CN113379565A - Comprehensive energy system optimization scheduling method based on distributed robust optimization method - Google Patents

Comprehensive energy system optimization scheduling method based on distributed robust optimization method Download PDF

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CN113379565A
CN113379565A CN202110635091.6A CN202110635091A CN113379565A CN 113379565 A CN113379565 A CN 113379565A CN 202110635091 A CN202110635091 A CN 202110635091A CN 113379565 A CN113379565 A CN 113379565A
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张群
王球
陈昌铭
诸晓骏
李泽森
王鑫
李妍
王青山
王琼
吴雪妍
林振智
杨莉
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Zhejiang University ZJU
Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a comprehensive energy system optimization scheduling method based on a distributed robust optimization method, which is characterized in that comprehensive demand response and heat supply network and air supply network pipeline energy storage are cooperatively modeled into virtual energy storage, so that the scheduling flexibility of a comprehensive energy system can be improved, and the uncertainty of the distributed renewable power output in the comprehensive energy system is processed by using the distributed robust optimization method based on Wassertein distance. The comprehensive energy system distribution robust optimization scheduling scheme obtained by the method has better economy and robustness, and the economy and the robustness of the comprehensive energy system distribution robust optimization scheduling scheme can be flexibly adjusted by changing the value of the confidence level and the number of historical samples of the output prediction error of the distributed renewable power supply.

Description

Comprehensive energy system optimization scheduling method based on distributed robust optimization method
The technical field is as follows:
the invention relates to the field of power systems, in particular to a comprehensive energy system optimization scheduling method based on a distributed robust optimization method.
Background art:
in the context of energy internet, Integrated Energy Systems (IES) have a multi-energy complementary characteristic, which can improve energy utilization efficiency, and the optimal scheduling thereof has become a research hotspot in recent years.
The uncertainty in the output of the distributed renewable power source may affect the economics and stability of the integrated energy system scheduling strategy. Common methods of dealing with distributed renewable power output uncertainty are random planning methods and robust optimization methods. However, the solution result of the stochastic programming method is too optimistic and the solution time is long, while the solution result of the robust optimization method is too conservative. Under the background, the distributed robust optimization method establishes a fuzzy set containing all possible probability distributions based on statistical information of random variables, and can overcome the defects of a random planning and robust optimization method, so that the output uncertainty of the distributed renewable power supply is effectively processed.
In the context of an integrated energy system, the traditional power demand response is expanded to an integrated demand response. In addition, the transmission delay characteristics of the heat supply network and the gas supply network can be modeled as pipeline energy storage. If the comprehensive demand response and the pipeline energy storage are cooperatively modeled into the virtual energy storage, greater flexibility can be provided for multi-energy complementation of the comprehensive energy system, and the economy of optimized scheduling of the comprehensive energy system is further improved.
The invention content is as follows:
the invention mainly solves the technical problem of providing a comprehensive energy system optimization scheduling method based on a distributed robust optimization method by adopting the distributed robust optimization method based on Wasserstein distance.
The technical scheme of the invention is as follows:
a comprehensive energy system optimization scheduling method based on a distributed robust optimization method comprises the following steps:
constructing a virtual energy storage model in the comprehensive energy system;
constructing a fuzzy probability distribution set of the output uncertainty of the distributed renewable power supply in the comprehensive energy system by adopting a Wasserstein distance-based distribution robust optimization method;
and constructing a comprehensive energy system distribution robust optimization scheduling model based on the virtual energy storage model and the fuzzy probability distribution set, and solving a comprehensive energy system optimization scheduling strategy based on a distribution robust optimization method.
Preferably, the virtual stored energy in the integrated energy system comprises integrated demand response, heat supply network pipeline stored energy and gas supply network pipeline stored energy.
Preferably, the constructing a virtual energy storage model in the integrated energy system includes:
firstly, modeling a comprehensive demand response, wherein the comprehensive demand response comprises a load interruption constraint and a load transfer constraint, and the load interruption constraint in the comprehensive demand response is expressed as follows:
Figure BDA0003104908170000021
in the formula, the superscript t represents the scheduling period t, and the same applies below;
Figure BDA0003104908170000022
is the interrupt power of the electrical load in the integrated demand response;
Figure BDA0003104908170000023
is the maximum proportion of electrical load interruptions;
Figure BDA0003104908170000024
is the electrical load in the integrated energy system;
the load shifting constraint in the integrated demand response is expressed as:
Figure BDA0003104908170000025
Figure BDA0003104908170000026
Figure BDA0003104908170000027
Figure BDA0003104908170000028
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000029
is the transferred power of the electrical load in the integrated demand response;
Figure BDA00031049081700000210
and
Figure BDA00031049081700000211
binary of shifted out and shifted in electric power respectively in integrated demand responseA coefficient;
Figure BDA00031049081700000212
and
Figure BDA00031049081700000213
respectively, the removed electric power and the moved electric power in the integrated demand response;
Figure BDA00031049081700000214
is the maximum proportion of electrical load transfer;
and then modeling the energy storage of the pipeline of the heat supply network, and modeling the temperature quasi-dynamics and the heat loss of the pipeline in the heat supply network by adopting a node method, wherein the temperature of the outlet hot water of the water supply pipeline p is expressed as follows:
Figure BDA00031049081700000215
Figure BDA00031049081700000216
Figure BDA00031049081700000217
Figure BDA00031049081700000218
in the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000219
and
Figure BDA00031049081700000220
the hot water temperatures at the inlet of the water supply pipe p at times t- (K-1) and t-K, respectively;
Figure BDA00031049081700000221
is the ambient temperature of the heating network; q. q.spAnd q isp+1The mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure BDA0003104908170000031
Figure BDA0003104908170000032
and τpThe time coefficients of the Kth mass block, the Kth mass block and the mass block at the outlet of the water supply pipeline p are respectively; k is a radical ofpAnd lpThe temperature loss coefficient and the length of the water supply pipe p, respectively;
the heating network pipeline energy storage is expressed as:
Figure BDA0003104908170000033
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000034
the heat supply network pipeline stores energy; c. CwIs the specific heat capacity of water; Δ t is the time interval between two adjacent scheduling times;
modeling the energy storage of the gas supply network pipeline, namely modeling the pipe storage and the average node pressure of the pipeline L in the gas supply network:
Figure BDA0003104908170000035
Figure BDA0003104908170000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000037
and
Figure BDA0003104908170000038
respectively, the inventory and average node pressure of the pipeline L in the gas supply network; zLIs a pipelineL(ii) a inventory factor of;
Figure BDA0003104908170000039
and
Figure BDA00031049081700000310
the gas inflow and gas outflow of the pipeline L in the gas supply network are respectively;
Figure BDA00031049081700000311
is a collection of pipes in an air supply network;
the gas supply network pipeline energy storage is expressed as
Figure BDA00031049081700000312
In the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000313
the gas supply network pipeline stores energy;
and finally, modeling virtual energy storage in the comprehensive energy system, and defining the virtual energy storage of the electric power, the heating power and the natural gas in the comprehensive energy system as the cooperation among the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage based on the model of the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage:
Figure BDA00031049081700000314
Figure BDA00031049081700000315
Figure BDA00031049081700000316
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000041
and
Figure BDA0003104908170000042
respectively, virtual energy storage for electricity, heat and natural gas.
Preferably, a Wasserstein distance-based distributed robust optimization method is applied to construct a fuzzy probability distribution set of the output uncertainty of the distributed renewable power supply in the comprehensive energy system, and the fuzzy probability distribution set comprises the following steps:
defining the prediction error of the output of the ith distributed renewable power source in the integrated energy system as deltai，δiFor random variables, note deltaiHas a true probability distribution of
Figure BDA0003104908170000043
Limited historical samples based on prediction error
Figure BDA0003104908170000044
Obtaining an empirical distribution
Figure BDA0003104908170000045
Wherein d iskTo represent
Figure BDA0003104908170000046
The Dirac measure of (a);
then by mixing
Figure BDA0003104908170000047
Setting the fuzzy set phi as a center to construct a fuzzy set phi; in the fuzzy set of values phi,
Figure BDA0003104908170000048
and
Figure BDA0003104908170000049
the distance between the two is measured by Wasserstein distance;
for a given tight support space xi and two probability distributions
Figure BDA00031049081700000410
And
Figure BDA00031049081700000411
wasserstein distance
Figure BDA00031049081700000412
Represented by the formula:
Figure BDA00031049081700000413
in the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000414
is to have an empirical distribution
Figure BDA00031049081700000415
A random variable of (a); j is at
Figure BDA00031049081700000416
And
Figure BDA00031049081700000417
a joint distribution which is an edge distribution;
Figure BDA00031049081700000418
is the distance of two random variables;
fuzzy sets
Figure BDA00031049081700000419
Is shown as
Figure BDA00031049081700000420
Fuzzy sets
Figure BDA00031049081700000421
Is regarded as having a radius
Figure BDA00031049081700000422
And are distributed empirically
Figure BDA00031049081700000423
A central Wasserstein ball;
wherein
Figure BDA00031049081700000424
Figure BDA00031049081700000425
In the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000426
is deltaiThe confidence of (2); η is an auxiliary variable;
Figure BDA00031049081700000427
is the average of historical samples of prediction error; n is a radical ofsamIs the number of historical samples of prediction error;
Figure BDA0003104908170000051
the result is obtained by a binary search method.
Preferably, a distributed robust optimization scheduling model of the integrated energy system is constructed based on the virtual energy storage model and the fuzzy probability distribution set, and an optimized scheduling strategy of the integrated energy system based on a distributed robust optimization method is solved, including:
the power deviation caused by the distributed renewable power source contribution prediction error is distributed to each gas turbine GT, and the actual output power of the ith GT at time t is expressed as:
Figure BDA0003104908170000052
wherein the actual output power and the planned output power of the ith GT are respectively
Figure BDA0003104908170000053
And
Figure BDA0003104908170000054
Figure BDA0003104908170000055
a prediction error for the distributed renewable power source output power;
Figure BDA0003104908170000056
is a column vector with all elements having a value of 1;
Figure BDA0003104908170000057
is a factor in the participation of the ith GT,
Figure BDA0003104908170000058
the objective function of the distributed robust optimization scheduling model of the integrated energy system is to minimize the total operating cost of the integrated energy system, namely:
Figure BDA0003104908170000059
Figure BDA00031049081700000510
Figure BDA00031049081700000511
Figure BDA00031049081700000512
Figure BDA00031049081700000513
Figure BDA00031049081700000514
wherein T is the number of scheduling moments; q. q.st＝eTδt；NGTIs the number of GT's in the integrated energy system;
Figure BDA00031049081700000515
and
Figure BDA00031049081700000516
the unit price of natural gas and electricity, respectively;
Figure BDA00031049081700000517
and
Figure BDA00031049081700000518
natural gas provided by a gas source and natural gas consumed by the ith GT, respectively;
Figure BDA00031049081700000519
is the power provided by the superior power grid;
Figure BDA00031049081700000520
and
Figure BDA00031049081700000521
is the cost coefficient of the ith GT;
Figure BDA00031049081700000522
and
Figure BDA00031049081700000523
unit prices of load interruption and load transfer in the comprehensive demand response are respectively;
introducing an auxiliary function h (q)tT) linearizing the distributed robust part of the objective function
Figure BDA0003104908170000061
The helper function is as follows:
Figure BDA0003104908170000062
Figure BDA0003104908170000063
according to the strong dual theory, the distribution robust part in the objective function is expressed as
Figure BDA0003104908170000064
Figure BDA0003104908170000065
In the formula, λtAnd
Figure BDA0003104908170000066
are all auxiliary variables;
the quadratic constraint is converted into a general matrix formula with three additional linear constraints using reconstruction linearization techniques, as follows:
Figure BDA0003104908170000067
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000068
is a symmetric matrix in which
Figure BDA0003104908170000069
ztAnd ctAre all auxiliary variables;
Figure BDA00031049081700000610
Figure BDA00031049081700000611
and
Figure BDA00031049081700000612
are each ytThe upper and lower limits of (d);
the comprehensive energy system distribution robust optimization scheduling model has the following constraint conditions:
1) distribution robust opportunity constraint: to ensure safe operation of the integrated energy system, the likelihood that the output power of the GT and the power of the distributed renewable power source deviate within their allowable ranges should be above a certain threshold; thus, the present invention employs a distributed robust opportunity constraint, as shown by the following two equations, the first of which represents the probability that the output power of the ith GT is within its range of at least 1- ε1,i(ii) a The second formula ensures that the probability that the reserve capacity of the output power of the ith GT satisfies its limit is at least 1-epsilon2,i；
Figure BDA0003104908170000071
Figure BDA0003104908170000072
In the formula, omegaGTIs a set of GT;
Figure BDA0003104908170000073
and
Figure BDA0003104908170000074
upper and lower limits, respectively, of the ith GT output power;
Figure BDA0003104908170000075
is the upper limit of the ith GT reserve capacity; epsilon1,iAnd ε2,iConfidence coefficients for the two constraints, respectively;
2) other constraints are: the method comprises the following steps of electric power balance constraint, thermal power balance constraint, natural gas balance constraint, power distribution network power flow constraint, heat supply network power flow constraint and air supply network power flow constraint;
and solving the established optimized scheduling model by using a CPLEX solver on the Matlab platform to obtain the distributed robust optimized scheduling scheme of the comprehensive energy system.
Preferably, the general form of the distributed robust opportunity constraint is:
Figure BDA0003104908170000076
in the formula, NJIs the number of uncertainty constraints;
then, the following CVaR approximation and relaxation method is adopted to linearize the general form of the robust opportunity constraint of distribution;
Figure BDA0003104908170000077
in the formula, ZCVaRIs a linearized distribution robust opportunity constraint set;
Figure BDA0003104908170000078
and
Figure BDA0003104908170000079
are all auxiliary variables.
Compared with the prior art, the invention has the following beneficial effects:
the method disclosed by the invention has the advantages that the comprehensive demand response and the pipeline energy storage of the heat supply network and the air supply network are cooperatively modeled into the virtual energy storage, the scheduling flexibility of the comprehensive energy system can be improved, and the uncertainty of the output of the distributed renewable power supply in the comprehensive energy system is processed by utilizing a Wasserstein distance-based distributed robust optimization method.
The comprehensive energy system distribution robust optimization scheduling method obtained by the method has better economy and robustness, and the economy and the robustness of the comprehensive energy system distribution robust optimization scheduling scheme can be flexibly adjusted by changing the value of the confidence level and the number of historical samples of the output prediction error of the distributed renewable power supply; the comprehensive demand response, the heat supply network and the gas supply network pipeline energy storage cooperate to fully exert the multi-energy complementary characteristic in the comprehensive energy system, and compared with a model which considers the comprehensive demand response or the pipeline energy storage alone, the comprehensive energy system distribution robust optimization scheduling scheme obtained by the method has lower operation cost and higher renewable energy consumption rate.
Description of the drawings:
FIG. 1 is a schematic overall flow chart of the present invention. (as abstract figure)
Fig. 2 is a diagram of an integrated energy system.
Fig. 3 is a diagram of an electric power optimal scheduling strategy.
Fig. 4 is a thermal power optimal scheduling strategy diagram.
Fig. 5 is a diagram of a natural gas optimal scheduling strategy.
FIG. 6 is a graph of sensitivity analysis of a distributed robust optimization method.
Fig. 7 is a wind curtailment and optical power curtailment diagram of different optimized scheduling models.
The specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The first embodiment is as follows:
the invention provides a comprehensive energy system optimization scheduling method based on a distributed robust optimization method, as shown in fig. 1, the implementation process comprises the following detailed steps:
step 1, constructing a virtual energy storage model in the comprehensive energy system. The virtual energy storage in the integrated energy system comprises integrated demand response, heat supply network pipeline energy storage and air supply network pipeline energy storage.
The integrated demand response is first modeled. The comprehensive demand response is composed of load interruption and load transfer of various energy sources, and the following load interruption constraint in the comprehensive demand response can be expressed as:
Figure BDA0003104908170000081
in the formula, the superscript t represents the scheduling period t, and the same applies below;
Figure BDA0003104908170000082
is the interrupt power of the electrical load in the integrated demand response;
Figure BDA0003104908170000083
is the maximum proportion of electrical load interruptions;
Figure BDA0003104908170000084
is the electrical load in the integrated energy system.
The load shifting constraint in the integrated demand response may be expressed as:
Figure BDA0003104908170000085
Figure BDA0003104908170000091
Figure BDA0003104908170000092
Figure BDA0003104908170000093
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000094
is the transferred power of the electrical load in the integrated demand response;
Figure BDA0003104908170000095
and
Figure BDA0003104908170000096
binary coefficients for the shifted-out electric power and the shifted-in electric power, respectively, in the integrated demand response;
Figure BDA0003104908170000097
and
Figure BDA0003104908170000098
respectively, the removed electric power and the moved electric power in the integrated demand response;
Figure BDA0003104908170000099
is the maximum proportion of electrical load transfer.
And modeling the heat supply network pipeline energy storage. The nodal method is used to model temperature quasi-dynamics and heat losses of the pipes in the heating network because it is computationally easy to process and has a high modeling accuracy.
Taking the water supply pipeline p as an example, the outlet hot water temperature can be expressed as:
Figure BDA00031049081700000910
Figure BDA00031049081700000911
Figure BDA00031049081700000912
Figure BDA00031049081700000913
in the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000914
and
Figure BDA00031049081700000915
are each at t- (K)-1) and the temperature of the hot water at the inlet of the water supply pipe p at time t-K;
Figure BDA00031049081700000916
is the ambient temperature of the heating network; q. q.spAnd q isp+1The mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure BDA00031049081700000917
Figure BDA00031049081700000918
and τpThe time coefficients of the Kth mass block, the Kth mass block and the mass block at the outlet of the water supply pipeline p are respectively; k is a radical ofpAnd lpThe temperature loss coefficient and the length of the water supply pipe p, respectively.
The quasi-dynamic temperature of the pipeline in the heat supply network can be modeled as pipeline energy storage, which is defined as
Figure BDA00031049081700000919
In the formula (I), the compound is shown in the specification,
Figure BDA00031049081700000920
the heat supply network pipeline stores energy; c. CwIs the specific heat capacity of water; at is the time interval between two adjacent scheduling times.
Modeling is carried out on the heat supply network pipeline energy storage. The piping in the gas supply network reflects the gas energy storage characteristics as follows:
Figure BDA0003104908170000101
Figure BDA0003104908170000102
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000103
and
Figure BDA0003104908170000104
respectively, the inventory and average node pressure of the pipeline L in the gas supply network; ZL is the inventory factor of the pipeline L;
Figure BDA0003104908170000105
and
Figure BDA0003104908170000106
the gas inflow and gas outflow of the pipeline L in the gas supply network are respectively;
Figure BDA0003104908170000107
is a collection of pipes in the air supply network.
Pipeline storage in a gas supply grid can be modeled as pipeline storage, which is defined as:
Figure BDA0003104908170000108
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000109
the energy is stored by the gas supply network pipeline.
The virtual stored energy in the integrated energy system is modeled below. Based on the above-mentioned model of synthesizing demand response, heat supply network pipeline energy storage and air supply network pipeline energy storage, with the electric power in the comprehensive energy system, the virtual energy storage definition of heating power and natural gas is for synthesizing the cooperation between demand response, heat supply network pipeline energy storage and the air supply network pipeline energy storage:
Figure BDA00031049081700001010
Figure BDA00031049081700001011
Figure BDA00031049081700001012
in the formula (I), the compound is shown in the specification,
Figure BDA00031049081700001013
and
Figure BDA00031049081700001014
respectively, virtual energy storage for electricity, heat and natural gas.
And 2, constructing a fuzzy probability distribution set of the output uncertainty of the distributed renewable power supply in the comprehensive energy system by using a Wasserstein distance-based distribution robust optimization method.
The prediction error of the output of the ith distributed renewable power supply in the integrated energy system is a random variable and is defined as deltai. In practice, δiTrue probability distribution of
Figure BDA00031049081700001015
Cannot be determined. However, a finite history sample of prediction errors
Figure BDA00031049081700001016
Some reliable probability information can be provided to obtain the empirical distribution
Figure BDA00031049081700001017
Wherein d iskTo represent
Figure BDA00031049081700001018
Dirac measure of (a). Then, can be obtained by
Figure BDA00031049081700001019
The fuzzy set Φ is constructed with the center. To construct a well-defined fuzzy set Φ, the Wasserstein distance is used for accurate measurement
Figure BDA0003104908170000111
And
Figure BDA0003104908170000112
the distance between them.
For a given tight support space xi and two probability distributions
Figure BDA0003104908170000113
And
Figure BDA0003104908170000114
wasserstein distance
Figure BDA0003104908170000115
Represented by the formula:
Figure BDA0003104908170000116
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000117
is to have an empirical distribution
Figure BDA0003104908170000118
A random variable of (a); j is at
Figure BDA0003104908170000119
And
Figure BDA00031049081700001110
a joint distribution which is an edge distribution;
Figure BDA00031049081700001111
is the distance between two random variables, using 1-norm | · | | luminance1Because it has excellent numerical scalability in the DRO problem.
Fuzzy sets according to the above definition
Figure BDA00031049081700001112
Can be expressed as
Figure BDA00031049081700001113
It should be noted that the method can be implemented by
Figure BDA00031049081700001114
It is regarded as having a radius
Figure BDA00031049081700001115
And are distributed empirically
Figure BDA00031049081700001116
A central Wasserstein ball.
Figure BDA00031049081700001117
The method is very important for the performance of a distributed robust optimization scheduling method based on Wasserstein distance, and can control the conservatism of a scheduling strategy. Construction of
Figure BDA00031049081700001118
A usable historical sample based on prediction error is needed, as follows:
Figure BDA00031049081700001119
Figure BDA00031049081700001120
in the formula (I), the compound is shown in the specification,
Figure BDA00031049081700001121
is deltaiThe confidence of (2); η is an auxiliary variable;
Figure BDA00031049081700001122
is the average of historical samples of prediction error; nsam is the number of historical samples of prediction error.
Figure BDA00031049081700001123
Can be obtained by a binary search method.
And 3, constructing a comprehensive energy system distribution robust optimization scheduling model based on the virtual energy storage model and the fuzzy probability distribution set, and solving a comprehensive energy system optimization scheduling strategy based on a distribution robust optimization method.
The power deviation caused by the distributed renewable power source contribution prediction error is distributed to each Gas Turbine (GT), and the actual output power of the ith GT at time t can be expressed as:
Figure BDA0003104908170000121
wherein the actual output power and the planned output power of the ith GT are respectively
Figure BDA0003104908170000122
And
Figure BDA0003104908170000123
Figure BDA0003104908170000124
a prediction error for the distributed renewable power source output power;
Figure BDA0003104908170000125
is a column vector with all elements having a value of 1;
Figure BDA0003104908170000126
is a factor in the participation of the ith GT,
Figure BDA0003104908170000127
the objective function of the distributed robust optimization scheduling model of the comprehensive energy system based on the distributed robust optimization method is to minimize the total operating cost of the comprehensive energy system, namely:
Figure BDA0003104908170000128
Figure BDA0003104908170000129
Figure BDA00031049081700001210
Figure BDA00031049081700001211
Figure BDA00031049081700001212
Figure BDA00031049081700001213
wherein T is the number of scheduling moments; q. q.st＝eTδt；NGTIs the number of GT's in the integrated energy system;
Figure BDA00031049081700001214
and
Figure BDA00031049081700001215
the unit price of natural gas and electricity, respectively;
Figure BDA00031049081700001216
and
Figure BDA00031049081700001217
natural gas provided by a gas source and natural gas consumed by the ith GT, respectively;
Figure BDA00031049081700001218
is the power provided by the superior power grid;
Figure BDA00031049081700001219
and
Figure BDA00031049081700001220
is the cost coefficient of the ith GT;
Figure BDA00031049081700001221
and
Figure BDA00031049081700001222
respectively, unit prices for load interruption and load shifting in the integrated demand response.
An objective function of a distributed robust optimization scheduling model of the comprehensive energy system based on the distributed robust optimization method is a 'min-max' problem and is difficult to directly solve.
To linearize the distributed robust part of the objective function, i.e.
Figure BDA00031049081700001223
Introducing an auxiliary function h (q)tT) is defined as
Figure BDA00031049081700001224
Figure BDA0003104908170000131
According to the strong dual theory, the distribution robust part in the objective function can be expressed as
Figure BDA0003104908170000132
Figure BDA0003104908170000133
In the formula, λtAnd
Figure BDA0003104908170000134
are all auxiliary variables.
Thus, the distribution robust part of the objective function has been converted to a linear formulation by strong dual theory and can be easily solved by commercial solvers. However, newly introduced quadratic constraints still need to be handled. The reconstruction linearization technique is effective in solving the quadratic constraint, therefore, the present invention applies the reconstruction linearization technique to convert the quadratic constraint into a general matrix formula with three additional linear constraints, as follows:
Figure BDA0003104908170000135
in the formula (I), the compound is shown in the specification,
Figure BDA0003104908170000136
is a symmetric matrix in which
Figure BDA0003104908170000137
ztAnd ctAre all auxiliary variables;
Figure BDA0003104908170000138
Figure BDA0003104908170000139
and
Figure BDA00031049081700001310
are each ytUpper and lower limits of (d).
The comprehensive energy system distribution robust optimization scheduling model based on the distribution robust optimization method has the following constraint conditions:
1) distribution robust opportunity constraint: to ensure safe operation of the integrated energy system, the likelihood that the output power of the GT and the power of the distributed renewable power source deviate within their allowable ranges should be above a certain threshold. Therefore, the present invention employs a distributed robust opportunity constraint, as shown in the following two equations. The first formula represents the output of the ith GTThe probability of the power being in its range being at least 1-epsilon1,i(ii) a The second formula ensures that the probability that the reserve capacity of the output power of the ith GT satisfies its limit is at least 1-epsilon2,i。
Figure BDA0003104908170000141
Figure BDA0003104908170000142
In the formula, omegaGTIs a set of GT;
Figure BDA0003104908170000143
and
Figure BDA0003104908170000144
upper and lower limits, respectively, of the ith GT output power;
Figure BDA0003104908170000145
is the upper limit of the ith GT reserve capacity; epsilon1,iAnd ε2,iRespectively, the confidence coefficients of the two constraints.
The two above distributed robust opportunistic constraints are non-convex constraints, which results in the model proposed by the present invention not being easily solved by commercial solvers. The CVaR approximation and relaxation method has proven to be effective in linearizing the opportunity constraints, so the present invention uses this method to linearize the two above distributed robust opportunity constraints. For ease of description, a general form of the distributed robust opportunity constraint is first given:
Figure BDA0003104908170000146
in the formula, NJIs the number of uncertainty constraints.
The general form of distributing the robust opportunity constraint is then linearized by the CVaR approximation and relaxation method as follows:
Figure BDA0003104908170000147
in the formula, ZCVaRIs a linearized distribution robust opportunity constraint set;
Figure BDA0003104908170000148
and
Figure BDA0003104908170000149
are all auxiliary variables.
2) Other constraints are: the method comprises electric power balance constraint, thermal power balance constraint, natural gas balance constraint, power distribution network power flow constraint, heat supply network power flow constraint and air supply network power flow constraint.
So far, a comprehensive energy system distribution robust optimization scheduling model based on a distribution robust optimization method is established. And solving the model by using a CPLEX solver on the Matlab platform to obtain the comprehensive energy system distribution robust optimization scheduling scheme.
The first application embodiment:
for further understanding of the present invention, the practical application of the present invention will be explained below by taking an integrated energy system consisting of an IEEE-33 node distribution network, a 44 node heating network and a 20 node gas supply network as an example.
The structure diagram of the comprehensive energy system consisting of an IEEE-33 node power distribution network, a 44 node heat supply network and a 20 node gas supply network is shown in figure 2, and the three energy networks of the power distribution network, the heat supply network and a natural gas network are coupled through a gas turbine GT, an electric gas conversion device P2G, an electric boiler EB and a cogeneration unit CHP in an energy hub.
The optimal scheduling strategy for electricity, heat and gas in the IES is shown in fig. 3-5. As can be seen from fig. 3, the DG contribution in the IES is sufficient during the entire dispatch period, so the IES does not need to buy power from the upper grid, and the RES output power needs to be reduced even in the evening or midday time periods when the RES contribution is large. Since the output power of Photovoltaic (PV) at 13:00 is large and the electricity price of 13:00 is low, at 13:00, 1.6MW of PV power is stored in VES and discharged during the high electricity price period of 16:00-21:00, which can reduce the operating cost of IES and light rejection. As can be seen from fig. 4, the EB is running at full power throughout the scheduling period to increase the renewable energy consumption rate. Since the CHP is operated in "on-demand" mode and the heat load is greater during the night than during the day, the CHP has greater thermal and electrical power during the night. As can be seen from fig. 2, the output power of Wind Turbine (WT) is larger at night, and the electrical load is lower, so that the larger electrical power of CHP at night may result in more wind curtailment. Thus, the VES releases thermal energy at 1:00-11:00 and 23:00-24:00 to reduce the CHP thermal power and thus reduce the WT output power. As can be seen from fig. 5, P2G, the gas source and the virtual energy storage together supply the natural gas load and the natural gas demand of the CHP and GT during the entire dispatch.
Table 1 shows a robust optimization method based on distribution
Figure BDA0003104908170000151
And comparing the operation cost of the comprehensive energy system between the stochastic programming method and the robust optimization method comprehensive energy system optimization scheduling model. As can be seen from table 1, the operation cost of the distributed robust optimization method is lower than that of the robust optimization method and higher than that of the stochastic programming method because the robust optimization method completely ignores probability information, and the stochastic programming method assumes an accurate probability distribution of uncertainty in the integrated energy system. In other words, the robust optimization method and the stochastic programming method respectively give out over-optimization and over-conservative scheduling strategies of the comprehensive energy system, the distributed robust optimization method establishes a fuzzy set containing all possible probability distributions based on historical samples of random variables in the comprehensive energy system, and compared with the stochastic programming method, the optimistic degree is lower, and the conservative degree is lower than that of the robust optimization method. As can be seen from table 1, the operation cost of the distributed robust optimization method decreases with the increase of the historical sample amount of the prediction error, that is, when the historical sample amount is smaller, the distributed robust optimization method adopts the conservative scheduling strategy of the image robust optimization method; conversely, when the historical sample size of the prediction error is largeThe distributed robust optimization method would use an optimistic scheduling strategy similar to the stochastic programming method. The reason is that when the historical sample size is small, the probability distribution which can be extracted is limited, so that the Wasserstein ball boundary is wider, and the scheduling strategy of the comprehensive energy system is more conservative; with the increase of the historical sample size, the radius of the Wasserstein ball is reduced, the fuzzy set is smaller, and the conservatism of the scheduling strategy of the comprehensive energy system is also reduced.
TABLE 1 comparison of integrated energy system operating costs between integrated energy system optimization scheduling models based on a distributed robust optimization method, a stochastic programming method, and a robust optimization method
Figure BDA0003104908170000161
In order to analyze the sensitivity of the model provided by the present invention to the confidence and the number of samples, the comparison between the operation cost of the integrated energy system and the Renewable Energy Consumption Level (RECL) at different confidence and the number of samples is shown in fig. 6. As can be seen from fig. 6, as the confidence level increases, the operation cost of the integrated energy system increases, and the RECL of the integrated energy system decreases, because as the confidence level β increases, the scheduling strategy of the integrated energy system tends to be more conservative. Furthermore, as the historical sample size increases, the operating cost of the integrated energy system decreases, while the RECL of the integrated energy system increases, because as the historical sample size increases, the fuzzy set shrinks and the conservatism of the integrated energy system scheduling strategy decreases. Therefore, the model can adjust the economy and robustness of the integrated energy system scheduling strategy according to the confidence coefficient and the historical sample number.
In order to verify the effectiveness of the model provided by the invention, an optimal scheduling model (M-WIP) of the comprehensive energy system without considering comprehensive demand response and pipeline energy storage, an optimal scheduling model (M-PESs) of the comprehensive energy system with considering pipeline energy storage, an optimal scheduling model (M-IDR) of the comprehensive energy system with considering comprehensive demand response and the model (M-VES) provided by the invention with considering virtual energy storage are compared. Table 2 shows the comparison of the M-WIP, the M-PESs, the M-IDR and the M-VES provided by the invention in the aspects of the running cost and the RECL of the integrated energy system, and the four models all use a Wasserstein distance-based distributed robust optimization method to process the uncertainty of the output of the distributed renewable power supply. As can be seen from Table 2, the operating cost of M-VES was 2.8%, 0.8% and 1.4% lower than M-WIP, M-PES and M-IDR, respectively. Furthermore, the RECL of M-VES was 5.8%, 1.4% and 3.4% higher than M-WIP, M-PES and M-IDR, respectively. This is because the virtual energy storage (i.e. the cooperation between the IDR and the pipeline energy storage) can fully utilize the complementary characteristics of multiple energies to enhance the scheduling flexibility of the integrated energy system, so that the operation cost of the integrated energy system can be reduced and the RECL can be improved. The comparison of the M-PES and the M-IDR shows that the comprehensive demand response and the pipeline energy storage can reduce the operation cost of the comprehensive energy system and improve the RECL of the REC, and the performance of the pipeline energy storage is superior to that of the comprehensive demand response.
TABLE 1 comparison of M-WIP, M-PESs, M-IDR and M-VES as proposed by the invention in terms of integrated energy system operating costs and RECL
Figure BDA0003104908170000171
FIG. 7 shows a comparison between M-WIP, M-PES, M-IDR and M-VES of the present invention for reducing wind curtailment. As can be seen from fig. 7, the wind curtailment and light curtailment of the distributed renewable power source occur at 1:00-14:00 and 23:00-24:00, since the distributed renewable power sources are very powerful and the electrical load is very low during these periods. Due to the lack of comprehensive demand response and pipeline energy storage, M-WIP cannot utilize the multi-energy complementation of the comprehensive energy system to promote renewable energy consumption, thus reducing 16.2MW of wind-solar output during the entire dispatch period. Pipeline energy storage and integrated demand response are used in the M-PES and M-IDR, respectively, so that RECL of the M-PES and M-IDR is improved. The M-VESs provided by the invention considers the synergistic effect between pipeline energy storage and comprehensive demand response so as to fully utilize the multi-energy complementary characteristic of a comprehensive energy system, so that the wind curtailment of the M-VESs is the lowest in the four models.

Claims (6)

1. A comprehensive energy system optimization scheduling method based on a distributed robust optimization method is characterized by comprising the following steps: the method comprises the following steps:
constructing a virtual energy storage model in the comprehensive energy system;
constructing a fuzzy probability distribution set of the output uncertainty of the distributed renewable power supply in the comprehensive energy system by adopting a Wasserstein distance-based distribution robust optimization method;
and constructing a comprehensive energy system distribution robust optimization scheduling model based on the virtual energy storage model and the fuzzy probability distribution set, and solving a comprehensive energy system optimization scheduling strategy based on a distribution robust optimization method.
2. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 1, wherein: the virtual energy storage in the integrated energy system comprises integrated demand response, heat supply network pipeline energy storage and air supply network pipeline energy storage.
3. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 2, wherein:
the method for constructing the virtual energy storage model in the comprehensive energy system comprises the following steps:
firstly, modeling a comprehensive demand response, wherein the comprehensive demand response comprises a load interruption constraint and a load transfer constraint, and the load interruption constraint in the comprehensive demand response is expressed as follows:
Figure FDA0003104908160000011
in the formula, the superscript t represents the scheduling period t, and the same applies below;
Figure FDA0003104908160000012
is the interrupt power of the electrical load in the integrated demand response;
Figure FDA0003104908160000013
is the maximum proportion of electrical load interruptions;
Figure FDA0003104908160000014
is the electrical load in the integrated energy system;
the load shifting constraint in the integrated demand response is expressed as:
Figure FDA0003104908160000015
Figure FDA0003104908160000016
Figure FDA0003104908160000017
Figure FDA0003104908160000018
in the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000019
is the transferred power of the electrical load in the integrated demand response;
Figure FDA00031049081600000110
and
Figure FDA00031049081600000111
binary coefficients for the shifted-out electric power and the shifted-in electric power, respectively, in the integrated demand response;
Figure FDA00031049081600000112
and
Figure FDA00031049081600000113
respectively, the removed electric power and the moved electric power in the integrated demand response;
Figure FDA00031049081600000114
is the maximum proportion of electrical load transfer;
and then modeling the energy storage of the pipeline of the heat supply network, and modeling the temperature quasi-dynamics and the heat loss of the pipeline in the heat supply network by adopting a node method, wherein the temperature of the outlet hot water of the water supply pipeline p is expressed as follows:
Figure FDA0003104908160000021
Figure FDA0003104908160000022
Figure FDA0003104908160000023
Figure FDA0003104908160000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000025
and
Figure FDA0003104908160000026
the hot water temperatures at the inlet of the water supply pipe p at times t- (K-1) and t-K, respectively;
Figure FDA0003104908160000027
is the ambient temperature of the heating network; q. q.spAnd q isp+1The mass flow rates of the water supply pipe p and the pipe connected to the outlet of the water supply pipe p, respectively;
Figure FDA0003104908160000028
and τpThe time coefficients of the Kth mass block, the Kth mass block and the mass block at the outlet of the water supply pipeline p are respectively; k is a radical ofpAnd lpThe temperature loss coefficient and the length of the water supply pipe p, respectively;
the heating network pipeline energy storage is expressed as:
Figure FDA0003104908160000029
in the formula (I), the compound is shown in the specification,
Figure FDA00031049081600000210
the heat supply network pipeline stores energy; c. CwIs the specific heat capacity of water; Δ t is the time interval between two adjacent scheduling times;
modeling the energy storage of the gas supply network pipeline, namely modeling the pipe storage and the average node pressure of the pipeline L in the gas supply network:
Figure FDA00031049081600000211
Figure FDA00031049081600000212
in the formula (I), the compound is shown in the specification,
Figure FDA00031049081600000213
and
Figure FDA00031049081600000214
respectively, the inventory and average node pressure of the pipeline L in the gas supply network; zLIs a pipelineL(ii) a inventory factor of;
Figure FDA00031049081600000215
and
Figure FDA00031049081600000216
the gas inflow and gas outflow of the pipeline L in the gas supply network are respectively;
Figure FDA00031049081600000217
is a collection of pipes in an air supply network;
the gas supply network pipeline energy storage is expressed as
Figure FDA0003104908160000031
In the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000032
the gas supply network pipeline stores energy;
and finally, modeling virtual energy storage in the comprehensive energy system, and defining the virtual energy storage of the electric power, the heating power and the natural gas in the comprehensive energy system as the cooperation among the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage based on the model of the comprehensive demand response, the heat supply network pipeline energy storage and the air supply network pipeline energy storage:
Figure FDA0003104908160000033
Figure FDA0003104908160000034
Figure FDA0003104908160000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000036
and
Figure FDA0003104908160000037
respectively, virtual energy storage for electricity, heat and natural gas.
4. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 1, wherein:
a distributed robust optimization method based on Wasserstein distance is applied to construct a fuzzy probability distribution set of the output uncertainty of a distributed renewable power supply in a comprehensive energy system, and the fuzzy probability distribution set comprises the following steps:
defining the prediction error of the output of the ith distributed renewable power source in the integrated energy system as deltai，δiFor random variables, note deltaiHas a true probability distribution of
Figure FDA0003104908160000038
Limited historical samples based on prediction error
Figure FDA0003104908160000039
Obtaining an empirical distribution
Figure FDA00031049081600000310
Wherein d iskTo represent
Figure FDA00031049081600000311
The Dirac measure of (a);
then by mixing
Figure FDA00031049081600000312
Setting the fuzzy set phi as a center to construct a fuzzy set phi; in the fuzzy set of values phi,
Figure FDA00031049081600000313
and
Figure FDA00031049081600000314
the distance between the two is measured by Wasserstein distance;
for a given tight support space xi and two probability distributions
Figure FDA00031049081600000315
And
Figure FDA00031049081600000316
wasserstein distance
Figure FDA00031049081600000317
Represented by the formula:
Figure FDA00031049081600000318
in the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000041
is to have an empirical distribution
Figure FDA0003104908160000042
A random variable of (a); j is at
Figure FDA0003104908160000043
And
Figure FDA0003104908160000044
a joint distribution which is an edge distribution;
Figure FDA0003104908160000045
is the distance of two random variables;
fuzzy sets
Figure FDA0003104908160000046
Is shown as
Figure FDA0003104908160000047
Fuzzy sets
Figure FDA0003104908160000048
Is regarded as having a radius
Figure FDA0003104908160000049
And are distributed empirically
Figure FDA00031049081600000410
A central Wasserstein ball;
wherein
Figure FDA00031049081600000411
Figure FDA00031049081600000412
In the formula (I), the compound is shown in the specification,
Figure FDA00031049081600000413
is deltaiThe confidence of (2); η is an auxiliary variable;
Figure FDA00031049081600000414
is the average of historical samples of prediction error; n is a radical ofsamIs the number of historical samples of prediction error;
Figure FDA00031049081600000415
the result is obtained by a binary search method.
5. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 1, wherein:
constructing a comprehensive energy system distribution robust optimization scheduling model based on the virtual energy storage model and the fuzzy probability distribution set, and solving a comprehensive energy system optimization scheduling strategy based on a distribution robust optimization method, wherein the comprehensive energy system optimization scheduling strategy comprises the following steps:
the power deviation caused by the distributed renewable power source contribution prediction error is distributed to each gas turbine GT, and the actual output power of the ith GT at time t is expressed as:
Figure FDA00031049081600000416
wherein the actual output power and the planned output power of the ith GT are respectively
Figure FDA00031049081600000417
And
Figure FDA00031049081600000418
Figure FDA00031049081600000419
a prediction error for the distributed renewable power source output power;
Figure FDA00031049081600000420
is a column vector with all elements having a value of 1;
Figure FDA00031049081600000421
is a factor in the participation of the ith GT,
Figure FDA00031049081600000422
the objective function of the distributed robust optimization scheduling model of the integrated energy system is to minimize the total operating cost of the integrated energy system, namely:
Figure FDA0003104908160000051
Figure FDA0003104908160000052
Figure FDA0003104908160000053
Figure FDA0003104908160000054
Figure FDA0003104908160000055
Figure FDA0003104908160000056
wherein T is the number of scheduling moments; q. q.st＝eTδt；NGTIs the number of GT's in the integrated energy system;
Figure FDA0003104908160000057
and
Figure FDA0003104908160000058
the unit price of natural gas and electricity, respectively;
Figure FDA0003104908160000059
and
Figure FDA00031049081600000510
natural gas provided by a gas source and natural gas consumed by the ith GT, respectively;
Figure FDA00031049081600000511
is the power supplied by the upper grid；
Figure FDA00031049081600000512
And
Figure FDA00031049081600000513
is the cost coefficient of the ith GT;
Figure FDA00031049081600000514
and
Figure FDA00031049081600000515
unit prices of load interruption and load transfer in the comprehensive demand response are respectively;
introducing an auxiliary function h (q)tT) linearizing the distributed robust part of the objective function
Figure FDA00031049081600000516
The helper function is as follows:
Figure FDA00031049081600000517
Figure FDA00031049081600000518
according to the strong dual theory, the distribution robust part in the objective function is expressed as
Figure FDA00031049081600000519
Figure FDA00031049081600000520
In the formula, λtAnd
Figure FDA00031049081600000521
are all auxiliary variables;
the quadratic constraint is converted into a general matrix formula with three additional linear constraints using reconstruction linearization techniques, as follows:
Figure FDA0003104908160000061
in the formula (I), the compound is shown in the specification,
Figure FDA0003104908160000062
is a symmetric matrix in which
Figure FDA0003104908160000063
ztAnd ctAre all auxiliary variables;
Figure FDA0003104908160000064
Figure FDA0003104908160000065
and
Figure FDA0003104908160000066
are each ytThe upper and lower limits of (d);
the comprehensive energy system distribution robust optimization scheduling model has the following constraint conditions:
1) distribution robust opportunity constraint: to ensure safe operation of the integrated energy system, the likelihood that the output power of the GT and the power of the distributed renewable power source deviate within their allowable ranges should be above a certain threshold; thus, the present invention employs a distributed robust opportunity constraint, as shown by the following two equations, the first of which represents the probability that the output power of the ith GT is within its range of at least 1- ε1,i(ii) a The second formula ensures that the probability that the reserve capacity of the output power of the ith GT satisfies its limit is at least 1-epsilon2,i；
Figure FDA0003104908160000067
Figure FDA0003104908160000068
In the formula, omegaGTIs a set of GT;
Figure FDA0003104908160000069
and
Figure FDA00031049081600000610
upper and lower limits, respectively, of the ith GT output power;
Figure FDA00031049081600000611
is the upper limit of the ith GT reserve capacity; epsilon1,iAnd ε2,iConfidence coefficients for the two constraints, respectively;
2) other constraints are: the method comprises the following steps of electric power balance constraint, thermal power balance constraint, natural gas balance constraint, power distribution network power flow constraint, heat supply network power flow constraint and air supply network power flow constraint;
and solving the established optimized scheduling model by using a CPLEX solver on the Matlab platform to obtain the distributed robust optimized scheduling scheme of the comprehensive energy system.
6. The integrated energy system optimization scheduling method based on the distributed robust optimization method according to claim 5, wherein: the general form of the distributed robust opportunity constraint is:
Figure FDA00031049081600000612
in the formula, NJIs the number of uncertainty constraints;
then, the following CVaR approximation and relaxation method is adopted to linearize the general form of the robust opportunity constraint of distribution;
Figure FDA0003104908160000071
in the formula, ZCVaRIs a linearized distribution robust opportunity constraint set;
Figure FDA0003104908160000072
and
Figure FDA0003104908160000073
are all auxiliary variables.
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