CN107563779A - A kind of deploying node method for solving - Google Patents
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Abstract
The present invention relates to a kind of deploying node method for solving, this method is based on direct current method B coefficients network loss modification and considers load side quotation, including：Determine direct current method B coefficients and power transfer factor SF；Establish the economic load dispatching model for including optimization aim, Unit commitment and trend constraint；Deploying node model is derived, determines deploying node；Determine the Incremental Transmission Loss of generator node and load bus；It is determined that marginal node and fully loaded circuit；Determine unknown fully loaded circuit shadow price μ and system power price λ；Determine the deploying node of non-marginal node.Technical scheme provided by the invention has wide applicability, it can be used for solving generator node, have the deploying node of the pure load bus of sensitiveness of quotation and the pure load bus of rigidity without quotation, suitable for the market price in each stage of Power Market Construction, the exploitation that detailed method for solving solves software for deploying node provides reference.
Description
Technical field
Fixed a price/go out clear technical field Marginal Pricing method for solving the present invention relates to electricity market, and in particular to a kind of node
Marginal Pricing method for solving.
Background technology
Deploying node is that one unit of certain node increase is active under current system running status, while ensures power system
Minimum power purchase expense needed for safe operation.The price of measurement dealing electricity, weighs Congested espense, cost of losses, is economic load dispatching
Accessory substance, ensure that total system power purchase expense is minimum, weigh the rare situation of system resource.Network loss is more difficult to simulate, often at present
It is rough network loss pro rata distribution.The solution of node electricity price has two difficulties：First, the selection of reference point influences node
Electricity price；Second network loss model is difficult to simulate, and the method network loss factor of network loss pro rata distribution is fixed value, and the actual network loss factor should be with
The different changes of electric network swim.
The currently research on deploying node concentrates on the DC power flow algorithm calculate node limit electricity for not considering network loss
Valency, or the method calculate node electricity price that adoption rate is shared, and the node side of an overwhelming majority research consideration generator node
The solution of border electricity price, the Solve problems of the deploying node of pure load bus are not accounted for, carry out deploying node model
Load side quotation is not accounted for during derivation, there is certain limitation using upper.
With going deep into for electricity market reform, supply of electric power will be changed from traditional scheduled mode to market mode, market
Power price under environment will be determined that deploying node is a kind of important market price method by market.Electric power city of China
The field transitional period, may there was only sub-load participation quotation, other still participate in market as rigid load, a report demand, do not offer
Lattice, it is contemplated that most nodes are pure rigid load bus, traditional processing side that model is substituted into using rigid load as fixed value
Method, the deploying node that cause pure rigid load bus can not be asked for, traditional processing method will be unsuitable for market ring
Border lower node Marginal Pricing model inference.Simultaneously as network loss is more difficult to simulate, what current research was commonly used is rough network loss
Pro rata distribution, acquisition is more simplified deploying node model.
The content of the invention
To solve above-mentioned deficiency of the prior art, it is an object of the invention to provide one kind to be based on direct current method B coefficient network loss
Amendment and the deploying node method for solving for considering load side quotation, this method will consider load side quotation, for not offering
Rigid load modeling when reasonably handled, and based on direct current method B coefficients consider network loss, derivation the wider array of section of applicability
Point Marginal Pricing model, to ensure that deploying node model can be applied to each stage of Power Market Construction, effectively ask
Solve the deploying node of generator node and pure load bus.
The purpose of the present invention is realized using following technical proposals：
The present invention provides a kind of deploying node method for solving, and it is theed improvement is that, methods described is based on direct current method B
Coefficient network loss modification and consideration load side quotation, comprise the steps：
The first step：Determine direct current method B coefficients and power transfer factor SF；
Second step：Establish the economic load dispatching model for including optimization aim, Unit commitment and trend constraint；
3rd step：Deploying node model is derived, determines deploying node, including generator node and load bus
Deploying node；
4th step：Determine the Incremental Transmission Loss of generator node and load bus；
5th step：It is determined that marginal node and fully loaded circuit；
6th step：According to the deploying node of marginal node, Incremental Transmission Loss and power transfer factor, determine unknown
Fully loaded circuit shadow price μ and system power price λ；
7th step：The node limit electricity of non-marginal node is determined according to fully loaded circuit shadow price μ and system power price λ
Valency.
Further, in the first step, the perunit value of line parameter circuit value is asked for according to basic parameter and network topology structure,
Reference point is selected, direct current method B coefficients and power transfer factor SF are asked according to line parameter circuit value perunit value respectively, the first step includes
Following step：
Step 1：Ask for the perunit value of line parameter circuit value：
Wherein, x*For the perunit value of line impedance, x is line impedance, XBFor the basic parameter of line impedance；
Step 2：Direct current method B coefficients are determined, including：
(1) power system network loss is decomposed into two parts related to voltage phase angle and related with voltage magnitude：
(2) assume that each busbar voltage amplitude is constant during the change of power system active power output, only considers related to voltage phase angle
Network loss change；Because voltage magnitude is 1, set voltage magnitude is 1, then：
GNNij=-gij
(3) the busbar voltage phase angle of DC power flow and the linear relationship of injecting power are utilized：
Pin=BNNθ
Power system network loss is expressed as to the function of each injecting power：
PL=θTGNNθ
=(BNN -1Pin)TGNN(BNN -1Pin)
=Pin T(BNN -1)TGNNBNN -1Pin
BNNij=-bij
Wherein, PLFor power system network loss, PLθFor the power system network loss part related to voltage phase angle, PLVFor power train
Network loss of the uniting part related to voltage magnitude, n are node total number, and i, j are respectively two nodes of branch road, Vi、VjRespectively branch road
The terminal voltage amplitude at both ends, θi、θjThe respectively terminal voltage phase angle at branch road both ends, gijFor branch road conductance；θ be voltage phase angle arrange to
Amount, θTFor the transposed vector of voltage phase angle column vector, GNNFor nodal-admittance matrix, GNNiiFor node self-conductance, GNNijFor i, j two
The transconductance of node；PinFor the net injecting power column vector of node, BNNFor node susceptance matrix, BNNiiRepresenting matrix BNNIt is diagonal
Line element, be it is all with i-node associated branch node from the summation of susceptance, BNNijOff diagonal element is represented, is ij branch roads two
The negative value of the mutual susceptance of node, bijRepresent branch road susceptance；
Step 3：Determine power transfer factor SF：
Fl=BlABNN -1Pin
Wherein, FlFor Line Flow column vector, BlFor branch road susceptance matrix, A is network associate matrix.
Further, in the second step, generator and load quote data are obtained according to data declaration, only report needs for setting
Seeking the rigid loads of lattice of not offering, to offer be 0, be used as variable in economic load dispatching model, rigid load is upper and lower in constraints
Limit take rigid load value, according to generator and include rigid load offer 0 load quote data, establish comprising optimization aim,
The economic load dispatching model of Unit commitment and trend constraint, and solve the economic load dispatching model；Under the economic load dispatching model is used
Formula represents：
min pTPG-pD TPD
S.T.eT(PG-PD)-PL=0
Wherein, p offers for generating set, pTFor generating set quotation p transposition, pDOffered for load, pD TFor load report
The transposition of valency, PGContributed for generating set,PG For generating set output lower limit,For the generator output upper limit, PDFor load work(
Rate,PD For load minimum power,For load peak power, PLFor power system network loss, SF is power transfer factor,Circuit
Trend limit, e=(1,1 ..., 1)T。
Further, the 3rd step is described according to the economic load dispatching model inference deploying node model of second step
3rd step comprises the steps：
Step (1)：Construct Lagrangian：
Wherein, L is Lagrangian, and λ is the Lagrange multiplier of system power price, i.e. power-balance constraint, and e is
Element is all 1 column vector, and μ is fully loaded circuit shadow price, i.e., Lagrange multiplier square corresponding to fully loaded Line Flow constraint
Battle array, p offer for generator, pDOffered for load, PGFor generator output,PG For generator output lower limit,For generator output
The upper limit, PDFor load power,PD For load minimum power,For load peak power, PLFor system losses, SF shifts for power
Matrix,Line Flow limit, τ 'G、τGRespectively the generator output upper limit, the Lagrange multiplier matrix of lower limit constraint, τ 'D、
τDRespectively the load power upper limit, the Lagrange multiplier matrix of lower limit constraint；PLFor power system network loss,
Step 2：Deploying portion Cook figure grace KKT conditions are as follows：
Wherein, PGiFor generating set i output, PDiFor load i power, piFor unit i quotation, pDiFor load i's
Quotation, μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, SFliWork(for branch road l to the net injecting power of node i
Rate transfer factor, τ 'Gi、τGiRespectively the unit i outputs upper limit, the Lagrange multiplier matrix of lower limit constraint, τ 'Di、τDiFor load
The i upper limit of the power, the Lagrange multiplier matrix of lower limit constraint,For the Incremental Transmission Loss to generator i,For to load
I Incremental Transmission Loss；
For reference mode, due toSFli=0, so for reference mode：
Step 3：Deploying node：
Wherein, ρGiThe deploying node of node, ρ where unit iDiThe node limit electricity of node where load i
Valency, the deploying node of reference point are：
ρGi=pi+τ′Gi-τGi=λ
ρDi=pDi-τ′Di+τDi=λ
For there was only the node of generator, deploying node ρGi, for there was only the node of load, deploying node
For ρDi；
There is the node of load again for existing generator, existI.e. deploying node has ρGi=
ρDi。
Further, the 4th step calculates generator node and load bus according to the 3rd step economic load dispatching optimum results
Incremental Transmission Loss；
If node n is reference point, calculated according to following formula：
PL=θTGNNθ
=(BNN -1Pin)TGNN(BNN -1Pin)
=Pin T(BNN -1)TGNNBNN -1Pin
=Pin T·B·Pin
The Incremental Transmission Loss of generator node and load bus is represented with following formula：
Wherein：PLFor power system network loss, θ is voltage phase angle column vector, GNNFor nodal-admittance matrix, BNNFor node susceptance
Matrix, PinFor the net injecting power column vector of node, B is direct current method B coefficient matrixes, PGiFor the output of generator node i, PDiFor
Load bus i power, Pin,iFor the net injecting power column vector P of nodeinElement, represent the net injecting power of node i, i=
1st, 2 ... n-1, n；Bi1Bi2…Bi,n-1It is coefficient matrix B element.
Further, the 5th step determines marginal node and fully loaded circuit according to second step economic load dispatching result；
Marginal node refers to that generator does not take the node of limit value for marginal unit or load of getting the bid；
The deploying node of marginal node is by for the quotation of the quotation of this node limit unit or marginal load, remaining section
The deploying node of point is amount to be asked；Shadow price corresponding to fully loaded circuit constraint is not 0, and for amount to be asked, remaining circuit is about
Shadow price corresponding to beam all 0；
According to optimization gained unit output and unit bound, judge unit output between unit output bound
When, existThe deploying node of node takes the quotation of marginal unit：
Load bus for participating in quotation, according to optimization gained acceptance of the bid load and load bound, judge that load is located at
When between bound, τ ' be presentD T=τD T=0, so the deploying node of the node takes the quotation of load：
Wherein：ρGiThe deploying node of node, p where unit iiFor unit i quotation, PLFor power system net
Damage, λ be system power price, i.e. power-balance constraint Lagrange multiplier, μlFor the drawing of the l articles Branch Power Flow limit constraint
Ge Lang multipliers, PGiFor generating set i output, SFliPower transfer factor for branch road l to the net injecting power of node i；τ
'G T、τG TThe respectively transposition for the Lagrange multiplier matrix that the unit output upper limit, lower limit constrain, τ 'D T、τD TFor in load power
The transposition for the Lagrange multiplier matrix that limit, lower limit constrain；
When judging that Line Flow reaches transmission of electricity limit, the circuit is fully loaded circuit, is fully loaded with shadow valency corresponding to circuit constraint
Lattice are not 0, for amount to be asked, shadow price all 0 corresponding to the constraint of remaining circuit.
Further, in the 6th step, according to the deploying node of node where marginal unit, Incremental Transmission Loss and
Power transfer factor, unknown shadow price μ and system power price λ are determined, including：
It is fully loaded with provided with m bar circuits, then m+1 marginal nodes is present, the unit output of marginal node is between bound
Or quotation load is between bound；If the numbering of marginal node is 1,2 ..., m, m+1, and it is reference point to select node n, full
Circuit number is carried then to have 1,2 ..., m, then：
Wherein：λ be system power price, i.e. power-balance constraint Lagrange multiplier, μlLimited for the l articles Branch Power Flow
Volume constraint Lagrange multiplier, l=1,2 ... m；SFliPower transfer factor for branch road l to the net injecting power of node i；i
=1,2 ... n-1, n；PinFor the net injecting power column vector of node, Pin,iFor the net injecting power column vector P of nodeinElement, table
Show the net injecting power of node i；
The node electricity price of marginal node takes the quotation of respective nodes, forms m+1 equation, and unknown quantity has m+1, is respectively
M shadow price μ and 1 system power price λ, solving equations, obtains all unknown quantitys.
Further, in the 7th step, the section of non-marginal node is solved according to shadow price μ and system power price λ
Point electricity price；
The node electricity price of non-marginal node is solved according to equation below：
Wherein：piFor unit i quotation, PLFor power system network loss, λ is system power price, i.e. power-balance constraint
Lagrange multiplier, μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, PGiFor generating set i output, SFli
Power transfer factor for branch road l to the net injecting power of node i, l=1,2 ... m；ρGiThe node side of node where unit i
Border electricity price, ρDiThe deploying node of node, P where load iDiFor load i power；τ′Gi、τGiRespectively unit i contributes
The upper limit, the Lagrange multiplier of lower limit constraint, τ 'Di、τDiThe Lagrange multiplier constrained for the load i upper limit of the power, lower limit.
Compared with immediate prior art, the excellent effect that technical scheme provided by the invention has is：
The present invention will consider load side quotation, reasonably be handled in modeling for the rigid load do not offered, and
Network loss is considered based on direct current method B coefficients, the wider array of deploying node model of applicability is derived, to ensure deploying node mould
Type can be applied to each stage of Power Market Construction, effectively solve the node limit electricity of generator node and pure load bus
Valency.
The present invention considers load side quotation and the modeling that more becomes more meticulous of network loss, carries out deploying node model and pushes away
Lead, and propose the detailed solution method of deploying node, the solution for market deploying node provides foundation and reference, is
Market guidance goes out designing and developing for clear software and provided fundamental basis.
Brief description of the drawings
Fig. 1 is the flow chart of deploying node method for solving provided by the invention；
Fig. 2 is that direct current method B coefficients provided by the invention derive schematic diagram；
Fig. 3 is the network topology structure figure of specific embodiment 1 provided by the invention；
Fig. 4 is the network topology structure figure of specific embodiment 2 provided by the invention.
Embodiment
The embodiment of the present invention is described in further detail below in conjunction with the accompanying drawings.
The following description and drawings fully show specific embodiments of the present invention, to enable those skilled in the art to
Put into practice them.Other embodiments can include structure, logic, it is electric, process and other change.Embodiment
Only represent possible change.Unless explicitly requested, otherwise single component and function are optional, and the order operated can be with
Change.The part of some embodiments and feature can be included in or replace part and the feature of other embodiments.This hair
The scope of bright embodiment includes the gamut of claims, and claims is all obtainable equivalent
Thing.Herein, these embodiments of the invention can individually or generally be represented that this is only with term " invention "
For convenience, and if in fact disclosing the invention more than one, the scope for being not meant to automatically limit the application is to appoint
What single invention or inventive concept.
The present invention provides a kind of deploying node based on direct current method B coefficients network loss modification and consideration load side quotation and asked
Solution method, its flow chart is as shown in figure 1, comprise the steps；
The first step：The perunit value of line parameter circuit value is asked for according to basic parameter and network topology structure, selects reference point, according to
Line parameter circuit value perunit value asks direct current method B coefficients and power transfer factor SF respectively.Direct current method B coefficients, it is that a kind of network loss modification is used
B coefficients, be the seventies propose a kind of algorithm.Belong to known term in the modeling of power system network loss.
Step 1：Seek direct current method B coefficients.Direct current method B coefficients derive schematic diagram as shown in Fig. 2 including：
(1) network loss is decomposed into two parts related to voltage phase angle and related with voltage magnitude：
Wherein, PLFor system losses, PLθFor the network loss part related to voltage phase angle, PLVIt is related to voltage magnitude for network loss
Part, n is node total number, and i, j are respectively two end points of branch road, Vi、VjThe respectively terminal voltage amplitude at branch road both ends, θi、
θjThe respectively terminal voltage phase angle at branch road both ends, gijFor branch road conductance.
(2) assume that each busbar voltage amplitude is constant during power plant's active power output change, only considers that the network loss related to phase angle becomes
Change, and the latter is dominant.Because voltage magnitude is about 1, it is assumed that voltage magnitude is all 1, then
GNNij=-gij
Wherein, PLFor system losses, PLθFor the network loss part related to voltage phase angle, n is node total number, and i, j are respectively
Two end points of branch road, θi、θjThe respectively terminal voltage phase angle at branch road both ends, gijFor branch road conductance, θ be voltage phase angle arrange to
Amount, GNNFor nodal-admittance matrix, GNNiiFor node self-conductance, GNNijFor the transconductance of two nodes.
(3) the busbar voltage phase angle of DC power flow and the linear relationship of injecting power are utilized：
Pin=BNNθ
Network loss is expressed as to the function of each injecting power：
PL=θTGNNθ
=(BNN -1Pin)TGNN(BNN -1Pin)
=Pin T(BNN -1)TGNNBNN -1Pin
BNNij=-bij
Wherein, PLFor power system network loss, PLθFor the power system network loss part related to voltage phase angle, PLVFor power train
Network loss of the uniting part related to voltage magnitude, n are node total number, and i, j are respectively two nodes of branch road, Vi、VjRespectively branch road
The terminal voltage amplitude at both ends, θi、θjThe respectively terminal voltage phase angle at branch road both ends, gijFor branch road conductance；θ be voltage phase angle arrange to
Amount, θTFor the transposed vector of voltage phase angle column vector, GNNFor nodal-admittance matrix, GNNiiFor node self-conductance, GNNijFor i, j two
The transconductance of node；PinFor the net injecting power column vector of node, BNNFor node susceptance matrix, BNNiiRepresenting matrix BNNIt is diagonal
Line element, be it is all with i-node associated branch node from the summation of susceptance, BNNijOff diagonal element is represented, is ij branch roads two
The negative value of the mutual susceptance of node, bijRepresent branch road susceptance；
Step 2：Seek power transfer factor SF.
Fl=BlABNN -1Pin
Wherein, FlFor Line Flow column vector, PinFor the net injecting power column vector of node, BNNFor node susceptance matrix, Bl
For branch road susceptance matrix, A is network associate matrix.
Second step：Generator, load quote data are obtained, for only reporting the do not offer rigid load of lattice of demand to need to be spy
Different processing, it is 0 to set its quotation, and in a model as variable, the bound of rigid load takes rigid load value in constraints,
According to the quote data of all generators and load (including rigid load quotation 0), establish comprising optimization aim, Unit commitment and
The Optimized model of trend constraint, and solve the model.
min pTPG-pD TPD
S.T.eT(PG-PD)-PL=0
Wherein, p offers for generator, pDOffered for load, PGFor generator output,PG For generator output lower limit,For
The generator output upper limit, PDFor load power,PD For load minimum power,For load peak power, PLFor system losses, SF
For power transfer matrix,Line Flow limit.
3rd step：According to the economic load dispatching model inference deploying node model of second step.
In view of China's electricity market transitional period, may only have sub-load to participate in quotation, other are still used as rigid load
Participate in market, only reporting demand, lattice of not offering.Load is modeled as rigid load in existing economic load dispatching model,
Load takes fixed value, if when deriving deploying node model, is still handled according to fixed value, and this type load is not reported
Valency, then this type load composition will not be contained in object function, the node for comprising only rigid load, will be unable to calculate the point
Deploying node.So when deriving deploying node model, need to offer for rigid load setting in object function
For 0, rigid load is as variable in a model, and the bound of load takes rigid load value in constraints, to ensure node side
Border Spot Price Model can be applied to each stage of China's Power Market Construction, effectively solve generator node, quotation load section
The deploying node of point and pure rigid load bus.
Step 1：Construct Lagrangian：
Wherein, L is Lagrangian, and λ is the Lagrange multiplier (also referred to as system power price) of power-balance constraint,
E is the column vector that element is all 1, and μ is Lagrange multiplier matrix (also referred to as shadow price matrix) corresponding to Line Flow constraint,
P offers for generator, pDOffered for load, PGFor generator output,PG For generator output lower limit,For on generator output
Limit, PDFor load power,PD For load minimum power,For load peak power, PLFor system losses, SF is that power shifts square
Battle array,Line Flow limit, τ 'G、τGThe respectively Lagrange multiplier matrix of generator output bound constraint, τ 'D、τDRespectively
For the Lagrange multiplier matrix of load power bound constraint.
Step 2：Deploying portion Cook figure grace (KKT) condition is as follows：
Wherein, PGiFor unit i output, PDiFor load i power, piFor unit i quotation, pDiFor load i report
Valency, λ are the Lagrange multiplier (also referred to as system power price) of power-balance constraint, μlConstrained for the l articles Branch Power Flow limit
Lagrange multiplier, SFliPower transfer factor for branch road l to the net injecting power of node i, τ 'Gi、τGiRespectively unit i goes out
The Lagrange multiplier of power bound constraint, τ 'Di、τDiThe Lagrange multiplier constrained for load i power bound,For
To generator i Incremental Transmission Loss,For the Incremental Transmission Loss to load i.
For reference mode, due toSFli=0, so for reference mode
Step 3：Deploying node：
Wherein, ρGiThe deploying node of node, ρ where unit iDiThe node limit electricity of node where load i
Valency, piFor unit i quotation, pDiFor load i quotation, λ is Lagrange multiplier (the also referred to as system power of power-balance constraint
Price), μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, SFliWork(for branch road l to the net injecting power of node i
Rate transfer factor, τ 'Gi、τGiThe respectively Lagrange multiplier of unit i outputs bound constraint, τ 'Di、τDiFor on load i power
The Lagrange multiplier of lower limit constraint,For the Incremental Transmission Loss to generator i,For the Incremental Transmission Loss to load i.
The node electricity price of reference point is
ρGi=pi+τ′Gi-τGi=λ
ρDi=pDi-τ′Di+τDi=λ
For there was only the node of generator, node electricity price ρGi, for there was only the node of load, node electricity price ρDi。
There is the node of load again for existing generator, existSo there is ρ in these nodesGi=
ρDi。
4th step：The network loss that all generator nodes and load bus are calculated according to the 3rd step economic load dispatching optimum results is micro-
Gaining rate.
If node n is reference point, Incremental Transmission Loss is asked according to following formula：
PL=θTGNNθ
=(BNN -1Pin)TGNN(BNN -1Pin)
=Pin T(BNN -1)TGNNBNN -1Pin
=Pin T·B·Pin
5th step：Determine that (generator is that marginal unit or acceptance of the bid are negative to marginal node according to second step economic load dispatching result
Lotus does not take the node (referred to hereinafter as marginal load) of limit value) and fully loaded circuit.The deploying node of marginal node will be this node
The quotation of marginal unit or the quotation of marginal load, the deploying node of remaining node is amount to be asked；Fully loaded circuit constraint pair
The shadow price answered is not 0, for amount to be asked, shadow price all 0 corresponding to the constraint of remaining circuit.
According to optimization gained unit output and unit bound, judge unit output between unit output bound
When, τ ' be presentG T=τG T=0, so the deploying node of the node takes the quotation of marginal unit：
Load bus for participating in quotation, according to optimization gained acceptance of the bid load and load bound, judge that load is located at
When between bound, τ ' be presentD T=τD T=0, so the deploying node of the node takes the quotation of load：
When judging that Line Flow reaches transmission of electricity limit, the circuit is fully loaded circuit.Shadow valency corresponding to fully loaded circuit constraint
Lattice are not 0, for amount to be asked, shadow price all 0 corresponding to the constraint of remaining circuit.
6th step：Deploying node, Incremental Transmission Loss and the power transfer factor of node, are asked according to where marginal unit
Solve unknown shadow price μ and system power price λ.
Assuming that there is m bar circuits to be fully loaded with, then exist the marginal nodes of m+1 (unit output of marginal node be located at bound it
Between or quotation load between bound).Assuming that the numbering of marginal node is 1,2 ..., m, m+1, selects node n as reference
Point, fully loaded circuit number are then to have 1,2 ..., m, then
Wherein：λ be system power price, i.e. power-balance constraint Lagrange multiplier, μlLimited for the l articles Branch Power Flow
Volume constraint Lagrange multiplier, l=1,2 ... m；SFliPower transfer factor for branch road l to the net injecting power of node i；i
=1,2 ... n-1, n；PinFor the net injecting power column vector of node, Pin,iFor the net injecting power column vector P of nodeinElement, table
Show the net injecting power of node i；
The node electricity price of marginal node takes the quotation of respective nodes, forms m+1 equation, and unknown quantity has m+1, is respectively
M shadow price μ and 1 system power price λ, solving equations, can obtain all unknown quantitys.
7th step：The node electricity price of non-marginal node is solved according to shadow price μ and system power price λ.
The node electricity price of non-marginal node is solved according to equation below：
Wherein：piFor unit i quotation, PLFor power system network loss, λ is system power price, i.e. power-balance constraint
Lagrange multiplier, μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, PGiFor generating set i output, SFli
Power transfer factor for branch road l to the net injecting power of node i, l=1,2 ... m；ρGiThe node side of node where unit i
Border electricity price, ρDiThe deploying node of node, P where load iDiFor load i power；τ′Gi、τGiRespectively unit i contributes
The upper limit, the Lagrange multiplier of lower limit constraint, τ 'Di、τDiThe Lagrange multiplier constrained for the load i upper limit of the power, lower limit.
Embodiment 1
The network topology structure figure of embodiment 1 provided by the invention is as shown in figure 3, contain：4 generators, 3 loads, and
Without pure load bus.Generator quotation parameter such as table 1, load quotation parameter such as table 2：
The generator of table 1 quotation parameter
| Generator | Capacity (MW) | Marginal cost ($/MWh) |
| A | 140 | 7.5 |
| B | 285 | 6 |
| C | 90 | 14 |
| D | 85 | 10 |
The load of table 2 quotation parameter
Select basic parameter SB=100MVA, VB=115KV.Line parameter circuit value such as table 3：
The circuit perunit parameter of table 3
| Branch road | Admittance parameter (p.u.) | Capacity (MW) |
| 1-2 | 3.12-j2.94 | 80 |
| 1-3 | 2.68-j5.32 | 220 |
| 2-3 | 2.81-j4.49 | 130 |
(1) it is reference point to select node 3, then
Nodal-admittance matrix：
Negative nodal point susceptance matrix：
Direct current method network loss B coefficients：
So system losses are：
Negative branch susceptance matrix：
Network associate matrix：
Power transfer factor SF：
(2) economic load dispatching model
min 7.5*PA+6*PB+14*PC+10*PD-14*L1-15*L2-0*L3
S.T.PA+PB+PC+PD-L1-L2-L3-PL=0
0.2504(PA+PB-L1)-0.2966(PC-L2)≤0.8
0.7496(PA+PB-L1)+0.2966(PC-L2)≤2.2
0.2504(PA+PB-L1)+0.7034(PC-L2)≤1.3
0≤PA≤1.4
0≤PB≤2.85
0≤PC≤0.9
0≤PD≤0.85
0≤L1≤0.5
0≤L2≤1
3≤L3≤3
The economic load dispatching result of table 4
| Generator | Power (p.u.) | Load | Power (p.u.) |
| PA | 0.617 | L1 | 0.5 |
| PB | 2.85 | —— | —— |
| PC | 0.9 | L2 | 0.98 |
| PD | 0.85 | L3 | 3 |
(3) Incremental Transmission Loss is calculated：
(4) marginal node and fully loaded circuit are determined according to economic load dispatching result.
Circuit 1-3 is judged to be fully loaded with circuit according to economic load dispatching result, then μ2≠0
Unit A output 61.7MW, then τ 'G1 T=τG1 T=0, so
Load L2 is 98MW, then τ 'D2 T=τD2 T=0
(5) calculate node Marginal Pricing：
Because the node electricity price of marginal node is
So
Solve
Because node 3 is reference point, so
ρ3=λ=17 $/MWH
Embodiment 2
The network topology structure figure of embodiment 2 provided by the invention is as shown in figure 4, contain：3 generators, 3 loads, section
Point 2 is pure load bus.Generator quotation parameter such as table 5, load quotation parameter such as table 6：
The generator of table 5 quotation parameter
| Generator | Capacity (MW) | Marginal cost ($/MWh) |
| A | 140 | 7.5 |
| B | 200 | 6 |
| C | 85 | 10 |
The load of table 6 quotation parameter
| Load | Minimum power (MW) | Peak power (MW) | Marginal cost ($/MWh) |
| L1 | 0 | 0.5 | 14 |
| L2 | 1 | 1 | —— |
| L3 | 0 | 2 | 15 |
Table 3 of the line parameter circuit value with embodiment 1.
(1) economic load dispatching model
min 7.5*PA+6*PB+10*PC-14*L1-0*L2-15*L3
S.T.PA+PB+PC-L1-L2-L3-PL=0
0.2504(PA+PB-L1)-0.2966(0-L2)≤0.8
0.7496(PA+PB-L1)+0.2966(0-L2)≤2.2
0.2504(PA+PB-L1)+0.7034(0-L2)≤1.3
0≤PA≤1.4
0≤PB≤2
0≤PC≤0.85
0≤L1≤0.5
1≤L2≤1
0≤L3≤2
The economic load dispatching result of table 7
| Generator | Power (p.u.) | Load | Power (p.u.) |
| PA | 0.51 | L1 | 0.5 |
| PB | 2 | L2 | 1 |
| PC | 0.85 | L3 | 1.485 |
(2) Incremental Transmission Loss is calculated
(3) marginal node and fully loaded circuit are determined according to economic load dispatching result.
Circuit 1-2 is judged to be fully loaded with circuit according to economic load dispatching result, then μ1≠0
Unit A output 51MW, then τ 'G1 T=τG1 T=0, so
Load L3 is 148.5MW, then τ 'D2 T=τD2 T=0
(4) calculate node Marginal Pricing
Because the node electricity price of marginal node is
So
Solve
Because node 3 is reference point, so
ρ2=λ-λ * (- 0.142)-μ1* (- 0.2966)=20.65 $/MWH
The present invention carries out network loss modification using direct current method B coefficients, and it is fine to consider that load side quotation carries out deploying node
Change modeling, the solution of the node electricity price for the pure rigid load bus for only reporting demand that considers not offering, node limit is described in detail
The method for solving of electricity price.The model has wide applicability, can be used for solving generator node, the pure load bus of quotation and
Do not offer the deploying node of pure load bus, suitable for the market price in each stage of Power Market Construction, detailed
The exploitation that method for solving can solve software for China's deploying node provides reference.
The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, although with reference to above-described embodiment pair
The present invention is described in detail, and those of ordinary skill in the art can still enter to the embodiment of the present invention
Row modification or equivalent substitution, these are applying without departing from any modification of spirit and scope of the invention or equivalent substitution
Within pending claims of the invention.
Claims (8)
1. a kind of deploying node method for solving, it is characterised in that methods described is based on direct current method B coefficients network loss modification and examined
Consider load side quotation, comprise the steps：
The first step：Determine direct current method B coefficients and power transfer factor SF；
Second step：Establish the economic load dispatching model for including optimization aim, Unit commitment and trend constraint；
3rd step：Deploying node model is derived, determines deploying node, including the section of generator node and load bus
Point Marginal Pricing；
4th step：Determine the Incremental Transmission Loss of generator node and load bus；
5th step：It is determined that marginal node and fully loaded circuit；
6th step：According to the deploying node of marginal node, Incremental Transmission Loss and power transfer factor, unknown be fully loaded with is determined
Circuit shadow price μ and system power price λ；
7th step：The deploying node of non-marginal node is determined according to fully loaded circuit shadow price μ and system power price λ.
2. deploying node method for solving as claimed in claim 1, it is characterised in that in the first step, according to benchmark
Parameter and network topology structure ask for the perunit value of line parameter circuit value, select reference point, ask straight respectively according to line parameter circuit value perunit value
Stream method B coefficients and power transfer factor SF, the first step comprise the steps：
Step 1：Ask for the perunit value of line parameter circuit value：
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<mo>*</mo>
</msup>
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<mi>x</mi>
<msub>
<mi>X</mi>
<mi>B</mi>
</msub>
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</mrow>
Wherein, x*For the perunit value of line impedance, x is line impedance, XBFor the basic parameter of line impedance；
Step 2：Direct current method B coefficients are determined, including：
(1) power system network loss is decomposed into two parts related to voltage phase angle and related with voltage magnitude：
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(2) assume that each busbar voltage amplitude is constant during the change of power system active power output, only considers the net related to voltage phase angle
Damage change；Because voltage magnitude is 1, set voltage magnitude is 1, then：
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GNNij=-gij
(3) the busbar voltage phase angle of DC power flow and the linear relationship of injecting power are utilized：
Pin=BNNθ
Power system network loss is expressed as to the function of each injecting power：
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BNNij=-bij
Wherein, PLFor power system network loss, PLθFor the power system network loss part related to voltage phase angle, PLVFor power system net
The damage part related to voltage magnitude, n are node total number, and i, j are respectively two nodes of branch road, Vi、VjRespectively branch road both ends
Terminal voltage amplitude, θi、θjThe respectively terminal voltage phase angle at branch road both ends, gijFor branch road conductance；θ is voltage phase angle column vector, θT
For the transposed vector of voltage phase angle column vector, GNNFor nodal-admittance matrix, GNNiiFor node self-conductance, GNNijFor the node of i, j two
Transconductance；PinFor the net injecting power column vector of node, BNNFor node susceptance matrix, BNNiiRepresenting matrix BNNDiagonal line element
Element, be it is all with i-node associated branch node from the summation of susceptance, BNNijOff diagonal element is represented, is the node of ij branch roads two
Mutual susceptance negative value, bijRepresent branch road susceptance；
Step 3：Determine power transfer factor SF：
Fl=BlABNN -1Pin
Wherein, FlFor Line Flow column vector, BlFor branch road susceptance matrix, A is network associate matrix.
3. deploying node method for solving as claimed in claim 1, it is characterised in that in the second step, according to data
Declare and obtain generator and load quote data, the do not offer rigid load quotation of lattice of a setting report demand is 0, in economic load dispatching
It is used as variable in model, the bound of rigid load takes rigid load value in constraints, according to generator and negative including rigidity
The quote data of lotus 0 load of quotation, establishes the economic load dispatching model for including optimization aim, Unit commitment and trend constraint, and ask
Solve the economic load dispatching model；The economic load dispatching model is represented with following formula：
min pTPG-pD TPD
S.T.eT(PG-PD)-PL=0
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Load minimum power,For load peak power, PLFor power system network loss, SF is power transfer factor,Line Flow limits
Volume, e=(1,1 ..., 1)T。
4. deploying node method for solving as claimed in claim 1, it is characterised in that the 3rd step is according to second step
Economic load dispatching model inference deploying node model, the 3rd step comprise the steps：
Step (1)：Construct Lagrangian：
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Wherein, L is Lagrangian, and λ is the Lagrange multiplier of system power price, i.e. power-balance constraint, and e is element
1 column vector is all, μ is fully loaded circuit shadow price, i.e., Lagrange multiplier matrix corresponding to fully loaded Line Flow constraint, p
Offered for generator, pDOffered for load, PGFor generator output,PG For generator output lower limit,For on generator output
Limit, PDFor load power,PD For load minimum power,For load peak power, PLFor system losses, SF is that power shifts square
Battle array,Line Flow limit, τ 'G、τGRespectively the generator output upper limit, the Lagrange multiplier matrix of lower limit constraint, τ 'D、τD
Respectively the load power upper limit, the Lagrange multiplier matrix of lower limit constraint；PLFor power system network loss,
Step 2：Deploying portion Cook figure grace KKT conditions are as follows：
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<mo>+</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mi>&Sigma;</mi>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
Wherein, PGiFor generating set i output, PDiFor load i power, piFor unit i quotation, pDiFor load i quotation,
μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, SFliThe power of the net injecting power of node i is shifted for branch road l
The factor, τ 'Gi、τGiRespectively the unit i outputs upper limit, the Lagrange multiplier matrix of lower limit constraint, τ 'Di、τDiFor load i power
The upper limit, the Lagrange multiplier matrix of lower limit constraint,For the Incremental Transmission Loss to generator i,For the net to load i
Damage tiny increment；
For reference mode, due toSo for reference mode：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
Step 3：Deploying node：
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
Wherein, ρGiThe deploying node of node, ρ where unit iDiThe deploying node of node where load i, reference
Point deploying node be：
ρGi=pi+τ′Gi-τGi=λ
ρDi=pDi-τ′Di+τDi=λ
For there was only the node of generator, deploying node ρGi, for there was only the node of load, deploying node is
ρDi；
There is the node of load again for existing generator, existI.e. deploying node has ρGi=ρDi。
5. deploying node method for solving as claimed in claim 1, it is characterised in that the 4th step passes through according to the 3rd step
Optimizing scheduling result of helping calculates the Incremental Transmission Loss of generator node and load bus；
If node n is reference point, calculated according to following formula：
PL=θTGNNθ
=(BNN -1Pin)TGNN(BNN -1Pin)
=Pin T(BNN-1)TGNNBNN-1Pin
=Pin T·B·Pin
The Incremental Transmission Loss of generator node and load bus is represented with following formula：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2</mn>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
</mtd>
<mtd>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mtable>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein：PLFor power system network loss, θ is voltage phase angle column vector, GNNFor nodal-admittance matrix, BNNFor node susceptance square
Battle array, PinFor the net injecting power column vector of node, B is direct current method B coefficient matrixes, PGiFor the output of generator node i, PDiIt is negative
The power of lotus node i, Pin,iFor the net injecting power column vector P of nodeinElement, represent the net injecting power of node i, i=1,
2nd ... n-1, n；Bi1Bi2…Bi,n-1It is coefficient matrix B element.
6. deploying node method for solving as claimed in claim 1, it is characterised in that the 5th step passes through according to second step
Ji scheduling result determines marginal node and fully loaded circuit；
Marginal node refers to that generator does not take the node of limit value for marginal unit or load of getting the bid；
The deploying node of marginal node by for the quotation of the quotation of this node limit unit or marginal load, remaining node
Deploying node is amount to be asked；Shadow price corresponding to fully loaded circuit constraint is not 0, for amount to be asked, the constraint pair of remaining circuit
The shadow price all 0 answered；
According to optimization gained unit output and unit bound, when judging that unit output is between unit output bound, deposit
The deploying node of node takes the quotation of marginal unit：
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
Load bus for participating in quotation, according to optimization gained acceptance of the bid load and load bound, judge load positioned at up and down
When between limit, existSo the deploying node of the node takes the quotation of load：
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
Wherein：ρGiThe deploying node of node, p where unit iiFor unit i quotation, PLFor power system network loss, λ is
The Lagrange multiplier of system power price, i.e. power-balance constraint, μlFor the Lagrange of the l articles Branch Power Flow limit constraint
Multiplier, PGiFor generating set i output, SFliPower transfer factor for branch road l to the net injecting power of node i；τG TPoint
Not Wei the unit output upper limit, lower limit constraint Lagrange multiplier matrix transposition,τD TFor the load power upper limit, lower limit about
The transposition of the Lagrange multiplier matrix of beam；
When judging that Line Flow reaches transmission of electricity limit, the circuit is fully loaded circuit, is fully loaded with shadow price corresponding to circuit constraint not
For 0, for amount to be asked, shadow price all 0 corresponding to the constraint of remaining circuit.
7. deploying node method for solving as claimed in claim 1, it is characterised in that in the 6th step, according to limit
Deploying node, Incremental Transmission Loss and the power transfer factor of node, determine unknown shadow price μ and system where unit
Energy value λ, including：
Be fully loaded with provided with m bar circuits, then m+1 marginal nodes be present, the unit output of marginal node between bound or
Load offer between bound；If the numbering of marginal node is 1,2 ..., m, m+1, and it is reference point to select node n, is fully loaded with line
Road numbering is to have 1,2 ..., m, then：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&rho;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>SF</mi>
<mn>11</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>SF</mi>
<mn>21</mn>
</msub>
<mo>-</mo>
<mo>...</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>m</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>m</mi>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&rho;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>SF</mi>
<mn>12</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>SF</mi>
<mn>22</mn>
</msub>
<mo>-</mo>
<mo>...</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>m</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>m</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>...</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mo>...</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>m</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein：λ be system power price, i.e. power-balance constraint Lagrange multiplier, μlFor the l articles Branch Power Flow limit about
The Lagrange multiplier of beam, l=1,2 ... m；SFliPower transfer factor for branch road l to the net injecting power of node i；I=1,
2nd ... n-1, n；PinFor the net injecting power column vector of node, Pin,iFor the net injecting power column vector P of nodeinElement, represent section
Point i net injecting power；
The node electricity price of marginal node takes the quotation of respective nodes, forms m+1 equation, and unknown quantity has m+1, is m respectively
Shadow price μ and 1 system power price λ, solving equations, obtains all unknown quantitys.
8. deploying node method for solving as claimed in claim 1, it is characterised in that in the 7th step, according to shadow
Price μ and system power price λ solves the node electricity price of non-marginal node；
The node electricity price of non-marginal node is solved according to equation below：
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>-</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>&rho;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>&lambda;</mi>
<mo>+</mo>
<mi>&lambda;</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>D</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mi>l</mi>
</munder>
<msub>
<mi>&mu;</mi>
<mi>l</mi>
</msub>
<msub>
<mi>SF</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
Wherein：piFor unit i quotation, PLFor power system network loss, λ is the glug of system power price, i.e. power-balance constraint
Bright day multiplier, μlFor the Lagrange multiplier of the l articles Branch Power Flow limit constraint, PGiFor generating set i output, SFliFor branch
Road l to the power transfer factor of the net injecting power of node i, l=1,2 ... m；ρGiThe node limit electricity of node where unit i
Valency, ρDiThe deploying node of node, P where load iDiFor load i power；τ′Gi、τGiRespectively in unit i outputs
Limit, the Lagrange multiplier of lower limit constraint, τ 'Di、τDiThe Lagrange multiplier constrained for the load i upper limit of the power, lower limit.
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