CN105281327B - Consider the large-scale distribution network optimal load flow calculation method of discrete and continuous decision variable - Google Patents
Consider the large-scale distribution network optimal load flow calculation method of discrete and continuous decision variable Download PDFInfo
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Abstract
The present invention is a kind of large-scale distribution network optimal load flow calculation method for considering discrete and continuous decision variable, its main feature is that, it is related to the mathematical model of complicated three-phase imbalance power distribution network including establishing, the contents such as the simplification process that the decomposition and three-phase imbalance distribution network loss that complicated optimal load flow calculates calculate, complicated optimum problem can be decomposed into mixed integer linear programming primal problem and non-linear feasible subproblem, decision optimizing and system security constraint are organically combined using the calculative strategy of mutual iteration, optimal load flow is nested into decision process, the quick calculating of extensive asymmetric trend is realized simultaneously.Suitable for the three-phase unbalanced load flow calculating of power distribution network, ring network structure, bi-directional current, discrete and continuous decision Real-time Decision and optimal load flow, there is scientific and reasonable, adaptable, the advantages that operation is accurate, speed is fast.
Description
Technical field
The present invention relates to distribution network technology field, be a kind of large-scale distribution network for considering discrete and continuous decision variable most
Excellent tidal current computing method.
Background technique
The operation of conventional electrical distribution net is static, passively.As wind-driven generator, photo-voltaic power supply, energy storage, microgrid etc. can be again
The raw energy accesses power distribution network, and power distribution network will be from radial, unidirectional trend, passive management to looped network, bi-directional current, active management
Method of operation transformation.Optimal load flow calculation method focuses primarily upon power transmission network at present, is not related to three-phase imbalance power distribution network, can not
The optimization problem containing extensive discrete and continuous decision variable is handled, is not able to satisfy the requirement calculated in real time.Active distribution network skill
Art is to solve the key technology of renewable energy grid integration, and active distribution network technology is in startup stage, Analysis of Policy Making at present
It is calculated separately with optimal load flow, the operation and requirement of real-time control of active distribution network can not be adapted to.
Summary of the invention
The object of the present invention is to which overcome the deficiencies in the prior art provides one using active distribution network technology as important support
Kind considers the large-scale distribution network optimal load flow calculation method of discrete and continuous decision variable, scientific and reasonable, adaptable,
Operation is accurate, speed is fast, especially suitable for three-phase imbalance distribution system analysis and decision.
Realize goal of the invention the technical solution adopted is that, a kind of large-scale distribution network considering discrete and continuous decision variable
Optimal load flow calculation method, characterized in that it includes the following contents:
1) it establishes and is related to the mathematical model of complicated three-phase imbalance power distribution network
Using minimum operating cost as target, foundation includes: three-phase imbalance power distribution network, distributed rotary generator, distribution
Formula wind-driven generator, photo-voltaic power supply, extensive energy storage, electric car energy storage, intelligent building, micro-grid system element, and consider to need
The mathematical model of response, the voltage of power grid and frequency adjustment and operation ancillary service is sought, includes discrete decision variable in model, connect
Continuous relationship and decision-making time range between decision variable, discrete decision variable and continuous decision variable,
Objective function:
Minimize f(ut,vt) (1)
Constraint condition:
Ht(xt,ut,wt)=0 (2)
Jt﹒ ut≥b (3)
Kt﹒ vt≥c (4)
Lt﹒ wt≥d (5)
G(xt)≥0 (6)
Wherein t ∈ T, and discrete decision variable and continuous decision variable have many applications, wherein load tap changer position
It sets, belongs to discrete decision variable ut；Unit Combination belongs to discrete decision variable；Load switch belongs to discrete decision variable；Have
The unit dispatch of function and the distributed generation system of reactive power belongs to continuous decision variable vt；Load side demand response, belongs to
Discrete decision variable；Home energy source management system belongs to continuous and discrete decision variable；The microgrid energy and ancillary service are attached
The continuous decision variable w addedt, other to be expressed as
Minimize: minimum value function；
F: objective cost function can be nonlinear cost curve；
xt: the state vector of node voltage；
ut: continuous decision variable vector；
vt: discrete decision variable vector；
T ∈ T: the time interval t in period T；
wt: additional continuous decision variable vector, such as the idle or capacitor group of inverter control；
Ht(): the three-phase unbalanced load flow equation in the t of interval；
Jt: linear matrix, and formula (3) is continuity decision variable utUpper and lower limit；
Kt: linear matrix, and formula (4) is discreteness decision variable vtUpper and lower limit；
Lt: linear matrix, and formula (5) is additional decision variable wtUpper and lower limit；
G (): the nonlinear function of power distribution system secure constraint.
2) decomposition that complicated optimal load flow calculates
When a part as constraint condition of formula (2), formula (1) solve it is difficult, using Benders method, by answering for upper section
Miscellaneous optimization problem is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce,
(i) primal problem
Objective function is formula (1), and constraint condition is formula (3), formula (4), since objective cost function f is able to carry out linearly
Change, and constraint equation (3), formula (4) be all it is linear, then primal problem is by formula (1), formula (3) and formula (4) as MIXED INTEGER
Linear programming method solves, and the optimal solution solved is expressed as
(ii) feasible subproblem
Primal problem optimal solutionWhen the number of iterations is 0, if generating state variable crosses the border, new constraint is generated
It condition and is included in the statement of primal problem, the then new optimal solution of primal problemIt is solved,
Then it passes again to feasible subproblem to solve, the iteration occurred between primal problem and feasible subproblem persistently carries out, until can
No longer detect that state variable is crossed the border in row subproblem, feasible subproblem is expressed as
Objective function:
F '=1 MinimizeT﹒ s (7)
Constraint condition:
Ht(xt,ut,wt)=0 (8)
Lt﹒ wt≥d (10)
G(xt)+s≥0 (11)
Due to constraint equation (6) and formula (9) be all it is nonlinear, using solution by iterative method, process are as follows: firstly, setting
Determine wtInitial valueThen, three-phase unbalanced load flow equation is solvedMust do well xtInitial valueMost
Afterwards, existSurrounding is linearized, and is obtained
Objective function:
F '=1 MinimizeT﹒ s (12)
Constraint condition:
WhereinFor partial differential operational factor, s is decision variable vector, and the element of matrix A isIllustrate control variable wtConstraint condition G (),That is the Jacobian matrix of G (x),By using uneven flow equation Ht()=0 carries out numerical value calculating；
Optimization problem formula (12)-formula (16) is one with decision variable Δ wtLinear programming problem, can use
Simplex method is solved, and decision variable is updatedIterative solution is executed, until the change of objective function
Change f in critical value predetermined, in iterative process, makes objective cost function value s*> 0 and constraint equation (14) drawing
Ge Lang multiplier is λ*, the new constraint condition that is added in primal problem are as follows:
The purpose of new constraint condition is that primal problem is forced to receive its decision so that helping to eliminate in feasible subproblem
Identified variable crosses the border；
3) the simplification process that three-phase imbalance distribution network loss calculates
The element of matrix A contains constraint condition, node voltage and bypass flow to node injecting power in formula (16)
Sensitirity va1ue, for three-phase imbalance power distribution system network, the derivation of analytic expression can become extremely difficult；In order to reduce
The complexity of calculating considers two hypothesis using approximate loss sensitivity analytic expression (18): (1) this phase power grid upstream branch and
Load is big to the influence being mutually lost；(2) distribution has enough reactive power supports, and the minor change of load will not cause big electricity
Deviation is pressed, i.e. voltage is constant, the two hypothesis meet power distribution network actual motion requirement, after assuming using two, is lost sensitive
Degree calculation amount will greatly simplify, and the network node n given for one can be with approximate representation in φ phase, loss sensitivity are as follows:
Wherein
Wherein
Dn-φIt is the φ phase load in network node n；
λn-φIt is the φ phase loss sensitivity in network node n；
WithIt is the set for flowing to the line and transformer of node n；
Ploss-lAnd Ploss-trIt is the piecewise smooth loss function of the load in line and transformer；
R and Z is line resistance and impedance respectively；
Re () takes the real part of complex variable；
φ indicates phase, and φ ∈ { a, b, c }；
V and subscript indicate: the node voltage of certain phase；
I and subscript indicate: the electric current of certain phase line or transformer；
θ and subscript indicate: the phase angle of current or voltage；
K and subscript indicate: being a constant parameters related with transformer voltage ratio.
The large-scale distribution network optimal load flow calculation method of the discrete and continuous decision variable of consideration of the invention, including establish
It is related to the mathematical model of complicated three-phase imbalance power distribution network, the decomposition that complicated optimal load flow calculates and three-phase imbalance power distribution network net
The contents such as simplification process calculated are damaged, complicated optimum problem can be decomposed into mixed integer linear programming primal problem and non-linear
Feasible subproblem is organically combined decision optimizing and system security constraint using the calculative strategy of mutual iteration, by optimal load flow
It is nested into decision process, while simplifying process using loss sensitivity, can be realized the quick of extensive asymmetric optimal load flow
It calculates.Suitable for the three-phase unbalanced load flow calculating of power distribution network, ring network structure, bi-directional current, discrete and continuous decision variable
Real-time Decision and optimal load flow have scientific and reasonable, adaptable, the advantages that operation is accurate, speed is fast.
Detailed description of the invention
Fig. 1 is active distribution network optimal load flow demonstration example；
Fig. 2 is the large-scale distribution network optimal load flow calculation method flow diagram for considering discrete and continuous decision variable.
Specific embodiment
Below with attached drawing and example, the invention will be further described.
Example shown in Fig. 1 is typical active distribution network structure, it may be verified that the discrete and continuous decision of consideration of the invention becomes
The validity of the large-scale distribution network optimal load flow calculation method of amount.Example is 21 node active distribution network test macros, includes
Distributed generation unit and energy-storage units total number be 8, type, configuration parameter are as shown in table 1:
1 distributed generation resource of table and energy-storage units configuration
Note: the parameter of photovoltaic indicates output peak power in table
Referring to Fig. 2, the large-scale distribution network optimal load flow calculation method of the discrete and continuous decision variable of consideration of the invention
Process are as follows: start；Initialize three-phase imbalance distribution network data；Solve mixed integer linear programming formula (1), formula (3), formula
(4)；Calculate linear sensitivity parameter；Solve linearisation subproblem formula (12)-formula (16)；Generate the new constraint equation of primal problem
(17)；Judge whether to restrain；Whether security constraint is met；Terminate.
The large-scale distribution network optimal load flow calculation method of the discrete and continuous decision variable of consideration of the invention, it include with
Lower content:
1) it establishes and is related to the mathematical model of complicated three-phase imbalance power distribution network
Using minimum operating cost as target, foundation includes: three-phase imbalance power distribution network, distributed rotary generator, distribution
Formula wind-driven generator, photo-voltaic power supply, extensive energy storage, electric car energy storage, intelligent building, micro-grid system element, and consider to need
The mathematical model of response, the voltage of power grid and frequency adjustment and operation ancillary service is sought, includes discrete decision variable in model, connect
Continuous relationship and decision-making time range between decision variable, discrete decision variable and continuous decision variable,
Objective function:
Minimize f(ut,vt) (1)
Constraint condition:
Ht(xt,ut,wt)=0 (2)
Jt﹒ ut≥b (3)
Kt﹒ vt≥c (4)
Lt﹒ wt≥d (5)
G(xt)≥0 (6)
Wherein t ∈ T, and discrete decision variable and continuous decision variable have many applications, wherein load tap changer position
It sets, belongs to discrete decision variable ut；Unit Combination belongs to discrete decision variable；Load switch belongs to discrete decision variable；Have
The unit dispatch of function and the distributed generation system of reactive power belongs to continuous decision variable vt；Load side demand response, belongs to
Discrete decision variable；Home energy source management system belongs to continuous and discrete decision variable；The microgrid energy and ancillary service are attached
The continuous decision variable w addedt, other to be expressed as
Minimize: minimum value function；
F: objective cost function can be nonlinear cost curve；
xt: the state vector of node voltage；
ut: continuous decision variable vector；
vt: discrete decision variable vector；
T ∈ T: the time interval t in period T；
wt: additional continuous decision variable vector, such as the idle or capacitor group of inverter control；
Ht(): the three-phase unbalanced load flow equation in the t of interval；
Jt: linear matrix, and formula (3) is continuity decision variable utUpper and lower limit；
Kt: linear matrix, and formula (4) is discreteness decision variable vtUpper and lower limit；
Lt: linear matrix, and formula (5) is additional decision variable wtUpper and lower limit；
G (): the nonlinear function of power distribution system secure constraint；
B, c, d are security constraint threshold value；
2) decomposition that complicated optimal load flow calculates
When a part as constraint condition of formula (2), formula (1) solve it is difficult, using Benders method, by answering for upper section
Miscellaneous optimization problem is decomposed into primal problem and feasible subproblem, then computational complexity will greatly reduce,
(i) primal problem
Objective function is formula (1), and constraint condition is formula (3), formula (4), since objective cost function f is able to carry out linearly
Change, and constraint equation (3), formula (4) be all it is linear, then primal problem is by formula (1), formula (3) and formula (4) as MIXED INTEGER
Linear programming method solves, and the optimal solution solved is expressed as
(ii) feasible subproblem
Primal problem optimal solutionWhen the number of iterations is 0, if generating state variable crosses the border, new constraint is generated
It condition and is included in the statement of primal problem, the then new optimal solution of primal problemIt is solved,
Then it passes again to feasible subproblem to solve, the iteration occurred between primal problem and feasible subproblem persistently carries out, until can
No longer detect that state variable is crossed the border in row subproblem, feasible subproblem is expressed as
Objective function:
F '=1 MinimizeT﹒ s (7)
Constraint condition:
Ht(xt,ut,wt)=0 (8)
Lt﹒ wt≥d (10)
G(xt)+s≥0 (11)
Due to constraint equation (6) and formula (9) be all it is nonlinear, using solution by iterative method, process are as follows: firstly, setting
Determine wtInitial valueThen, three-phase unbalanced load flow equation is solvedMust do well xtInitial valueMost
Afterwards, existSurrounding is linearized, and is obtained
Objective function:
F '=1 MinimizeT﹒ s (12)
Constraint condition:
WhereinFor partial differential operational factor, s is decision variable vector, and the element of matrix A isIllustrate control variable wtConstraint condition G (),That is the Jacobian matrix of G (x),By using uneven flow equation Ht()=0 carries out numerical value calculating；
Optimization problem formula (12)-formula (16) is one with decision variable Δ wtLinear programming problem, can use
Simplex method is solved, and decision variable is updatedIterative solution is executed, until the change of objective function
Change f in critical value predetermined, in iterative process, makes objective cost function value s*> 0 and constraint equation (14) drawing
Ge Lang multiplier is λ*, the new constraint condition that is added in primal problem are as follows:
The purpose of new constraint condition is that primal problem is forced to receive its decision so that helping to eliminate in feasible subproblem
Identified variable crosses the border；
3) the simplification process that three-phase imbalance distribution network loss calculates
The element of matrix A contains constraint condition, node voltage and bypass flow to node injecting power in formula (16)
Sensitirity va1ue, for three-phase imbalance power distribution system network, the derivation of analytic expression can become extremely difficult；In order to reduce
The complexity of calculating considers two hypothesis using approximate loss sensitivity analytic expression (18): (1) this phase power grid upstream branch and
Load is big to the influence being mutually lost；(2) distribution has enough reactive power supports, and the minor change of load will not cause big electricity
Deviation is pressed, i.e. voltage is constant, the two hypothesis meet power distribution network actual motion requirement, after assuming using two, is lost sensitive
Degree calculation amount will greatly simplify, and the network node n given for one can be with approximate representation in φ phase, loss sensitivity are as follows:
Wherein
Wherein
Dn-φIt is the φ phase load in network node n；
λn-φIt is the φ phase loss sensitivity in network node n；
WithIt is the set for flowing to the line and transformer of node n；
Ploss-lAnd Ploss-trIt is the piecewise smooth loss function of the load in line and transformer；
R inputs other variables；
Re () takes the real part of complex variable；
φ indicates phase, and φ ∈ { a, b, c }；
V and subscript indicate: the node voltage of certain phase；
I and subscript indicate: the electric current of certain phase line or transformer；
θ and subscript indicate: the phase angle of current or voltage；
K and subscript indicate: being a constant parameters related with transformer voltage ratio.
Specific embodiment, the big rule of the discrete and continuous decision variable of consideration of the invention are combined according to formula (1)~formula (6)
Mould power distribution network optimal load flow calculation method, including the following contents:
1) it establishes and is related to the mathematical model of Complicated Distribution Network
Objective function: formula (1) may be expressed as:
Constraint condition: it may be expressed as: by formula (2)~formula (6)
nmin≤ni,t≤nmax (28)
Vi.min≤Vi(t)≤Vi.max (31)
P in formulaPV-iAnd QPV-iIt is the active power and reactive power at photovoltaic generating system node i, i=1 ..., N, N is
Interstitial content, N=21 in this example；PE-iAnd QE-iIt is active power and reactive power of the energy storage device in i-th of node；PL-i
And QL-iIt is active power and reactive power of the load in i-th of node；PiAnd QiIt is the injection active power and nothing of i-th of node
Function power；R is the resistance connected at bus i；Vi、VjVoltage at expression node i, j；δi、δjIt is the phase angle of node i, j voltage；
θijIt is node i, admittance Y between jijPhase angle；VrefIt is on-load regulator transformer reference voltage, generally takes 1.0p.u.；ni,tIt is
T period on-load transformer tap changer no-load voltage ratio at node i；Δn,nminAnd nmaxIt is that on-load transformer tap changer becomes respectively
The change rate of ratio, no-load voltage ratio minimum value and no-load voltage ratio maximum value；Ei(t) it is energy-storage travelling wave tube is stored at node i energy；Ei.maxIt is storage
The maximum value of energy element storage energy；RE-iIt (t) is the energy conversion rate of energy-storage system t period at node i；ηchAnd ηdisRespectively
Efficiency is charged and discharged for energy-storage system；PE-i, QE-iIt is the active and idle function that energy-storage system is interacted with power grid at node i respectively
Rate；P E.rated-i,It is the bound of energy-storage travelling wave tube output power at node i；UE-iIt is exchanged for energy-storage system at node i
Side voltage effective value；The upper limit value allowed for energy-storage system charge and discharge at node i；Vi.min,Vi.maxRespectively at node i
Voltage minimum and maximum security constraint value.Example to simplify the analysis, this example threephase load according to symmetrical treatment, calculating process without
Difference.
2) decomposition that complicated optimal load flow calculates
When a part as constraint condition of three-phase unbalanced load flow formula (2), formula (1) solve it is difficult, using Benders
The complicated optimum problem of upper section is decomposed into primal problem and feasible subproblem by method, then computational complexity will greatly reduce.
(i) primal problem
Shown in objective function such as formula (1), and shown in constraint condition such as formula (3), formula (4).Since objective cost function f can be with
Linearized, and constraint equation (3) and formula (4) be all it is linear, then primal problem, formula (1), formula (3) and formula (4) can be made
For mixed integer linear programming, i.e. MILP method solves, and the optimal solution solved is expressed asBy imitative
True analysis, acquiring optimal value is 137.3940, this moment uA6=0.997p.u., uA10=1.001p.u., uA19=1.003p.u.,
And the optimal solution is convergent.
(ii) feasible subproblem
Primal problem optimal solutionWhen the number of iterations is 0, if generating state variable crosses the border, new pact is generated
It beam condition and is included in the statement of primal problem, the then new optimal solution of primal problemTo be asked
Solution, such as in network shown in Fig. 1, when subproblem is crossed the border, intermediate solution at this time includes: that network loss value is 27.4kW；And bus
Voltage at subbus is 1.052p.u., is crossed the border, and the voltage at bus A6 is 1.049p.u., and the voltage of bus A17
For 1.036p.u. etc..Then it passes again to feasible subproblem to solve, the iteration occurred between primal problem and feasible subproblem is held
It is continuous to carry out, until no longer detecting that state variable is crossed the border in feasible subproblem.The objective function of feasible subproblem such as formula (7) institute
Show, and shown in constraint condition such as formula (8)~formula (11).Due to constraint equation (8)~formula (11) be all it is nonlinear, using repeatedly
It is solved for method, process are as follows: firstly, setting control wtInitial valueThen, three-phase unbalanced load flow equation is solvedIt must do wellFinally,Surrounding is linearized, and is obtained shown in objective function such as formula (12), about
Shown in beam condition such as formula (13)~formula (16).Wherein the element of matrix A isIllustrate control variable wt
Constraint condition G (),That is the Jacobian matrix of G (x),It can be by using uneven flow equation Ht
()=0 carries out numerical value calculating.
Optimization problem formula (12)~formula (16) is one with decision variable Δ wtLinear programming problem, can use
Simplex method is solved, and decision variable is updatedIterative solution is executed, until the change of objective function
Change f in critical value predetermined, in iterative process, makes objective cost function value S*> 0 and constraint equation (16)
Lagrange's multiplier is λ*, it is added to shown in the new constraint condition such as formula (17) in primal problem.The purpose of new constraint condition is urgent
So that primal problem is received its decision and crosses the border so that the identified variable in feasible subproblem can be helped to eliminate.
3) the simplification process that three-phase imbalance distribution network loss calculates
The element of matrix A contains constraint condition, node voltage and bypass flow to node injecting power in formula (14)
Sensitirity va1ue, for three-phase imbalance power distribution system network, the derivation of analytic expression can become extremely difficult；In order to reduce
The complexity of calculating uses approximate loss sensitivity analytic expression (18).
It can be seen that solution iteration from the process of Fig. 2 and both needed iteration between primal problem and feasible subproblem,
Need the iteration of feasible subproblem itself.Active distribution network according to Fig. 1 passes through calculating, it can be deduced that the network loss before optimization
For 25.6kW, and the network loss after optimizing is 7.1kW, and by the comparison of optimization front and back network loss value, we are it can be found that by excellent
Change, network loss value is substantially reduced, and Utilities Electric Co. reduces costs by each component parameters of coordinated control, realizes energy conservation.
The present invention relates to asymmetrical three-phase power distribution network optimal load flow computation model and solution strategies, it can be used for solving one kind
Distribution system planning and Operation Decision problem.By using engineering approximation, sensitivity parameter matrix is modified, is realized
The Efficient Solution of feasible subproblem.
Design conditions, legend, table in the embodiment of the present invention etc. are only used for that the present invention is further illustrated, not thoroughly
It lifts, does not constitute the restriction to claims, the enlightenment that those skilled in the art obtain according to embodiments of the present invention,
It would occur to other substantially equivalent substitutions without creative work, all fall in the scope of protection of the present invention.
Claims (1)
1. a kind of large-scale distribution network optimal load flow calculation method for considering discrete and continuous decision variable, characterized in that it is wrapped
Include the following contents:
1) it establishes and is related to the mathematical model of complicated three-phase imbalance power distribution network
Using minimum operating cost as target, foundation includes: three-phase imbalance power distribution network, distributed rotary generator, distributed wind
Power generator, photo-voltaic power supply, extensive energy storage, electric car energy storage, intelligent building, micro-grid system element, and consider that demand is rung
Answer, the mathematical model of the adjustment of the voltage of power grid and frequency and operation ancillary service, in model comprising discrete decision variable, it is continuous certainly
Relationship and decision-making time range between plan variable, discrete decision variable and continuous decision variable,
Objective function:
Minimize f(ut,vt) (1)
Constraint condition:
Ht(xt,ut,wt)=0 (2)
Jt﹒ ut≥b (3)
Kt﹒ vt≥c (4)
Lt﹒ wt≥d (5)
G(xt)≥0 (6)
Wherein t ∈ T, and discrete decision variable and continuous decision variable have many applications, wherein load tap changer position, belongs to
In discrete decision variable；Unit Combination belongs to discrete decision variable；Load switch belongs to discrete decision variable；It is active and idle
The unit dispatch of the distributed generation system of power belongs to continuous decision variable；Load side demand response belongs to discrete decision change
Amount；The microgrid energy and ancillary service are additional continuous decision variable, other to be expressed as
Minimize: minimum value function；
F: objective cost function can be nonlinear cost curve；
xt: the state vector of node voltage；
ut: continuous decision variable vector；
vt: discrete decision variable vector；
T ∈ T: the time interval t in period T；
wt: additional continuous decision variable vector, such as the idle or capacitor group of inverter control；
Ht(): the three-phase unbalanced load flow equation in the t of interval；
Jt: linear matrix, and formula (3) is continuous decision variable upper and lower limit；
Kt: linear matrix, and formula (4) is discrete decision variable upper and lower limit；
Lt: linear matrix, and formula (5) is additional continuous decision variable upper and lower limit；
G (): the nonlinear function of power distribution system secure constraint；
Objective function: formula (1) may be expressed as:
Constraint condition: it may be expressed as: by formula (2)~formula (6)
nmin≤ni,t≤nmax (9)
Vi.min≤Vi(t)≤Vi.max (12)
In formula, PPV-iAnd QPV-iIt is the active power and reactive power at photovoltaic generating system node i, i=1 ..., N, N is node
Number；PE-iAnd QE-iIt is active power and reactive power of the energy storage device in i-th of node；PL-iAnd QL-iIt is load at i-th
The active power and reactive power of node；PiAnd QiIt is the injection active power and reactive power of i-th of node；R is at bus i
The resistance of connection；Vi、VjVoltage at expression node i, j；δi、δjIt is the phase angle of node i, j voltage；θijIt is node i, is led between j
Receive YijPhase angle；VrefIt is on-load regulator transformer reference voltage, generally takes 1.0p.u.；ni,tBe at node i the t period have load adjust
Pressure transformer tap no-load voltage ratio；Δn,nminAnd nmaxIt is the change rate of on-load transformer tap changer no-load voltage ratio respectively, no-load voltage ratio is most
Small value and no-load voltage ratio maximum value；Ei(t) it is energy-storage travelling wave tube is stored at node i energy；Ei.maxIt is energy-storage travelling wave tube storage energy
Maximum value；RE-iIt (t) is the energy conversion rate of energy-storage system t period at node i；ηchAnd ηdisRespectively energy-storage system charging and
Discharging efficiency；PE-i, QE-iIt is the active and reactive power that energy-storage system is interacted with power grid at node i respectively；P E.rated-i,It is the bound of energy-storage travelling wave tube output power at node i；UE-iIt is effective that side voltage is exchanged for energy-storage system at node i
Value；The upper limit value allowed for energy-storage system charge and discharge at node i；Vi.min,Vi.maxRespectively at node i voltage minimum and
Maximum security constraint value；
2) decomposition that complicated optimal load flow calculates
When a part as constraint condition of formula (2), formula (1) solve it is difficult, it is using Benders method, the complexity of upper section is excellent
Changing PROBLEM DECOMPOSITION is primal problem and feasible subproblem, then computational complexity will greatly reduce,
(i) primal problem
Objective function is formula (1), and constraint condition is formula (3), formula (4), since objective cost function f is able to carry out linearisation,
And constraint equation (3), formula (4) be all it is linear, then primal problem by formula (1), formula (3) and formula (4) be used as MIXED INTEGER line
Property planing method solve, the optimal solution solved is expressed as
(ii) feasible subproblem
Primal problem optimal solutionWhen the number of iterations is 0, if generating state variable crosses the border, new constraint condition is generated
And it is included in the statement of primal problem, then the new optimal solution of primal problemIt is solved, then
It passes again to feasible subproblem to solve, the iteration occurred between primal problem and feasible subproblem persistently carries out, until in feasible son
No longer detect that state variable is crossed the border in problem, feasible subproblem is expressed as
Objective function:
F '=1 MinimizeT﹒ s (13)
Constraint condition:
Ht(xt,ut,wt)=0 (14)
Lt﹒ wt≥d (16)
G(xt)+s≥0 (17)
Due to constraint equation (6) and formula (15) be all it is nonlinear, using solution by iterative method, process are as follows: firstly, setting wt
Initial valueThen, three-phase unbalanced load flow equation is solvedMust do well xtInitial valueFinally,Surrounding is linearized, and is obtained
Objective function:
F '=1 MinimizeT﹒ s (18)
Constraint condition:
WhereinFor partial differential operational factor, s is decision variable vector, and the element of matrix A isTable
Additional continuous decision variable w is showntConstraint condition G (),That is the Jacobian matrix of G (x),Pass through
Use uneven flow equation Ht()=0 carries out numerical value calculating；
Optimization problem formula (18)-formula (22) is one with decision variable Δ wtLinear programming problem, simplex can be used
Method is solved, and additional continuous decision variable is updatedIterative solution is executed, until target letter
Several variation f are in critical value predetermined, in iterative process, make objective cost function value s*> 0 and constraint equation
(20) Lagrange's multiplier is λ*, the new constraint condition that is added in primal problem are as follows:
The purpose of new constraint condition is that primal problem is forced to receive its decision so that helping to eliminate to be known in feasible subproblem
Not Chu variable cross the border；
3) the simplification process that three-phase imbalance distribution network loss calculates
The element of matrix A contains the spirit of constraint condition, node voltage and bypass flow to node injecting power in formula (22)
Sensitivity value, for three-phase imbalance power distribution system network, the derivation of analytic expression can become extremely difficult；It is calculated to reduce
Complexity, using approximate loss sensitivity analytic expression, consider two hypothesis: (1) this phase power grid upstream branch and load are to this
Mutually the influence of loss is big；(2) distribution has enough reactive power supports, and the minor change of load will not cause big voltage deviation,
I.e. voltage is constant, the two hypothesis meet power distribution network actual motion requirement, after assuming using two, loss sensitivity calculation amount
It will greatly simplify, the network node n given for one can be with approximate representation in φ phase, loss sensitivity are as follows:
Wherein
|Il-b|·Rl-φb·cos(θI-l-b-θI-n-φ)+|Il-c|·Rl-φc·cos(θI-l-c-θI-n-φ)} (25)
Wherein
Dn-φIt is the φ phase load in network node n；
λn-φIt is the φ phase loss sensitivity in network node n；
WithIt is the set for flowing to the line and transformer of node n；
Ploss-lAnd Ploss-trIt is the piecewise smooth loss function of the load in line and transformer；
R and Z respectively indicate resistance and impedance；
Re () takes the real part of complex variable；
φ indicates phase, and φ ∈ { a, b, c }；
V and subscript indicate: the node voltage of certain phase；
I and subscript indicate: the electric current of certain phase line or transformer；
θ and subscript indicate: the phase angle of current or voltage；
K and subscript indicate: being a constant parameters related with transformer voltage ratio.
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