CN105186578B - There is the distributed automatic scheduling method of power system accurately calculating network loss ability - Google Patents

There is the distributed automatic scheduling method of power system accurately calculating network loss ability Download PDF

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CN105186578B
CN105186578B CN201510543029.9A CN201510543029A CN105186578B CN 105186578 B CN105186578 B CN 105186578B CN 201510543029 A CN201510543029 A CN 201510543029A CN 105186578 B CN105186578 B CN 105186578B
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electromotor
power
network loss
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cost
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CN105186578A (en
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赵善驰
吴英俊
岳东
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Nanjing Post and Telecommunication University
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Abstract

The invention discloses a kind of distributed automatic scheduling method of power system having and accurately calculating network loss ability, the invention used electricity-tracing method and electrical dissection to obtain the power attenuation of every electromotor, provide a kind of method calculating network loss more accurately, the present invention uses two-layer consistency algorithm, marginal cost is finally reached unanimity, each node has its respective load and generating information, result in each of which and have respective power deviation, lower level uses average homogeneity to carry out the consistent of guaranteed output deviation, the incremental cost that higher level uses incremental cost concordance to realize every electromotor reaches unanimity, the present invention can solve the Economic Dispatch Problem in power system in the case of reducing communications cost by this distributed AC servo system algorithm.

Description

There is the distributed automatic scheduling method of power system accurately calculating network loss ability
Technical field
The present invention relates to the control method of a kind of generators in power systems power, be specifically related to one and there is accurately calculating network loss energy The power system distributed scheduling scheme of power, belongs to Economic Dispatch technical field.
Background technology
Emerging intelligent grid framework contribute to inquiring into further in distribution system some substantially challenge, such as economic load dispatching (ED).Economic load dispatching refers to that generating set is minimum in operating cost and meets under the power constraints of electromotor total need Power is asked to distribute to each generating set.Traditional solution includes λ iterative method and gradient search procedure, and both approaches is main For solving when cost function is situation during convex function.It is non-convex letter that the more complicated method of other is used for solving cost function Situation during number, including genetic algorithm (GA), particle cluster algorithm (PSO) also has newly improved particle cluster algorithm (IPSO).Pass through These methods make the performance of economic load dispatching and application be obtained for improvement, and the most traditional centralized framework electrical network is to distributed Intelligent grid change, equally, also there occurs same transformation in corresponding decision-making and network field.Master controller generally needs The communications facility wanting high bandwidth collects the information of whole system, further needs exist for a degree of communication the highest, therefore when a fault Point out current, arise that stability problem.And, the topological structure of following electrical network and communication network is all variable, and this is just It is the lowest that the efficiency making centerized fusion becomes.Therefore, a kind of new algorithm accurately calculating network loss is studied significant.
Summary of the invention
The technical problem to be solved is under conditions of electromotor meets certain operation constraint, accurately calculates network loss and merit Rate deviation, in the case of reducing communications cost, solves the Economic Dispatch Problem in power system.
The present invention solves above-mentioned technical problem by the following technical solutions:
A kind of have the distributed automatic scheduling method of power system accurately calculating network loss ability, is calculated by distributed two-layer concordance Method, loss allocation is accurately given each electromotor by use electricity-tracing method and electrical dissection, it is achieved marginal cost is consistent, Concretely comprising the following steps of the method:
Step 1: input system parameter, limits P including peak powermax, minimum power limit Pmin, and to marginal cost and send out Electrical power gives initial value and carries out initialization operation;
Step 2: use distributed two-layer consistency algorithm, update incremental cost IC of each electromotori
Step 3: use electricity-tracing method, electrical dissection to try to achieve the network loss apportioned by each electromotor
Step 4: calculate the power deviation Δ P of each electromotori
Step 5: judge whether the generated output of electromotor meets peak power and limit PmaxP is limited with minimum powerminRequirement, If meeting the requirement that peak power limits and minimum power limits, then calculate electromotor output under this incremental cost PGi;If limited beyond peak power and the requirement of minimum power restriction, then the output of this electromotor being set as, it is maximum Output PGi,maxOr minimum output power PGi,min
Step 6: solve global power deviation delta PG, it is judged that its absolute value whether in the range of error of regulation in advance, if it is satisfied, Then terminate;Otherwise, then 2 are gone to step.
Further, a kind of distributed automatic scheduling method of power system with accurately calculating network loss ability of the present invention, described Distributed two-layer consistency algorithm in step 2, is that the sequencing according to computing arranges lower level and higher level, Qi Zhong In lower level, each node has its respective information on load and electromotor information, there is different power deviations, transports at lower level With average homogeneity algorithm, the power deviation of each node is made to reach a meansigma methods;Incremental cost is used unanimously to calculate in higher level Method, updates the information of each electromotor neighbours, makes the incremental cost of each electromotor reach unanimity.
Further, a kind of distributed automatic scheduling method of power system with accurately calculating network loss ability of the present invention, described Electricity-tracing method described in step 3, is to use Kirchhoff's law, obtains the node admittance side of each node in electric power networks Journey, then utilizes direction of energy method or method for estimating state, obtains the equivalent parallel admittance of each load bus, then obtains The load equivalent parallel impedance being made up of load equivalent parallel admittance, combines terminal busbar voltage, finally obtains each branch road electricity Stream.
Further, a kind of distributed automatic scheduling method of power system with accurately calculating network loss ability of the present invention, described Electrical dissection in step 3, is that every branch road obtains after subdivision some subpaths, subpath electric current and be equal to The originally electric current in path, uses Ohm's law, obtains the impedance of each single sub path.
Further, a kind of distributed automatic scheduling method of power system with accurately calculating network loss ability of the present invention, described In step 3, the computing formula of the network loss apportioned by each electromotor is:
p l o s s j = Σ i = 1 L { J B i j I j I B i [ r e a l ( Z B i ) ] } ,
Wherein, JBi jFor jth electromotor at the electric current distribution factor of i-th branch road, IjIt is the electric current of jth electromotor, IBi It is the electric current of i-th branch road, ZBiBeing the impedance of i-th branch road, L is circuitry number.
Further, a kind of distributed automatic scheduling method of power system with accurately calculating network loss ability of the present invention, described Power deviation Δ P in step 4iMore new regulation be:I=1 ..., n, wherein, wijIt is one Element in individual renewal matrix W, W=I-μ Lij, I is the unit matrix of a n × n, and μ is to update weight, LijIt is La Pu Element in the matrix L of Lars, Δ pi[k+1] is i-th+1 power deviation of node kth, Δ pj[k] is jth node kth time Power deviation.
The present invention uses above technical scheme compared with prior art, has following technical effect that
(1) the invention propose a kind of electricity-tracing method and electrical dissection to calculate network loss, compare other meter The method calculating network loss, result of calculation is more accurate, uses two-layer consistency algorithm so that system is no longer by single leader Impact, each node could act as leader, and the suitability is more extensive;
(2) present invention can solve to consider in electrical network network loss feelings by the way of distributed AC servo system in the case of reducing communications cost Economic Dispatch Problem under condition.
(3) present invention is more suitable for solving topologies change and adapting to the feature of plug and play.
(4) present invention has higher robustness and more preferable extensibility, and can better adapt to multinode situation.
Accompanying drawing explanation
Fig. 1 is the IEEE6 node standard power network of the present invention.
Fig. 2 is the communication topology figure of the present invention.
Fig. 3 is the electrical dissection schematic diagram of the present invention, and wherein (a) is the schematic diagram of original power transmission line, and (b) is subpath Schematic diagram.
Fig. 4 is the electrical dissection schematic diagram of the present invention, and wherein (a) is electric current and the schematic diagram of impedance, (b) of original power transmission line It is electric current and the schematic diagram of impedance of subpath after subdivision.
Fig. 5 is the sub-network schematic diagram after decomposing.Wherein (a) is the sub-network schematic diagram of the G1 after decomposing, after (b) is decomposition The sub-network schematic diagram of G4, (c) is the sub-network schematic diagram of the G6 after decomposing.
Fig. 6 is that tiny increment changes over curve chart.
Fig. 7 is that generator power changes over curve chart.
Fig. 8 is that electromotor general power changes over curve chart with total load.
Fig. 9 is the schematic flow sheet of the inventive method.
Detailed description of the invention
Embodiments of the present invention are described below in detail, and the example of described embodiment is shown in the drawings, the most from start to finish phase Same or similar label represents same or similar element or has the element of same or like function.Retouch below with reference to accompanying drawing The embodiment stated is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
As it is shown in figure 9, the present invention provides a kind of distributed automatic scheduling method of power system having and accurately calculating network loss ability, Idiographic flow is as follows:
First, the relation between element (bus and transmission line) and each element in power system of setting up with G is (between element Carry out communication for information by communications facility) model.Definition G=(v, ε, A), v={v1,v2,...,vnBRepresent vertex set, It is the set expression limit collection on different summit pair, A=[aij]∈Rn×nRepresent adjacency matrix, electric power unit during wherein n represents power system The number of part, R represents set of real numbers.Directed graph refers to that the limit of figure is directive.The bus of figure vertex representation power system, While the transmission line represented between bus, adjacency matrix represents the weight on limit.If bus i receives the information from bus j, say The bright weight that exists is aijLimit (vj,vi).In the presence of corresponding limit, the element a of adjacency matrixijFor on the occasion of, otherwise be negative.As Really bus i can receive the information from bus j, and bus j is thus referred to as the neighbours of bus i.NiRepresent the neighbours' of bus i Set, its radix isSize is defined as:
Position according to electromotor and load draws the communication topology figure of power system.The figure that the present invention uses is directed graph, wherein Including polygon and from ring.Definition adjacency matrix A={aijIt is:
a i j = 1 / d i ‾ , j ∈ N i 0 , j ∉ N i
1, the cost function of first definition electromotor i is:
Ci(PGi)=αiiPGiiP2 Gi (1)
Wherein PGiRepresent the output of i-th electromotor, Ci(PGi) represent that electromotor i is P at outputGiShi Suoxu's Cost, αi、βi、γiFor positive constant.
Economic Dispatch Problem refers to that electromotor, under conditions of meeting a series of operation constraint, makes the generating of whole Operation of Electric Systems The optimization problem of cost minimization, it may be assumed that
M i n Σ i ∈ S G C i ( P G i )
S . T . Σ i ∈ S G P G i - Σ j ∈ S D P D j - P l o s s = 0 - - - ( 2 )
PGi,min≤PGi≤PGi,max, i ∈ SG (3)
Wherein, SGRepresent electromotor set, SDRepresent collections of loads, PDjRepresent the output of load j, PlossRepresent electric power The loss power of system, PGi,minRepresent the minimum output power of i-th electromotor, PGi,maxRepresent that the maximum of i-th electromotor is defeated Go out power.Utilize classical method of Lagrange multipliers to solve, make X represent the Lagrange multiplier corresponding with equality constraint, do not examine When considering constraint (2) and (3), above-mentioned RegionAlgorithm for Equality Constrained Optimization can be converted into:
L = Σ i ∈ S G C i ( P G i ) - X ( Σ i ∈ S G P G i - Σ j ∈ S D P D j - P l o s s ) = 0 - - - ( 4 )
Respectively to variable PGiLocal derviation is asked just to obtain optimality condition with X, it may be assumed that
∂ L ∂ P G i = ∂ C i ∂ P G i - X ( 1 - ∂ p l o s s ∂ P G i ) = 0 ∂ L ∂ X = Σ i ∈ S G P G i - Σ j ∈ S D P D j - P l o s s = 0 - - - ( 5 )
The above formula i.e. equation of comptability, can obtain according to the equation of comptability:
X = ∂ C i ∂ P G i / ( 1 - ∂ p l o s s ∂ P G i ) - - - ( 6 )
WhereinIt is referred to as Incremental Transmission Loss, the micro-increasing to the output of i-th electromotor of the loss power of expression power system Rate.
OrderRepresent loss factor, then
Thus the output of i-th electromotor is:
P G i = X / PF i - β i 2 γ i - - - ( 7 )
2, electricity-tracing method, electrical dissection is utilized to try to achieve the network loss apportioned by every electromotor accurately:
If the bus admittance matrix of each node is YV=I in circuit, wherein, Y represents that node admittance, V represent node voltage, I represents node current, uses a ready-made direction of energy method or method for estimating state, and the equivalent parallel admittance of load bus is:
Yi=(pi-jQi)/|Vi|2 (8)
Wherein Pi,Qi,ViIt is respectively active power, reactive power and the voltage of load bus, increases right to Y matrix of these equatioies Angle element, obtains:
YGV=IG (9)
Here IGThe diagonal matrix being made up of the electric current of electromotor, IG=[I1,I2,I3,...,IM,...,0]T, I1,I2,I3,...,IMIt is respectively stream Cross electromotor 1,2 ..., the electric current of M, YGFor load equivalent parallel impedance.
For each branch road, the electric current flowing through them can be obtained I by terminal busbar voltageB=ZL -1SV。
Wherein IB=[IB1,IB2..., IBi,...,IBL]T,ZL -1Being the diagonal matrix of a L*L, S is a L*N connection matrix
Formula (9) is substituted into,
IB=ZL -1SYG -1IG (10)
Above formula is rewritten into:
I B 1 = J B 1 1 I 1 + J B 1 2 I 2 + .... + J B 1 M I M I B 2 = J B 2 1 I 1 + J B 2 2 I 2 + .... + J B 2 M I M . . . I B i = J B i 1 I 1 + J B i 2 I 2 + .... + J B i M I M . . . I B l = J B l 1 I 1 + J B l 2 I 2 + .... + J B l M I M - - - ( 11 )
Wherein JBi j=(Zki-Zli)/ZBiFor jth electromotor at the electric current distribution factor of i-th branch road, Zki、ZliIt is ZLIn Element, ZBiIt it is the impedance of i-th branch road.
Here, we define: Vk-Vl=I1Z1=I2Z2=...=IMZM
Being obtained subpath impedance by above formula is:
Z i = V k - V l I i - - - ( 12 )
Wherein, i=1,2 ..., M, Vk,VlFor initiating terminal voltage, IiFor electric current.
The impedance in the i-th single sub path of jth electromotor is:
Z B i j = I B i J B i j I j Z B i - - - ( 13 )
Wherein JBi j=(Zki-Zli)/ZBiFor electromotor at the electric current distribution factor of subcircuits, Zki、ZliIt is ZLIn element.
To sum up, the computing formula of available network loss is:
p l o s s j = Σ i = 1 L { J B i j I j I B i [ r e a l ( Z B i ) ] } - - - ( 14 )
3. the information of utilization two-layer concordance distributed algorithm more new neighbor:
If incremental cost IC of electromotor iiFor:
X = ∂ C i ∂ P G i / ( 1 - ∂ p l o s s ∂ P G i ) - - - ( 15 )
Incremental cost IC from electromotor iiMore new formula be:
X i [ k + 1 ] = Σ f = 1 n d i f X f [ k ] , i = 1 , 2... n - - - ( 16 )
Wherein difRepresent row stochastic matrix DnIn element.
Incremental cost IC of main generator iiMore new formula be:
X i [ k + 1 ] = Σ f = 1 n d i f X f [ k ] + ϵΔP G , i = 1 , 2... n - - - ( 17 )
Wherein difRepresent row stochastic matrix DnIn element, Δ PGRepresent the difference between total demand power and real output Value, it may be assumed thatI=1,2...n, wherein PDRepresenting total demand power, ε is convergence coefficient.
Thus can obtain, the output of i-th electromotor is constrained to:
X i = X i - l o w e r , P G i < P G i , m i n X i &lsqb; k + 1 &rsqb; = &Sigma; f = 1 n d i f X f &lsqb; k &rsqb; , P G i , m i n < P G i < P G i , m a x X i = X i - u p p e r , P G i > P G i , m a x - - - ( 18 )
Wherein Xi-lowerRepresent the minima of the incremental cost of electromotor i, Xi-upperRepresent the maximum of the incremental cost of electromotor i Value, PGi,minRepresent the minimum power of electromotor i output, PGi,maxRepresent the peak power of electromotor i output.
The power deviation of every electromotor is:
&Delta;p i &lsqb; k + 1 &rsqb; = &Sigma; i = 1 n w i j &Delta;p j &lsqb; k &rsqb; , i = 1 , ... , n , - - - ( 19 )
Wherein, wijIt is an element updated in matrix W, W=I-μ Lij, I is the unit matrix of a n × n, and μ is more New weight, LijIt is the element in Laplacian Matrix L, Δ pi[k+1] is i-th+1 power deviation of node kth, Δ pj[k] is Jth node kth time power deviation.
Below in conjunction with the accompanying drawings technical scheme is described in further detail.
The present invention is as a example by 6 bus-bar systems, including 3 electromotors and 3 loads, the most as shown in Figure 1.Its communication Topological diagram is as shown in Figure 2.
Step one: input system parameter, gives initial value to marginal cost and generated output and carries out initialization operation;
Wherein, the parameter of system is as shown in table 1.
Table 1:
Here, choosing total load is 210MW, and initial marginal cost is respectively 8.59 $/MW, 9.25 $/MW, 8.89 $/MW.
Step 2: use distributed two-layer consistency algorithm, update the incremental cost of each electromotor;
Here selecting G1 is leader, as follows from the renewal of electromotor:
X i &lsqb; k + 1 &rsqb; = &Sigma; f = 1 n d i f X f &lsqb; k &rsqb; , i = 1 , 2... n
I.e.
The renewal of main generator 1 is as follows:
X 1 &lsqb; k + 1 &rsqb; = &Sigma; f = 1 n d 1 f X f &lsqb; k &rsqb; + &epsiv;&Delta;P G
In formula
Step 3, uses electricity-tracing method, electrical dissection to try to achieve the network loss apportioned by every electromotor accurately;
Wherein, as shown in Table 2, wherein r is resistance to the line parameter circuit value of 6 bus-bar systems, and x is reactance, and b is susceptance.
Table two:
Branch road Beginning node End-node r/pu x/pu b/pu
1 2 0.08 0.36 0.01
1 4 0.12 0.52 0.00
2 3 0.02 0.12 0.02
2 4 0.09 0.40 0.01
3 6 0.07 0.30 0.00
4 5 0.03 0.22 0.01
5 6 0.28 0.64 0.02
Use electricity-tracing method, electrical dissection to be calculated the resistance value of subpath and final every electromotor network loss is divided Joining value, concrete exploded view is shown in that Fig. 3, Fig. 4, Fig. 5 are the sub-network schematic diagrams of G1, G4, the G6 after decomposing, and it calculates knot Fruit is as shown in table three, table four, table five:
Table three:
Table four:
Table five:
Step 4: update the power deviation Δ P of each electromotori
Use distributed consensus algorithm, more new regulation be:
&Delta;p i &lsqb; k + 1 &rsqb; = &Sigma; j = 1 n w i j &Delta;p j &lsqb; k &rsqb; , i = 1 , ... , n ,
That is:
Step 5: judge whether the generated output of electromotor reaches it and limit requirement, without reaching its limit value requirement, then counts Calculate electromotor output under this incremental cost;If it exceeds its limit value requirement, then the output of electromotor is set Maximum or minimum output power for it;
Constraints is as follows, after updating, carries out judging and carry out next step in order to lower formula and calculates:
X i = X i - l o w e r , P G i < P G i , m i n X i &lsqb; k + 1 &rsqb; = &Sigma; f = 1 n d i f X f &lsqb; k &rsqb; , P G i , m i n < P G i < P G i , m a x X i = X i - u p p e r , P G i > P G i , m a x
Step 6, solves global power deviation, it is judged that its absolute value whether in the range of error that it specifies, if it is satisfied, then Algorithm terminates;Otherwise, then two are gone to step.
CalculateJudge | Δ pG| whether in the range of error that it specifies, if it is satisfied, then terminate; Otherwise, then going to step two, repetitive cycling operates, until meeting condition, it is achieved consistent.
Based on to data, use the operation of said method step cycle, calculating final incremental cost concordance is 9.02 $/MW.
Time of running in simulation analysis is 83 seconds, and emulation uses MATLAB R2010a, and computer is Corei53.20Ghz, 4G RAM, simulation result is as shown in Fig. 6, Fig. 7, Fig. 8.

Claims (2)

1. one kind has the distributed automatic scheduling method of power system accurately calculating network loss ability, it is characterised in that by distribution Formula two-layer consistency algorithm, loss allocation is accurately given each electromotor by use electricity-tracing method and electrical dissection, real Existing marginal cost is consistent, concretely comprising the following steps of the method:
Step 1: input system parameter, limits P including peak powermax, minimum power limit Pmin, and to marginal cost and send out Electrical power gives initial value and carries out initialization operation;
Step 2: use distributed two-layer consistency algorithm, update incremental cost IC of each electromotori, particularly as follows: according to The sequencing of computing arranges lower level and higher level, wherein in lower level each node have its respective information on load and , there is different power deviations in electromotor information, uses average homogeneity algorithm at lower level, make the power deviation of each node Reach a meansigma methods;Use incremental cost unification algorism in higher level, update the information of each electromotor neighbours, make each The incremental cost of platform electromotor reaches unanimity;
Step 3: use electricity-tracing method, electrical dissection to try to achieve the network loss apportioned by each electromotorParticularly as follows: Use Kirchhoff's law, obtain the Nodal admittance equation of each node in electric power networks, then utilize direction of energy method or Method for estimating state, obtains the equivalent parallel admittance of each load bus, then obtains the load being made up of load equivalent parallel admittance Equivalent parallel impedance, combines terminal busbar voltage, finally obtains each branch current;Every branch road is obtained after subdivision Some subpaths, subpath electric current and equal to the electric current in original path, use Ohm's law, obtain the resistance of each single sub path Anti-, the computing formula of the network loss apportioned by each electromotor is:
p l o s s j = &Sigma; i = 1 L { J B i j I j I B i &lsqb; r e a l ( Z B i ) &rsqb; } ,
Wherein, JBi jFor jth electromotor at the electric current distribution factor of i-th branch road, IjIt is the electric current of jth electromotor, IBi It is the electric current of i-th branch road, ZBiBeing the impedance of i-th branch road, L is circuitry number;
Step 4: calculate the power deviation Δ P of each electromotori
Step 5: judge whether the generated output of electromotor meets peak power and limit PmaxP is limited with minimum powerminRequirement, If meeting the requirement that peak power limits and minimum power limits, then calculate electromotor output under this incremental cost PGi;If limited beyond peak power and the requirement of minimum power restriction, then the output of this electromotor being set as, it is maximum Output PGi,maxOr minimum output power PGi,min
Step 6: solve global power deviation delta PG, it is judged that its absolute value whether in the range of error of regulation in advance, if it is satisfied, Then terminate;Otherwise, then 2 are gone to step.
A kind of distributed automatic scheduling method of power system with accurately calculating network loss ability the most according to claim 1, It is characterized in that, power deviation Δ P in described step 4iMore new regulation be:
&Delta;p i &lsqb; k + 1 &rsqb; = &Sigma; i = 1 n w i j &Delta;p j &lsqb; k &rsqb; , i = 1 , ... , n
Wherein, wijIt is an element updated in matrix W, W=I-μ Lij, I is the unit matrix of a n × n, and μ is more New weight, LijIt is the element in Laplacian Matrix L, Δ pi[k+1] is i-th+1 power deviation of node kth, Δ pj[k] is Jth node kth time power deviation.
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