CN108985561A - A kind of active power distribution network isolated island division methods based on chance constraint - Google Patents
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Abstract
A kind of active power distribution network isolated island division methods based on chance constraint: according to selected distribution system, incoming line parameter, load level, network topology connection relationship, system operation voltage level and the limitation of branch active power, confidence parameter, controllable and uncontrollable distributed generation resource on-position, capacity, load prediction curve, system failure moment, reference voltage and reference power initial value；Uncontrollable distributed generation resource generated output is subjected to discretization, obtains the discrete probability distribution parameter of uncontrollable distributed generation resource generated output；Establish the active power distribution network isolated island partitioning model based on chance constraint；System load flow constraint, node voltage probability constraints and branch active power probability constraints are converted, MIXED INTEGER nonlinear model is obtained；MIXED INTEGER nonlinear model is solved using interior point method；Export solving result.The present invention can make the isolated island partition strategy for meeting different demands, make system safety operation while ensuring part important load reliable power supply.
Description
Technical field
The present invention relates to a kind of active power distribution network isolated island division methods.More particularly to a kind of based on the active of chance constraint
Power distribution network isolated island division methods.
Background technique
As the high proportion of distributed generation resource accesses extensively, the operation of distribution system and scheduling mode have occurred deep and hold
Long variation.Isolated operation is a kind of special method of operation of active distribution system, can under extreme fault condition by point
Cloth power supply is that the important load in system is powered, and effectively improves the power supply reliability and elasticity of distribution system.
However, operation characteristic is by environment after the uncontrollable distributed generation resource access active power distribution network such as a large amount of blower, photovoltaics
It is affected and there is apparent randomness and fluctuation, problems can be brought for the safe operation of power distribution network, such as node electricity
Press out-of-limit, branch current overload etc..During power distribution network isolated operation, contributes when uncontrollable distributed generation resource and differed with predicted value
When more, controlled distribution formula power supply is often difficult to ensure by the power regulation of itself in isolated island region since its capacity is limited
Power-balance is difficult to operate normally so as to cause the isolated island strategy pre-established, so that voltage out-of-limit, electric current mistake in power distribution network
Load problem is more prominent, seriously affects distribution system safety in operation and power supply reliability.Therefore, to contain uncontrollable distribution
The power distribution network of formula power supply carries out to fully consider the power output uncertain influence to isolated operation strategy when isolated island division.
Currently, existing meter and distributed generation resource are contributed, probabilistic isolated island division methods are broadly divided into robust optimization
Algorithm, two class of stochastic programming.Wherein, robust optimization algorithm replaces uncontrollable distributed generation resource generated output with uncertain set
Probability be definitely distributed, using the Optimal Operation Strategies under most severe scene as the operation reserve of system, when to guarantee system
When interior based model for load duration as much as possible is powered, obtained result is more conservative.Stochastic programming rule is mostly by uncontrollable distributed electrical
The uncertain information in source is described with the mode of scene probability distribution, when carrying out isolated island division by stochastic programming, is adopted mostly
With Chance-constrained Model, which allows to obtain isolated operation strategy and is unsatisfactory for constraint condition to a certain extent, but constrains item
The probability that part is set up is not less than a certain confidence level.However, the existing active power distribution network isolated island division side based on chance constraint
Method mostly uses greatly the two-phase algorithm of " heuristic/intelligent algorithm+verification ", and such method the number of iterations is more, calculating process is numerous
It is trivial and be difficult to find that globally optimal solution, there is certain limitation.
Therefore, it is badly in need of a kind of mathematic programming methods for capableing of direct solution, active matches to solve based on chance constraint
Power grid isolated island partitioning model is sufficiently coordinated system and is transported safely to make the isolated island partition strategy that can satisfy different demands
Capable confidence level and load restoration are horizontal, make system safety operation while ensuring part important load reliable power supply.
Summary of the invention
The technical problem to be solved by the invention is to provide it is a kind of can satisfy active power distribution network different demands based on machine
The active power distribution network isolated island division methods that can be constrained.
The technical scheme adopted by the invention is that: a kind of active power distribution network isolated island division methods based on chance constraint, packet
Include following steps:
1) according to selected distribution system, incoming line parameter, load level, network topology connection relationship, system operation
Voltage level and the limitation of branch active power, confidence parameter, controllable and uncontrollable distributed generation resource on-position, capacity, load
Prediction curve, system failure moment, reference voltage and reference power initial value；
2) uncontrollable distributed generation resource generated output is subjected to discretization, obtains uncontrollable distributed generation resource generated output
Discrete probability distribution parameter；
3) the active power distribution network isolated island partitioning model based on chance constraint is established, comprising: power distribution system in setting a period of time
The burden with power amount that system restores is up to objective function, considers radial constraint, system load flow constraint, network reconfiguration respectively about
Beam, node voltage probability constraints, branch active power probability constraints, uncontrollable distributed generation resource operation constraint and controlled distribution formula
Power supply operation constraint；
4) system load flow constraint, node voltage probability constraints and branch active power probability constraints are converted, is obtained
MIXED INTEGER nonlinear model；
5) the MIXED INTEGER nonlinear model that step 4) obtains is solved using interior point method；
6) export step 5) solving result, including meet any confidence level distribution system burden with power amount of recovery,
Block switch and interconnection switch state, each node restore load coefficient.
The method that uncontrollable distributed generation resource generated output described in step 2) carries out discretization is as follows:
In formula, f (x) is the probability density function of uncontrollable distributed generation resource generated output；X is uncontrollable distributed generation resource
Generated output；M is the discrete scene of uncontrollable distributed generation resource generated output；P (m) is uncontrollable distributed electrical under m scene
The generated output in source；F [P (m)] indicates that uncontrollable distributed generation resource generated output is the probability of P (m)；Q is discretization step-length；
ΩsFor the set of scene m.
The constraint of system load flow described in step 3) is as follows:
In formula, ΩbFor the set of branch；Pt,ji,m、Qt,ji,mRespectively t period, the wattful power flowed through on m scene branch ji
Rate and reactive power；Pt,i,m、Qt,i,mRespectively the sum of t period, the active power injected on m scenario node i and reactive power
The sum of；The active power and reactive power that load consumes respectively in t period node i；λiTo be born in node i
The recovery coefficient of lotus, λi∈ { 0,1 }, λi=1 indicates load restoration in node i, λiLoad does not restore in=0 expression node i；Respectively the t period, on m scenario node i the injection of controlled distribution formula power supply active power and reactive power；Respectively the t period, on m scenario node i uncontrollable distributed generation resource injection active power and reactive power；
ut,i,mFor voltage magnitude square on t period, m scenario node i；it,ij,mFor t period, m scene branch ij current amplitude square；Rij
For the resistance of branch ij, XijFor the reactance of branch ij.
Node voltage probability constraints described in step 3) are as follows:
In formula, Pr{ } indicates the probability that a certain event is set up；ε is confidence parameter；Respectively voltage amplitude
The bound of value；ut,i,mFor voltage magnitude square on t period, m scenario node i.
Branch active power probability constraints described in step 3) are as follows:
In formula, Pr{ } indicates the probability that a certain event is set up；ε is confidence parameter；Respectively branch has
The bound of function power；Pt,ij,mFor the active power flowed through on t period, m scene branch ij.
Conversion described in step 4) includes:
Introduce 0-1 variable zt,m, by system load flow constraint, node voltage probability constraints and branch active power probability constraints
Combine and be converted into MIXED INTEGER nonlinear model:
In formula, zt,mFor the binary variable of introducing, zt,m=0 indicates to be included in when solving optimal isolated operation strategy
Scene m, zt,m=1 expression is not counted when solving optimal isolated operation strategy and scene m；πt,mOccur for t period scene m general
Rate；M indicates a great constant；ΩbFor the set of branch；Pt,ji,m、Qt,ji,mRespectively t period, m scene branch ji are upper
The active power and reactive power crossed；Pt,i,m、Qt,i,mRespectively the sum of t period, the active power injected on m scenario node i with
And the sum of reactive power；The active power and reactive power that load consumes respectively in t period node i；λiFor
The recovery coefficient of load, λ in node ii∈ { 0,1 }, λi=1 indicates load restoration in node i, λi=0 indicates load in node i
Do not restore；Respectively t period, the active power of controlled distribution formula power supply injection and idle on m scenario node i
Power；Respectively t period, the active power of uncontrollable distributed generation resource injection and idle on m scenario node i
Power；uT, i, mFor voltage magnitude square on t period, m scenario node i；iT, iJ,mIt is flat for t period, m scene branch ij current amplitude
Side；RijFor the resistance of branch ij, XijFor the reactance of branch ij；ε is confidence parameter；Respectively voltage magnitude
Bound；The respectively bound of branch active power.
A kind of active power distribution network isolated island division methods based on chance constraint of the invention, it is uncontrollable based on solving to contain
The active power distribution network isolated island partition problem of distributed generation resource fully considers network topology constraint, system load flow constraint, node voltage
Probability constraints, branch active power probability constraints, uncontrollable distributed generation resource operation constraint and the operation of controlled distribution formula power supply are about
Beam establishes the active power distribution network isolated island partitioning model based on chance constraint, and mathematics essence is that mixed integer nonlinear programming is asked
Topic, is solved using interior point method, obtains meeting node voltage and the isolated island of branch active power probability confidence level divides plan
Slightly.The present invention can make the isolated island partition strategy for meeting different demands, sufficiently coordinate the confidence level of system safety operation
With load restoration level, make system safety operation while ensuring part important load reliable power supply.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the active power distribution network isolated island division methods based on chance constraint of the present invention；
Fig. 2 is improved 33 node example structure chart of IEEE；
Fig. 3 is load prediction curve；
Fig. 4 is the probability density function profiles figure of photovoltaic unit generation power at 9；
Fig. 5 is the discrete probabilistic probability distribution graph of photovoltaic unit generation power at 9；
Fig. 6 is the system jam at 9, the isolated island partition strategy schematic diagram of scene 1；
Fig. 7 is the system jam at 9, the isolated island partition strategy schematic diagram of scene 2；
Fig. 8 is the system jam at 9, the isolated island partition strategy schematic diagram of scene 3；
Fig. 9 is the system jam at 9, load restoration level and confidence level correlativity schematic diagram.
Specific embodiment
Below with reference to embodiment and attached drawing to a kind of active power distribution network isolated island division side based on chance constraint of the invention
Method is described in detail.
As shown in Figure 1, a kind of active power distribution network isolated island division methods based on chance constraint of the invention, including walk as follows
It is rapid:
1) according to selected distribution system, incoming line parameter, load level, network topology connection relationship, system operation
Voltage level and the limitation of branch active power, confidence parameter, controllable and uncontrollable distributed generation resource on-position, capacity, load
Prediction curve, system failure moment, reference voltage and reference power initial value；
2) uncontrollable distributed generation resource generated output is subjected to discretization, obtains uncontrollable distributed generation resource generated output
Discrete probability distribution parameter；The method that the uncontrollable distributed generation resource generated output carries out discretization is as follows:
In formula, f (x) is the probability density function of uncontrollable distributed generation resource generated output；X is uncontrollable distributed generation resource
Generated output；M is the discrete scene of uncontrollable distributed generation resource generated output；P (m) is uncontrollable distributed electrical under m scene
The generated output in source；F [P (m)] indicates that uncontrollable distributed generation resource generated output is the probability of P (m)；Q is discretization step-length；
ΩsFor the set of scene m.
3) the active power distribution network isolated island partitioning model based on chance constraint is established, comprising: power distribution system in setting a period of time
The burden with power amount that system restores is up to objective function, considers radial constraint, system load flow constraint, network reconfiguration respectively about
Beam, node voltage probability constraints, branch active power probability constraints, uncontrollable distributed generation resource operation constraint and controlled distribution formula
Power supply operation constraint；Wherein,
(1) distribution system service restoration burden with power amount is up to objective function and is expressed as in a period of time described in
In formula, ΩτFor the set of distribution system isolated operation time；ΩnFor the set of all nodes of distribution system；λiFor
The recovery coefficient of load, λ in node ii∈ { 0,1 }, λi=1 indicates load restoration in node i, λi=0 indicates load in node i
Do not restore；For the burden with power in t period node i.
(2) the radial constraint representation described in is
αij=βij+βji, ij ∈ Ωb (3)
αij∈ { 0,1 } (6)
0≤βij≤ 1,0≤βji≤1 (7)
In formula, ΩbIndicate the set of all branches of distribution system；ΩrWhen indicating distribution system isolated operation, isolated island is supported
The node set of voltage and frequency；αijIndicate branch ij upper switch cut-offs state, αij=1 indicates to close the switch, αij=0 table
Show that switch disconnects；βijIndicate the relationship of node i and node j, βij=1 expression node j is the father node of node i, otherwise βij=0.
(3) the system load flow constraint described in is as follows:
In formula, PT, ji, m、QT, ji, mRespectively t period, the active power and reactive power that flow through on m scene branch ji；
PT, i, m、QT, i, mRespectively the sum of t period, the active power injected on m scenario node i and reactive power；Point
Not Wei in t period node i load consumption active power and reactive power；Respectively t period, m scenario node
The active power and reactive power of the upper controlled distribution formula power supply injection of i；Respectively the t period, on m scenario node i
The active power and reactive power of uncontrollable distributed generation resource injection；uT, i, mFor t period, m scenario node i voltage magnitude square；
iT, ij, mFor t period, m scene branch ij current amplitude square；RijFor the resistance of branch ij, XijFor the reactance of branch ij.
(4) the network reconfiguration constraint representation described in is
-Mαij≤PT, ij, m≤Mαij (13)
-Mαij≤QT, ij, m≤Mαij (14)
0≤it,ji,m≤Mαij (15)
In formula, M indicates a great constant.
(5) the node voltage probability constraints described in are expressed as
In formula, Pr{ } indicates the probability that a certain event is set up；ε is confidence parameter；Respectively voltage magnitude
Bound.
(6) the branch active power probability constraints described in are expressed as
In formula,The respectively bound of branch active power.
(7) the controlled distribution formula power supply described in runs constraint representation
In formula,Indicate the capacity of controlled distribution formula power supply in node i；For the operation of distributed generation resource in node i
Minimum power factor.
(8) the uncontrollable distributed generation resource described in runs constraint representation
In formula,Indicate the capacity of uncontrollable distributed generation resource in node i.
4) system load flow constraint, node voltage probability constraints and branch active power probability constraints are converted, is obtained
MIXED INTEGER nonlinear model；The conversion includes:
Introduce 0-1 variable zt,m, by system load flow constraint, node voltage probability constraints and branch active power probability constraints
Combine and be converted into MIXED INTEGER nonlinear model:
In formula, zt,mFor the binary variable of introducing, zt,m=0 indicates to be included in when solving optimal isolated operation strategy
Scene m, zt,m=1 expression is not counted when solving optimal isolated operation strategy and scene m；πt,mOccur for t period scene m general
Rate；M indicates a great constant.
5) the MIXED INTEGER nonlinear model that step 4) obtains is solved using interior point method；
6) export step 5) solving result, including meet any confidence level distribution system burden with power amount of recovery,
Block switch and interconnection switch state, each node restore load coefficient.
For the embodiment of the present invention, the impedance value of circuit element, load cell first in input 33 node system of IEEE
Active power, reactive power, network topology connection relationship, confidence parameter, load prediction curve, distributed electrical source dates, calculate
Example structure is as shown in Fig. 2, detail parameters are shown in Table 1, table 2, table 3；Assuming that permanent three-phase occurs at the morning 9 between branch 1-2
Failure, Fault Isolation time are 1 hour；The reference voltage of system is set as 12.66kV, reference power 1MVA；It should for verifying
The validity of method is analyzed using following 3 kinds of scenes.
Scene 1: confidence level is 100% corresponding isolated island partition strategy；
Scene 2: confidence level is 90% corresponding isolated island partition strategy；
Scene 3: confidence level is 80% corresponding isolated island partition strategy；
It is assumed that the uncontrollable distributed generation resource of distribution system access is photovoltaic unit, and photovoltaic unit generation power
Probability density function is as shown in Figure 4 at the morning 9.Using the discretization method mentioned of the present invention by photovoltaic unit generation power into
Row is discrete, and obtained generated output discrete probability distribution is as shown in Figure 5.It is solved using the method for the present invention, under 3 kinds of scenes
Active power distribution network isolated island partition strategy is as shown in Fig. 6,7,8, wherein solid node indicates that the node load restores, hollow node
Indicate that the node load does not restore；Load restoration amount is from the correlation of confidence level as shown in figure 9, the load of different confidence levels
See Table 4 for details for recovery situation；In order to verify the invention validity, Monte Carlo test is carried out to the isolated island partition strategy of 3 kinds of scenes,
It the results are shown in Table 5.
Executing the computer hardware environment that optimization calculates is IntelICoreIi5-3470CPU, dominant frequency 3.20GHz, interior
Save as 4GB；Software environment is 7 operating system of Windows.
The present invention can be set up according to node voltage and branch active power constraint condition it can be seen from Fig. 6,7,8
Probability confidence level formulates the isolated island partition strategy of corresponding active power distribution network.When confidence level difference, the isolated island of power distribution network
Partition strategy is different, and load restoration amount is also different, the particularly relevant relationship of load restoration level and confidence level as shown in figure 9,
Specific load restoration situation is shown in Table 3.As can be seen that the burden with power of distribution system restores horizontal with the raising of confidence level
It gradually decreases, this is because confidence level is higher, the applicable scene of isolated operation strategy is more, except meeting photovoltaic unit generation function
Outside the higher scene of rate, isolated operation strategy also must satisfy the lower scene of photovoltaic unit generation power, so as to cause load
Amount of recovery decreases.In order to verify effectiveness of the invention, Monte Carlo test is carried out to 3 kinds of scenes, the results are shown in Table 5.By
Table 5 is it is found that the isolated island fortune that the active power distribution network isolated island division methods proposed by the present invention based on chance constraint can guarantee
Row strategy is run with the probabilistic safety for being higher than a certain confidence level.Method of the invention is capable of effective coordination system safety operation
Relationship between confidence level and load restoration level, and formulates corresponding isolated island partition strategy according to different needs, to matching
Electrical system safety operation is of great significance with reliable power supply.
1 IEEE33 node example load on-position of table and power
2 IEEE33 node example line parameter circuit value of table
3 distributed generation resource configuring condition of table
The load restoration situation of the different confidence levels of table 4
5 Monte Carlo test result of table
Claims (6)
1. a kind of active power distribution network isolated island division methods based on chance constraint, which comprises the steps of:
1) according to selected distribution system, incoming line parameter, load level, network topology connection relationship, system working voltage
The limitation of horizontal and branch active power, confidence parameter, controllable and uncontrollable distributed generation resource on-position, capacity, load prediction
Curve, system failure moment, reference voltage and reference power initial value；
2) uncontrollable distributed generation resource generated output is subjected to discretization, obtains the discrete of uncontrollable distributed generation resource generated output
Probability distribution parameters；
3) the active power distribution network isolated island partitioning model based on chance constraint is established, comprising: distribution system is extensive in setting a period of time
Multiple burden with power amount is up to objective function, considers radial constraint, system load flow constraint, network reconfiguration constraint, section respectively
Point voltage probability constraints, branch active power probability constraints, uncontrollable distributed generation resource operation constraint and controlled distribution formula power supply
Operation constraint；
4) system load flow constraint, node voltage probability constraints and branch active power probability constraints are converted, is mixed
Integral nonlinear model；
5) the MIXED INTEGER nonlinear model that step 4) obtains is solved using interior point method；
6) solving result for exporting step 5), distribution system burden with power amount of recovery, segmentation including meeting any confidence level
Switch and interconnection switch state, each node restore load coefficient.
2. a kind of active power distribution network isolated island division methods based on chance constraint according to claim 1, which is characterized in that
The method that uncontrollable distributed generation resource generated output described in step 2) carries out discretization is as follows:
In formula, f (x) is the probability density function of uncontrollable distributed generation resource generated output；X is the hair of uncontrollable distributed generation resource
Electrical power；M is the discrete scene of uncontrollable distributed generation resource generated output；P (m) is uncontrollable distributed generation resource under m scene
Generated output；F [P (m)] indicates that uncontrollable distributed generation resource generated output is the probability of P (m)；Q is discretization step-length；ΩsFor
The set of scene m.
3. a kind of active power distribution network isolated island division methods based on chance constraint according to claim 1, which is characterized in that
The constraint of system load flow described in step 3) is as follows:
In formula, ΩbFor the set of branch；Pt,ji,m、Qt,ji,mRespectively the t period, the active power that flows through on m scene branch ji and
Reactive power；Pt,i,m、Qt,i,mRespectively the sum of t period, the active power injected on m scenario node i and reactive power it
With；The active power and reactive power that load consumes respectively in t period node i；λiFor load in node i
Recovery coefficient, λi∈ { 0,1 }, λi=1 indicates load restoration in node i, λiLoad does not restore in=0 expression node i；Respectively the t period, on m scenario node i the injection of controlled distribution formula power supply active power and reactive power；Respectively the t period, on m scenario node i uncontrollable distributed generation resource injection active power and reactive power；
ut,i,mFor voltage magnitude square on t period, m scenario node i；it,ij,mFor t period, m scene branch ij current amplitude square；Rij
For the resistance of branch ij, XijFor the reactance of branch ij.
4. a kind of active power distribution network isolated island division methods based on chance constraint according to claim 1, which is characterized in that
Node voltage probability constraints described in step 3) are as follows:
In formula, Pr{ } indicates the probability that a certain event is set up；ε is confidence parameter；Respectively voltage magnitude is upper
Lower limit；ut,i,mFor voltage magnitude square on t period, m scenario node i.
5. a kind of active power distribution network isolated island division methods based on chance constraint according to claim 1, which is characterized in that
Branch active power probability constraints described in step 3) are as follows:
In formula, Pr{ } indicates the probability that a certain event is set up；ε is confidence parameter；Respectively branch wattful power
The bound of rate；Pt,ij,mFor the active power flowed through on t period, m scene branch ij.
6. a kind of active power distribution network isolated island division methods based on chance constraint according to claim 1, which is characterized in that
Conversion described in step 4) includes:
Introduce 0-1 variable zt,m, system load flow constraint, node voltage probability constraints and branch active power probability constraints are combined
It is converted into MIXED INTEGER nonlinear model:
In formula, zt,mFor the binary variable of introducing, zt,m=0 indicates to be included in scene when solving optimal isolated operation strategy
M, zt,m=1 expression is not counted when solving optimal isolated operation strategy and scene m；πt,mThe probability occurred for t period scene m；M
Indicate a great constant；ΩbFor the set of branch；Pt,ji,m、Qt,ji,mRespectively the t period, flow through on m scene branch ji
Active power and reactive power；Pt,i,m、Qt,i,mRespectively the sum of t period, the active power injected on m scenario node i and nothing
The sum of function power；The active power and reactive power that load consumes respectively in t period node i；λiFor section
The recovery coefficient of load, λ on point ii∈ { 0,1 }, λi=1 indicates load restoration in node i, λi=0 indicates that load is not in node i
Restore；Respectively t period, the active power of controlled distribution formula power supply injection and idle function on m scenario node i
Rate；Respectively t period, the active power of uncontrollable distributed generation resource injection and idle function on m scenario node i
Rate；ut,i,mFor voltage magnitude square on t period, m scenario node i；it,ij,mFor t period, m scene branch ij current amplitude square；
RijFor the resistance of branch ij, XijFor the reactance of branch ij；ε is confidence parameter；Respectively voltage magnitude is upper and lower
Limit； The respectively bound of branch active power.
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