non-convex constraint and Benders decomposition algorithm, realizes the dispersion solution of the centralized optimization objective function and constraint of the power network and the natural gas network, thereby completing the optimization calculation of the data of the electric-gas interconnection system, improving the data calculation efficiency of the electric-gas interconnection system, reducing the data transmission quantity and solving the technical problems of low calculation efficiency and large data transmission quantity in the existing processing of the data of the power network and the gas network.
In an embodiment of the present invention, applying a nonlinear non-convex constraint process to the second parameter data to obtain a relaxation variable of the natural gas network includes:
processing the second parameter data by adopting a natural gas pipeline gas flow formula to obtain a transmission characteristic constant of the natural gas pipeline;
processing the second parameter data and the transmission characteristic constant by adopting non-convex constraint to obtain a constraint inequality of the natural gas;
performing reduced term linearization processing on the constraint inequality in a first-order Taylor expansion mode to obtain a linearization constraint inequality;
and carrying out iterative processing on the second parameter data and the transmission characteristic constant for multiple times to obtain a relaxation variable meeting the linearization constraint inequality.
In the embodiment of the invention, the natural gas pipeline gas flow formula is as follows:
the constraint inequality is: the constraint inequality is:
the linearized constraint inequality is:
in the formula,. DELTA.xijIs the space step length between the natural gas pipeline node i and the node j, M2In order to be a constant of the transfer characteristic,
for the gas pressure at location d between natural gas pipeline node i and node j at time t,
for the gas pressure at position d +1 between natural gas pipeline node i and node j at time t,
for the amount of gas flow between natural gas pipeline node i and node j at position d at time t,
the gas pressure after k-1 iterations at the position d between the natural gas pipeline node i and the node j at the time t,
for the gas flow after k-1 iterations at position d between natural gas pipeline node i and node j at time t,
and k is a natural number greater than zero, and is a relaxation variable at a position d between the natural gas pipeline node i and the node j at the time t, namely the relaxation variable of the natural gas network.
In the embodiment of the present invention, the natural gas pipeline gas flow formula may also be:
in the formula, M1For another transmission characteristic constant, Δ t is the time step between node i and node j of the natural gas pipeline.
It should be noted that the constraint inequality
Is a standard second order cone constraint, which is convex in nature; and the inequality of constraint
Is a difference constraint of a convex function, i.e. is a non-convex constraint.
In an embodiment of the present invention, the obtaining the penalty function and the penalty factor by performing n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data according to the relaxation variable and by using a Benders decomposition algorithm includes:
performing relaxation treatment on the first parameter data and the energy coupling data by adopting a convex quadratic constraint inequality to obtain a natural gas network variable and a natural gas flow;
if the objective function of the natural gas network has a solution, obtaining a solution vector, and processing the natural gas network variable and the natural gas flow by adopting a coupling constraint formula to obtain a Benders cut constraint inequality;
if the objective function of the natural gas network has no solution, increasing the fuel gas relaxation variable of the coupling constraint, and processing the natural gas network variable, the natural gas flow and the energy coupling data by adopting the natural gas network constraint of the Benders decomposition algorithm to obtain a feasible Benders cut constraint inequality;
carrying out iteration processing on the Benders cut constraint inequality and the feasibility Benders cut constraint inequality n times by adopting the power network constraint of the Benders decomposition algorithm to obtain an upper boundary and a lower boundary of the target function;
if the upper boundary and the lower boundary meet the optimal solution condition, obtaining a penalty factor;
and constituting a penalty function by a penalty factor, an optimization target of the energy coupling data and a relaxation variable.
In the embodiment of the present invention, the convex quadratic constraint inequality is: f. ofGT，a,t≥h2,a(PGT，a,t)2+h1,aPGT,a,t+h0,a，a∈ΩGT，
a∈ΩGT(ii) a In the formula (f)GT，a，tThe natural gas flow h consumed by the gas turbine set a at the moment t0，aIs the first consumption characteristic coefficient h of the gas turbine set a1，aIs the second consumption characteristic coefficient, h, of the gas turbine unit a2，aIs the third consumption characteristic coefficient of the gas unit a, a is the serial number of the gas unit, omegaGTIs a collection of gas-fired units, PGT，a，tThe active power of the gas turbine set a at the moment t,
is a natural gas network variable.
In the embodiment of the present invention, the objective function is:
the coupling constraint is:
s.t.
the Benders cut constraint inequality is: fgas(gn)+Fpower(p)+(λn)TE(p-pn)≤μ；
In the formula, FgasFor the purpose of a natural gas network,
is the relaxation variable between natural gas pipeline node i and node j at time t at position d, omegadFor a collection of natural gas pipeline locations, ΩpipeIs a set between different nodes i and j, T is a set of moments, pkA is a penalty factor after the kth iteration, a is the number of the gas turbine set, omegaGTIs the set of gas units, b is the number of the electric-to-gas units, omegaP2GIs a collection of electric gas-converting machine sets,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
as a natural gas network variable, hP2GIs the conversion coefficient of electricity to gas,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tMu is real variable, g is active power consumed by the electric gas conversion unit b after the nth iteration at the moment tnIs the solution vector of the nth iteration, E is the coefficient matrix of coupling constraint, FpowerFor a power network objective, p is a decision vector for the power network objective,
as a result of the nth iteration, lambdanCoupled to the contracted multiplier vector in the nth iteration.
In an embodiment of the invention, the natural gas network constraints are:
min v
s.t. natural gas network constraints
The feasible Benders cuts the constraint inequality as:
the power network constraints are:
minμ
s.t. power network constraints
Fgas(gn)+Fpower(p)+(λn)TE(p-pn)≤μ
The optimal solution conditions are as follows: i UB-LB|≤ε|LB|；
In the formula etacIs the gas relaxation variable of the c coupled constraint and is more than 0, v is the sum of all the gas relaxation variables, UBIs the upper boundary of the objective function, LBIs the lower boundary of the objective function, epsilon is the convergence parameter of the optimal solution,
as a function of the natural gas network variables,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
the gas relaxation variable for the c-th coupling constraint of gas train a,
the gas relaxation variable of the coupling constraint of the c-th of the electric gas conversion unit b,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tActive power h consumed by the electric gas-converting unit b after the nth iteration at the moment tP2GIs the conversion coefficient of electricity to gas,
coupling a constrained multiplier vector under the constraint of a natural gas network in the nth iteration, E is a coefficient matrix of the coupling constraint, p is a decision vector of a power network target,
as a result of the nth iteration, mu is a real variable, lambdanFor coupled-bound multiplier vectors in the nth iteration, FpowerFor the purpose of the power network, FgasFor natural gas network purposes, gnIs the solution vector of the nth iteration.
In the embodiment of the invention, because unnecessary natural gas consumption inevitably causes the increase of the operation cost and the carbon emission of the electric-gas interconnection system, the first parameter data, the second parameter data and the energy coupling data are subjected to nonlinear non-convex constraint by adopting a convex quadratic constraint inequality with a compact function to obtain the natural gas network variable and the natural gas flow; then, the centralized optimization of the data in the electricity-gas interconnection system is divided into a main problem of the optimal power flow of the power network and a sub problem of the optimal power flow of the natural gas network through a Benders decomposition algorithm based on the natural gas network variables and the natural gas flow, and the centralized optimization of the data in the electricity-gas interconnection system is realized through alternately iterating the main problem and the sub problem; finally, in the natural gas network optimal power flow subproblem, penalty factors are obtained in different modes mainly through whether a target function of the natural gas network has a solution or not, and the penalty functions are formed through the penalty factors, the optimization target of the energy coupling data and relaxation variables; the optimization result by the convergence condition is obtained in step S4 and step S5.
It should be noted that the natural gas target network in the target function of the natural gas network refers to the sum of the gas source cost, the natural gas storage cost, and the penalty term for the relaxation variable of the natural gas pipeline flow equation. G in the objective function of the natural gas network is a decision vector of the natural gas network optimal power flow subproblem, which is also called a solution vector of the objective function.
Mainly refers to the result of the nth iteration of the optimal power flow main problem of the power network. The natural gas network optimal power flow subproblem is expressed by adopting an objective function, and the alternative iteration main problem and the alternative iteration subproblem are realized by coupling a constraint equation and a Benders cut constraint inequality or a natural gas network constraint and a feasibility Benders cut constraint inequality. Substituting the generated Benders cut constraint inequality and the feasibility Benders cut constraint inequality into a power network constraint of a main problem in an iteration process to solve to obtain an upper boundary of an objective function iteration n times and a lower boundary of an iteration n +1 times; in the iterative processing process, the main problem and the sub-problems are solved repeatedly, namely the upper boundary and the lower boundary of the objective function are corrected step by step, and only if the upper boundary and the lower boundary meet the optimal solution condition, the optimal solution optimized in the data set in the electric-gas interconnection system is obtained, and the penalty factor of the optimal solution is obtained.
In the embodiment of the present invention, the method for accelerating the convex-concave optimization of the data of the electrical-pneumatic interconnection system is described by taking an electrical-pneumatic interconnection system in which an IEEE39 node power network and a belgium 20 node natural gas network are coupled as a case, and includes: the parameters influencing the convergence effect mainly comprise the initial value rho of the penalty factor0Dynamic adjustment of coefficient vc(refer to the gas relaxation variables), convergence tolerance ε1And ε2Setting the convergence tolerance to ε1＝10-4，ε2＝10-3To ensure the convergence accuracy, the convergence condition S4 has an epsilon of 10-5. Initial value rho based on penalty factor0Dynamic adjustment of coefficient vcThe impact on the convergence performance of the inner and outer layer algorithms (i.e., the nonlinear non-convex constraint and Benders decomposition algorithms).
For penalty factor initial value ρ0Target value and penalty factor initial value ρ0The ratio between the target value and the target value will influence the final effect of the algorithm, the target value is fixed in thousand orders, and rho is set0At 1X 10-4The convergence effect of the inner and outer layer algorithms is shown in table 1, varying from-10.
TABLE 1
As can be seen from Table 1 above, for PCCP-Benders, the smaller the magnitude of the initial value, the better the solution quality, when ρ0When the target value is more than or equal to 1, the result of the target value is slightly poor; when rho 010, the total iteration times are more, and the calculation time consumption is correspondingly increased; the above results show that the initial penalty of the nonlinear non-convex constraint on the relaxation domain cannot be too heavy, so that the algorithm searches in a more ideal region at the initial stage, thereby ensuring the convergence effect. In this embodiment, p may be calculated by comprehensively considering the target value and the number of iterations0Is arranged as 10-3。
Fig. 3 is a schematic diagram of a gas relaxation variable and an iteration number of an accelerated convex dispersion optimization method for data of an electrical-electrical interconnection system according to an embodiment of the present invention, and fig. 4 is a schematic diagram of a gas relaxation variable and an iteration number of an accelerated convex dispersion optimization method for data of an electrical-electrical interconnection system according to an embodiment of the present invention.
For dynamically adjusting coefficient vcThe penalty factor of the nonlinear non-convex constraint accelerates the convergence rate at the later stage of the iteration by dynamic adjustment, as shown in fig. 3. For PCCP-Benders, the coefficient v is dynamically adjustedcThe larger value leads the punishment to be increased too fast, the iteration times to be increased and the convergence result to be not ideal, and as can be seen from figure 3, the value of the value can have better convergence result and less convergence result between 2 and 4The number of iterations of (c).
Thus, the coefficient v is dynamically adjustedcUniformly taking a proper value vcChanging the carbon transaction price from $ 0 to $ 60/t, wherein the iteration process and time consumption of the PCCP-Benders are shown in FIG. 4, and as can be seen from FIG. 4, the PCCP-Benders algorithm has stable iteration characteristics and short convergence time, and when the 1 st iteration is used for solving the initial point, the iteration frequency of the inner layer electrical decoupling (Benders decomposition algorithm) is more, but the electrical decoupling frequency in the subsequent iterations is stabilized to be 2; the time for solving the initial point in the PCCP-Benders in the early stage is more than 75% of the total calculation time, but the subsequent iteration can be completed only by 5-7 s. PCCP-Benders are superior in computational efficiency because the natural gas system has sufficient capacity for gas consumption of gas units and variations in electricity to natural gas output, and the objective function of the optimization problem is a linear function, so sub-problems are usually solved and more optimality cut constraints can be generated. The optimality cut constraints are superposed in the main problem, and the PCCP-Benders can be guided to converge quickly. Then, the existing interior point method (IPOPT), the second-order cone programming method (SCOP), the mixed integer linear programming Method (MILP) and the PCCP centralized algorithm are respectively adopted to carry out centralized solution on the multi-period dynamic power flow model of the electricity-gas interconnection system, and the centralized solution is compared with the PCCP-Benders distributed solution, and the comparison result is shown in the table 2.
TABLE 2
As can be seen from the centralized optimization data in Table 2, the results of the three methods except the MILP method were calculated. The IPOPT algorithm does not find the optimal solution, and the result is a compromise solution. The optimized target value of the SOCP algorithm is minimum, but the dynamic airflow constraint of the natural gas pipeline is only inequality constrained by an equation
Convex relaxation is not compact and the calculation result does not satisfy all the constraints. For the dispersive optimization of the electric-gas decoupling, the PCCP-Benders can obtain a junction with almost centralized optimizationAnd the method is not much different from the centralized PCCP in the aspect of calculation time. Therefore, by adopting a proper decomposition algorithm and an acceleration strategy, the privacy of the information in the main body can be protected, and meanwhile, a high-quality result and calculation speed can be obtained.
In the embodiment of the invention, on the basis of ensuring the information privacy and the self-control rights of the power network and the natural gas network, the method for accelerating the convex-dispersed optimization of the data of the electric-gas interconnection system can accurately calculate the flow of the natural gas network and obtain a high-quality solution of the operation of the electric-gas interconnection system, namely a relaxation variable and a penalty factor.
Example two:
fig. 5 is a block diagram of an apparatus for accelerated convex distribution optimization of electrical-to-electrical interconnection system data according to an embodiment of the present invention.
As shown in fig. 5, an embodiment of the present invention further provides an apparatus for accelerating the convex dispersion optimization of data of an electrical-electrical interconnection system, including: the system comprises a data acquisition module 10, a constraint processing module 20, a decomposition processing module 30 and an optimization output module 40;
the data processing module 10 is configured to acquire first parameter data of a power network, second parameter data of a natural gas network, and energy coupling data of the power network and the natural gas network;
the constraint processing module 20 is configured to perform nonlinear non-convex constraint processing on the second parameter data to obtain a slack variable of the natural gas network;
the decomposition processing module 30 is configured to perform iteration processing on the first parameter data, the second parameter data and the energy coupling data for n times by using a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor;
an optimization output module 40, configured to output an optimization result if both the relaxation variable and the penalty function satisfy the convergence condition;
wherein the convergence condition is as follows:
in the formula，ε1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1Is a penalty function for k-1 iterations.
It should be noted that the modules in the second embodiment correspond to the steps in the first embodiment, and the steps in the first embodiment have been described in detail in the first embodiment, and the contents of the modules in the second embodiment are not described in detail in this second embodiment.
Example three:
the embodiment of the invention provides an accelerating convex dispersion optimization device for data of an electric-gas interconnection system, which comprises a processor and a memory;
a memory for storing the program code and transmitting the program code to the processor;
and the processor is used for executing the acceleration convex dispersion optimization method of the electric-electric interconnection system data according to the instructions in the program codes.
It should be noted that the processor is configured to execute the steps of the aforementioned method for accelerated convex hull optimization of electrical-to-electrical interconnect system data according to instructions in the program code. Alternatively, the processor, when executing the computer program, implements the functions of each module/unit in each system/apparatus embodiment described above.
Illustratively, a computer program may be partitioned into one or more modules/units, which are stored in a memory and executed by a processor to accomplish the present application. One or more modules/units may be a series of computer program instruction segments capable of performing specific functions, which are used to describe the execution of a computer program in a terminal device.
The terminal device may be a desktop computer, a notebook, a palm computer, a cloud server, or other computing devices. The terminal device may include, but is not limited to, a processor, a memory. Those skilled in the art will appreciate that the terminal device is not limited and may include more or fewer components than those shown, or some components may be combined, or different components, e.g., the terminal device may also include input output devices, network access devices, buses, etc.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable gate array (FPGA) or other Programmable logic device, discrete gate or transistor logic device, discrete hardware component, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The storage may be an internal storage unit of the terminal device, such as a hard disk or a memory of the terminal device. The memory may also be an external storage device of the terminal device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the terminal device. Further, the memory may also include both an internal storage unit of the terminal device and an external storage device. The memory is used for storing computer programs and other programs and data required by the terminal device. The memory may also be used to temporarily store data that has been output or is to be output.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. An accelerated convex dispersion optimization method for data of an electric-gas interconnection system is characterized by comprising the following steps:
s1, acquiring first parameter data of a power network, second parameter data of a natural gas network and energy coupling data of the power network and the natural gas network;
s2, performing nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network;
s3, carrying out n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor;
s4, if the relaxation variable and the penalty function both meet the convergence condition, outputting an optimization result;
wherein the convergence condition is:
in the formula, epsilon1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1Is a penalty function for k-1 iterations.
2. The method of accelerated convex dispersion optimization of electrical-to-electrical interconnection system data of claim 1, comprising: and S5, if the relaxation variable and/or the penalty function do not meet the convergence condition, updating the penalty factor, and executing the step S3 again.
3. The method of claim 1, wherein the obtaining slack variables of the natural gas network by applying nonlinear non-convex constraint processing to the second parameter data comprises:
processing the second parameter data by adopting a natural gas pipeline gas flow formula to obtain a transmission characteristic constant of the natural gas pipeline;
processing the second parameter data and the transmission characteristic constant by adopting non-convex constraint to obtain a constraint inequality of the natural gas;
performing reduced term linearization processing on the constraint inequality in a first-order Taylor expansion mode to obtain a linearization constraint inequality;
and performing multiple iteration processing on the second parameter data and the transmission characteristic constant to obtain a relaxation variable meeting the linearization constraint inequality.
4. The method for accelerated convex dispersion optimization of electrical-to-electrical interconnection system data of claim 3, wherein the natural gas pipeline gas flow formula is:
the constraint inequality is:
the linearization constraint inequality is:
in the formula,. DELTA.xijIs the space step length between the natural gas pipeline node i and the node j, M2In order to be a constant of the transfer characteristic,
for the gas pressure at location d between natural gas pipeline node i and node j at time t,
for the gas pressure at position d +1 between natural gas pipeline node i and node j at time t,
for the amount of gas flow between natural gas pipeline node i and node j at position d at time t,
the gas pressure after k-1 iterations at the position d between the natural gas pipeline node i and the node j at the time t,
for the gas flow after k-1 iterations at position d between natural gas pipeline node i and node j at time t,
and k is a natural number greater than zero, and is a relaxation variable at a position d between the natural gas pipeline node i and the node j at the time t, namely the relaxation variable of the natural gas network.
5. The method of claim 1, wherein the obtaining a penalty function and a penalty factor by performing n iterations on the first parameter data, the second parameter data, and the energy coupling data according to the relaxation variables and using a Benders decomposition algorithm comprises:
performing relaxation treatment on the first parameter data and the energy coupling data by adopting a convex quadratic constraint inequality to obtain a natural gas network variable and a natural gas flow;
if the target function of the natural gas network has a solution, obtaining a solution vector, and processing the natural gas network variable and the natural gas flow by adopting a coupling constraint formula to obtain a Benders cut constraint inequality;
if the objective function of the natural gas network has no solution, increasing the fuel gas relaxation variable of the coupling constraint, and processing the natural gas network variable, the natural gas flow and the energy coupling data by adopting the natural gas network constraint of the Benders decomposition algorithm to obtain a feasible Benders cut constraint inequality;
carrying out iteration processing on the Benders cut constraint inequality and the feasibility Benders cut constraint inequality for n times by adopting the power network constraint of the Benders decomposition algorithm to obtain an upper boundary and a lower boundary of the target function;
if the upper boundary and the lower boundary meet the optimal solution condition, obtaining a penalty factor;
and constituting a penalty function by the penalty factor, the optimization target of the energy coupling data and the relaxation variable.
6. The method of accelerated convex decentralized optimization of data of an electrical-electrical interconnection system according to claim 5, characterized in that said convex quadratic constraint inequality is: f. ofGT,a,t≥h2，a(PGT，a,t)2+h1,aPGT,a,t+h0,a，a∈ΩGT，
a∈ΩGT(ii) a In the formula (f)GT，a，tThe natural gas flow h consumed by the gas turbine set a at the moment t0，aIs the first consumption characteristic coefficient h of the gas turbine set a1，aIs the second consumption characteristic coefficient, h, of the gas turbine unit a2，aIs the third consumption characteristic coefficient of the gas unit a, a is the serial number of the gas unit, omegaGTIs a collection of gas-fired units, PGT，a，tThe active power of the gas turbine set a at the moment t,
is a natural gas network variable.
7. The method of accelerated convex-dispersive optimization of electrical-to-electrical interconnection system data according to claim 5, wherein said objective function is:
the coupling constraint is as follows:
s.t.
the Benders cuts the inequality of constraint as: fgas(gn)+Fpower(p)+(λn)TE(p-pn)≤μ；
In the formula, FgasFor the purpose of a natural gas network,
is the relaxation variable between natural gas pipeline node i and node j at time t at position d, omegadFor a collection of natural gas pipeline locations, ΩpipeIs a set between different nodes i and j, T is a set of moments, pkA is a penalty factor after the kth iteration, a is the number of the gas turbine set, omegaGTIs the set of gas units, b is the number of the electric-to-gas units, omegaP2GIs a collection of electric gas-converting machine sets,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
for natural gas networksVariable, hP2GIs the conversion coefficient of electricity to gas,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tMu is real variable, g is active power consumed by the electric gas conversion unit b after the nth iteration at the moment tnIs the solution vector of the nth iteration, E is the coefficient matrix of coupling constraint, FpowerFor a power network objective, p is a decision vector for the power network objective,
as a result of the nth iteration, lambdanCoupled to the contracted multiplier vector in the nth iteration.
8. The method of accelerated convex decentralized optimization of electrical-to-electrical interconnection system data according to claim 5, characterized in that said natural gas network constraints are:
min v
s.t. natural gas network constraints
The feasible Benders cuts the inequality of constraint as:
the power network constraints are:
min μ
s.t. power network constraints
The optimal solution conditions are as follows: i UB-LB|≤ε|LB|；
In the formula etacFor the c-th coupled constraint, v is the sum of the individual gas relaxation variables, UBIs the upper boundary of the objective function, LBIs the lower boundary of the objective function, epsilon is the convergence parameter of the optimal solution,
as a function of the natural gas network variables,
the natural gas flow consumed by the gas unit a after the nth iteration at the time t,
the gas relaxation variable for the c-th coupling constraint of gas train a,
the gas relaxation variable of the coupling constraint of the c-th of the electric gas conversion unit b,
is the natural gas flow f converted by the electric gas conversion unit b after the nth iteration at the time tP2G，b，tActive power h consumed by the electric gas-converting unit b after the nth iteration at the moment tP2GIs the conversion coefficient of electricity to gas,
coupling a constrained multiplier vector under the constraint of a natural gas network in the nth iteration, E is a coefficient matrix of the coupling constraint, p is a decision vector of a power network target,
as a junction after the nth iterationFruit, μ is a real variable, λnFor coupled-bound multiplier vectors in the nth iteration, FpowerFor the purpose of the power network, FgasFor natural gas network purposes, gnIs the solution vector of the nth iteration.
9. An apparatus for accelerated convex dispersion optimization of data in an electrical-to-electrical interconnection system, comprising: the system comprises a data acquisition module, a constraint processing module, a decomposition processing module and an optimized output module;
the data processing module is used for acquiring first parameter data of the power network, second parameter data of the natural gas network and energy coupling data of the power network and the natural gas network;
the constraint processing module is used for carrying out nonlinear non-convex constraint processing on the second parameter data to obtain a relaxation variable of the natural gas network;
the decomposition processing module is used for carrying out n times of iterative processing on the first parameter data, the second parameter data and the energy coupling data by adopting a Benders decomposition algorithm according to the relaxation variables to obtain a penalty function and a penalty factor;
the optimization output module is used for outputting an optimization result if the relaxation variable and the penalty function both meet a convergence condition;
wherein the convergence condition is:
in the formula, epsilon1And ε2Are all convergence tolerances, δ is the relaxation variable, WkPenalty function for the kth iteration, Wk-1Is a penalty function for k-1 iterations.
10. An accelerated convex dispersion optimization device for data of an electric-gas interconnection system is characterized by comprising a processor and a memory;
the memory is used for storing program codes and transmitting the program codes to the processor;
the processor is configured to execute the method for accelerated convex-concave optimization of electrical-electrical interconnection system data according to any one of claims 1 to 8 according to instructions in the program code.
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