CN111401664A - Robust optimization scheduling method and device for comprehensive energy system - Google Patents

Robust optimization scheduling method and device for comprehensive energy system Download PDF

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CN111401664A
CN111401664A CN202010316566.0A CN202010316566A CN111401664A CN 111401664 A CN111401664 A CN 111401664A CN 202010316566 A CN202010316566 A CN 202010316566A CN 111401664 A CN111401664 A CN 111401664A
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刘洋
赵瑞锋
郭文鑫
王海柱
卢建刚
李波
王可
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Abstract

The application discloses a robust optimization scheduling method and device for an integrated energy system, comprising the following steps: clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set; establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, wherein the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage; solving a day-ahead planned scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply amount interval; and solving the real-time operation scheduling to obtain the output value of the decision-making unit and the gas supply amount of the natural gas. The problem of IEGS coordination optimization under the uncertain environment of wind power output is solved.

Description

Robust optimization scheduling method and device for comprehensive energy system
Technical Field
The application relates to the technical field of power dispatching, in particular to a robust optimization dispatching method and device for an integrated energy system.
Background
In recent years, with the introduction of concepts such as "energy internet", the integration and transformation of various energy forms have become a hot point of research at home and abroad. An Integrated Electrical and Gas System (IEGS) is a modern energy system that is electricity-centric and integrates a natural gas system. Compared with other primary energy sources, the natural gas has the characteristics of cleanness and environmental protection, and has practical significance in researching the mutual influence between the natural gas and a power system. In recent years, students at home and abroad have some basic researches on the optimized operation of IEGS. At present, the main research array is an IEGS planning method considering various energy storages such as electric energy storage, P2G and the like, but the research considering the influence of the uncertainty of wind power output on the IEGS coordination optimization is less.
In order to deal with the problem of wind power uncertainty in the IEGS, some scholars propose stochastic optimization and robust optimization techniques, but the above methods have respective limitations. The disadvantage of random optimization is that the number of scenes is too large, which makes the calculation difficult, and the exact distribution of uncertain parameters is often difficult to obtain. The robust optimization overcomes the defect of large random optimization calculation amount, only one uncertain set is used for representing, but due to neglecting probability information, the scheduling plan of the method is often too conservative.
With the development of the data management technology facing comprehensive energy, transparent unified data storage and access are realized. Scholars at home and abroad have the opportunity to obtain massive and diverse comprehensive energy system big data to solve the robustness problem of the optimized scheduling of the comprehensive energy system. In recent years, scholars at home and abroad improve the generation mode of an uncertain set in robust optimization through a data-driven method, and provide methods of the uncertain set considering moment uncertainty, the uncertain set based on Wasserstein distance, the uncertain set based on principal component analysis and the like so as to reduce the conservative property of classical robust optimization. However, the above method implicitly assumes that fuzzy concentrated distributions are similar, and the actual wind power prediction error distribution is extremely complex, is related to many factors such as weather, wind power plant, power grid, and the like, and presents a multi-modal characteristic, and the above method is difficult to apply.
Disclosure of Invention
The application provides a robust optimization scheduling method and device for an integrated energy system, and solves the problem of IEGS coordination optimization in an uncertain environment of wind power output.
In view of the above, a first aspect of the present application provides an integrated energy system robust optimization scheduling method, including:
clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set;
establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, wherein the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage;
solving the day-ahead plan scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply amount interval;
and solving the real-time operation scheduling to obtain the output value of the decision-making unit and the gas supply quantity of the natural gas.
Optionally, the clustering of the wind power prediction error sample set by using the infinite dimension gaussian mixture model to obtain the data-driven wind power prediction error uncertainty set specifically comprises:
clustering a multi-wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model:
Figure BDA0002459804860000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002459804860000022
is in the N dimensionThe quantity, representing the prediction error of N wind farms at time t,
Figure BDA0002459804860000023
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure BDA0002459804860000024
Deducing a data-driven wind power prediction error uncertain set as follows according to a wind power plant prediction error clustering result:
Figure BDA0002459804860000025
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikCharacterizing;scorresponding to the spatial budget in classical robust optimization.
Optionally, the establishing of the robust optimized dispatching model of the electrical integrated energy system according to the wind power prediction error uncertainty set specifically includes:
Figure BDA0002459804860000031
Figure BDA0002459804860000032
y＝{Pg,t,Pi,b,t,Pt +,Pt -,ωm,t,vsp,t,gfmn,t}∈C2,t
t∈U
Figure BDA0002459804860000033
in the formula, F1、F2The cost of the day-ahead planning and scheduling stage and the real-time operation and scheduling are respectively; u. ofg,tThe running state of the unit g at the moment t is shown; y isg,tStarting the unit g at the time t; z is a radical ofg,tStopping the unit g at the moment t;
Figure BDA0002459804860000034
Pg,trespectively an upper bound of an output interval and a lower bound of the output interval of the unit g at the moment t; v. ofsp,t、
Figure BDA0002459804860000035
The upper limit and the lower limit of the output interval of the natural gas well sp at the time t are respectively. Pg,tThe actual output of the unit g at the time t is obtained; omegam,tThe air pressure of the air supply node m at the time t; v. ofsp,tThe gas supply quantity of a natural gas well sp at the time t is obtained; gfmn,tThe natural gas flow from the gas supply node m to the node n at the moment t; p+(t) is the wind power of the abandoned wind at the moment t; p-(t) is the load shedding power at time t.tAnd predicting errors of the output of each wind power plant at the moment t. C1Scheduling feasible fields of phases for a day-ahead plan, C2,tAnd scheduling the feasible domain of the tth optimization problem for real-time operation.
Optionally, the objective function of the day-ahead planning and scheduling is as follows:
F1＝CST+CRUN
Figure BDA0002459804860000036
Figure BDA0002459804860000037
in the formula, CSTThe cost of starting and stopping the unit is shown,
Figure BDA0002459804860000038
respectively representing the cost required by the unit g for starting and stopping each time; cRUNRepresents the operating costs of the unit, wherein
Figure BDA00024598048600000310
Representing the operating costs required by the unit g per unit time interval.
Optionally, the constraint conditions of the day-ahead planned scheduling include a unit output interval constraint, a unit climbing event constraint, a unit start-stop and operation state logic constraint, and a unit shortest continuous operation/outage time constraint.
Optionally, the objective function of the real-time operation stage is:
F2,t＝Ccoil,t+Cgas,t+Cunb,t
Figure BDA0002459804860000039
Figure BDA0002459804860000041
Cunb,t＝c+P+(t)+c-P-(t)
in the formula, Ccoil,tFor the cost of the system to fire coal during the period t, agIs a secondary cost coefficient term of the coal-fired unit g, bgIs a primary item of the cost coefficient of the coal-fired unit g; cgas,tGas cost, rho, for the system t periodgasIn order to be the price of the natural gas,
Figure BDA0002459804860000042
the gas consumption of the gas unit g in the time period t is measured; cunb,tSum of penalty cost for load shedding and wind curtailment for period t, wherein c+A unit penalty charge for wind abandonment, c-The cost is punished for load shedding unit.
Optionally, the constraint conditions of the real-time operation stage include power system constraints and natural gas system constraints; the power system constraints comprise power line transmission capacity constraints, electric energy balance constraints, unit output upper and lower limit constraints, abandoned air volume upper limit constraints and load shedding upper limit constraints; the natural gas system constraints comprise gas unit feasible regions, natural gas dynamic power flow constraints, gas transmission node gas pressure constraints, natural gas well gas supply upper and lower limit constraints, node natural gas balance constraints and node natural gas load equations.
Optionally, the robust optimization scheduling model is subjected to convex processing by using a second-order cone relaxation technology, and is solved by using a column constraint generation algorithm.
The second aspect of the present application provides an integrated energy system robust optimization scheduling apparatus, the apparatus comprising:
the clustering module is used for clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set;
the model establishing module is used for establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, and the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage;
the first solving module is used for solving the day-ahead plan scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply interval;
and the second solving module is used for solving the real-time operation scheduling to obtain the output value of the decision unit and the gas supply quantity of the natural gas.
Optionally, the clustering module specifically includes:
clustering a multi-wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model:
Figure BDA0002459804860000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002459804860000044
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure BDA0002459804860000045
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs that distributionWeight of, satisfy
Figure BDA0002459804860000051
Deducing a data-driven wind power prediction error uncertain set as follows according to a wind power plant prediction error clustering result:
Figure BDA0002459804860000052
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikCharacterizing;scorresponding to the spatial budget in classical robust optimization.
According to the technical scheme, the method has the following advantages:
the embodiment of the application provides a robust optimization scheduling method and device for an integrated energy system, and the method comprises the steps of clustering a wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set; establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, wherein the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage; solving a day-ahead planned scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply amount interval; and solving the real-time operation scheduling to obtain the output value of the decision-making unit and the gas supply amount of the natural gas.
According to the method, the multiple wind power plant prediction errors are clustered through the infinite dimension Gaussian mixture model, and a data-driven wind power prediction error uncertainty set is established. Establishing an IEGS two-stage robust optimization scheduling model, wherein the first stage is a day-ahead plan level, and deciding a unit start-stop and output interval and a natural gas supply interval; and the second stage is a real-time operation level, and the output value of the unit and the gas supply quantity of the natural gas are determined. The problem of IEGS coordination optimization under the uncertain environment of wind power output is solved, and the economy is better on the premise of ensuring the safety compared with the traditional robust optimization method. Compared with a steady-state model, the dynamic natural gas flow equation can better exert the gas storage potential of the natural gas pipeline.
Drawings
FIG. 1 is a flowchart of a method of an embodiment of a robust optimized dispatching method for an integrated energy system according to the present application;
FIG. 2 is a schematic diagram of an embodiment of an integrated energy system robust optimization scheduling apparatus according to the present application;
FIG. 3 is a flow chart of solving a steady state distribution of distribution weights in an infinite dimension Gaussian mixture model by using a Metropolis-Hasting sampling algorithm in the present application;
fig. 4 is a flowchart of solving the convex robust optimized scheduling model by using the column constraint generation algorithm according to the present application.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, 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 application.
Referring to fig. 1, fig. 1 is a flowchart illustrating a method of an embodiment of a robust optimal scheduling method for an integrated energy system according to the present application, where fig. 1 includes:
101. and clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set.
It should be noted that in the IEGS, there is uncertainty in the output of renewable energy sources such as wind power, and there is an error between the predicted output value of wind power and the actual output value. Therefore, the following multi-wind farm wind power prediction error sample sets are considered:
Figure BDA0002459804860000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002459804860000062
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure BDA0002459804860000063
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure BDA0002459804860000064
Since the wind power prediction technology takes the time correlation into account, DyThe samples in (1) are mutually independent in time, but due to the influence of geographical distribution, a certain degree of correlation still exists between prediction errors of all wind power plants. The classical robust optimization method uses a polyhedron to wrap the error sample set:
Figure BDA0002459804860000065
in the formula, zeta is an uncertain parameter; II-1、‖·‖∞Respectively 1-norm and infinity-norm; is a space budget for controlling the size and shape of the polyhedron.
The size and shape of the polyhedron can be controlled by artificially selecting parameters. However, the method is easy to be involved in both conservative and robust features, an excessively large uncertain set easily covers more zero probability regions, so that the scheduling result is excessively conservative, and an excessively small uncertain set cannot wrap more outliers, so that the scheduling result is poor in robustness. And when the number of wind farms exceeds 3, the method of manually selecting parameters is difficult to work due to the difficulty of visualization.
The root of the above problems is that the wind power prediction error is influenced by many factors such as wind speed, a fan and a power grid, and the characteristics of multiple peaks and multiple modes of the uncertain set described by limited parameters are difficult to reflect. Therefore, the method of nonparametric Bayes is adopted firstly, and an Infinite Gaussian Mixture Model (IGMM) is used for clustering the wind power prediction error sample set:
Figure BDA0002459804860000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002459804860000072
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure BDA0002459804860000073
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure BDA0002459804860000074
Because the number of the components in the model is infinite, the model is essentially a data-driven method, the category number of the wind power prediction error cluster can be adjusted in a self-adaptive manner according to different sample sets, and the category number can also grow along with the increase of the sample points.
Since the number of components in an IGMM is infinite, it is necessary to introduce a random process as a distribution weight π on top of the IGMMkPrior distribution, the present application selects Chinese Restaurant Process (CRP), which is defined as: there are numerous tables in the restaurant, numbered 1,2, …, and customers walk into the restaurant in sequence and choose the tables to sit on according to the following random process:
1. a first customer selects a first table;
2. the nth customer
Figure BDA0002459804860000075
To select an unmanned table to sit on
Figure BDA0002459804860000076
Probability of selecting a person's table to sit onWherein c is the number of people existing at the table.
G is said to be subject to Chinese restaurant process CRP (α). where α is the dispersion factor, in IGMM, CRP is used as { π }kA priori, its standard form is as follows:
Figure BDA0002459804860000077
cj～Categorical({πk}k＝1,...,∞)
{ηk}k＝1,...,∞～G0
{πk}k＝1,...,∞～CRP(α)
the meaning of the model is that each sample y in the data setiGenerated by first weighting pi of each class distribution according to Chinese restaurant process CRP (α)kSampling, and then distributing G according to the reference0For parameter { ηkSample and then y is weighted according to the distributioniClass c ofiSampling and finally obtaining a likelihood function
Figure BDA0002459804860000081
For yiThe value of (a) is sampled. The key to the model is to compute the posterior distribution p (c)1,...,cN|y1,...,yN) And p (η)1,...,ηN|y1,...,yN) Because the distribution can not be directly sampled, the invention adopts Metropolis-Hasting sampling algorithm to indirectly sample and takes ηk＝(μk,Φk)，
Figure BDA0002459804860000082
G0＝NIW(μ0λ, Φ, ν), wherein NIW represents a Normal Inverse Weishate (Normal-Inverse-Wishart) distribution, is (μk,Φk) The a-priori parameters in NIW are taken
Figure BDA0002459804860000083
Φ＝DyDy T，λ＝ν＝NtThe algorithm is shown in fig. 3.
The sampling formula in fig. 3 is:
Figure BDA0002459804860000084
Figure BDA0002459804860000085
P(η*|yi)∝F(yi,η*)G0(η*)
Figure BDA0002459804860000086
the weight { pi ] is obtained through Metropolis-Hasting sampling calculationkThe steady state distribution of }, and μk，Φk. The following wind power prediction error clustering results can be obtained:
Figure BDA0002459804860000087
wherein n isc＝|{πkIs the total number of elements, since ncRather than being specified in advance, the uncertain set can adaptively increase the number of components in the set as the data set grows.
According to the clustering result of the wind power prediction errors, the following uncertain set of wind power prediction errors can be deduced:
Figure BDA0002459804860000088
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikAnd (5) characterizing.sCorresponding to the spatial budget in classical robust optimization, withsIncrease, set UkIncreasing that the wind power prediction error belongs to the set UkThe higher the confidence of (A), the more conservative the corresponding dispatch plan, when takensWhen 3, corresponding to UkThe confidence of (c) is 99.73%.
102. And establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, wherein the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage.
It should be noted that the IEGS data-driven robust optimal scheduling (DDRUC) based on the uncertainty set is a two-stage optimization model, and the first stage is a scheduling stage of a day-ahead plan and is used for deciding the operation state of a unit, the start and stop of the unit, the output interval of the unit, and the output interval of a natural gas well; and the second stage is an adjustment plan of the least favorable scene with uncertain wind power prediction errors corresponding to the IEGS, namely real-time operation scheduling, and is used for decision variables, wherein the variables comprise the actual output of a unit, the gas supply quantity of a natural gas well, the node air pressure, the flow of a gas supply pipeline, the load shedding power and the wind curtailment power. The robust optimization scheduling model is shown as a formula:
Figure BDA0002459804860000091
Figure BDA0002459804860000092
y＝{Pg,t,Pi,b,t,Pt +,Pt -,ωm,t,vsp,t,gfmn,t}∈C2,t
t∈U
Figure BDA0002459804860000093
in the formula, F1、F2The cost of the day-ahead planning and scheduling stage and the real-time operation and scheduling are respectively; u. ofg,tThe running state of the unit g at the moment t is shown; y isg,tStarting the unit g at the time t; z is a radical ofg,tStopping the unit g at the moment t;
Figure BDA0002459804860000094
Pg,trespectively an upper bound of an output interval and a lower bound of the output interval of the unit g at the moment t;v sp,t、
Figure BDA0002459804860000095
the upper limit and the lower limit of the output interval of the natural gas well sp at the time t are respectively. Pg,tThe actual output of the unit g at the time t is obtained; omegam,tThe air pressure of the air supply node m at the time t; v. ofsp,tThe gas supply quantity of a natural gas well sp at the time t is obtained; gfmn,tThe natural gas flow from the gas supply node m to the node n at the moment t; p+(t) is the wind power of the abandoned wind at the moment t; p-(t) is the load shedding power at time t.tAnd predicting errors of the output of each wind power plant at the moment t. C1Scheduling feasible fields of phases for a day-ahead plan, C2,tAnd scheduling the feasible domain of the tth optimization problem for real-time operation.
103. And solving a day-ahead planned scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply amount interval.
It should be noted that, in the present application, the objective function of the schedule stage of the day ahead plan is specifically:
F1＝CST+CRUN
Figure BDA0002459804860000096
Figure BDA0002459804860000097
in the formula, CSTThe cost of starting and stopping the unit is shown,
Figure BDA0002459804860000098
respectively representing the cost required by the unit g for starting and stopping each time; cRUNRepresents the operating costs of the unit, wherein
Figure BDA0002459804860000099
Representing the operating costs required by the unit g per unit time interval.
In a specific implementation mode, the constraint conditions of the planning and scheduling stage in the application day ahead comprise a unit output interval constraint, a unit climbing event constraint, a unit start-stop and running state logic constraint and a unit shortest continuous running/stop time constraint; also included is a natural gas well output constraint.
The unit output interval constraint is as follows:
Figure BDA0002459804860000101
wherein
Figure BDA0002459804860000102
Is the minimum technical output of the unit g,
Figure BDA0002459804860000103
is the maximum technical output of the unit g, ug,t is the running state of the unit g at the moment t;
the unit climbing event constraint is as follows:
Figure BDA0002459804860000104
Figure BDA0002459804860000105
wherein RUg、RDgThe power limit values of the climbing and the landslide of the unit g are respectively;
Figure BDA0002459804860000106
Pg,trespectively an upper bound of an output interval and a lower bound of the output interval of the unit g at the moment t; y isg,tStarting the unit g at the time t; z is a radical ofg,tStopping the unit g at the moment t;
the unit start-stop and running state logic constraint is as follows:
ug,t-ug,t-1＝yg,t-zg,t
yg,t+zg,t≤1
the shortest continuous operation/shutdown time constraint of the unit is as follows:
Figure BDA0002459804860000107
Figure BDA0002459804860000108
Figure BDA0002459804860000109
Figure BDA00024598048600001010
Figure BDA00024598048600001011
Figure BDA00024598048600001012
in the formula (I), the compound is shown in the specification,
Figure BDA00024598048600001013
for the minimum continuous run time of the unit g,
Figure BDA00024598048600001014
for the minimum continuous off-time of the unit g, TUg,0For the time at the beginning of the day, T, when the unit g has been continuously operatedDg,0The time that the unit g has been continuously shut down at the beginning of the day.
Natural gas well output constraints include:
Figure BDA0002459804860000111
103. and solving real-time operation scheduling to obtain the output value of the decision-making unit and the gas supply quantity of the natural gas.
It should be noted that, in the present application, the objective function of real-time operation scheduling is:
F2,t＝Ccoil,t+Cgas,t+Cunb,t
Figure BDA0002459804860000112
Figure BDA0002459804860000113
Cunb,t＝c+P+(t)+c-P-(t)
in the formula, Ccoil,tFor the cost of the system to fire coal during the period t, agIs a secondary cost coefficient term of the coal-fired unit g, bgIs a primary item of the cost coefficient of the coal-fired unit g; cgas,tGas cost, rho, for the system t periodgasIn order to be the price of the natural gas,
Figure BDA0002459804860000114
the gas consumption of the gas unit g in the time period t is measured; cunb,tSum of penalty cost for load shedding and wind curtailment for period t, wherein c+A unit penalty charge for wind abandonment, c-The cost is punished for load shedding unit.
In a specific embodiment, the constraint conditions of the real-time operation scheduling comprise power system constraint and natural gas system constraint; the power system constraints comprise power line transmission capacity constraints, electric energy balance constraints, unit output upper and lower limit constraints, abandoned air volume upper limit constraints and load shedding upper limit constraints; the natural gas system constraints comprise gas unit feasible regions, natural gas dynamic power flow constraints, gas transmission node gas pressure constraints, natural gas well gas supply upper and lower limit constraints, node natural gas balance constraints and node natural gas load equations.
Wherein the power line transmission capacity constraint in the power system constraint is:
Figure BDA0002459804860000115
Figure BDA0002459804860000116
wherein N isbAs the total number of nodes, the number of nodes,
Figure BDA0002459804860000118
for the injected power at the ith node at time t,
Figure BDA0002459804860000117
is the transmission capacity, T, of the j-th lineijDistributing j rows and j columns of elements of the ith row of the matrix for the power flow, wherein the j rows and j columns of elements correspond to the power flow influence of the injected power of the ith node on the jth line; gi、ωi、diA generator set, a wind power plant set, a load set, P, of the ith node respectivelyω(t) is a predicted value before the output day of the wind power plant omega at the time t,t(ω) is the prediction error of wind farm ω at time t, Pd(t) is a predicted value of the load d at time t.
The electric energy balance constraint is as follows:
Figure BDA0002459804860000121
the upper and lower limits of the unit output are restricted as follows:
Figure BDA0002459804860000122
the upper limit of the abandoned air volume is constrained as follows:
Figure BDA0002459804860000123
the upper limit of the load shedding is constrained as follows:
Figure BDA0002459804860000124
the feasible region constraint of the gas turbine set in the natural gas system constraint is as follows:
Figure BDA0002459804860000125
Figure BDA0002459804860000126
the natural gas dynamic power flow constraint is as follows:
Figure BDA0002459804860000127
Figure BDA0002459804860000128
Figure BDA0002459804860000129
in the formula (I), the compound is shown in the specification,
Figure BDA00024598048600001210
fuel cost for the gas turbine g during time t, αgFor fixed operating cost per unit, βg,bMarginal cost, P, for gas train section bg,b,tForce value, P, segmented for t period bg,tIs the summed force out value for the t period. The variation of the node air pressure in unit time is in a linear relation with the gradient of the natural gas flow, the gradient of the natural gas flow is approximately represented by the difference of the flow at the head end and the tail end of the pipeline, and therefore the natural gas flow can be simplified into a first formula in a natural gas dynamic power flow constraint, wherein omegam,tIs the natural gas pressure at node m, gf, during the period tmn,tThe flow of natural gas from node m to node n is for a period of time t.
The air pressure constraint of the air transmission node is as follows:
Figure BDA00024598048600001211
ωref＝ω0
the natural gas well gas supply upper and lower limits are constrained as follows:
Figure BDA00024598048600001212
the node natural gas balance constraint is as follows:
Figure BDA00024598048600001213
the node natural gas load equation is as follows:
Figure BDA0002459804860000131
wherein the equation
Figure BDA0002459804860000132
Representing the coupled change in node pressure over time, degrades to a steady state natural gas flow if the left side of the equation is 0.
Natural gas dynamic power flow constraint equation:
Figure BDA0002459804860000133
Figure BDA0002459804860000134
is a Weymouth equation, and expresses that the natural gas flow is determined by the node air pressure at two ends of a pipeline, wherein C1,mn、C2,mnRepresents the overall characteristics of the pipe (including temperature, length, diameter, coefficient of friction);
Figure BDA0002459804860000135
respectively, the lower limit and the upper limit, omega, of the air pressure at the air supply node mrefAs reference node pressure, ω0GS (m), GN (m), GU (m) are respectively a natural gas well assembly, a gas supply node assembly, a gas turbine assembly and DG (g) connected to a gas supply node mm,tRepresenting the resident natural gas load of node m at time t.
According to the method, the multiple wind power plant prediction errors are clustered through the infinite dimension Gaussian mixture model, and a data-driven wind power prediction error uncertainty set is established. Establishing an IEGS two-stage robust optimization scheduling model, wherein the first stage is a day-ahead plan level, and deciding a unit start-stop and output interval and a natural gas supply interval; and the second stage is a real-time operation level, and the output value of the unit and the gas supply quantity of the natural gas are determined. The problem of IEGS coordination optimization under the uncertain environment of wind power output is solved, and the economy is better on the premise of ensuring the safety compared with the traditional robust optimization method. Compared with a steady-state model, the dynamic natural gas flow equation can better exert the gas storage potential of the natural gas pipeline.
The above is an embodiment of the robust optimization scheduling method for an integrated energy system according to the present application, and the method further includes:
and carrying out convex treatment on the robust optimization scheduling model by adopting a second-order cone relaxation technology, and solving by adopting a column constraint generation algorithm.
It should be noted that, in a specific embodiment, the present application is directed to a scheduled electro-pneumatic energy system, and a simultaneous solution is adopted to solve the scheduling problem of IEGS in the future. Because the Weymouth equation in the natural gas system has the characteristic of non-convex nonlinearity, and is difficult to directly apply a commercial solver to solve, the Weymouth equation is relaxed into convex second-order conical constraint:
Figure BDA0002459804860000136
the relaxed second-order cone-shaped constraint has a four-layer structure of min-max-max-min, and the method decomposes the two-order cone-shaped constraint into a main problem and a sub-problem, wherein the main problem is as follows:
Figure BDA0002459804860000141
s.t.Ax≤d
wherein x is a decision variable of a day-ahead planning and scheduling stage in a formula robust optimization scheduling model, and a is a cost coefficient vectorD is a right-end vector, A is a constant matrix, and d and A describe a constraint condition set C1，qt(x) And taking the objective function value after the optimal reaction for the t-th sub-problem and the response function of the t-th sub-problem with respect to x, namely given x.
And traversing a component k of the wind power prediction error uncertain set to { 1., n ═ 1 ·cH, response function q of each sub-questiont(x) By finding { qt,k(x) The maximum in (f) is obtained, i.e.:
Figure BDA0002459804860000142
wherein q ist,k(x) For the scenetFrom the kth uncertain set (denoted ast,k) The optimal value of the tth sub-problem is specifically as follows:
Figure BDA0002459804860000143
s.t.t,k TΜk t,k+Hk t,k≤gk
Figure BDA0002459804860000144
the constant matrixes Λ and c can be obtained by derivation of an objective function in the real-time operation stage of the second stage and introducing a relaxation variable stSo that the subproblem always has a feasible solution, M is a sufficiently large number. M (mum)k、Hk、gkAnd (4) a constant matrix deduced for the wind power prediction error uncertainty set. C. D, et、E、G、ftIt can be derived through sub-problem power system constraints. The sum of the values of Ω (x,t) Expressed at a given x,tTime sub-problem response strategy yt、stThe feasible domain of (a), can be obtained by the KKT condition:
Figure BDA0002459804860000145
wherein mu and lambda are dual variables and signs of inequality constraint and equality constraint of the subproblem respectively
Figure BDA0002459804860000146
Represents the Hardamard product; constraining
Figure BDA0002459804860000151
And
Figure BDA0002459804860000152
in a bilinear form, the method cannot be directly solved and can be converted into a mixed integer linear constraint in the following way:
Figure BDA0002459804860000153
through the above transformation, the main problem and the sub-problems can be solved iteratively through a column constraint generation algorithm C & CG, and a specific solving algorithm is shown in fig. 4.
The above is an embodiment of the robust optimal scheduling method for an integrated energy system according to the present application, and the present application further includes an embodiment of an apparatus for robust optimal scheduling for an integrated energy system, as shown in fig. 2, including:
the clustering module is used for clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set;
the model establishing module is used for establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, and the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage;
the first solving module is used for solving the day-ahead plan scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply interval;
and the second solving module is used for solving the real-time operation scheduling to obtain the output value of the decision unit and the gas supply amount of the natural gas.
In a specific embodiment, the clustering module specifically includes:
clustering a multi-wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model:
Figure BDA0002459804860000154
in the formula (I), the compound is shown in the specification,
Figure BDA0002459804860000155
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure BDA0002459804860000156
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure BDA0002459804860000157
Deducing a data-driven wind power prediction error uncertain set as follows according to a wind power plant prediction error clustering result:
Figure BDA0002459804860000158
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikAnd (5) characterizing.sCorresponding to the spatial budget in classical robust optimization.
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.
The terms "first," "second," "third," "fourth," and the like in the description of the application and the above-described figures, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions in actual implementation, for example, multiple modules 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.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each module may exist alone physically, or two or more modules are integrated into one unit. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode.
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 application may be substantially implemented or contributed to by the prior art, or all or part of the technical solution may be embodied in 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 application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should 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 in the embodiments of the present application.

Claims (10)

1. A robust optimization scheduling method for an integrated energy system is characterized by comprising the following steps:
clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set;
establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, wherein the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage;
solving the day-ahead plan scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply amount interval;
and solving the real-time operation scheduling to obtain the output value of the decision-making unit and the gas supply quantity of the natural gas.
2. The robust optimization scheduling method for the integrated energy system according to claim 1, wherein the clustering is performed on the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model, and the obtaining of the data-driven wind power prediction error uncertainty set specifically comprises:
clustering a multi-wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model:
Figure FDA0002459804850000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002459804850000012
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure FDA0002459804850000013
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure FDA0002459804850000014
Deducing a data-driven wind power prediction error uncertain set as follows according to a wind power plant prediction error clustering result:
Figure FDA0002459804850000015
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikCharacterizing;scorresponding to the spatial budget in classical robust optimization.
3. The robust optimal scheduling method for the integrated energy system according to claim 1, wherein the building of the robust optimal scheduling model for the electrical integrated energy system according to the wind power prediction error uncertainty set specifically comprises:
Figure FDA0002459804850000021
Figure FDA0002459804850000022
y＝{Pg,t,Pi,b,t,Pt +,Pt -,ωm,t,vsp,t,gfmn,t}∈C2,t
Figure FDA0002459804850000023
in the formula, F1、F2The cost of the day-ahead planning and scheduling stage and the real-time operation and scheduling are respectively; u. ofg,tThe running state of the unit g at the moment t is shown; y isg,tStarting the unit g at the time t; z is a radical ofg,tStopping the unit g at the moment t;
Figure FDA0002459804850000024
P g,trespectively an upper bound of an output interval and a lower bound of the output interval of the unit g at the moment t;v sp,t、
Figure FDA0002459804850000025
respectively an upper limit of an output interval and a lower limit of the output interval of the natural gas well sp at the time t; pg,tThe actual output of the unit g at the time t is obtained; omegam,tThe air pressure of the air supply node m at the time t; v. ofsp,tThe gas supply quantity of a natural gas well sp at the time t is obtained; gfmn,tThe natural gas flow from the gas supply node m to the node n at the moment t; p+(t) is the wind power of the abandoned wind at the moment t; p-(t) load shedding power at time t;tpredicting errors of the output of each wind power plant at the time t; c1Scheduling feasible fields of phases for a day-ahead plan, C2,tAnd scheduling the feasible domain of the tth optimization problem for real-time operation.
4. The robust optimized scheduling method for integrated energy systems according to claim 1, wherein the objective function of the day-ahead planned scheduling is:
F1＝CST+CRUN
Figure FDA0002459804850000026
Figure FDA0002459804850000027
in the formula, CSTThe cost of starting and stopping the unit is shown,
Figure FDA0002459804850000028
respectively representing the cost required by the unit g for starting and stopping each time; cRUNRepresents the operating costs of the unit, wherein
Figure FDA0002459804850000029
Representing the operating costs required by the unit g per unit time interval.
5. The robust optimization scheduling method of the integrated energy system according to claim 4, wherein the constraint conditions of the day-ahead planned scheduling include a unit output interval constraint, a unit climbing event constraint, a unit start-stop and operation state logic constraint and a unit shortest continuous operation/stop time constraint.
6. The robust optimal scheduling method for the integrated energy system according to claim 1, wherein the objective function of the real-time operation stage is as follows:
F2,t＝Ccoil,t+Cgas,t+Cunb,t
Figure FDA0002459804850000031
Figure FDA0002459804850000032
Cunb,t＝c+P+(t)+c-P-(t)
in the formula, Ccoil,tFor the cost of the system to fire coal during the period t, agIs a secondary cost coefficient term of the coal-fired unit g, bgIs a primary item of the cost coefficient of the coal-fired unit g; cgas,tGas cost, rho, for the system t periodgasIn order to be the price of the natural gas,
Figure FDA0002459804850000033
the gas consumption of the gas unit g in the time period t is measured; cunb,tSum of penalty cost for load shedding and wind curtailment for period t, wherein c+A unit penalty charge for wind abandonment, c-The cost is punished for load shedding unit.
7. The robust optimized dispatching method for the integrated energy system according to claim 6, wherein the constraint conditions of the real-time operation stage comprise power system constraints and natural gas system constraints; the power system constraints comprise power line transmission capacity constraints, electric energy balance constraints, unit output upper and lower limit constraints, abandoned air volume upper limit constraints and load shedding upper limit constraints; the natural gas system constraints comprise gas unit feasible region constraints, natural gas dynamic power flow constraints, gas transmission node gas pressure constraints, natural gas well gas supply upper and lower limit constraints, node natural gas balance constraints and node natural gas load equations.
8. The method for robust optimal scheduling of an integrated energy system according to claim 1, further comprising using a second order cone relaxation technique to perform a convex operation on the robust optimal scheduling model and using a column constraint generation algorithm to perform a solution operation.
9. An integrated energy system robust optimization scheduling device, comprising:
the clustering module is used for clustering the wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model to obtain a data-driven wind power prediction error uncertain set;
the model establishing module is used for establishing a robust optimization scheduling model of the electrical comprehensive energy system according to the wind power prediction error uncertain set, and the robust optimization scheduling model comprises a day-ahead plan scheduling stage and a real-time operation scheduling stage;
the first solving module is used for solving the day-ahead plan scheduling stage to obtain a decision unit start-stop and output interval and a natural gas supply interval;
and the second solving module is used for solving the real-time operation scheduling to obtain the output value of the decision unit and the gas supply quantity of the natural gas.
10. The robust optimized scheduling device of integrated energy systems according to claim 9, wherein the clustering module specifically comprises:
clustering a multi-wind power prediction error sample set by adopting an infinite dimension Gaussian mixture model:
Figure FDA0002459804850000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002459804850000042
is an N-dimensional vector and represents the prediction errors of N wind power plants at the time t,
Figure FDA0002459804850000043
represents the mean value of μk∈RnCovariance matrix of phik∈RnnGaussian distribution of (n) (. pi.)kIs the weight of the distribution, satisfies
Figure FDA0002459804850000044
Deducing a data-driven wind power prediction error uncertain set as follows according to a wind power plant prediction error clustering result:
Figure FDA0002459804850000045
uncertain set U is ncThe combination of the ellipsoid-shaped uncertain sets and the correlation of the multi-wind-power-plant wind power output prediction are determined by a covariance matrix phikCharacterizing;scorresponding to the spatial budget in classical robust optimization.
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