CN112865100B - Double-layer P2P trading method capable of protecting private information based on augmented Benders decomposition - Google Patents

Double-layer P2P trading method capable of protecting private information based on augmented Benders decomposition Download PDF

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CN112865100B
CN112865100B CN202110391262.5A CN202110391262A CN112865100B CN 112865100 B CN112865100 B CN 112865100B CN 202110391262 A CN202110391262 A CN 202110391262A CN 112865100 B CN112865100 B CN 112865100B
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夏元兴
徐青山
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Southeast University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses a double-layer P2P trading method capable of protecting private information based on augmented Benders decomposition, and the operation of a power distribution network is cooperatively optimized by using the augmented Benders decomposition technology and a community microgrid. The method comprises the following steps: the P2P transaction is divided into two layers, namely, a power distribution network layer and a community-level micro-network layer according to different transaction ranges. Modeling the two layers into a main problem and a sub problem respectively, and optimizing by adopting the augmented Benders decomposition; in the double-layer transaction model, an external model is established by an upper layer model from the perspective of a power distribution network system operator, and a convex alternating current optimal power flow model is established by utilizing a power distribution network power flow model so as to ensure the optimal operation of a power grid; the internal model is established at the lower layer from the perspective of energy producers and consumers, and the whole system transmits power according to an economic optimal scheme because the community-level microgrid has small transmission power and a simple circuit structure and neglects tidal current constraint.

Description

Double-layer P2P trading method capable of protecting private information based on augmented Benders decomposition
Technical Field
The invention belongs to the technical field of P2P transaction, and particularly relates to a double-layer P2P transaction method based on augmented Benders decomposition.
Background
In recent years, with the increasing popularization of distributed power generation resources and the continuous progress of information communication technology, a power distribution network transaction form based on P2P (Peer-to-Peer) is becoming popular. The energy trading form allows the energy producer and consumer to directly trade the electric power, thereby improving the consumption rate of renewable energy at the user end. Since most of participants of the P2P transaction consume energy locally, few users need power from an upper grid, so the transaction scheme can reduce the transmission pressure of a transmission trunk line and the scheduling complexity of the upper grid. Therefore, the popularization of the P2P (peer-to-peer) based power distribution network transaction has strong practical significance and economic value.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a double-layer P2P trading method based on augmented Benders decomposition, which can effectively protect the privacy information of each community microgrid and efficiently and accurately meet the requirements of two trading parties.
The purpose of the invention can be realized by the following technical scheme: a double-layer P2P transaction method capable of protecting private information based on augmented Benders decomposition comprises the following steps:
1) establishing a double-layer transaction model based on the characteristics of a transaction range, wherein the double-layer transaction model comprises an upper layer model and a lower layer model, the upper layer model comprises a power distribution network layer, the lower layer model comprises a community-level microgrid layer, the power distribution network layer is modeled as a main problem, the power distribution network layer is modeled as a sub-problem, and the optimization is carried out by adopting augmented Benders;
2) Acquiring data, namely acquiring user load, real-time electricity price and power grid data, and transmitting the acquired data serving as parameters into the double-layer transaction model;
3) optimizing an upper layer model, establishing an external model for the upper layer model from the perspective of a power distribution network system operator, and establishing a convex alternating current optimal power flow model by using a power distribution network power flow model;
4) optimizing a lower model, and establishing an internal model of the lower model from the perspective of an energy producer and consumer;
5) and respectively optimizing the main problem and the sub-problems by using the augmented Benders decomposition, and solving the optimal solution of the sub-problems.
As a further scheme of the invention, the user load data comprises year-round load data of users in each community-level microgrid, the data acquisition interval is minimum 15 minutes, and the real-time electricity price adopts a national uniform peak-valley average three-time electricity price;
the power grid data comprise the connection relation between each micro-power grid and a superior power distribution network, the resistance and reactance value of each branch, and the upper limit of the transmission power of each branch.
As a further scheme of the invention, in the step 1), the specific steps are as follows: analyzing the transaction process of the distribution network level P2P, establishing an objective function of an optimization model, wherein energy producers and consumers exist in the community-level microgrid, the outside of the microgrid is a superior grid, a distribution network operator is responsible for operating the whole distribution network system, and a microgrid manager is responsible for managing each microgrid, because in the transaction process of the distribution network level P2P, the distribution network operator needs to be responsible for the safe and stable operation of both transaction parties and the grid, the model centralized optimization transaction party's total income should be established:
Figure GDA0003648714040000021
Figure 915676DEST_PATH_FDA0003614144490000022
pnm≥0,
Figure GDA0003648714040000031
pmn≤0,
Figure GDA0003648714040000032
In the formula: xisysE omega is a decision variable set for optimizing the power distribution network; the set of buyers and sellers in the energy transaction is N respectivelys,Nb,Ω＝card(Ns)×card(Nb) To represent a set of transactions that may occur between the buyer and seller; cnRepresenting a cost utility function for the nth energy producer and consumer; p is a radical ofnmRepresenting the amount of power that seller n delivers to buyer m; the power supplied by the seller to all the buyers is limited to the upper and lower limits of the seller's electricity production
Figure GDA0003648714040000033
Within, the sum of the power of the buyer and the seller is 0 to ensure the power balance in the system, and the positive power direction is set from the seller to the buyer.
Utility function C of energy producer and consumernModeling
Figure GDA0003648714040000034
In the formula: pnPower produced or consumed by energy producers or consumers, an,bn,cnRespectively reporting prior parameters for each of the producers and the consumers.
Second order cone relaxation (re l axed-SOCP) model of distribution grid level power flow:
Figure GDA0003648714040000035
s.t.
Figure GDA0003648714040000036
Figure GDA0003648714040000037
Figure GDA0003648714040000038
Figure GDA0003648714040000039
Figure GDA00036487140400000310
Figure GDA0003648714040000041
Figure GDA0003648714040000042
Figure GDA0003648714040000043
in the formula:
Figure GDA0003648714040000044
is a set of decision variables of the power distribution network,
Figure GDA0003648714040000045
as a function of the cost of each of the producers and consumers,
Figure GDA0003648714040000046
and the electricity purchasing cost is carried out on the community micro-grid to a superior distribution network. The constraint conditions are respectively active balance, reactive balance and line head and tailThe upper limit of the transmission capacity at two ends is restricted, the relaxation model of the node voltage and the upper limit of the power generation of each energy producer and consumer are restricted, and the upper limit and the lower limit of the active power and the reactive power of each node are restricted.
Figure GDA0003648714040000047
Is the active power flow with the generation node b on the line l, R lIs the resistance value of the line l, alIs the square of the current on the line l,
Figure GDA0003648714040000048
is the active output of the node b and,
Figure GDA0003648714040000049
is the amount of electricity sold by the node b,
Figure GDA00036487140400000410
is the power demand of node b, GbIs the conductance of node b, vbSquared as the voltage at node b.
Figure GDA00036487140400000411
Is a reactive power flow with a generating node b on the line l, XlIs the reactance value of line l, BbFor the susceptance value of the node b,
Figure GDA00036487140400000412
is the square of the upper limit of the transmission capacity of line l;
in order to maintain the safe and stable operation of the power distribution network, punishment of network blocking is carried out on transactions occurring in the network, and the punishment cost UC of the network blocking can be calculated as follows:
Figure GDA00036487140400000413
Figure GDA00036487140400000414
Figure GDA00036487140400000415
in the formula:
Figure GDA00036487140400000416
respectively are dual variables of corresponding constraints in the above formula, and the flowing power p when the line is blocked can be obtained by calculating the line l with network blockagewThe penalty cost UC;
and finally, uniformly optimizing the power distribution network model and the second-order cone relaxation model to obtain the optimal solution of the P2P trading process under the condition that the power grid operates safely and stably.
As a further scheme of the present invention, the power flow model of the power distribution network in step 3) specifically includes:
second-order cone relaxation model for distribution network-level power flow
Figure GDA0003648714040000051
s.t.
Figure GDA0003648714040000052
Figure GDA0003648714040000053
Figure GDA0003648714040000054
Figure GDA0003648714040000055
Figure GDA0003648714040000056
Figure GDA0003648714040000057
Figure GDA0003648714040000058
In the formula:
Figure GDA0003648714040000059
is a set of decision variables of the power distribution network,
Figure GDA00036487140400000510
as a function of the cost of each of the producers and consumers,
Figure GDA00036487140400000511
the power purchasing cost from a community micro-grid to a superior distribution network is realized by respectively adopting the constraint conditions of active balance and reactive balance on a line l, upper limit constraint of transmission capacity at the first end and the last end of the line, relaxation model of node voltage, upper limit of power generation of each energy producer and consumer, upper limit constraint of active and reactive limits of each node,
Figure GDA00036487140400000512
Is the active power flow with the generation node b on the line l, RlIs the resistance value of the line l, alIs the square of the current on the line l,
Figure GDA00036487140400000513
is the active output of the node b and,
Figure GDA00036487140400000514
is the amount of electricity sold by the node b,
Figure GDA00036487140400000515
is the power demand of node b, GbIs the conductance of node b, vbWhich is the square of the voltage at node b,
Figure GDA0003648714040000061
is the reactive power flow with the generation node b on the line l, XlIs the reactance value of line l, BbFor the susceptance value of the node b,
Figure GDA0003648714040000062
which is the square of the upper limit of the transmission capacity of line i.
As a further aspect of the present invention, the step 4) includes:
analyzing a model in the community-level microgrid, and establishing an optimization model and corresponding constraint conditions;
because the producers and consumers in each community have the right to negotiate, receive and reject transactions, the goal of the model in the microgrid is to establish a stable transaction scheme that is acceptable to all participants, and the model is as follows:
Figure GDA0003648714040000063
Figure GDA0003648714040000064
σs+σb＝1
Figure GDA0003648714040000065
SOCn(t)＝SOCn(t-1)+pn×Δt,
Figure GDA0003648714040000066
Figure GDA0003648714040000067
Figure GDA0003648714040000068
Figure GDA0003648714040000069
Figure GDA00036487140400000610
Figure GDA00036487140400000611
Figure GDA00036487140400000612
in the formula:
Figure GDA00036487140400000613
is a decision variable of the underlying model,
Figure GDA00036487140400000614
to describe the boolean variables of the transaction state, when the seller selects transaction w,
Figure GDA00036487140400000615
otherwise
Figure GDA00036487140400000616
Figure GDA00036487140400000617
Is arranged and
Figure GDA00036487140400000618
the consistency is kept between the first and the second,
Figure GDA00036487140400000619
and
Figure GDA00036487140400000620
optimum prices, SOC, for seller and buyer, respectively, in a transactionn(t)For the state of charge of the nth energy storage device at time t,
Figure GDA00036487140400000621
and
Figure GDA00036487140400000622
lower and upper limits, respectively, of the energy storage state of charge, the transaction w selected by the buyer must be completed by the seller in each transaction, and so
Figure GDA0003648714040000071
The values can only be (1,1), (0,1) and (0, 0);
due to uncertainty of new energy output and load, the load of part of communities needs the output support of the microgrid of other communities, and therefore the input and output power of the community-level microgrid can be modeled as follows:
Figure GDA0003648714040000072
in the formula:
Figure GDA0003648714040000073
is the power supplied by the other micro-grid,
Figure GDA0003648714040000074
the two parameters are calculated by an upper layer model, and the two parameters are power supplied by the microgrid to other communities.
As a further aspect of the present invention, the augmented Benders decomposition specifically comprises: solving the main problem and the sub-problems by using an augmented Benders decomposition algorithm, and realizing privacy information protection through dual information exchanged between the main problem and the sub-problems;
reconstructing the original problem into a matrix form:
Figure GDA0003648714040000075
s.t.
G(x)≥d
Bnx+Cnyn+Dnzn≥d,
Figure GDA0003648714040000076
zn∈{0,1}n,
Figure GDA0003648714040000077
in the formula: a isT,
Figure GDA0003648714040000078
Constant coefficient matrixes respectively representing corresponding variables, x is a matrix corresponding to decision variables in an upper layer distribution network model, yn,znContinuous decision variables and Boolean decision variables in the lower community-level microgrid are represented respectively, and constraint conditions in other models are reconstructed into a matrix form and written in the model;
the main problem is broken down from the above equation and converted into:
Figure GDA0003648714040000079
s.t.
G(x)≥d
θn≥0,
Figure GDA00036487140400000710
wherein the cutting plane of the main problem can be generated as:
GCPn(x)≥0,
Figure GDA0003648714040000081
in the formula: thetanThe operation cost of the nth community-level micro-grid calculated from the perspective of the power distribution network operator is calculated, and the optimal solution is obtained after the calculation result is completed
Figure GDA0003648714040000082
Is transmitted to the lower sub-problem for further solving;
the feasible region inspection subproblem and the optimal solution inspection subproblem are uniformly modeled and optimized in the part, and the model is built as follows:
Figure GDA0003648714040000083
Figure GDA0003648714040000084
Figure GDA0003648714040000085
Figure GDA0003648714040000086
zn∈{0,1}n
sn≥0,ξn,ζn≥0
in the formula: sn,ξn,ζnRelaxation variables for feasible solution and optimal solution corresponding to sub-problem respectively, if optimal solution snIf not, a feasible cut set needs to be complemented back to the main problem to ensure the model of the main problem is feasible, otherwise, an optimal cut set needs to be complemented back to the main problem to ensure the effectiveness of the solution, and a relaxation variable xin,ζnCharacterize and show
Figure GDA0003648714040000087
Degree of deviation from optimal solution true value, if ξn,ζnIf not 0, the optimal cut set needs to be complemented back to the main problem for solving, otherwise, the feasible cut set needs to be complemented back to the main problem, and the sub-problems of the unified modeling of the part can simultaneously generate the optimal cut and the feasible cut, so that the method is faster compared with the sub-problems of the original algorithm,
will thetanAnd x are written together as a matrix, the main problemCan be reconstructed as follows:
Figure GDA0003648714040000088
H(x')≥d'
GCPn(x′)≥0,
Figure GDA0003648714040000089
in the formula: x' ═ θnX is a decision variable under a unified model, H represents a constraint set in the model, d' is a parameter set of corresponding constraints, and similarly, subproblems can also be written in a unified form as follows:
Figure GDA0003648714040000091
Figure GDA0003648714040000092
zn∈{0,1}n,s'n≥0
in the formula: sn,ξn,ζnA decision variable corresponding to the sub-problem;
Solving the Benders cut set and the feasible domain recovery cut set,
by taking the Boolean type variable z of the original problemnRelaxation is a continuous variable, and the sub-problem can be written as follows:
Figure GDA0003648714040000093
Figure GDA0003648714040000094
Figure GDA0003648714040000095
Figure GDA0003648714040000096
s′n≥0
in the formula:
Figure GDA0003648714040000097
for newly introduced Boolean type variable, to relax the Boolean type variable z in the original problemnBy separating the boolean variables and the continuous variables, the original model can be written as follows:
Figure GDA0003648714040000098
according to strong dual theory, the minimization model inside the brackets can be replaced by its dual model:
Figure GDA0003648714040000099
according to the min-max inequality, the inner and outer models can be swapped in order as follows:
Figure GDA00036487140400000910
the part of the internal model directly related to the decision variables is
Figure GDA00036487140400000911
Can use maximization model 1TωnTo replace it with a new one in the form of a new one,
the inner and outer layers can thus be modeled uniformly as follows:
Figure GDA00036487140400000912
Figure GDA00036487140400000913
Figure GDA00036487140400000914
0≤αn≤1,ωn≤0,ωn≤βn
by solving this model, the unified Benders cut set can be expressed as:
Figure GDA0003648714040000101
in the formula:
Figure GDA0003648714040000102
are respectively the optimal solutions of the unified subproblems,
the model contains integer variables, and the feasible region recovery cut set needs to be returned to the original main problem to ensure that the dual gap is eliminated if the optimal solution is adopted
Figure GDA0003648714040000103
If the requirement of the feasible region is met, the feasible region recovery subproblem can be obtained from the following model:
Figure GDA0003648714040000104
zn∈{0,1}n
in the formula: objective function
Figure GDA0003648714040000105
Represents the optimal solution x' and the feasible solution
Figure GDA0003648714040000106
The difference between them, the expression is as follows:
Figure GDA0003648714040000107
In the formula: x'h,
Figure GDA0003648714040000108
Respectively, represent a matrix x',
Figure GDA0003648714040000109
each element of phihDenotes the normalization factor of x 'h, if x'h|>0, normalization factor is | x'hIf x'hI is 0, the normalization factor is a small positive number τ>0，
And returning the two solved cut sets to the main problem to obtain the optimal solution of the original problem.
The invention has the beneficial effects that: the P2P transaction of each micro-grid in the power distribution network is modeled by using the method of augmenting Benders decomposition, so that the power utilization satisfaction of energy producers and consumers is improved while the safe and stable operation of the whole power distribution network is ensured. The used augmented Benders decomposition algorithm protects the privacy information of each microgrid user and has higher use value
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a schematic view of the power flow of a single line connected to a single community-level microgrid;
FIG. 3 is a schematic diagram of the power flow of a plurality of lines connected to a plurality of community-level micro grids;
FIG. 4 is a schematic diagram of a distribution grid-microgrid two-tier dispatch;
FIG. 5 is a graphical representation of utility functions of energy storage, generator, and load.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Referring to fig. 1, it shows a flowchart of the two-layer model structure based on augmented Benders decomposition and its corresponding algorithm of the present invention, the method includes the following steps:
1) Establishing a double-layer transaction model based on the characteristics of a transaction range, wherein the double-layer transaction model comprises an upper layer model and a lower layer model, the upper layer model comprises a power distribution network layer, the lower layer model comprises a community-level microgrid layer, the power distribution network layer is modeled as a main problem, the power distribution network layer is modeled as a sub-problem, and the optimization is carried out by adopting augmented Benders;
2) acquiring data, namely acquiring user load, real-time electricity price and power grid data, and transmitting the acquired data serving as parameters into the double-layer transaction model; the user load data comprises year-round load data of users in each community-level microgrid, and the data acquisition interval is minimum 15 minutes. The real-time electricity price adopts the national uniform peak-valley average three-time electricity price. The power grid data comprise the connection relation between each micro-power grid and a superior power distribution network, the resistance and reactance value of each branch and the upper limit of the transmission power of each branch.
3) Optimizing an upper layer model, establishing an external model for the upper layer model from the perspective of a power distribution network system operator, and establishing a convex alternating current optimal power flow model by using a power distribution network power flow model;
4) optimizing a lower layer model, and establishing an internal model of the lower layer model from the perspective of an energy producer and consumer;
5) And respectively optimizing the main problem and the sub-problems by using the augmented Benders decomposition, and solving the optimal solution of the sub-problems.
Further, analyzing the transaction process of the distribution network level P2P, and establishing an objective function of an optimization model;
the structure of the microgrid connected with the power distribution network is shown in fig. 2 and fig. 3, an energy producer and an energy consumer exist inside the community-level microgrid, the outside of the microgrid is a higher-level microgrid, a power distribution network operator is responsible for operating the whole power distribution network system, and a microgrid manager is responsible for managing each microgrid.
Because the distribution network operator needs to be responsible for the safe and stable operation of the transaction parties and the power grid in the distribution network level P2P transaction process, a model should be established for centralized optimization of the total income of the transaction parties
Figure GDA0003648714040000121
Figure GDA0003648714040000122
pnm≥0,
Figure GDA0003648714040000123
pmn≤0,
Figure GDA0003648714040000124
In the formula: xisysSelecting omega as a decision variable set for optimizing the power distribution network; the set of the buyer and the two parties in the energy transaction is N respectivelys,Nb,Ω＝card(Ns)×card(Nb) To represent a set of transactions that may occur between the buyer and seller; cnRepresenting a cost utility function for the nth energy producer and consumer; p is a radical ofnmRepresenting the amount of power that the seller n delivers to the buying room m; the power supplied by the seller to all the buyers is limited to the upper and lower limits of the seller's electricity production
Figure GDA0003648714040000125
Within, the sum of the power of the buyer and the seller is 0 to ensure the power balance in the system, and the positive power direction is set from the seller to the buyer.
Utility function C of energy producer and consumernModeling
Figure GDA0003648714040000126
In the formula: pnPower produced or consumed by energy producers or consumers, an,bn,cnRespectively reporting prior parameters for each of the producers and the consumers.
Second order cone relaxation (re l axed-SOCP) model for distribution network level power flow
Figure GDA0003648714040000127
s.t.
Figure GDA0003648714040000128
Figure GDA0003648714040000131
Figure GDA0003648714040000132
Figure GDA0003648714040000133
Figure GDA0003648714040000134
Figure GDA0003648714040000135
Figure GDA0003648714040000136
Figure GDA0003648714040000137
In the formula:
Figure GDA0003648714040000138
is a set of decision variables of the power distribution network,
Figure GDA0003648714040000139
as a function of the cost of each of the producers and consumers,
Figure GDA00036487140400001310
and the electricity purchasing cost is carried out on the community micro-grid to a superior distribution network. The constraint conditions are respectively active balance and reactive balance on the line l, upper limit constraint of transmission capacity at the head end and the tail end of the line, relaxation model of node voltage, upper limit of power generation of each energy producer and consumer, and upper limit constraint of active and reactive limits of each node.
Figure GDA00036487140400001311
Is the active power flow with the generation node b on the line l, RlIs the resistance value of the line l, alIs the square of the current on the line i,
Figure GDA00036487140400001312
is the active output of the node b and,
Figure GDA00036487140400001313
is the amount of electricity sold by the node b,
Figure GDA00036487140400001314
is the power demand of node b, GbIs the conductance of node b, vbThe voltage at node b is squared.
Figure GDA00036487140400001315
Is the reactive power flow with the generation node b on the line l, XlIs the reactance value of line l, BbFor the susceptance value of the node b,
Figure GDA00036487140400001316
which is the square of the upper limit of the transmission capacity of line i.
In order to maintain the safe and stable operation of the power distribution network, the invention punishs network blocking on the transaction occurring in the network. The network congestion penalty cost UC may be calculated as follows:
Figure GDA0003648714040000141
Figure GDA0003648714040000142
Figure GDA0003648714040000143
In the formula:
Figure GDA0003648714040000144
respectively are dual variables of corresponding constraints in the above formula, and the flowing power p when the line is blocked can be obtained by calculating the line l with network blockagewThe penalty cost UC.
And finally, uniformly optimizing the power distribution network model and the second-order cone relaxation model to obtain the optimal solution of the P2P trading process under the condition that the power grid operates safely and stably.
Analyzing a model in the community-level microgrid, and establishing an optimization model and corresponding constraint conditions;
the two-layer scheduling structure formed by the distribution network and the micro-grid is shown in figure 4 and accords with the structure of the augmented Benders decomposition used by the invention.
Because the producers and consumers in each community have the right to negotiate, accept and reject transactions, the model in the microgrid aims to establish a stable transaction scheme that all participants can accept. The model is as follows:
Figure GDA0003648714040000145
Figure GDA0003648714040000151
σs+σb＝1
Figure GDA0003648714040000152
SOCn(t)＝SOCn(t-1)+pn×Δt,
Figure GDA0003648714040000153
Figure GDA0003648714040000154
Figure GDA0003648714040000155
Figure GDA0003648714040000156
Figure GDA0003648714040000157
Figure GDA0003648714040000158
Figure GDA0003648714040000159
in the formula:
Figure GDA00036487140400001510
is a decision variable of the underlying model,
Figure GDA00036487140400001511
to describe the boolean variables of the transaction state, when the seller selects transaction w,
Figure GDA00036487140400001512
otherwise
Figure GDA00036487140400001513
Figure GDA00036487140400001514
Is arranged and
Figure GDA00036487140400001515
and (5) the consistency is achieved.
Figure GDA00036487140400001516
And
Figure GDA00036487140400001517
optimum prices, SOC, for seller and buyer, respectively, in a transactionn(t) is the state of charge of the nth energy storage device at time t,
Figure GDA00036487140400001518
and
Figure GDA00036487140400001519
respectively, the lower and upper limits of the energy storage state of charge. In each transaction, the transaction w selected by the buyer must be completed by the seller, and so
Figure GDA00036487140400001520
Values can only be (1,1), (0,1) and (0, 0).
Due to uncertainty of new energy output and load, the load of part of communities needs the output support of the microgrid of other communities, and therefore the input and output power of the community-level microgrid can be modeled as follows:
Figure GDA00036487140400001521
in the formula:
Figure GDA00036487140400001522
is the power supplied by the other micro-grid,
Figure GDA00036487140400001523
is the power supplied by the microgrid to other communities. These two parameters are calculated by the upper layer model.
The joint scheduling model of the upper layer and the lower layer:
Figure GDA0003648714040000161
the constraints and variable descriptions have been given above.
Solving the double-layer problem by using an augmented Benders decomposition algorithm, modeling a community-level microgrid as a subproblem, modeling a distribution network-level problem as a main problem, and realizing privacy information protection through dual information exchanged between the main and subproblems;
reconstructing the original problem into a matrix form:
Figure GDA0003648714040000162
s.t.
G(x)≥d
Bnx+Cnyn+Dnzn≥d,
Figure GDA0003648714040000163
zn∈{0,1}n,
Figure GDA0003648714040000164
in the formula: a isT,
Figure GDA0003648714040000165
Constant coefficient matrixes respectively representing corresponding variables, x is a matrix corresponding to decision variables in an upper layer distribution network model, yn,znAnd the continuous decision variables and the Boolean decision variables in the lower community-level micro-grid are represented respectively. The constraints in other models are also reconstructed and written in the model in the form of a matrix.
The main question can be split from the overall question and converted into:
Figure GDA0003648714040000166
s.t.
G(x)≥d
θn≥0,
Figure GDA0003648714040000167
Wherein the cutting plane of the main problem can be generated as:
GCPn(x)≥0,
Figure GDA0003648714040000168
in the formula: thetanThe operation cost of the nth community-level micro-grid calculated from the perspective of the power distribution network operator is calculated, and the optimal solution is obtained after the calculation result is completed
Figure GDA0003648714040000171
Is passed to the lower sub-problem for further resolution.
The feasible domain inspection sub-problem and the optimal solution inspection sub-problem are uniformly modeled and optimized in the part, and the model is as follows:
Figure GDA0003648714040000172
Figure GDA0003648714040000173
Figure GDA0003648714040000174
Figure GDA0003648714040000175
zn∈{0,1}n
sn≥0,ξn,ζn≥0
in the formula: sn,ξn,ζnRelaxation variables for feasible solution and optimal solution corresponding to sub-problem respectively, if optimal solution snInstead of 0, a feasible cut set needs to be complemented back to the main problem to ensure that the model of the main problem is feasible. Otherwise, an optimal cut set needs to be complemented back to the main problem to ensure the validity of the solution. Relaxation variable xin,ζnCharacterize and show
Figure GDA0003648714040000176
Degree of deviation from optimal solution true value, if ξn,ζnIf not, the optimal cut set needs to be complemented back to the main problem for solving, otherwise, the feasible cut set needs to be complemented back to the main problem. The sub-problems of the unified modeling of the part can generate the optimal cut and the feasible cut simultaneously, so that the method is faster compared with the sub-problems of the original algorithm.
Will thetanAnd x are uniformly written into a matrix, and the main problem can be reconstructed as follows:
Figure GDA0003648714040000177
H(x')≥d'
GCPn(x′)≥0,
Figure GDA0003648714040000178
in the formula: x' ═ θnX is a decision variable under the unified model, G represents a constraint set of the model, and d' is a parameter set of corresponding constraints. Similarly, the subproblems may also be uniformly written in the form of a matrix as follows:
Figure GDA0003648714040000179
Figure GDA00036487140400001710
zn∈{0,1}n,s'n≥0
In the formula: sn,ξn,ζnThe decision variables corresponding to the sub-problems.
Solving a Benders cut set and a feasible domain recovery cut set:
the unified Benders cut sets including the feasible cut sets and the optimal cut sets in the invention can be obtained by solving the original unified subproblems. By using the Boolean type variable z of the original problemnRelaxation is a continuous variable, and sub-problems can be written as follows:
Figure GDA0003648714040000181
Figure GDA0003648714040000182
Figure GDA0003648714040000183
Figure GDA0003648714040000184
s′n≥0
in the formula:
Figure GDA0003648714040000185
for newly introduced Boolean type variable, for relaxing the Boolean type variable z in the original problemn. By separating the Boolean-type variables from the continuous-type variables, the original model can be written as follows:
Figure GDA0003648714040000186
according to strong dual theory, the minimization model inside the brackets can be replaced by its dual model:
Figure GDA0003648714040000187
according to the min-max inequality, the inner and outer models can be swapped in order as follows:
Figure GDA0003648714040000188
the part of the internal model directly related to the decision variables is
Figure GDA0003648714040000189
Can use the maximization model 1TωnTo replace it.
The inner and outer layers can thus be modeled uniformly as follows:
Figure GDA00036487140400001810
Figure GDA00036487140400001811
Figure GDA00036487140400001812
0≤αn≤1,ωn≤0,ωn≤βn
by solving this model, the unified Benders cut set can be expressed as:
Figure GDA00036487140400001813
in the formula:
Figure GDA0003648714040000191
respectively, are the optimal solutions of the unified subproblems.
Because the corresponding model of the invention contains integer variables, the feasible domain recovery cut set needs to be returned to the original main problem to ensure that the dual gap is eliminated. If the optimal solution is
Figure GDA0003648714040000192
If the requirement of the feasible region is met, the feasible region recovery subproblem can be obtained from the following model:
Figure GDA0003648714040000193
zn∈{0,1}n
in the formula: objective function
Figure GDA0003648714040000194
Represents the optimal solution x' and the feasible solution
Figure GDA0003648714040000195
The difference between them, the expression is as follows:
Figure GDA0003648714040000196
in the formula: x'h,
Figure GDA0003648714040000197
Respectively, represent a matrix x',
Figure GDA0003648714040000198
element of (b), phihRepresents x'hThe normalization factor of (1). If x'h|>0, normalization factor is | x'hIf x'hI is 0, the normalization factor is a small positive number τ>0。
And returning the two solved cut sets to the main problem to obtain the optimal solution of the original problem.
The energy efficiency model of the cost of the energy producer and consumer established by the invention is shown in figure 5, and the cost is lower for the generator when the power generation is less, and the satisfaction is higher for the consumer when the load is more. The energy storage device can be either an energy producer (discharging) or an energy consumer (charging), so its energy model exists between the two quadrants.
The invention is suitable for the double-layer P2P transaction of a power distribution network and a microgrid, improves the decision making speed by applying the enhanced Benders decomposition algorithm from the perspective of the power distribution network, protects the power consumption privacy of each community-level microgrid from the perspective of microgrid producers and consumers, provides a new idea for the P2P energy transaction, and effectively improves the local consumption rate of new energy.
It will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (6)

1. A double-layer P2P transaction method capable of protecting private information based on augmented Benders decomposition, the method comprises the following steps:
1) establishing a double-layer transaction model based on the characteristics of a transaction range, wherein the double-layer transaction model comprises an upper layer model and a lower layer model, the upper layer model comprises a power distribution network layer, the lower layer model comprises a community-level microgrid layer, the power distribution network layer is modeled as a main problem, the power distribution network layer is modeled as a sub-problem, and the augmented Benders are adopted for optimization;
2) acquiring data, namely acquiring user load, real-time electricity price and power grid data, and transmitting the acquired data serving as parameters into the double-layer transaction model;
3) Optimizing an upper layer model, establishing an external model for the upper layer model from the perspective of a power distribution network system operator, and establishing a convex alternating current optimal power flow model by using a power distribution network power flow model;
4) optimizing a lower model, and establishing an internal model of the lower model from the perspective of an energy producer and consumer;
5) and respectively optimizing the main problem and the sub-problems by adopting the augmented Benders decomposition, and solving the optimal solution of the sub-problems.
2. The double-layer P2P transaction method capable of protecting privacy information based on augmented Benders decomposition as claimed in claim 1, wherein in step 2), the user load comprises year-round load data of users in each community-level microgrid, and the data collection interval is minimum 15 minutes;
the real-time electricity price adopts the national uniform peak-valley average three-time electricity price;
the power grid data comprise the connection relation between each micro-power grid and a superior power distribution network, the resistance and reactance value of each branch and the upper limit of the transmission power of each branch.
3. The double-layer P2P transaction method capable of protecting private information based on augmented Benders decomposition as claimed in claim 1, wherein the specific steps in step 1) are as follows: analyzing the transaction process of the distribution network level P2P, establishing an objective function of an optimization model, wherein energy producers and consumers exist in the community-level microgrid, the outside of the microgrid is a superior grid, a distribution network operator is responsible for operating the whole distribution network system, and a microgrid manager is responsible for managing each microgrid, because in the transaction process of the distribution network level P2P, the distribution network operator needs to be responsible for the safe and stable operation of both transaction parties and the grid, the model centralized optimization transaction party's total income should be established:
Figure FDA0003614144490000021
Figure FDA0003614144490000022
Figure FDA0003614144490000023
Figure FDA0003614144490000024
In the formula: xisysE omega is a decision variable set for optimizing the power distribution network; the set of buyers and sellers in the energy transaction is N respectivelys,Nb,Ω＝card(Ns)×card(Nb) To represent a set of transactions that may occur between the buyer and seller; cnRepresenting a cost utility function for the nth energy producer and consumer; p is a radical ofnmRepresenting the amount of power that seller n delivers to buyer m; the power supplied by the seller to all the buyers is limited to the upper and lower limits of the seller's electricity production
Figure FDA0003614144490000025
The sum of the power of the buyer and the seller is 0 to ensure the power balance in the system, and the positive power direction is set from the seller to the buyer;
utility function C of energy producer and consumernModeling
Figure FDA0003614144490000026
In the formula: pnPower produced or consumed by energy producers or consumers, an,bn,cnRespectively reporting prior parameters for each of the producers and the consumers;
second order cone relaxation (delayed-SOCP) model of distribution network level power flow:
Figure FDA0003614144490000027
s.t.
Figure FDA0003614144490000028
Figure FDA0003614144490000031
Figure FDA0003614144490000032
Figure FDA0003614144490000033
Figure FDA0003614144490000034
Figure FDA0003614144490000035
Figure FDA0003614144490000036
in the formula:
Figure FDA0003614144490000037
is a set of decision variables of the power distribution network,
Figure FDA0003614144490000038
as a function of the cost of each of the producers and consumers,
Figure FDA0003614144490000039
the electricity purchasing cost from the community micro-grid to a superior distribution network is lowered; the constraint conditions are respectively active balance and reactive balance on a line l, upper limit constraint of transmission capacity at the head end and the tail end of the line, relaxation models of node voltage, upper limit of power generation of energy producers and consumers, and upper limit constraint of active and reactive power of each node;
Figure FDA00036141444900000310
is the active power flow with the generation node b on the line l, R lIs the resistance value of the line l, alIs the square of the current on the line l,
Figure FDA00036141444900000311
is the active output of the node b and,
Figure FDA00036141444900000312
is the amount of electricity sold by the node b,
Figure FDA00036141444900000313
is the power demand of node b, GbIs the conductance of node b, vbIs the voltage at node b squared;
Figure FDA00036141444900000314
is the reactive power flow with the generation node b on the line l, XlIs the reactance value of line l, BbFor the susceptance value of the node b,
Figure FDA00036141444900000315
is the square of the upper limit of the transmission capacity of line l;
in order to maintain the safe and stable operation of the power distribution network, punishment of network blocking is carried out on transactions occurring in the network, and the punishment cost UC of the network blocking can be calculated as follows:
Figure FDA00036141444900000316
Figure FDA00036141444900000317
Figure DA00036141444966997168
respectively are dual variables of corresponding constraints in the above formula, and the flowing power p when the line is blocked can be obtained by calculating the line l with network blockagewThe penalty cost UC;
and finally, uniformly optimizing the power distribution network model and the second-order cone relaxation model to obtain the optimal solution of the P2P trading process under the condition that the power grid operates safely and stably.
4. The double-layer P2P transaction method capable of protecting private information based on augmented Benders decomposition as claimed in claim 1, wherein the power distribution network power flow model in step 3) specifically comprises:
second-order cone relaxation model for distribution network-level power flow
Figure FDA0003614144490000042
s.t.
Figure FDA0003614144490000043
Figure FDA0003614144490000044
Figure FDA0003614144490000045
Figure FDA0003614144490000046
Figure FDA0003614144490000047
Figure FDA0003614144490000048
Figure FDA0003614144490000049
In the formula:
Figure FDA00036141444900000410
is a set of decision variables of the power distribution network,
Figure FDA00036141444900000411
As a function of the cost of each of the producers and consumers,
Figure FDA00036141444900000412
the power purchasing cost from a community micro-grid to a superior distribution network is realized by respectively adopting the constraint conditions of active balance and reactive balance on a line l, upper limit constraint of transmission capacity at the first end and the last end of the line, relaxation model of node voltage, upper limit of power generation of each energy producer and consumer, upper limit constraint of active and reactive limits of each node,
Figure FDA0003614144490000051
is the active power flow with the generation node b on the line l, RlIs the resistance value of the line l, alIs the square of the current on the line i,
Figure FDA0003614144490000052
is the active output of the node b and,
Figure FDA0003614144490000053
is the amount of electricity sold by the node b,
Figure FDA0003614144490000054
is the power demand of node b, GbIs the conductance of node b, vbWhich is the square of the voltage at node b,
Figure FDA0003614144490000055
is the reactive power flow with the generation node b on the line l, XlIs the reactance value of line l, BbFor the susceptance value of the node b,
Figure FDA0003614144490000056
which is the square of the upper limit of the transmission capacity of line i.
5. The method of double-layered P2P transaction for protecting private information based on augmented Benders decomposition as claimed in claim 1, wherein said step 4) comprises:
analyzing a model in the community-level microgrid, and establishing an optimization model and corresponding constraint conditions;
because the producers and consumers in each community have the right to negotiate, receive and reject transactions, the goal of the model in the microgrid is to establish a stable transaction scheme that is acceptable to all participants, and the model is as follows:
Figure FDA0003614144490000057
Figure FDA0003614144490000058
σs+σb＝1
Figure FDA0003614144490000059
Figure FDA00036141444900000510
Figure FDA00036141444900000511
Figure FDA00036141444900000512
Figure FDA00036141444900000513
Figure FDA00036141444900000514
Figure FDA00036141444900000515
Figure FDA00036141444900000516
In the formula:
Figure FDA0003614144490000061
is a decision variable of the underlying model,
Figure FDA0003614144490000062
to describe the boolean variables of the transaction state, when the seller selects transaction w,
Figure FDA0003614144490000063
otherwise
Figure FDA0003614144490000064
Figure FDA0003614144490000065
Is arranged and
Figure FDA0003614144490000066
the consistency is kept between the two parts,
Figure FDA0003614144490000067
and
Figure FDA0003614144490000068
optimum prices, SOC, for seller and buyer, respectively, in a transactionn(t) is the state of charge of the nth energy storage device at time t,
Figure FDA0003614144490000069
and
Figure FDA00036141444900000610
lower and upper limits, respectively, of the energy storage state of charge, the transaction w selected by the buyer must be completed by the seller in each transaction, and so
Figure FDA00036141444900000611
Values can only be (1,1), (0,1) and (0, 0);
due to uncertainty of new energy output and load, the load of part of communities needs the output support of the microgrid of other communities, so the input and output power of the community-level microgrid can be modeled as follows:
Figure FDA00036141444900000612
in the formula:
Figure FDA00036141444900000613
is the power supplied by the other microgrid,
Figure FDA00036141444900000614
the two parameters are calculated by an upper layer model, and the two parameters are power supplied by the microgrid to other communities.
6. The method for double-layer P2P trading with privacy information protected based on augmented Benders decomposition as claimed in claim 1, wherein in step 5), the augmented Benders decomposition specifically comprises:
solving the main problem and the sub-problems by using an augmented Benders decomposition algorithm, and realizing privacy information protection through dual information exchanged between the main problem and the sub-problems;
Reconstructing the original problem into a matrix form:
Figure FDA00036141444900000615
s.t.
G(x)≥d
Figure FDA00036141444900000618
Figure FDA00036141444900000616
in the formula:
Figure FDA00036141444900000617
constant coefficient matrixes respectively representing corresponding variables, x is a matrix corresponding to decision variables in an upper layer distribution network model, yn,znContinuous decision variables and Boolean decision variables in the lower community-level microgrid are represented respectively, and constraint conditions in other models are reconstructed into a matrix form and written in the model;
the main problem is broken down from the above equation and converted into:
Figure FDA0003614144490000071
s.t.
G(x)≥d
Figure FDA0003614144490000072
wherein the cutting plane of the main problem can be generated as:
Figure FDA0003614144490000073
in the formula: thetanThe operation cost of the nth community-level micro-grid calculated from the perspective of the power distribution network operator is calculated, and the optimal solution is obtained after the calculation result is completed
Figure FDA0003614144490000074
Is transmitted to the lower layer subproblem to be further solved;
the feasible domain inspection sub-problem and the optimal solution inspection sub-problem are uniformly modeled and optimized in the part, and the model is as follows:
Figure FDA0003614144490000075
Figure FDA0003614144490000076
Figure FDA0003614144490000077
Figure FDA0003614144490000078
zn∈{0,1}n
sn≥0,ξn,ξn≥0
in the formula: sn,ξn,ζnRelaxation variables for feasible solution and optimal solution corresponding to sub-problem respectively, if optimal solution snIf not, a feasible cut set needs to be complemented back to the main problem to ensure the model of the main problem is feasible, otherwise, an optimal cut set needs to be complemented back to the main problem to ensure the effectiveness of the solution, and a relaxation variable xin,ζnCharacterize and show
Figure FDA0003614144490000079
Degree of deviation from optimal solution true value, if ξ n,ζnIf not 0, the optimal cut set needs to be complemented back to the main problem for solving, otherwise, the feasible cut set needs to be complemented back to the main problem, and the sub-problems of the unified modeling of the part can simultaneously generate the optimal cut and the feasible cut, so that the method is faster compared with the sub-problems of the original algorithm,
will thetanAnd x are uniformly written into a matrix, and the main problem can be reconstructed as follows:
Figure FDA0003614144490000081
H(x')≥d'
Figure FDA0003614144490000082
in the formula: x' ═ θnX is a decision variable under a unified model, H represents a constraint set of the model, d' is a parameter set of corresponding constraints, and similarly, subproblems can also be written in a unified form as follows:
Figure FDA0003614144490000083
Figure FDA0003614144490000084
zn∈{0,1}n,s'n≥0
in the formula: sn,ξn,ζnA decision variable corresponding to the sub-problem;
the Benders cut set and the feasible domain recovery cut set are solved,
by using the Boolean type variable z of the original problemnRelaxation is a continuous variable, and sub-problems can be written as follows:
Figure FDA0003614144490000085
Figure FDA0003614144490000086
Figure FDA0003614144490000087
Figure FDA0003614144490000088
in the formula:
Figure FDA0003614144490000089
for newly introduced Boolean type variable, for relaxing the Boolean type variable z in the original problemnBy separating the boolean variables and the continuous variables, the original model can be written as follows:
Figure FDA00036141444900000810
according to strong dual theory, the minimization model inside the brackets can be replaced by its dual model:
Figure FDA00036141444900000811
according to the min-max inequality, the inner and outer models can be swapped in order as follows:
Figure FDA00036141444900000812
the part of the internal model directly related to the decision variables is
Figure FDA00036141444900000813
Can use the maximization model 1TωnTo replace it with a new one in the form of a new one,
the inner and outer layers can thus be modeled uniformly as follows:
Figure FDA0003614144490000091
Figure FDA0003614144490000092
Figure FDA0003614144490000093
0≤αn≤1,ωn≤0,ωn≤βn
by solving this model, the unified Benders cut set can be expressed as:
Figure FDA0003614144490000094
in the formula:
Figure FDA0003614144490000095
are respectively the optimal solutions of the unified subproblems,
the above model contains integersNumber variable, feasible domain recovery cut-sets need to be returned to the original master problem to ensure that dual gaps are eliminated if the optimal solution is
Figure FDA0003614144490000096
If the requirement of the feasible region is met, the feasible region recovery subproblem can be obtained from the following model:
Figure FDA0003614144490000097
zn∈{0,1}n
in the formula: objective function
Figure DA00036141444967124828
Representing an optimal solution
Figure DA00036141444967134539
And feasible solution
Figure DA00036141444967142907
The difference between them, the expression is as follows:
Figure DA00036141444967157618
in the formula:
Figure FDA0003614144490000099
respectively represent matrices
Figure FDA00036141444900000910
Each element of (1), phihRepresents x'hIf x'h|>0, normalization factor is | x'hIf x'hI is 0, the normalization factor is a small positive number τ>0，
And returning the two solved cut sets to the main problem to obtain the optimal solution of the original problem.
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CN109980636A (en) * 2019-03-21 2019-07-05 上海电力学院 Based on the geomantic omen fire coordination optimization dispatching method for improving Benders decomposition method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105226651A (en) * 2015-10-22 2016-01-06 上海交通大学 A kind of consider risk containing large-scale wind power Transmission Expansion Planning in Electric system
CN109980636A (en) * 2019-03-21 2019-07-05 上海电力学院 Based on the geomantic omen fire coordination optimization dispatching method for improving Benders decomposition method

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