CN111753441A - Convex solving method for multi-target dynamic model of electric-gas coupling system - Google Patents

Convex solving method for multi-target dynamic model of electric-gas coupling system Download PDF

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CN111753441A
CN111753441A CN202010669457.7A CN202010669457A CN111753441A CN 111753441 A CN111753441 A CN 111753441A CN 202010669457 A CN202010669457 A CN 202010669457A CN 111753441 A CN111753441 A CN 111753441A
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convex
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黄霆
张敏
袁健华
吴杰
李伟伦
徐晓轶
马骏
袁松
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Nantong Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The application provides a convex solving method of an electric-gas coupling system multi-target dynamic model, which is based on a Gaussian smoke mass diffusion theory and constructs the electric-gas coupling system multi-target optimal dynamic energy model considering the time-space distribution of unit pollutant emission. And aiming at the constructed model, a solving algorithm based on consideration of decision preference and a convex-concave penalty process is provided. The algorithm is based on generalized membership optimization considering decision preference, and can coordinate a plurality of mutually conflicting targets; the method is suitable for converting an economic target, a carbon emission target and an atmospheric pollutant concentration reduction target in the model into a single target problem; and the problem of non-convex constraint conditions of the model can be solved by a convex-concave penalty process, the solving speed of the optimization task is obviously improved, and the electric-gas coupled dynamic model considering the space-time distribution of the atmospheric pollutants can be quickly and efficiently solved.

Description

Convex solving method for multi-target dynamic model of electric-gas coupling system
Technical Field
The invention belongs to the field of electric-gas coupling of an electric power system, and particularly relates to a convex solving method of a multi-target dynamic model of an electric-gas coupling system.
Background
In recent years, due to the development of technologies such as gas turbine units, cogeneration, electricity-to-gas conversion and the like, various energy networks are coupled with one another to gradually form a whole, the traditional power dispatching is gradually transited to the optimized dispatching of an integrated energy system, and an effective way is provided for reducing carbon emission and reducing the emission of atmospheric pollutants, wherein an electricity-gas coupling system formed by coupling the power network and a natural gas network is a basic form of the integrated energy system.
At present, a scheduling main body is transited from a power network to an electric-gas coupling system for coupling the power network with a natural gas network, but a scheduling mode considering economic and environmental factors still maintains the same form as the original mode, namely CO2 generated by power generation and atmospheric pollutants are controlled from the perspective of total emission control, and the tolerance capacity of different environments to emission and the self-cleaning capacity of different environments to the emission are ignored.
Disclosure of Invention
The invention provides an electric-gas coupling system multi-target dynamic model considering atmospheric pollutant space-time distribution and a convex solving method thereof. The method is based on generalized membership optimization considering decision preference, and can coordinate a plurality of mutually conflicting targets; the method is suitable for converting an economic target, a carbon emission target and an atmospheric pollutant concentration reduction target in the model into a single target problem; and the problem of non-convex constraint conditions of the model can be solved by a convex-concave penalty process, the solving speed of the optimization task is obviously improved, and the electric-gas coupled dynamic model considering the space-time distribution of the atmospheric pollutants can be quickly and efficiently solved.
The invention particularly relates to a convex solving method of a multi-target dynamic model of an electric-gas coupling system, which specifically comprises the following steps:
acquiring diffusion parameters, wind speed, unit and monitoring point positions, unit parameters, air source correlation coefficients and electric and gas loads;
calculating the optimal number of segments of the scheduling period;
selecting an M value for a convex-concave punishing process;
carrying out fuzzy processing on the target function by utilizing the membership function;
relaxing a non-convex equation of the model, namely a consumption characteristic equation and a dynamic equation of the pipeline airflow into convex quadratic constraint;
neglecting the convex function difference constraint of the dynamic equation of the pipeline airflow to calculate an initial point target value;
solving the SOCP problem of the convexity to obtain a kth iteration variable and a target value;
judging whether a convergence criterion is reached, and if so, outputting a multi-objective optimization result; otherwise, returning to the previous step and continuing the iteration.
Furthermore, the multi-objective dynamic model of the electric-gas coupling system considers the space-time distribution of pollutant emission of the unit, the scheduling time interval is divided into D emission time intervals, each emission time interval releases a smoke group to represent pollutants emitted in the time interval, and the quality of the smoke group in all the emission time intervals in each scheduling time interval is equal, so that discrete smoke groups can approximately represent continuous smoke flow.
Furthermore, in the multi-target dynamic model of the electric-gas coupling system, the concentration contribution of the smoke mass to the monitoring point in the tau period is calculated by using the diffusion coefficient, and the time-varying problem of the diffusion coefficient under the varying atmospheric stability is considered.
Further, a solving algorithm considering decision preference and a convex-concave penalty process is adopted, a membership function is utilized to carry out fuzzy processing on an economic target, a carbon emission target and an atmospheric pollutant concentration reduction target, the minimum value of all target membership degrees considering the decision preference is introduced, and the model is converted into a single-target optimization model.
Further, the solution algorithm considering the decision preference and the convex-concave penalty process directly relaxes the consumption characteristic equation of the generator into convex quadratic constraint, converts the dynamic equation of the pipeline airflow into a standard second-order cone constraint and a typical convex function difference constraint, and then utilizes the convex-concave penalty process to carry out convexity, so that the solution process can be converged.
Compared with the prior art, the technical scheme of the invention has the following beneficial technical effects: based on the Gaussian smoke mass diffusion theory, the economic and environmental benefits of the electric-gas coupling system are fully exerted, and the multi-target optimal dynamic energy model of the electric-gas coupling system considering the time-space distribution of unit pollutant emission is constructed. The proposed solving algorithm based on consideration of decision preference and convex-concave penalty process has low dependence degree on an optimization model, not only can effectively solve the non-convex optimization problem of a dynamic equation containing the pipeline airflow, but also can meet the requirements of a plurality of targets.
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FIG. 1 is a flow chart of a method for solving the convexity of a multi-objective dynamic model of an electric-pneumatic coupling system according to the present invention;
FIG. 2 is a node electrical load and a node natural gas load;
FIG. 3 is an example city distribution map.
Detailed Description
The detailed description of the embodiment of the method for solving the convexity of the multi-target dynamic model of the electric-gas coupling system is provided below with reference to the accompanying drawings.
Referring to fig. 1, fig. 2 and fig. 3, the invention relates to an electric-gas coupling system multi-objective dynamic model considering the space-time distribution of atmospheric pollutants and a convex solving method thereof. The method starts from a Gaussian smoke mass diffusion model, a power plant pollutant emission model considering environment tolerance is constructed, and then the multi-target dynamic problem of the electric-gas coupling system considering the space-time distribution of atmospheric pollutants is solved. The method comprises the following steps:
step S1, acquiring diffusion parameters, wind speed, unit and monitoring point positions, unit parameters, air source correlation coefficients and electric and gas loads;
the example uses the IPGS of an IEEE 39 node power network coupled with a Belgian 20 node natural gas network as a simulation. The network has 10 generator sets, wherein 1, 7 and 8 are gas generator sets, and the rest are coal generator sets. The natural gas network with 20 nodes, the nodes 1 and 8 of the network are respectively provided with a gas source, and the gas units are respectively positioned at the nodes 4, 10 and 12.
TABLE 1 diffusion parameters
Figure BDA0002581710180000031
Table 2 wind speeds in the examples
Figure BDA0002581710180000032
TABLE 3 Unit position data
Figure BDA0002581710180000041
TABLE 4 location data of monitoring points
Figure BDA0002581710180000042
TABLE 5 Unit parameters coal-fired unit coal consumption coefficient t/MWh
Figure BDA0002581710180000043
Output parameter of coal-fired unit
Figure BDA0002581710180000044
Coefficient of emission of coal-fired unit
Figure BDA0002581710180000051
Gas consumption coefficient m of gas turbine3/MWh
Figure BDA0002581710180000052
Output parameter of gas turbine
Figure BDA0002581710180000053
Emission coefficient of gas turbine
Figure BDA0002581710180000054
In step S2, the optimal number of segments of the scheduling period is calculated.
The optimal number of segments is determined by simulation for simple scenarios: placing a pollution source with constant discharge rate, setting J monitoring points, increasing the segment number D from 1, and respectively calculating the average pollution concentration C of each monitoring point in the next scheduling periodj(D) The current number of segments D is determined to be the optimum number of segments when the following condition is satisfied.
Figure BDA0002581710180000055
DmaxTaken here as 500 for the maximum number of segments acceptable; zeta1,ζ2The convergence tolerance was 0.01.
Step S3, selecting the M value of the convex-concave penalty process;
the objective function lambda introduces a large scale factor M to prevent the penalty term from deteriorating the original objective function value too much. Essentially, the objective function M λ and the initial penalty factor ρ0The ratio between will affect the convergence speed and the final result of the optimization process. Therefore, when ρ0When the M value is determined, the size of the M value becomes a key factor influencing the convergence of the algorithm.
Step S4, fuzzy processing is carried out on the objective function by utilizing the membership function;
Figure BDA0002581710180000061
in the formula: the subscript "m" denotes the mth target; mu.smIs fmDegree of membership of, also denoted fmThe degree of satisfaction of;
Figure BDA0002581710180000062
and fmIs acceptable fmA maximum value and a minimum value. Each f is optimized separatelymFrom the individual single-target optimization results
Figure BDA0002581710180000063
And fm。
Let the weight vector representing the importance of the target be ω and λ be the minimum of all target membership values that account for decision preference, representing the membership value of the least satisfactory target, then:
Figure BDA0002581710180000064
in order to fully coordinate a plurality of mutually conflicting objectives and enable the objective which is the most unsatisfying objective to be satisfied as much as possible, the multi-objective optimization model can be converted into a single-objective optimization model which maximizes lambda
obj＝max λ
S5, relaxing a non-convex equation of the model, namely a consumption characteristic equation and a dynamic equation of the pipeline airflow into convex quadratic constraint;
the following formula is the consumption characteristic equation of the generator
Figure BDA0002581710180000065
Figure BDA0002581710180000066
Is converted into convex secondary constraint through direct relaxation
Figure BDA0002581710180000067
Figure BDA0002581710180000068
The following equation is the dynamic equation of the pipeline airflow
Figure BDA0002581710180000069
Transforming the non-convex part into an inequality and then convex the non-convex part, i.e. the formula
Figure BDA00025817101800000610
Convex with penalty convex-concave process and simultaneously introduce relaxation variable
Figure BDA0002581710180000071
Step S6, calculating initial point target value by neglecting convex function difference constraint of dynamic equation of pipeline airflow
Setting a convergence tolerance1And2and a dynamically adjusted proportion v of penalty factorsc. Let k equal to 1, initialize ρ1。
Step S7, solving the SOCP problem of the convexity to obtain the k iteration variable and the target value
Step S8, judging whether the convergence criterion is reached, if so, outputting a multi-objective optimization result; otherwise, returning to the previous step and continuing the iteration.
Through the steps, the multi-objective dynamic model of the electric-gas coupling system considering the space-time distribution of the atmospheric pollutants can be solved, and simultaneously, the optimization of multiple objectives is realized.
Compared with the prior art, the electric-gas coupling system multi-target dynamic model considering the space-time distribution of the atmospheric pollutants and the convex solving method thereof have the following advantages and effects:
(1) compared with the traditional economic cost scheduling method, the electric-gas coupling system multi-target dynamic model considering the space-time distribution of the atmospheric pollutants and the convex solving method thereof provided by the invention simultaneously consider cost and environmental factors, and optimize and coordinate a plurality of mutually conflicting targets through the generalized membership degree, so that the IPGS is sacrificed at lower cost, the reduction of carbon emission and the reduction of the contribution of the concentration of the atmospheric pollutants are realized.
(2) The electric-gas coupling system multi-target dynamic model considering the atmospheric pollutant space-time distribution and the convex solving method thereof, which are designed by the invention, treat different areas according to the environment tolerance capability by considering the dynamic model considering the atmospheric pollutant space-time distribution, so that the contribution of IPGS to the atmospheric pollutant concentration at the center and the periphery of a low-tolerance city is remarkably reduced, and the influence on the life quality of residents is effectively reduced.
(3) The electric-gas coupling system multi-target dynamic model considering the atmospheric pollutant space-time distribution and the convexity solution method thereof have ideal effect on treating the non-convexity of the natural gas flow dynamic equation by adopting the convex-concave penalty process, can obtain the result almost close to the global optimal solution by less calculation time, and have advantages compared with the conventional method in both the solution time and the target result.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (5)

1. A convex solving method for a multi-target dynamic model of an electric-gas coupling system is characterized by comprising the following steps: the method specifically comprises the following steps:
acquiring diffusion parameters, wind speed, unit and monitoring point positions, unit parameters, air source correlation coefficients and electric and gas loads;
calculating the optimal number of segments of the scheduling period;
selecting an M value for a convex-concave punishing process;
carrying out fuzzy processing on the target function by utilizing the membership function;
relaxing a non-convex equation of the model, namely a consumption characteristic equation and a dynamic equation of the pipeline airflow into convex quadratic constraint;
neglecting the convex function difference constraint of the dynamic equation of the pipeline airflow to calculate an initial point target value;
solving the SOCP problem of the convexity to obtain a kth iteration variable and a target value;
judging whether a convergence criterion is reached, and if so, outputting a multi-objective optimization result; otherwise, returning to the previous step and continuing the iteration.
2. The method for solving the convexity of the multi-objective dynamic model of the electric-pneumatic coupling system as claimed in claim 1, wherein the multi-objective dynamic model of the electric-pneumatic coupling system considers the time-space distribution of the emission of the pollutants of the unit, the scheduling period is subdivided into D emission periods, each emission period releases a smoke mass to represent the pollutants emitted in the period, and the quality of the smoke mass in all the emission periods in each scheduling period is equal, so that the discrete smoke mass can approximately represent the continuous smoke flow.
3. The method for solving the convexity of the multi-objective dynamic model of the electric-gas coupling system as claimed in claim 2, wherein in the multi-objective dynamic model of the electric-gas coupling system, the diffusion coefficient is used for calculating the concentration contribution of the smoke mass to the monitoring point in the period of tau, and the time-varying problem of the diffusion coefficient under the varying atmospheric stability is considered.
4. The convex solving method of the multi-target dynamic model of the electric-gas coupling system as claimed in claim 1, wherein a solving algorithm taking decision preference and penalty convex-concave process into account is adopted, a membership function is used for fuzzy processing of an economic target, a carbon emission target and an atmospheric pollutant concentration reduction target, the minimum value of the membership of all targets taking decision preference into account is introduced, and the model is converted into a single-target optimization model.
5. The method for solving the convexity of the multi-target dynamic model of the electric-gas coupling system as claimed in claim 4, wherein the solution algorithm taking decision preference and penalty convex-concave process into account directly relaxes the consumption characteristic equation of the generator into convex quadratic constraint, converts the dynamic equation of the pipeline gas flow into a standard second-order cone constraint and a typical convex function difference constraint, and then performs convexity by using the penalty convex-concave process, so that the solution process can be converged.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113221325A (en) * 2021-04-13 2021-08-06 西华大学 Multi-source energy storage type regional comprehensive energy low-carbon operation optimization method considering electricity to gas

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113221325A (en) * 2021-04-13 2021-08-06 西华大学 Multi-source energy storage type regional comprehensive energy low-carbon operation optimization method considering electricity to gas
CN113221325B (en) * 2021-04-13 2023-05-02 西华大学 Multi-source energy storage type regional comprehensive energy low-carbon operation optimization method considering electric conversion

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