CN106026105B - A kind of Optimal Power Flow Problems control method based on the concave-convex optimisation technique of punishment - Google Patents
A kind of Optimal Power Flow Problems control method based on the concave-convex optimisation technique of punishment Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract
The invention discloses a kind of based on the Optimal Power Flow Problems control method for punishing concave-convex optimisation technique, comprising the following steps: acquisition power system network parameter first determines the mathematical model of optimal load flow control problem；Followed by punishment thought and Taylor expansion, the current approximate convex problem of optimal power flow problems is obtained；Then it iteratively solves the approximate convex problem of optimal load flow control and obtains each bus injecting power value；It is last that Optimal Power Flow Problems control is completed according to the bus injecting power value being calculated.The present invention can make system performance loss minimum using concave-convex optimisation technique design Optimal Power Flow Problems are punished under the premise of guaranteeing power flow equation feasibility.
Description
Technical field
The present invention relates to technical field of power systems, and in particular to a kind of electric system based on the concave-convex optimization thought of punishment
Optimal load flow control method.
Background technique
Optimization Problems In Power Systems, including planning, dispatch, run on control, target is security of system and economy
Balance and compromise.As one of most important one problem, optimal load flow (Optimal Power Flow, OPF) control is
Refer to that the structural parameters of electric system and load condition have all given timing, adjusts available control variable (such as generator output work
Rate, adjustable transformer tap etc.) to find all operation constraint conditions are able to satisfy, and make a certain performance indicator of system (such as
Cost of electricity-generating or via net loss) power flowcontrol when reaching minimum value.In recent years, with smart grid, distributed generation technology,
The fast development of distribution type electric energy memory technology improves economy under the premise of meeting power system security as much as possible,
It rationally controls this classical problem using resource distribution and existing equipment and becomes again to reduce the optimal load flow of energy consumption and grind
Study carefully hot spot.
Since the 1960s, powerful tool of the optimal load flow as Operation of Electric Systems and analysis, always again
It is concerned.By nearly development in 50 years, numerous optimal methods are introduced sequentially into the field, such as: linear programming, quadratic programming,
Non-Linear Programming and Newton method and decoupling method etc..But optimal load flow is a typical nonlinear optimal problem, and due to about
It is complicated that the complexity of beam calculates it, and difficulty is larger.Currently, document [M.Farivar and S.H.Low, " Branch
Flow model:Relaxations and convexification (parts I, II), " IEEE Trans.Power
Syst., vol.28, no.3, pp.2554-2572,2013] in propose using convex relaxation method --- SOCP relaxation solves most
Excellent Power Flow Problem, however it is tight that it only demonstrates the relaxation under certain condition.For non-convex optimal power flow problems, convex pine
Relaxation method even all not can guarantee to obtain the feasible solution of problem.Therefore, the present invention proposes the optimal tide based on the concave-convex optimization of punishment
Method of flow control.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of electric system based on concave-convex optimization thought
Optimal load flow control method, the method for the present invention consider the control problem of inverter in distributed power generation, it is ensured that in iteration
Power System Performance loss monotone decreasing always in the process can be realized reduction while reaching each constraint requirements of electric system
The purpose of Power System Performance loss completes Optimal Power Flow Problems control.Specifically includes the following steps:
Step 1: obtaining power system network parameter: the bus set N and set N after removal root bus+=N { 0 }；Electricity
Net set of fingers ξ；The impedance z of branch between busij,Each bus nodes injecting power siConstraint set Si；It is female
Square v of line voltage range valueiLower limitv iAnd the upper limit
Step 2: initialization the number of iterations k=0, maximum number of iterations Kmax, convergence precision tol；Set initial pointDetermine penalty coefficient β；lijIt indicates from bus i to square of the current amplitude of bus j；SijIndicate bus i
To the trend of the line transmitting terminal between j；
Step 3: Taylor expansion is utilized, the approximate convex problem of optimal power flow problems is obtained:
Optimized variable: s, S, v, l, s0
Wherein | a |,The amplitude, conjugation and real part of plural a are respectively indicated with Re (a)；It indicates at bus i
System performance loss caused by injecting power；
Step 4: Solve problems (P1) obtain current calculated resultJudge whether to reach convergence
Precision:Or whether reach maximum number of iterations: k > Kmax；If so, the injecting power of output bus, meter
System performance loss is calculated, step 5 is executed；Otherwise the number of iterations k=k+1 is enabled, step 3 and 4 is repeated.
Step 5: optimal load flow control is completed according to the bus injecting power being calculated.
Further, Solve problems (P1) obtain calculated result in the step 4Solution party
Method is interior-point algohnhm.
Optimal load flow is constructed first the invention has the advantages that: the method for the present invention and corresponds to planning problem, is thought followed by punishment
Think and Taylor expansion, obtains the current approximate convex problem of optimal power flow problems；Then it is approximate iteratively to solve optimal load flow control
Convex problem obtains each bus injecting power value；It is last that the optimal tide of electric system is completed according to the bus injecting power value being calculated
Flow control.The present invention can guarantee that power flow equation is feasible using concave-convex optimisation technique design Optimal Power Flow Problems are punished
Property under the premise of make system performance loss minimum.
Detailed description of the invention
Fig. 1 is the system model figure that the embodiment of the present invention uses this method.
Fig. 2 is the specific flow chart that the embodiment of the present invention uses this method.
Fig. 3 is the target value of the embodiment of the present invention and the relational graph of the number of iterations.
Fig. 4 is system restriction of embodiment of the present invention feasibility criterion and the number of iterations relational graph.
Specific embodiment
In order to keep the objects and effects of the present invention clearer, with reference to the accompanying drawing to the specific embodiment party of the method for the present invention
Formula is described in detail.
As shown in Figure 1, considering radial power distribution network, it is made of the line of bus and connection bus.In the network
Root node is substation bus bar (for convenience of description, hereinafter referred to as root bus), is connected with power transmission network.Root bus uses fixation
Voltage, while will be from the electric power distribution received in transmission network to other buses.The present invention defines the root bus as mother
Line 0, other buses are 1 ..., n；In addition, N:={ 0 ..., n } is enabled to indicate all buses in power grid, N is defined+:=N { 0 }；
(i, j) indicates that bus i is connected with bus j, and direction is i → j, and bus j is on the exclusive path of bus i and bus 0.Enable ξ table
The set for showing all branches in network indicates vector branch i → j to any (i, j) ∈ ξ.
For any bus i ∈ N, v is enablediIndicate square of the voltage amplitude value at bus i.As described above, substation is female
The voltage of line is fixed value v0.Define si=pi+iqiIndicate the injecting power at bus i, wherein pi, qi respectively indicate injection
Active power and reactive power.In addition, defining PiFor bus i to the exclusive path between bus 0, for Radial network, Pi
It is unique.For any line (i, j) ∈ ξ, l is enabledijIt indicates from bus i to square of the current amplitude of bus j, zij=
rij+ixijIndicate bus i, the impedance of line between j；Enable Sij=Pij+iQijIndicate the tide of the line transmitting terminal between bus i to j
It flows (or power flow), wherein PijAnd QijRespectively indicate active power stream and reactive power flow.In addition, being used for plural a ∈ CIndicate the conjugation of a.
Given network topology (N, ξ), impedance z and substation bus bar voltage v0When, then other electrical network parameters (s, S, v,
L, s0) can be expressed as follows by the branch flow model (branch flow model) of radial network:
Formula (1a) and (1b) are power balance equations, and formula (1c) and (1d) are the identical transformations of ohm formula.
The present invention considers following several power distribution network controllable devices: distributed generator, inverter, controllable load, such as electricity
Motor-car, intelligent appliance, shunt capacitor.In practical applications, power grid is injected by control shunt capacitor and inverter
Reactive power adjusts voltage.After setting injecting power s, other electrical parameter (S, v, l, s can be determined by formula (1)0)。
According to the different type of controllable device, power grid median generatrix i ∈ N+Injecting power siWith different constraint set
Si, it may be assumed that
si∈Si, i ∈ N+ (2)
According to device type definition set SiAre as follows:
1. if siRepresent a rated capacity asShunt capacitor, then
If siRepresent a maximum generating watt asSolar energy electroplax, be by a capacityInverter connect with power grid, that
?
2. if siRepresenting a power factor is η, active power consumption in sectionThe adjustable negative of consecutive variations
It carries, then
Note that siIt can indicate the total injecting power of multiple above equipments.
In addition, it is necessary to by square v of the voltage amplitude value of bus iiControl is in preset voltage lower limit valuev iAnd voltage
Upper limit valueBetween, that is, it needs to meet
Under conditions of power flow constraint, voltage constraint, injecting power constraint, optimal power flow problems be can be described as follows:
Optimized variable: s, S, v, l, s0
si∈Si, i ∈ N+(3e)
Wherein in objective functionIndicate system performance loss caused by bus i injecting power.If for appointing
Anticipate i ∈ N, there is fi(x)=x, thenIndicate the total-power loss in power grid.
Due to existing such as Non-convex constraint, above-mentioned optimal power flow problems be non-convex optimization problem,
It is difficult to solve.Document [M.Farivar and S.H.Low, " Branch flow model:Relaxations and
Convexification (parts I, II), " IEEE Trans.Power Syst., vol.28, no.3, pp.2554-2572,
2013] it is proposed in and solves optimal power flow problems using SOCP relaxation method, however only demonstrate the relaxation under certain condition
It is tight.For one optimal power flow problems, convex relaxation method even all not can guarantee to obtain the feasible solution of problem.Therefore,
The present invention proposes the optimal load flow control method based on the concave-convex optimization of punishment.
By taking non-convex constraint (3d) as an example, two inequality constraints are converted by (3d) first:
Wherein the former is convex constraint, and the latter is non-convex constraint.Target is moved it to by introducing penalty term for the latter
In function, punishment problem is obtained:
It can be proved that when punishment parameter β is greater than some threshold value.Problem (4) can be solved by bumps optimization.
Specifically, S is givenijAnd viCurrent value S_preijAnd v_prei, the penalty term in problem (4) is subjected to line by Taylor expansion
Property is approached, it may be assumed that
Available following convex problem,
Above-mentioned convex problem is iteratively solved until algorithmic statement, available optimal load flow control result.
Fig. 2 gives the flow chart of the above-mentioned Optimal Power Flow Problems control method based on concave-convex optimisation technique.Specifically
Ground can be described as follows:
A kind of Optimal Power Flow Problems control method based on the concave-convex optimisation technique of punishment, this method include following step
It is rapid:
Step 1: obtaining power system network parameter: the bus set N and set N after removal root bus+=N { 0 }；Electricity
Net set of fingers ξ；The impedance z of branch between busij,Each bus nodes injecting power siConstraint set Si；It is female
Square v of line voltage range valueiLower limitvI and the upper limit
Step 2: initialization the number of iterations k=0, maximum number of iterations Kmax, convergence precision tol；Set initial pointDetermine penalty coefficient β；lijIt indicates from bus i to square of the current amplitude of bus j；SijIndicate bus i
To the trend of the line transmitting terminal between j；
Step 3: Taylor expansion is utilized, the approximate convex problem of optimal power flow problems is obtained:
Optimized variable: s, S, v, l, s0
Wherein | a |,The amplitude, conjugation and real part of plural a are respectively indicated with Re (a)；It indicates at bus i
System performance loss caused by injecting power；
Step 4: Solve problems (P1) obtain current calculated resultJudge whether to reach convergence
Precision:Or whether reach maximum number of iterations: k > Kmax；If so, the injecting power of output bus, meter
System performance loss is calculated, step 5 is executed；Otherwise the number of iterations k=k+1 is enabled, step 3 and 4 is repeated.
Step 5: optimal load flow control is completed according to the bus injecting power being calculated.
Further, Solve problems (P1) obtain calculated result in the step 4Solution party
Method is interior-point algohnhm.
Technical solution of the present invention is further elaborated below by specific example.In experiment, using SCE-47 and
SCE-56 network system carries out proof of algorithm.Specifically, using following experiment parameter:
1. setting minimum power losses as target, and the voltage V of substation bus bar0For the reference voltage of a unit
Value；
2. the setting for injecting power restrained boundary, any bus i ∈ N in power grid+Place there may be multiple equipment,
Such as shunt capacitance, tunable load, solar energy electroplax；Assuming that there is D in power grid in totaliA equipment and to be numbered be 1,
2 ..., Di；For d=1,2 ..., Di, sidIndicate the injecting power of equipment d.
It is loaded if equipment d is one, and known active power consumption p and reactive power consumption q, then s at this timeid=-p-
i·q；If the apparent energy peak value S of known load dpeak, then sid=-Speakexp(jθ).Wherein, (0.9) θ=arccos,
At this point, the injecting power s of loadidA namely constant；
If equipment d is that a capacity isCapacitor, then having
If equipment d is that a capacity isPhotovoltaic battery plate, then
According to the above setting, bus i total injecting power is at this time
Other parameters setting is as follows: determining each reference capacity value, initialization bus sum N, electricity according to power grid actual conditions
Hinder rij, reactance xijAnd the capacity of relevant device type or active power consumption value at bus, concurrently set power transformation tiny node
Power be a unit reference power value, enable iteration total degree Kmax=20, vmaxEqual to 1.1 cell voltage base values, vminIt is equal to
0.9 cell voltage base value, convergence precision tol=0.001, punishment parameter β=0.001 initialize bus voltage upper limit
Lower voltage limitIn addition, in the present embodiment, definitionTo constrain feasibility criterion, when value is close to 0
Illustrate to have arrived feasible.
Fig. 3,4 are simulation results figures by Matlab to designed method.
The calculating knot that the method for the present invention is applied in SCE-47 bus-bar system and SCE-56 bus-bar system is set forth in Fig. 3
Fruit.The result of SOCP relaxation method is also given in order to compare, in figure.It can be seen from the figure that the method for the present invention can be quick
Convergence makes system total power consumption with the number of iterations while meeting electric power system tide equation, power and voltage and constraining
Constantly reduce until restraining, and the optimal load flow control method based on concave-convex optimisation technique has reached and the optimal tide based on SOCP
The almost the same target value of method of flow control illustrates that technical solution of the present invention can be realized optimal load flow control.
Fig. 4 is set forth in SCE-47 bus-bar system and SCE-56 bus-bar system using after the method for the present invention, model
Middle constraint feasibility criterion and the number of iterations relational graph.It can be seen from the figure that with the increase of the number of iterations, constraint condition by
Gradually met, and after iteration the 2nd time, the method for the present invention can meet constraint feasibility criterion.
The present invention is not only limited to above-mentioned specific embodiment, one technical staff of this field is disclosed interior according to the present invention
Hold, the present invention can be implemented using other a variety of specific embodiments.Therefore, all using design structure and think of of the invention
Road does the design of some simple variations or change, both falls within the scope of the present invention.
Claims (2)
1. a kind of based on the Optimal Power Flow Problems control method for punishing concave-convex optimisation technique, which is characterized in that this method packet
Include following steps:
Step 1: obtaining power system network parameter: the bus set N and set N after removal root bus+=N { 0 }；Grid branch
Set ξ；The impedance z of branch between busij,Each bus nodes injecting power siConstraint set Si；Busbar voltage
Square v of range valueiLower limit viAnd the upper limit
Step 2: initialization the number of iterations k=0, maximum number of iterations Kmax, convergence precision tol；Set initial point
Determine penalty coefficient β；lijIt indicates from bus i to square of the current amplitude of bus j；SijIndicate the line between bus i to j
The trend of transmitting terminal；
Step 3: Taylor expansion is utilized, the approximate convex problem of optimal power flow problems is obtained:
Optimized variable: s, S, v, l, s0
Wherein fiIndicate system performance loss caused by injecting power at bus i；
Step 4: Solve problems (P1) obtain current calculated resultJudge whether to reach convergence precision:Or whether reach maximum number of iterations: k > Kmax；If so, the injecting power of output bus, computing system
Performance loss, executes step 5；Otherwise the number of iterations k=k+1 is enabled, step 3 and 4 is repeated；
Step 5: optimal load flow control is completed according to the bus injecting power being calculated.
2. a kind of Optimal Power Flow Problems control method based on the concave-convex optimisation technique of punishment according to claim 1,
It is characterized in that, Solve problems (P1) obtain calculated result in the step 4Solution be interior
Point algorithm.
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| CN102508950A (en) * | 2011-10-14 | 2012-06-20 | 广东电网公司电力科学研究院 | Regional dispatching automatic system and method for communication between regional dispatching automatic system and remote monitoring diagnosis centre |
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| CN102508950A (en) * | 2011-10-14 | 2012-06-20 | 广东电网公司电力科学研究院 | Regional dispatching automatic system and method for communication between regional dispatching automatic system and remote monitoring diagnosis centre |
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