CN116187035A - Variable mass flow combined heat and power system operation method based on multiple uncertainty sets - Google Patents

Variable mass flow combined heat and power system operation method based on multiple uncertainty sets Download PDF

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CN116187035A
CN116187035A CN202310067532.6A CN202310067532A CN116187035A CN 116187035 A CN116187035 A CN 116187035A CN 202310067532 A CN202310067532 A CN 202310067532A CN 116187035 A CN116187035 A CN 116187035A
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邓莉荣
冯然
符杨
李振坤
张智泉
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Abstract

The invention relates to a variable mass flow combined heat and power system operation method based on a multiple uncertainty set, which comprises the following steps: step S1, a robust operation model of a variable mass flow combined heat and power system IEHS is established, an objective function comprises the total cost of a minimized generator set of the deterministic combined heat and power system IEHS and the minimum resource rescheduling adjustment cost considering a prediction error, wherein the prediction error is restrained by adopting a multi-element uncertainty set; and S2, processing double constraint conditions of robust optimization problems under an IEHS model of the variable mass flow combined heat and power system by adopting a contracted McCormick algorithm to obtain an optimal operation result. Compared with the prior art, the invention has the advantages of good flexibility and high safety.

Description

Variable mass flow combined heat and power system operation method based on multiple uncertainty sets
Technical Field
The invention relates to the technical field of operation of a combined heat and power system, in particular to a variable mass flow combined heat and power system operation method based on a multi-element uncertain set.
Background
The comprehensive energy system has important significance for integrating renewable energy and improving energy efficiency. The electric power system EPS and the district heating system DHS are increasingly closely connected, the combined heat and power system IEHS develops rapidly, and the flexibility can be provided through the technical schemes of renewable energy power generation-heating units, comprehensive system operation, market mechanisms and the like, so that the combined heat and power system has great potential. The system operation is a basic and effective function for managing the IEHS of the combined heat and power system.
The variable-flow temperature heating regulation mode has more advantages over the constant-flow temperature heating regulation mode in terms of the flexibility of the district heating network.
With the continuous expansion of renewable energy power generation scale, the existing method for determining the IEHS of the combined heat and power system has a solving limitation on the problem of uncertainty.
Stochastic programming SP is a classical approach to resolve uncertainty with the aim of optimizing the expectations of economic objectives. However, the system operator is sometimes more concerned about security, i.e. robustness of the system operation, than economy. Typically, a robust optimized RO replaces the scenario in a stochastic programming SP with an uncertainty set without prior knowledge of the underlying probability distribution. Robust optimization RO converts uncertainty parameters as deterministic problems into deterministic problems in order to find the optimal value in the worst case uncertainty in the worst possible scenario, with moderate computational cost, but the worst case solution is too conservative. To overcome the conservation, the scholars designed various variants of robust optimized ROs, roughly divided into two field-class methods, namely, constructing uncertainty sets and designing solution algorithms.
To construct the uncertainty set, scholars have proposed special forms of uncertainty sets of box, sphere, budget, ellipsoid, and polyhedron. For example: 1) Employing a distributed, decentralized, robust optimization RO, wherein the uncertainty set is represented by a box shape; in order to reduce the conservation of the robust solution, the spatial correlation of the output of the uncertain wind power output and wind energy is considered in the uncertain set structure, and the correlation of the wind power plant is assumed to be a linear relation, so that the t distribution is obeyed. 2) The adoption of the space-time flexibility requirement envelope provides a less conservative but still robust solution; respectively obtaining a time trend and a spatial correlation of renewable energy power generation through time sequence analysis and principal component analysis; although Renewable Energy Sources (RES) for each time interval are modeled with mean, bias, and time series effects, correlations between different time intervals have not been described. 3) A spatio-temporal sparse correlation matrix, which is sparse in that only the temporal correlation between successive time intervals is considered; it assumes that the hill climbing constraint limits only two consecutive time intervals. However, this is not the case in reality; even if the time interval is greater than 2, there is a time correlation.
In the field of solving algorithm design, the method comprises a random p-RO method, data-driven random robust optimization, two-stage robust optimization planning and the like. The two-stage robust optimization planning (also called as adjustable Adaptive Robust Optimization (ARO)) is well applied to the field of energy system operation. The ARO algorithm is mainly of two types. The first class of algorithms is to solve the ARO problem in a two-layer optimization, where the upper layer is to minimize the total cost and handle the "here-and-now" decision variables; the lower layer is to deal with the max-min optimization problem, solving the "wait-and-see" decision variables in the worst uncertainty case. The second type of algorithm is to assume that the lower level decision variables obey a priori decision rules, which in this document are typically linear functions or piecewise linear functions (also known as affine strategies) that are not deterministic. Such algorithms are easy to implement but may lead to suboptimal results compared to the first class.
Based on the above analysis, robust operation of variable mass flow cogeneration systems still presents the following challenges:
1) When the IEHS is operated, the renewable energy source long-term power generation lacks an effective multi-element uncertain set construction method considering the long-term power generation characteristics of the renewable energy source;
2) There is a lack of solution algorithms that computationally embody the multivariate uncertainty analysis in the optimization.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a variable mass flow combined heat and power system operation method with good flexibility and high safety based on a multiple uncertainty set.
The aim of the invention can be achieved by the following technical scheme:
step S1, a robust operation model of a variable mass flow combined heat and power system IEHS is established, an objective function comprises the total cost of a minimized generator set of the deterministic combined heat and power system IEHS and the minimum resource rescheduling adjustment cost considering a prediction error, wherein the prediction error is restrained by adopting a multi-element uncertainty set;
and S2, solving a robust optimization problem under an IEHS model of the variable mass flow thermoelectric combined system by adopting a contracted McCormick algorithm to obtain an optimal operation result.
Preferably, the step S1 further includes using affine policies, specifically:
1) the renewable energy power generation amount of each unit i at the time t is expressed as:
Figure BDA0004073627590000031
wherein ,
Figure BDA0004073627590000032
is the actual power of the renewable energy, +.>
Figure BDA0004073627590000033
Is the predicted value of renewable energy sources, xi i,t Prediction error for renewable energy;
2) Assuming that the rescheduling output of each adjustable generator at time t is in linear relation with the total prediction error of renewable energy sources, all renewable energy sources are expressed as random vectors at time t
Figure BDA0004073627590000034
wherein ,
Figure BDA0004073627590000035
is the quantity of renewable energy sources in the system, and the total prediction error at the time t is 1 T ξ t Where 1 is an all-column vector.
Preferably, the robust operation model under the IEHS model of the variable mass flow combined heat and power system in step S1 is specifically:
1) Objective function:
Figure BDA0004073627590000036
in the formula ,
Figure BDA0004073627590000037
for the total cost function of the deterministic thermoelectric combined system IEHS operation optimization model, x is the decision variable of the deterministic thermoelectric combined system IEHS operation optimization model, the subscript t is the time index,/-and #>
Figure BDA0004073627590000038
For the active power output of thermal power generating unit j, < >>
Figure BDA0004073627590000039
Is the active power output of the cogeneration unit j;
Figure BDA00040736275900000310
For the thermal power output of the cogeneration unit j, < >>
Figure BDA00040736275900000311
Is the heat power output of the heating boiler j, +.>
Figure BDA00040736275900000312
Is the power purchased from the external network at interface j, +.>
Figure BDA00040736275900000313
Is the power sold to the external grid at interface j;
Figure BDA00040736275900000320
For the run time period index, t is the time index; ζ is the prediction error; the decision variable y is a flexible resource adjustment factor;
Figure BDA00040736275900000314
The adjustment factors are respectively the adjustment factors of the heat power output of the heat supply boiler, the adjustment factors of the active power output of the cogeneration unit, the adjustment factors of the heat power output of the cogeneration unit and the adjustment factors of the active power output of the thermal power unit;
Figure BDA00040736275900000315
For the cost factor of the heating boiler i,
Figure BDA00040736275900000316
for the cost factor of the cogeneration unit i, < >>
Figure BDA00040736275900000317
Is the cost coefficient of the thermal power unit i;
Figure BDA00040736275900000318
respectively collecting a heating boiler, a cogeneration unit and a thermal power unit;
2) Operational constraints, including district heating system constraints, power system constraints, tunable flexible resource constraints, node power constraints, prediction error constraints, and flexible resource adjustment factor constraints.
Preferably, the node power constraint includes a relation constraint of the active power, the reactive power, the yield of the thermal power and the flexible resource of the actual node, and the expression is:
Figure BDA00040736275900000319
Figure BDA0004073627590000041
Figure BDA0004073627590000042
in the formula ,
Figure BDA0004073627590000043
adjustment factors of the actual active power, reactive power, thermal yield of the respective corresponding node i, +.>
Figure BDA0004073627590000044
The adjustment factors of active power output of the cogeneration unit, reactive power output of the cogeneration unit and thermal power output of the cogeneration unit are respectively +.>
Figure BDA0004073627590000045
The adjustment factors of the active power output of the thermal power generating unit and the reactive power output of the thermal power generating unit are respectively,
Figure BDA0004073627590000046
the adjustment factors of the purchased electric quantity at the interface j and the adjustment factors of the sold electric quantity at the interface j are respectively +.>
Figure BDA0004073627590000047
For the adjustment factor of the heat power output of the heating boiler j, < >>
Figure BDA0004073627590000048
The electric heat transfer coefficient of the heat supply boiler j;
Figure BDA0004073627590000049
Respectively collecting a heating boiler, a cogeneration unit and a thermal power unit;
Figure BDA00040736275900000410
The number of renewable energy sources connected to node i is indicated.
Preferably, the district heating system constraint is expressed as:
Figure BDA00040736275900000411
Figure BDA00040736275900000412
Figure BDA00040736275900000413
Figure BDA00040736275900000414
Figure BDA00040736275900000415
Figure BDA00040736275900000416
Figure BDA00040736275900000417
Figure BDA00040736275900000418
wherein c is the specific heat capacity of water, v is the heat transfer coefficient per unit length, L ji Is the length of the pipeline, and the subscript t is the time;
Figure BDA00040736275900000419
respectively an inlet node set and an outlet node set;
Figure BDA00040736275900000420
Respectively corresponding to auxiliary variables->
Figure BDA00040736275900000434
and
Figure BDA00040736275900000421
Wherein%>
Figure BDA00040736275900000422
Figure BDA00040736275900000423
For the actual mass flow of water in the pipe ik, < > is>
Figure BDA00040736275900000424
Is an auxiliary variable +.>
Figure BDA00040736275900000425
Is the actual value of (2);
Figure BDA00040736275900000426
Adjustment factor for the actual thermal yield of node i, < ->
Figure BDA00040736275900000427
An adjustment factor corresponding to the thermal load of node i;
Figure BDA00040736275900000428
The adjustment factors of the mass flow of the water of the pipelines ji, ik respectively;
Figure BDA00040736275900000429
For the actual outlet temperature of node i, +.>
Figure BDA00040736275900000430
Respectively the upper limit and the lower limit of the outlet temperature of the node i;
Figure BDA00040736275900000431
For the actual mass flow of water in the pipe ji, < + >>
Figure BDA00040736275900000432
The upper and lower limits of the mass flow of water in the pipe ji, respectively.
Preferably, the power system constraint is expressed as:
Figure BDA00040736275900000433
Figure BDA0004073627590000051
Figure BDA0004073627590000052
Figure BDA0004073627590000053
in the formula ,
Figure BDA0004073627590000054
the adjustment factors g of the actual active power and the reactive power output of the node i respectively ij +jb ij Is the admittance, g, of the line ij ii +jb ii Is the shunt admittance of busbar i, +.>
Figure BDA0004073627590000055
Is a collection of bus bars;
Figure BDA0004073627590000056
Adjustment factors of voltage amplitude, voltage phase angle of bus i, respectively, +.>
Figure BDA0004073627590000057
The adjustment factors of the voltage amplitude and the voltage phase angle of the bus j are respectively;
Figure BDA0004073627590000058
For the maximum transmission power of branch ij, < +.>
Figure BDA0004073627590000059
The actual voltage amplitude and phase angle of bus i, V i max 、V i min Is the upper and lower limits of the voltage amplitude of the bus i.
Preferably, the adjustable flexible resource constraint is expressed as:
Figure BDA00040736275900000510
Figure BDA00040736275900000511
Figure BDA00040736275900000512
Figure BDA00040736275900000513
in the formula ,
Figure BDA00040736275900000514
for the actual heat output of the heating boiler i, < >>
Figure BDA00040736275900000515
The upper and lower limits of the heat output quantity of the heat supply boiler i are respectively set;
Figure BDA00040736275900000516
The actual active power and reactive power output of the cogeneration unit i are respectively +.>
Figure BDA00040736275900000517
The operation feasible region parameter of the cogeneration unit i is as follows;
Figure BDA00040736275900000518
is the actual active power of the thermal power generating unit i, P i TU,max 、P i TU,min The upper limit and the lower limit of active power output of the thermal power unit i are respectively;
Figure BDA00040736275900000519
and
Figure BDA00040736275900000520
The lower and upper limits of the heat of the flexible heat load i are respectively;
Figure BDA00040736275900000521
The adjustment factor of the thermal load of the corresponding node i,
Figure BDA00040736275900000522
the upper and lower limits of the flexible thermal load i, respectively. />
Preferably, the prediction error constraint is expressed as:
Figure BDA00040736275900000523
Figure BDA00040736275900000524
where xi is the prediction error,
Figure BDA00040736275900000525
in the case of a multiple uncertainty set, I.I 2 Representing a second norm; Γ is a proportional parameter; μ is the expectation of the value of ζ; Λ is represented by Σ -1 An upper triangular matrix decomposed by cholesky, and a covariance matrix with a value of Σ being xi; vec (ζ) represents a vector expression of ζ.
Preferably, said step S2 comprises the following sub-steps:
step S21, compact form of robust operation model under the variable mass flow combined heat and power system ies model:
objective function:
Figure BDA00040736275900000526
wherein ,
Figure BDA0004073627590000061
indexing for an operation period;
Figure BDA0004073627590000062
A set of flexible resources with adjustable power output; x, y and xi are decision variables; c (C) i,t Cost coefficients for the tunable flexible resources; zeta type toy t Is a prediction error; subscript t is time;
operational constraints, comprising:
1) Inequality constraints associated with uncertain parameters:
A(y t )ξ t ≤b(x t ) (25)
in the formula ,A(yt) and b(xt ) Affine mapping used to represent times y and x;
2) Bilinear constraints:
Figure BDA0004073627590000063
in the formula ,
Figure BDA0004073627590000064
as an auxiliary variable, +.>
Figure BDA0004073627590000065
Is an auxiliary variable +.>
Figure BDA0004073627590000066
C is the specific heat capacity of water, m ik,t 、
Figure BDA0004073627590000067
The mass flow rate of the water in the pipeline ik, the actual mass flow rate of the water in the pipeline ik and tau are respectively as follows i,t 、
Figure BDA0004073627590000068
The outlet temperature of the node i and the actual outlet temperature of the node i are respectively;
3) Convex constraints with deterministic parameters:
x,y∈Ω (27)
wherein omega is a decision variable convex constraint set;
4) Prediction error constraint:
Figure BDA0004073627590000069
where xi is the prediction error,
Figure BDA00040736275900000610
is a multiple uncertainty set;
step S32, introducing an auxiliary variable matrix S into the objective function, wherein the expression is as follows:
Figure BDA00040736275900000611
in the formula ,si,t Auxiliary variables corresponding to the adjustable flexible resource i;
increasing the operating constraint:
C i,t y i,t 1 T ξ t ≤s i,t (30)
and S33, converting the robust operation model by adopting a tightening McCormick method and a dual theory, respectively converting a max-min structure in the objective function and inequality constraint related to uncertain parameters into a convex formula, and carrying out optimization solving.
Preferably, the robust operation model converted in the step S33 is:
objective function:
Figure BDA00040736275900000612
operation constraint:
Figure BDA00040736275900000613
Figure BDA0004073627590000071
Figure BDA0004073627590000072
Figure BDA0004073627590000073
x,y∈Ω (36)
in the formula ,
Figure BDA0004073627590000074
is a pipeline set,/->
Figure BDA0004073627590000075
A set of inequality constraints for the uncertain parameter;
Figure BDA0004073627590000076
Comprises->
Figure BDA0004073627590000077
Is->
Figure BDA0004073627590000078
To->
Figure BDA0004073627590000079
Entry, the rest zero,>
Figure BDA00040736275900000710
the number of renewable energy sources connected to the node i is represented by T, which is the time; I.I 2 Is the second norm.
Compared with the prior art, the invention has the following advantages:
1) The adoption of the multiple uncertainty sets derived from the GARCH model considers the long-term time correlation of the power generation output of the renewable energy source, reduces the conservation of robust optimization, improves the flexibility for the operation of a heat supply regulation mode with variable mass flow, and improves the safety of the system operation;
2) Based on the dual theory, the robust operation problem with multiple uncertain sets is converted into a processable deterministic convex planning problem, and the difficulty of solving the optimization problem is reduced.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a generalized affine strategy framework schematic;
FIG. 3 is a cogeneration system IEHS with a 6 bus EPS and an 8 node DHS;
FIG. 4 is a schematic diagram of a two-dimensional uncertainty set of different lead time correlations;
FIG. 5 is an autocorrelation of wind power;
fig. 6 is a graph of the results of a day-ahead robust operation for small scale cases with variable mass flow.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
Examples
As shown in fig. 1, the embodiment provides a method for operating a variable mass flow combined heat and power system based on a plurality of uncertain sets, which comprises the following steps:
step S1, a robust operation model of a variable mass flow combined heat and power system IEHS is established, an objective function comprises the total cost of a minimized generator set of the deterministic combined heat and power system IEHS and the minimum resource rescheduling adjustment cost considering a prediction error, wherein the prediction error is restrained by adopting a multi-element uncertainty set;
and S2, processing double constraint conditions of robust optimization problems under an IEHS model of the variable mass flow combined heat and power system by adopting a contracted McCormick algorithm to obtain an optimal operation result.
Next, the method in this embodiment will be described in detail.
Problem (one) is presented
1. Deterministic integrated heat and power system IEHS operation model
While meeting the operation constraints of the power system EPS and the district heating system DHS, the fuel cost and the power transaction cost between other connected power systems are minimized, and the reconstruction model expression is:
objective function:
Figure BDA0004073627590000081
where F is the total cost function in a deterministic operation problem; the subscript t is the time index and,
Figure BDA0004073627590000082
the active power output of the thermal power generating unit TUj is +.>
Figure BDA0004073627590000083
Is the active power output of the cogeneration unit CHPj;
Figure BDA0004073627590000084
For the thermal power output of the cogeneration unit j, < >>
Figure BDA0004073627590000085
Is the heat power output of the heating boiler j, +.>
Figure BDA0004073627590000086
Is the power purchased from the external grid at interface j,
Figure BDA0004073627590000087
is the power sold to the external grid at interface j;
operation constraint:
Figure BDA0004073627590000088
Figure BDA0004073627590000089
Figure BDA00040736275900000810
in the formula ,
Figure BDA00040736275900000811
is the thermal power output of node i, +.>
Figure BDA00040736275900000812
and
Figure BDA00040736275900000813
Is an auxiliary variable defined as
Figure BDA00040736275900000814
m ij Is the mass flow, τ, of water in the DHS pipe that is transported from node i to node j i Is the exit temperature of node i, τ ji Is the pipe outlet temperature from node j to node i, < >>
Figure BDA00040736275900000815
Is the active/reactive power output at bus i, V i and θi Voltage amplitude of bus iValues and phase angles;
Figure BDA00040736275900000816
is the reactive power output of TU/CHPi.
Equations (2 a), (2 b), (2 c) are compact forms of deterministic operation equations in power system EPS, district heating system DHS and node power relations, respectively. Since the operational inequality is closely related to randomness in the system, the operational inequality will be described in the following section.
2. Affine strategy under random renewable energy
the renewable energy source generating power of each unit i at the moment t is expressed as:
Figure BDA0004073627590000091
wherein ,
Figure BDA0004073627590000092
is the actual renewable energy power generation, +.>
Figure BDA0004073627590000093
Is the predicted value of the generated power of renewable energy sources, and is zeta i,t Is the prediction error. If the prediction is 100% accurate then ζ i,t =0. However, this is not typically the case. In order for the tunable generator to adjust the output according to the prediction error, an affine strategy, also called a linear decision rule, is used.
The strategy assumes that the rescheduling output of each adjustable generator at time t has a linear relationship with the total prediction error of the renewable energy source. The random vector of prediction errors at time t for all renewable energy sources is represented as
Figure BDA0004073627590000094
wherein ,
Figure BDA0004073627590000095
Is the amount of renewable energy in the system; at t timeTotal prediction error of 1 T ξ t Wherein 1 is an all-column vector.
All flexible resources in the IEHS of the cogeneration system will provide the ability to adjust to compensate for output bias of renewable energy sources, including thermal power plants, cogeneration plants, heating boilers, and flexible heat loads such as heating, ventilation, and air conditioning (HVAC). HVAC can regulate the required thermal energy by regulating the temperature in the comfort zone, thereby acting as a thermal storage to achieve thermal power balance. Fig. 2 is a generalized affine strategy framework.
Figure BDA0004073627590000096
Figure BDA0004073627590000097
Figure BDA0004073627590000098
Figure BDA0004073627590000099
Figure BDA00040736275900000910
Figure BDA00040736275900000911
Figure BDA00040736275900000912
in the formula ,
Figure BDA00040736275900000913
is an adjustment factor for flexible resources.
Figure BDA00040736275900000914
The requirement is greater than or equal to zero;
Figure BDA00040736275900000915
is the actual active/reactive power output of the cogeneration unit i, < >>
Figure BDA00040736275900000916
Is the active/reactive power output of the actual thermal power generating unit i,/, the power supply is a power supply system>
Figure BDA00040736275900000917
Is the actual purchase and sales power from the external network at interface i, < >>
Figure BDA00040736275900000918
Is the actual active/reactive power generation at busbar i,/->
Figure BDA00040736275900000919
Is the actual thermal power output of the cogeneration unit i, < >>
Figure BDA00040736275900000920
Is the actual heat output of the heating boiler i, < >>
Figure BDA00040736275900000921
Is the actual thermal power output of node i.
It should be noted that the total heat load
Figure BDA00040736275900000922
Mainly from the adjustable air conditioning unit.
The adjustment relation between the output of the active power, the reactive power and the thermal power of the actual node and the flexible resource is as follows:
Figure BDA0004073627590000101
Figure BDA0004073627590000102
Figure BDA0004073627590000103
in the formula ,
Figure BDA0004073627590000104
the RES number connected to the node i is indicated. The same node power relationships as in the equation (2 c) are revealed in the equations (4 a) to (4 c). Wherein (1)>
Figure BDA0004073627590000105
Adjustment factors of the actual active power, reactive power, thermal yield of the corresponding node i, +.>
Figure BDA0004073627590000106
The RES number connected to the node i is indicated. In addition, except for the flexible resource adjusting its output according to the new energy real-time output, all other decision/state variables need to adjust their values to meet the network constraint:
Figure BDA0004073627590000107
Figure BDA0004073627590000108
Figure BDA0004073627590000109
in the formula ,
Figure BDA00040736275900001010
voltage phase angle and power of bus iAdjustment factor of amplitude of voltage,/->
Figure BDA00040736275900001011
Is the adjustment factor of the outlet temperature of node i, < >>
Figure BDA00040736275900001012
Is the adjustment factor of the pipe outlet temperature from node j to node i, +.>
Figure BDA00040736275900001013
Is an adjustment factor for the mass flow of water in the pipeline that is transmitted from node i to node j;
Figure BDA00040736275900001014
Is the actual voltage amplitude and phase angle of bus i,
Figure BDA00040736275900001015
is the actual outlet temperature of node i, +.>
Figure BDA00040736275900001016
Is the actual outlet temperature of the pipeline from node j to node i, < >>
Figure BDA00040736275900001017
Is the actual mass flow of water in the pipe that is transferred from node i to node j.
3. Adjustment in district heating system DHS
The constraint of equation (2 b) in the deterministic model provides a district heating system DHS model without taking into account uncertain prediction errors.
After the prediction error is considered, the adjustment of the district heating system DHS model is as follows:
Figure BDA00040736275900001018
Figure BDA00040736275900001019
Figure BDA00040736275900001020
Figure BDA00040736275900001021
Figure BDA00040736275900001022
Figure BDA00040736275900001023
Figure BDA00040736275900001024
Figure BDA00040736275900001025
wherein c is the specific heat capacity of water, v is the heat transfer coefficient per unit length, L ji Is the length of the pipeline, and the subscript t is the time;
Figure BDA00040736275900001026
respectively an inlet node set and an outlet node set;
Figure BDA00040736275900001027
Respectively corresponding to auxiliary variables->
Figure BDA00040736275900001028
and
Figure BDA0004073627590000111
Wherein%>
Figure BDA0004073627590000112
Figure BDA0004073627590000113
For the actual mass flow of water in the pipe ik, < > is>
Figure BDA0004073627590000114
Is an auxiliary variable +.>
Figure BDA0004073627590000115
Is the actual value of (2);
Figure BDA0004073627590000116
The adjustment factors of the actual thermal power output and the thermal load of the node i are respectively;
Figure BDA0004073627590000117
The adjustment factors of the mass flow of the water of the pipelines ji, ik respectively;
Figure BDA0004073627590000118
For the actual outlet temperature of node i, +.>
Figure BDA0004073627590000119
Respectively the upper limit and the lower limit of the outlet temperature of the node i;
Figure BDA00040736275900001110
For the actual mass flow of water in the pipe ji, < + >>
Figure BDA00040736275900001111
The upper and lower limits of the mass flow of water in the pipe ji, respectively. />
4. Adjustment in an EPS model of a power system
The constraint in equation (2 a) is power system EPS modeling performed without considering prediction errors.
To take into account the prediction error, the following constraints are required:
Figure BDA00040736275900001112
Figure BDA00040736275900001113
Figure BDA00040736275900001114
Figure BDA00040736275900001115
in the formula ,
Figure BDA00040736275900001116
the adjustment factors g of the actual active power output and the reactive power output of the node i respectively ij +jb ij Is the admittance, g, of the line ij ii +jb ii Is the shunt admittance of busbar i, +.>
Figure BDA00040736275900001117
Is a collection of bus bars;
Figure BDA00040736275900001118
Adjustment factors of voltage amplitude, voltage phase angle of bus i, respectively, +.>
Figure BDA00040736275900001119
The adjustment factors of the voltage amplitude and the voltage phase angle of the bus j are respectively;
Figure BDA00040736275900001120
For the maximum transmission power of branch ij, < +.>
Figure BDA00040736275900001121
The actual voltage amplitude and phase angle of bus i, V i max 、V i min Is a bus barUpper and lower limits of the i voltage amplitude.
5. Energy regulation
Tunable flexible resources include HB, CHP, TU and flexible thermal loads, such as HVAC.
Figure BDA00040736275900001122
Figure BDA00040736275900001123
Figure BDA00040736275900001124
Figure BDA00040736275900001125
in the formula ,
Figure BDA00040736275900001126
for the actual heat output of the heating boiler i, < >>
Figure BDA00040736275900001127
The upper and lower limits of the heat power output of the heat supply boiler i are respectively set;
Figure BDA00040736275900001128
The actual active power and reactive power output of the cogeneration unit i are respectively +.>
Figure BDA00040736275900001129
The operation feasible region parameter of the cogeneration unit i is as follows;
Figure BDA00040736275900001130
Is the active power of the thermal power generating unit i, P i TU,max 、P i TU,min The upper and lower limits of active power output of the thermal power unit i are respectively set;
Figure BDA0004073627590000121
and
Figure BDA0004073627590000122
The lower and upper limits of the heat of the flexible heat load i are respectively;
Figure BDA0004073627590000123
Is the adjustment factor of the thermal load of the node i.
6. Robust operation problems in an IEHS of a cogeneration system
In robust optimization, the possible implementation of prediction errors is typically limited to an uncertainty set. Since renewable energy errors are considered to have a strong temporal correlation, a set of multiple uncertainties defined by means and covariance is required. In order to obtain a multi-element uncertainty set, the invention adopts point prediction based on a machine learning method as a mean value, adopts a GARCH model to predict a covariance matrix, and adopts a Monte Carlo based method to estimate a proportion parameter. Multiple uncertainty set
Figure BDA0004073627590000124
The following is shown: />
Figure BDA0004073627590000125
Wherein x is 2 Representing a second norm, i.e
Figure BDA0004073627590000126
Γ is referred to as a scaling parameter. μ is the expectation of the value of ζ. Λ is represented by Σ -1 Upper triangular matrix decomposed by cholesky, Σ being the covariance matrix of ζ; vec (ζ) represents a vector expression of ζ by superimposing each column of v with the next column.
The robust optimization problem is to find the minimum target value in the worst case of uncertain parameters. Based on the deterministic model and the adjustment analysis caused by the prediction error, the overall robust problem is rewritten as:
Figure BDA0004073627590000127
equation in DHS model: (2b) (6 a) - (6 d) (10 b)
Equation in EPS: (2a) (7 a) - (7 b) (10 c)
Equation in energy: (8) (10 d)
Node power equation: (2c) (4 a) - (4 c) (10 e)
Inequality: (6f) - (6 h), (7 c) - (7 d), (8) (10 f)
Figure BDA0004073627590000128
Figure BDA0004073627590000129
wherein
Figure BDA00040736275900001210
For the run time period index, +.>
Figure BDA00040736275900001211
Is the cost factor of the heating boiler i, +.>
Figure BDA00040736275900001212
Is the cost factor of cogeneration unit i, < >>
Figure BDA00040736275900001213
Is the cost coefficient of the thermal power unit i, +.>
Figure BDA00040736275900001214
Is a set of heating boilers, < >>
Figure BDA00040736275900001215
Is a set of cogeneration units, +.>
Figure BDA00040736275900001216
Is a collection of thermal power generating units.
The objective function of the robustness problem is split into two parts. The first part is to minimize the total generator set cost F without taking into account prediction errors. The detailed formulas for the objective function F and the decision variable x come from deterministic running formulas. The second part is to minimize the cost of resource rescheduling to compensate for the energy imbalance caused by random prediction errors. The decision variable y is an adjustment factor which,
Figure BDA0004073627590000131
note that (10 g) limits the prediction error to an uncertainty set, (10 h) ensures that the adjustment factor of the flexible resource is zero or more
(II) solution
1. Compact form of robust optimization problem
The difficulty of solving problem (10) is in two aspects: first, a multiple uncertainty set (10 g) of prediction errors, and second, a bilinear constraint. The latter can be solved using a compact mccomick algorithm.
Therefore, a solution technology of the RO problem with a multiple uncertainty set is being studied with an emphasis. In particular, the RO problem is converted to a deterministic convex problem using the dual theory.
First, a compact form consistent with the robust optimization problem equation (10) is given:
Figure BDA0004073627590000132
s.t.A(y t )ξ t ≤b(x t )(11b)
Figure BDA0004073627590000133
x,y∈Ω(11d)
Figure BDA0004073627590000134
wherein
Figure BDA0004073627590000135
Is a flexible set of resources with adjustable power output, in this embodiment,/i>
Figure BDA0004073627590000136
Figure BDA0004073627590000137
A(y t) and b(xt ) Affine mappings representing y and x at time t, respectively; -an objective function (11 a) representation (10 a); (11 b) is an inequality constraint associated with the uncertainty parameter; (11 c) is a bilinear constraint; (11 d) summarizing only convex constraints with deterministic parameters. (11 e) is an uncertainty set constraint.
2. Introducing an auxiliary variable matrix s
An auxiliary variable matrix s is introduced into the objective function, and the calculation complexity of the objective function is reduced in a max-min mode.
Figure BDA0004073627590000138
s.t.C i,t y i,t 1 T ξ t ≤s i,t (12b)
A(y t )ξ t ≤b(x t )(12c)
Figure BDA0004073627590000139
x,y∈Ω(12e)
Figure BDA0004073627590000141
3. According to the dual theory, the conversion problem
Figure BDA0004073627590000142
Figure BDA0004073627590000143
Figure BDA0004073627590000144
Figure BDA0004073627590000145
Figure BDA0004073627590000146
x,y∈Ω(13f)
wherein
Figure BDA0004073627590000147
Is a pipeline set,/->
Figure BDA0004073627590000148
A set of inequality constraints for the uncertain parameter;
Figure BDA0004073627590000149
Comprises->
Figure BDA00040736275900001410
Is->
Figure BDA00040736275900001411
To->
Figure BDA00040736275900001412
The entries, the remainder are zero. Up to now, in the formula (13)The max-min structure in the scalar function and the inequality constraint associated with the uncertainty parameter are converted to convex formulas, respectively. To address the bilinear constraint, equation (13 d), a compact mccomick method may be used. The detailed conversion from equation (12) to equation (13) and the tightening mccomick method are omitted for reasons of space limitations.
(III) application instance
1. Description of the examples
In order to verify the validity of the proposed model and algorithm, several case studies were performed. First, two cases are compared to illustrate the importance of considering the temporal correlation of reproducible prediction errors.
Case 1: the polygon uncertainty set generates a multivariate prediction interval using a marginal (univariate) prediction interval and a multivariate scene as inputs. The time correlation is not taken into account.
Case 2: an ellipsoid uncertainty set based on the GARCH model, predicting a covariance matrix using the GARCH model. Taking into account time correlation
Both cases were tested in two IEHS systems. One is a small scale system with 6 bus EPS and 8 node DHS as shown in figure 3. Another example is a large system in the pari island, comprising a modified 118 busbar EPS and a 33 node DHS.
Details of these two IEHS's can be found in literature (H.Sun, Q.Guo, B.Zhang, W.Wu, B.Wang, X.Shen, and J.Wang, "Integrated energy management system: concept, design, and demonstration in china," IEEE Electrification Magazine, vol.6, no.2, pp.42-50,2018). Wind power data is provided by 2014 global energy forecast campaigns. The data set selected was from 1/2012/1/11/30/2013. The first 500 days of hour data were used as training data, and the last 125 days of data were used as prediction data.
2. Time correlation of multiple uncertainty sets
FIG. 4 is a schematic diagram of a two-dimensional multivariate uncertainty set. The lead time is defined as the period of time from the release of the prediction to the occurrence of the predicted phenomenon. The volume of the collection can be adjusted by a scaling parameter. The time dependence of RES is revealed with a coverage of 90% instead of 100%. It is noted that modifying the scaling parameters is also one way to reduce conservation. Compared to the polyhedral set, it is noted that the distribution of the prediction error points shows a strong positive correlation between the outputs of the adjacent two time periods, thereby proving that it is necessary to consider the time correlation. With 90% coverage, it can be observed that the collection constructed using the GARCH model has a more appropriate volume and better elliptical tilt than the polyhedral collection. In addition, fig. 4 also shows the aggregate shape at different lead times. It can be concluded that the correlation of the data generated when the lead time is equal to 1 with the data when the lead time is equal to 3 is smaller than the data when the lead time is equal to 2. This is reasonable because the autocorrelation will decrease over time as shown in fig. 5. In this embodiment, however, the autocorrelation is still strong until the lag time exceeds 20.
3) Robust running base results
Fig. 6 shows the results of the day-ahead robust operation of the variable mass flow IEHS, including the power output of each production unit, the power exchange with the grid, the worst case for renewable energy power, and the mass flow of typical pipelines. Because the solution method proposed by the present invention is used, the robust problem is convex planning, and thus can be effectively solved using off-the-shelf commercial solvers.
4. Robust operation under different uncertainty sets
Table 1 gives the optimal values of RO for different uncertainty set formulas. A polyhedral set refers to an uncertainty set shaped like a polyhedron or box. It ignores the temporal correlation of the prediction errors of different time periods. Thus, it is more conservative than the optimal results based on the uncertainty set of the GARCH model, both in small-scale and large-scale cases.
TABLE 1 optimal values of RO for different uncertainty set formulas
Uncertainty set Polyhedral set Ellipsoid collection
Description of the invention Irrespective of time correlation Taking into account time correlation
Optimum (Small-scale case) 156792.65$ 141328.17$
Optimum value (Large-scale case) 2208416.46$ 2159437.65$
In summary, the method of the invention improves flexibility for heating operation with variable mass flow and improves safety for robust operation; the long-term time correlation of the power generation output of the renewable energy sources is considered by adopting a multi-element uncertainty set derived from the GARCH model, so that the conservation of robust optimization is reduced; based on the dual theory, the robust operation problem with multiple uncertain sets is converted into a processable deterministic convex planning problem, and the difficulty of optimizing and solving is reduced.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.

Claims (10)

1. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets, the method comprising the steps of:
step S1, a robust operation model of a variable mass flow combined heat and power system IEHS is established, and an objective function comprises the total cost of a minimized generator set of the deterministic combined heat and power system IEHS and the minimum resource rescheduling adjustment cost for considering a prediction error, wherein the prediction error is restrained by a multi-element uncertainty set;
and S2, solving a robust optimization problem under an IEHS model of the variable mass flow thermoelectric combined system by adopting a contracted McCormick algorithm to obtain an optimal operation result.
2. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets according to claim 1, wherein said step S1 further comprises making a linear decision using affine strategies, in particular:
1) the renewable energy source of each unit i at time t is expressed as:
Figure FDA0004073627580000011
wherein ,
Figure FDA0004073627580000012
is the actual power of the renewable energy, +.>
Figure FDA0004073627580000013
Is the power predictive value of renewable energy and zeta i，t Prediction error for renewable energy;
2) Defining that the rescheduling output of each adjustable generator at the moment t is in linear relation with the total power prediction error of renewable energy sources, and expressing the power prediction error of all the renewable energy sources at the moment t as a random vector
Figure FDA0004073627580000014
wherein ,
Figure FDA0004073627580000015
is the quantity of renewable energy sources in the system, and the total prediction error deviation at the time t is 1 T ξ t Where 1 is an all-column vector.
3. A method for operating a variable mass flow combined heat and power system based on a multiple uncertainty set according to claim 2, wherein the robust operation optimization model under the variable mass flow combined heat and power system IEHS model in step S1 is specifically:
1) Objective function:
Figure FDA0004073627580000016
in the formula ,
Figure FDA0004073627580000017
for the total cost function of the deterministic thermoelectric combined system IEHS operation optimization model, x is the decision variable of the deterministic thermoelectric combined system IEHS operation optimization model, the subscript t is the time index,/-and #>
Figure FDA0004073627580000018
For the active power output of thermal power generating unit j, < >>
Figure FDA0004073627580000019
Is the active power output of the cogeneration unit j;
Figure FDA00040736275800000110
For the thermal power output of the cogeneration unit j, < >>
Figure FDA00040736275800000111
Is the heat power output of the heating boiler j, +.>
Figure FDA0004073627580000021
Is the power purchased from the external network at interface j, +.>
Figure FDA0004073627580000022
Is the power sold to the external grid at interface j;
Figure FDA0004073627580000023
Indexing for an operation period; ζ is the uncertainty prediction error; the decision variable y is a flexible resource adjustment factor;
Figure FDA0004073627580000024
The adjustment factors are respectively the adjustment factors of the heat power output of the heat supply boiler, the adjustment factors of the active power output of the cogeneration unit, the adjustment factors of the heat power output of the cogeneration unit and the adjustment factors of the active power output of the thermal power unit;
Figure FDA0004073627580000025
For the cost factor of the heating boiler i +.>
Figure FDA0004073627580000026
For the cost factor of the cogeneration unit i, < >>
Figure FDA0004073627580000027
Is the cost coefficient of the thermal power unit f;
Figure FDA0004073627580000028
Respectively collecting a heating boiler, a cogeneration unit and a thermal power unit;
2) Operational constraints, including district heating system constraints, power system constraints, tunable flexible resource constraints, node power constraints, prediction error constraints, and flexible resource adjustment factor constraints.
4. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 3, wherein the node power constraints comprise real node active power, reactive power, thermal power yield versus flexible resource constraints expressed as:
Figure FDA0004073627580000029
Figure FDA00040736275800000210
Figure FDA00040736275800000211
in the formula ,
Figure FDA00040736275800000212
adjustment factors of the actual active power, reactive power, thermal power yield, respectively corresponding to node i,/->
Figure FDA00040736275800000213
The adjustment factors of active power output of the cogeneration unit, reactive power output of the cogeneration unit and thermal power output of the cogeneration unit are respectively +.>
Figure FDA00040736275800000214
The power supply system is characterized in that the power supply system is respectively a thermal power unit active power output adjustment factor and a thermal power unit reactive power output adjustment factor, < ->
Figure FDA00040736275800000215
The adjustment factors of the purchased electric quantity at the interface j and the adjustment factors of the sold electric quantity at the interface j are respectively +.>
Figure FDA00040736275800000216
For the adjustment factor of the heating power output of the heating boiler j, < >>
Figure FDA00040736275800000217
The electric heat transfer coefficient of the heat supply boiler j;
Figure FDA00040736275800000218
Respectively collecting a heating boiler, a cogeneration unit and a thermal power unit;
Figure FDA00040736275800000219
The number of renewable energy sources connected to node i is indicated.
5. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 3, wherein the district heating system constraints are expressed as:
Figure FDA00040736275800000220
Figure FDA00040736275800000221
Figure FDA00040736275800000222
Figure FDA00040736275800000223
Figure FDA00040736275800000224
Figure FDA0004073627580000031
Figure FDA0004073627580000032
Figure FDA0004073627580000033
wherein c is the specific heat capacity of water, v is the heat transfer coefficient per unit length, L ji Is the length of the pipeline, and the subscript t is the time;
Figure FDA0004073627580000034
respectively an inlet node set and an outlet node set;
Figure FDA0004073627580000035
Respectively corresponding to auxiliary variables->
Figure FDA0004073627580000036
and
Figure FDA0004073627580000037
Wherein%>
Figure FDA0004073627580000038
For the actual mass flow of water in the pipe ik, < > is>
Figure FDA0004073627580000039
Is an auxiliary variable +.>
Figure FDA00040736275800000310
Is the actual value of (2);
Figure FDA00040736275800000311
The adjustment factors of the actual thermal power output and the thermal load of the node i are respectively;
Figure FDA00040736275800000312
The adjustment factors of the mass flow of the water of the pipelines ji, ik respectively;
Figure FDA00040736275800000313
For the actual outlet temperature of node i, +.>
Figure FDA00040736275800000314
Respectively the upper limit and the lower limit of the outlet temperature of the node i;
Figure FDA00040736275800000315
For the actual mass flow of water in the pipe ji, < + >>
Figure FDA00040736275800000316
The upper and lower limits of the mass flow of water in the pipe ji, respectively. />
6. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 3, wherein the power system constraints are expressed as:
Figure FDA00040736275800000317
Figure FDA00040736275800000318
Figure FDA00040736275800000319
Figure FDA00040736275800000320
in the formula ,
Figure FDA00040736275800000321
the adjustment factors g of the actual active power output and the reactive power output of the node i respectively ij +jb ij Is the admittance, g, of the line ij ii +jb ii Is the shunt admittance of busbar i, +.>
Figure FDA00040736275800000322
Is a collection of bus bars;
Figure FDA00040736275800000323
Adjustment factors of voltage amplitude, voltage phase angle of bus i, respectively, +.>
Figure FDA00040736275800000324
The adjustment factors of the voltage amplitude and the voltage phase angle of the bus j are respectively;
Figure FDA00040736275800000325
For the maximum transmission power of branch ij, < +.>
Figure FDA00040736275800000326
The actual voltage amplitude and phase angle of bus i, V i max 、V i min Is the upper and lower limits of the voltage amplitude of the bus i.
7. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 3, wherein the adjustable flexible resource constraints are expressed as:
Figure FDA00040736275800000327
Figure FDA00040736275800000328
Figure FDA00040736275800000329
Figure FDA00040736275800000330
in the formula ,
Figure FDA0004073627580000041
for the actual heat output of the heating boiler i, < >>
Figure FDA0004073627580000042
The upper and lower limits of the heat power output of the heat supply boiler i are respectively set;
Figure FDA0004073627580000043
The actual active power and reactive power output of the cogeneration unit i are respectively,
Figure FDA0004073627580000044
the operation feasible region parameter of the cogeneration unit i is as follows;
Figure FDA0004073627580000045
For the active power output of the thermal power generating unit i, < >>
Figure FDA0004073627580000046
The upper and lower limits of active power output of the thermal power unit i are respectively set;
Figure FDA0004073627580000047
and
Figure FDA0004073627580000048
The lower and upper limits of the heat of the flexible heat load i are respectively;
Figure FDA0004073627580000049
Is the adjustment factor of the heat of the flexible heat load.
8. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 3, wherein the prediction error constraint is expressed as:
Figure FDA00040736275800000410
Figure FDA00040736275800000411
where xi is the prediction error,
Figure FDA00040736275800000412
in the case of a multiple uncertainty set, I.I 2 Representing a second norm; Γ is a proportional parameter; μ is the expectation of the value of ζ; a is formed by -1 An upper triangular matrix decomposed by cholesky, and a covariance matrix with a value of Σζ; vec (ζ) represents a vector expression of ζ.
9. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets of claim 8, wherein said step S2 comprises the sub-steps of:
step S21, compact form of robust operation model under the variable mass flow combined heat and power system ies model:
objective function:
Figure FDA00040736275800000413
wherein ,
Figure FDA00040736275800000414
indexing for an operation period;
Figure FDA00040736275800000415
A set of flexible resources with adjustable power output; x, y and xi are decision variables; c (C) i，t Cost coefficients for the tunable flexible resources; zeta type toy t Is a prediction error; subscript t is time;
operational constraints, comprising:
1) Inequality constraints associated with uncertain parameters:
A(y t )ξ t ≤b(x t ) (25)
in the formula ,A(yt) and b(xt ) Affine mapping used to represent times y and x;
2) Bilinear constraints:
Figure FDA00040736275800000416
in the formula ,
Figure FDA00040736275800000417
is an auxiliary variable +.>
Figure FDA00040736275800000418
Is>
Figure FDA00040736275800000419
c is the specific heat capacity of water, m ik，t 、
Figure FDA00040736275800000420
The mass flow and the pipe of the water in the pipeline jkThe actual mass flow rate of water in the channel jk, τ i，t 、
Figure FDA00040736275800000421
The outlet temperature of the node i and the actual outlet temperature of the node i are respectively;
3) Convex constraints with deterministic parameters:
x，y∈Ω (27)
wherein omega is a decision variable convex constraint set;
4) Prediction error constraint:
Figure FDA0004073627580000051
where xi is the prediction error,
Figure FDA0004073627580000052
is a multiple uncertainty set;
step S32, introducing an auxiliary variable S into the objective function, wherein the expression is as follows:
Figure FDA0004073627580000053
in the formula ,si，t Auxiliary variables corresponding to the adjustable flexible resource i;
increasing the operating constraint:
C i，t y i，t 1 T ξ t ≤s i，t (30)
and S33, converting the robust operation model by adopting a tightening McCormick method and a dual theory, respectively converting a max-min structure in the objective function and inequality constraint related to uncertain parameters into a convex formula, and carrying out optimization solving.
10. A method of operating a variable mass flow cogeneration system based on a plurality of uncertainty sets according to claim 9, wherein said robust operation model converted in step S33 is:
objective function:
Figure FDA0004073627580000054
operation constraint:
Figure FDA0004073627580000055
Figure FDA0004073627580000056
Figure FDA0004073627580000057
Figure FDA0004073627580000058
x，y∈Ω (36)
in the formula ,
Figure FDA0004073627580000059
is a pipeline set,/->
Figure FDA00040736275800000510
A set of inequality constraints for the uncertain parameter;
Figure FDA00040736275800000511
Included
Figure FDA00040736275800000512
Is->
Figure FDA00040736275800000513
To->
Figure FDA00040736275800000514
Entry, the rest zero,>
Figure FDA00040736275800000515
the number of renewable energy sources connected to the node i is represented by T, which is the time; I.I 2 Is the second norm. />
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CN116644866A (en) * 2023-07-27 2023-08-25 国网江西省电力有限公司经济技术研究院 Comprehensive energy system robust optimization method and system considering wind-light uncertainty

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