CN108173265A - A kind of power distribution network network reconstruction method based on linearisation trend - Google Patents
A kind of power distribution network network reconstruction method based on linearisation trend 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
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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
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The present invention proposes a kind of power distribution network network reconstruction method based on linearisation trend, belongs to technical field of power system operation control.This method initially sets up the power distribution network network reconfiguration model being made of object function and constraints；Object function and constraints are converted respectively, master mould is converted into a MINLP model model；To the model solution after conversion, each branch open and-shut mode variable is obtained, and respective switch action is carried out according to solving result and realizes network reconfiguration.Calculating speed of the present invention is fast, and convergence is good, is suitably applied among the scenes such as the real-time network reconstruct of power distribution network.
Description
Technical field
The present invention relates to a kind of power distribution network network reconstruction methods based on linearisation trend, belong to Operation of Electric Systems control
Technical field.
Background technology
Power distribution network is the important component of electric system, and compared with the power transmission network of loop-net operation, although power distribution network has ring
Road interconnection, but interconnection is typically in off-state at runtime, and network architecture is radial.Therefore in power distribution network
In, the variation of network structure is to carry out basis and the important means of various power distribution network applications.
The network reconfiguration of power distribution network is that adjustment control network structure all kinds of is matched to optimize including loss minimization, load balancing etc.
Operation of power networks refers to calibration method, it realizes specific purpose by the opening and closing of branch in network and the variation of network structure.
The network reconfiguration model of power distribution network belongs to the nonlinear programming problem of MIXED INTEGER, all possible network structure with
The exponential growth of branch number can be cut-off by whole network, belong to np hard problem.Therefore it needs to realize distribution by approximate model
The Efficient Solution of net network reconfiguration.
Currently used power distribution network network reconstruction method has the heuritic approaches such as genetic algorithm, all possible by searching for
Reconfiguration scheme obtains feasible solution, disadvantage is that being difficult to obtain optimal solution, and when operating conditions change, generally requires to adjust
Whole algorithm parameter to adapt to new situation again.
Invention content
The purpose of the present invention is the shortcomings to overcome prior art, it is proposed that a kind of distribution based on linearisation trend
Net network reconstruction method.This method is as a reference point by the flow state of current power grid, to the nonlinear terms in power flow equation into
Row is approximate, obtains linear Three-phase Power Flow model, network reconfiguration side is quickly obtained by solving MINLP model problem
Case.Calculating speed of the present invention is fast, and convergence is good, is suitably applied among the scenes such as the real-time network reconstruct of power distribution network.
A kind of power distribution network network reconstruction method based on linearisation trend proposed by the present invention, which is characterized in that this method
Include the following steps：
(1) power distribution network network reconfiguration model is established, which is made of object function and constraints；Specific steps are such as
Under：
(1-1) determines the object function of power distribution network network reconfiguration model；
For the target of power distribution network network reconfiguration to minimize via net loss, expression formula is as follows：
In above formula, IijFor the electric current of branch ij, rijFor branch ij resistance；
(1-2) determines the constraints of power distribution network network reconfiguration model, specific as follows：
The radial operation constraint of (1-2-1) power distribution network, expression formula are as follows：
In above formula, xijFor branch ij open and-shut mode variables arbitrary in power distribution network, 0 representative is cut-off, and 1 represents closure；NnodeIt is
The number of all nodes, N in systemrootIt is root node number in system；
(1-2-2) power distribution network node power Constraints of Equilibrium, expression formula are as follows：
In above formula, first equation represents the balance of the active power of node k, and second equation represents the idle of node k
The balance of power；pgk、pkmIt is the active power of branch gk and branch km respectively, qgk、qkmIt is the nothing of branch gk and branch km respectively
Work(power,It is the burden with power of node k,It is the load or burden without work of node k；Wherein k is a node of arbitrary selection, and g is
Node k upstream nodes are numbered, and m is node k downstream nodes number；
(1-2-3) branch power constrains, and expression formula is as follows：
In above formula, pij,max,qij,maxRespectively the active power upper limit of branch ij and the reactive power upper limit；
(1-2-4) branch voltage equation constrains, and expression formula is as follows：
In above formula,Represent that point removes, v, I and s are three-dimensional column vector forms, represent voltage, the electric current of three-phase respectively
And power, zgkIt is the three-phase impedance matrix of branch gk, is 3 × 3 symmetrical complex matrix, * represents the conjugation of plural number, vkAnd vgRespectively
Represent the voltage of node k and node g, igkRepresent the electric current of branch gk, sgkRepresent the power of branch gk；
(1-2-5) node voltage bound constrains, and expression formula is as follows：
vk,min≤|vk|≤vk,max
In above formula, vk,min,vk,maxThe respectively lower voltage limit and the upper limit of node k；
(2) model established to step (1) converts；It is as follows：
(2-1) converts the object function of power distribution network network reconfiguration model；
It is approximately the quadratic sum of branch active power and reactive power by branch current square, then object function is converted into：
(2-2) selectes reference state, and the constraint of branch voltage equation is linearized；
By branch voltage equation both sides take conjugation and with former constraint expression formula dot product, obtain：
In above formula, | vg|2, | vk|2Square of the voltage magnitude of node g and node k is represented respectively；
Selected reference state represents the value of reference state with subscript 0, whereinThe voltage of node g reference states is represented,WithThe active power of branch gk reference states and the reactive power of reference state are represented respectively；
Quadratic term progress Taylor expansion is obtained：
Wherein, RgkAnd XgkIt is 3 × 3 matrix,It is 3 × 1 vector, value is shown below, and diag is represented will be to
Amount is converted into diagonal matrix：
In above formula,WithIt is impedance parameter, expression formula is as follows：
(2-3) decouples integer variable and continuous variable；
The constraint of power distribution network node power Constraints of Equilibrium is rewritten, expression formula is as follows：
Branch power constraint is rewritten, expression formula is as follows：
For the branch voltage equation for the linearisation that step (2-2) obtains, relaxed, be rewritten as using large M：
In above formula, M is positive number；
(3) model after step (2) conversion is solved；
After the conversion of step (2), the object function expression formula of model is as follows：
Constraints is as follows：
Model after conversion is a MINLP model model, to the model solution, obtains each branch opening and closing
State variable xij, 0, which represents branch ij, cut-offs, and 1 represents branch ij closures, and carry out respective switch action according to solving result and realize
Network reconfiguration.
The features of the present invention and advantageous effect are：
This method is by establishing power distribution network network reconfiguration model, by branch voltage equation nonlinear in model in reference point
Single order expansion linearisation is carried out at power, while integer variable and continuous variable are decoupled, the mixing for being difficult to solve is whole
Number nonlinear programming problem is converted into MINLP model problem solving.Therefore, which calculates
Speed is fast, and convergence is good, while can guarantee the optimality of result compared to heuritic approach, is suitably applied the Real-time Network of power distribution network
Among the scenes such as network reconstruct.
Description of the drawings
Fig. 1 is the overall flow block diagram of the method for the present invention.
Specific embodiment
A kind of power distribution network network reconstruction method based on linearisation trend proposed by the present invention, below in conjunction with the accompanying drawings and specifically
Embodiment is further described as follows.
A kind of power distribution network network reconstruction method based on linearisation trend proposed by the present invention, for the radial fortune of power distribution network
The network characteristic of row and three-phase imbalance, overall flow is as shown in Figure 1, include the following steps：
(1) power distribution network network reconfiguration model is established, which is made of object function and constraints；Specific steps are such as
Under：
(1-1) determines the object function of power distribution network network reconfiguration model；
The target of power distribution network network reconfiguration is typically chosen in minimum via net loss, and model objective function expression formula is as follows：
In above formula, IijFor the electric current of branch ij, rijFor branch ij resistance；
(1-2) determines the constraints of power distribution network network reconfiguration model, specific as follows：
The radial operation constraint of (1-2-1) power distribution network, expression formula are as follows：
In above formula, xijFor branch ij open and-shut mode variables arbitrary in power distribution network, 0 representative is cut-off, and 1 represents closure；NnodeIt is
The number of all nodes, N in systemrootIt is root node in system (feeder line) number.
(1-2-2) power distribution network node power Constraints of Equilibrium, expression formula are as follows：
In above formula, first equation represents the balance of the active power of node k, and second equation represents the idle of node k
The balance of power；pgkAnd pkmIt is the active power of branch gk and branch km respectively, qgkAnd qkmIt is branch gk and branch km respectively
Reactive power,It is the burden with power of node k,It is the load or burden without work of node k；Wherein k is one arbitrarily chosen in power distribution network
A node, g are node k upstream nodes numbers, and m is node k downstream nodes number
(1-2-3) branch power constrains, and expression formula is as follows：
In above formula, pij,max,qij,maxRespectively the active power upper limit of branch node k and the reactive power upper limit；
(1-2-4) branch voltage equation constrains, and expression formula is as follows：
In above formula,Represent that point removes, v, I and s are three-dimensional column vector forms, represent the voltage of three-phase, electric current respectively
And power, zgkIt is the three-phase impedance matrix of branch gk, is 3 × 3 symmetrical complex matrix, the headend node that subscript g represents branch is compiled
Number, subscript k represents the endpoint node number of branch, and * represents the conjugation of plural number, vkAnd vgThe electricity of node k and node g is represented respectively
Pressure, igkRepresent the electric current of branch gk, sgkRepresent the power of branch gk.
(1-2-5) node voltage bound constrains, and expression formula is as follows：
vk,min≤|vk|≤vk,max
In above formula, vk,min,vk,maxThe respectively lower voltage limit and the upper limit of node k.
(2) model established to step (1) converts；It is as follows：
(2-1) converts the object function of power distribution network network reconfiguration model；
It is approximately that branch is active by branch current square since node voltage perunit value each in power distribution network is approximately 1
The quadratic sum of power and reactive power, i.e. object function are converted into：
(2-2) selectes reference state, and the constraint of branch voltage equation is linearized；
By branch voltage equation both sides take conjugation and with former constraint expression formula dot product, obtain：
In above formula, | vg|2, | vk|2Square of the voltage magnitude of node g and node k is represented respectively.
In order to carry out linearization approximate to branch voltage equation, need to select a reference state, in actual operation may be used
Using by the current state of electric system as the value that reference state with reference to state, is represented with subscript 0, including：Represent node g ginsengs
The voltage value of state is examined,The active power of branch gk reference states and the reactive power of reference state are represented respectively
Quadratic term progress Taylor expansion is obtained：
Wherein, RgkAnd XgkIt is 3 × 3 matrix,It is 3 × 1 vector, value is shown below, and diag is represented will be to
Amount is converted into diagonal matrix：
In above formula,WithIt is impedance parameter, expression formula is as follows：
(2-3) decouples integer variable and continuous variable；
There is integer variable x in power distribution network node power Constraints of Equilibriumgk,xkmWith the continuous variable p of powergk,pkm,
qgk,qkmThe form of multiplication, this non-linear form of different variable products increase the solution difficulty of Optimized model.Therefore it is right
The constraint of node power Constraints of Equilibrium is rewritten, and expression formula is as follows：
Branch power constraint is rewritten, expression formula is as follows：
For the branch voltage equation of the linearisation in (2-2), when circuit i-j is disconnected, the disconnected branches both end voltage
Should there be direct relation, therefore be relaxed using large M, is rewritten as：
M represents sufficiently large positive number, and size should be at 100 times or more of normal voltage amplitude, if so branch g-k breaks
Open (xijFor 0) then Mij100 times or more for normal voltage amplitude so that | vg|2-|vk|2It is limited in normal voltage amplitude
Between 100 times and hundred times of the negative one of normal voltage amplitude, this constraint can always meet, and be equivalent to the section at disconnected branches both ends
There is no any direct limitation between point voltage.If branch gk is closed (xgkFor 1) then constraints above is equivalent to the branch linearized
Voltage equation.
(3) model after step (2) conversion is solved；
After the conversion of step (2), the object function expression formula of model is as follows：
Constraints is as follows：
Model after conversion is a MINLP model model, can be solved by a variety of business such as Gurobi, Cplex
Device utilizes branch and bound method Efficient Solution, solving the result is that each branch open and-shut mode variable xij, 0 represents branch i-j
It cut-offs, 1 represents branch ij closures, and respective switch action can be carried out according to solving result and realizes network reconfiguration.
Claims (1)
1. a kind of power distribution network network reconstruction method based on linearisation trend, which is characterized in that this method includes the following steps：
(1) power distribution network network reconfiguration model is established, which is made of object function and constraints；It is as follows：
(1-1) determines the object function of power distribution network network reconfiguration model；
For the target of power distribution network network reconfiguration to minimize via net loss, expression formula is as follows：
In above formula, IijFor the electric current of branch ij, rijFor branch ij resistance；
(1-2) determines the constraints of power distribution network network reconfiguration model, specific as follows：
The radial operation constraint of (1-2-1) power distribution network, expression formula are as follows：
In above formula, xijFor branch ij open and-shut mode variables arbitrary in power distribution network, 0 representative is cut-off, and 1 represents closure；NnodeIt is system
In all nodes number, NrootIt is root node number in system；
(1-2-2) power distribution network node power Constraints of Equilibrium, expression formula are as follows：
In above formula, first equation represents the balance of the active power of node k, and second equation represents the reactive power of node k
Balance；pgk、pkmIt is the active power of branch gk and branch km respectively, qgk、qkmIt is the idle work(of branch gk and branch km respectively
Rate,It is the burden with power of node k,It is the load or burden without work of node k；Wherein k is a node of arbitrary selection, and g is node k
Upstream node is numbered, and m is node k downstream nodes number；
(1-2-3) branch power constrains, and expression formula is as follows：
In above formula,pij,max,qij,maxRespectively the active power upper limit of branch ij and the reactive power upper limit；
(1-2-4) branch voltage equation constrains, and expression formula is as follows：
In above formula,Represent that point removes, v, I and s are three-dimensional column vector forms, represent the voltage, electric current and work(of three-phase respectively
Rate, zgkIt is the three-phase impedance matrix of branch gk, is 3 × 3 symmetrical complex matrix, * represents the conjugation of plural number, vkAnd vgIt represents respectively
The voltage of node k and node g, igkRepresent the electric current of branch gk, sgkRepresent the power of branch gk；
(1-2-5) node voltage bound constrains, and expression formula is as follows：
vk,min≤|vk|≤vk,max
In above formula, vk,min,vk,maxThe respectively lower voltage limit and the upper limit of node k；
(2) model established to step (1) converts；It is as follows：
(2-1) converts the object function of power distribution network network reconfiguration model；
It is approximately the quadratic sum of branch active power and reactive power by branch current square, then object function is converted into：
(2-2) selectes reference state, and the constraint of branch voltage equation is linearized；
By branch voltage equation both sides take conjugation and with former constraint expression formula dot product, obtain：
In above formula, | vg|2, | vk|2Square of the voltage magnitude of node g and node k is represented respectively；
Selected reference state represents the value of reference state with subscript 0, whereinThe voltage of node g reference states is represented,WithThe active power of branch gk reference states and the reactive power of reference state are represented respectively；
Quadratic term progress Taylor expansion is obtained：
Wherein, RgkAnd XgkIt is 3 × 3 matrix,It is 3 × 1 vector, value is shown below, and diag represents to turn vector
Turn to diagonal matrix：
In above formula,WithIt is impedance parameter, expression formula is as follows：
(2-3) decouples integer variable and continuous variable；
The constraint of power distribution network node power Constraints of Equilibrium is rewritten, expression formula is as follows：
Branch power constraint is rewritten, expression formula is as follows：
For the branch voltage equation for the linearisation that step (2-2) obtains, relaxed, be rewritten as using large M：
In above formula, M is positive number；
(3) model after step (2) conversion is solved；
After the conversion of step (2), the object function expression formula of model is as follows：
Constraints is as follows：
Model after conversion is a MINLP model model, to the model solution, obtains each branch open and-shut mode
Variable xij, 0, which represents branch ij, cut-offs, and 1 represents branch ij closures, and carry out respective switch action according to solving result and realize network
Reconstruct.
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| CN109256772A (en) * | 2018-10-16 | 2019-01-22 | 清华大学 | A kind of optimal convex optimization method cut-off of electric system power transmission network |
| CN109473980A (en) * | 2018-11-30 | 2019-03-15 | 中国电力科学研究院有限公司 | A kind of reconstructing method and system of power distribution network |
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| CN111130118A (en) * | 2020-01-09 | 2020-05-08 | 清华大学 | Optimal power flow calculation method of power system based on piecewise linearization |
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| CN113364054A (en) * | 2021-05-17 | 2021-09-07 | 国家电网有限公司 | Power distribution network interval network reconstruction model optimization method based on second-order cone relaxation method |
| CN113949063A (en) * | 2021-10-25 | 2022-01-18 | 国网天津市电力公司电力科学研究院 | Fault isolation and recovery reconstruction method for power distribution network |
| CN114156867A (en) * | 2021-11-11 | 2022-03-08 | 国网北京市电力公司 | Power distribution network interval network reconstruction model optimization method and device |
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| CN109713694A (en) * | 2019-01-25 | 2019-05-03 | 南方电网科学研究院有限责任公司 | Network dynamic reconstruction method for three-phase asymmetric power distribution network |
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| CN113364054A (en) * | 2021-05-17 | 2021-09-07 | 国家电网有限公司 | Power distribution network interval network reconstruction model optimization method based on second-order cone relaxation method |
| CN113364054B (en) * | 2021-05-17 | 2024-04-30 | 国家电网有限公司 | Power distribution network interval network reconstruction model optimization method based on second order cone relaxation method |
| CN113949063A (en) * | 2021-10-25 | 2022-01-18 | 国网天津市电力公司电力科学研究院 | Fault isolation and recovery reconstruction method for power distribution network |
| CN113949063B (en) * | 2021-10-25 | 2024-08-27 | 国网天津市电力公司电力科学研究院 | Fault isolation and recovery reconstruction method for power distribution network |
| CN114156867A (en) * | 2021-11-11 | 2022-03-08 | 国网北京市电力公司 | Power distribution network interval network reconstruction model optimization method and device |
| CN114156867B (en) * | 2021-11-11 | 2024-04-09 | 国网北京市电力公司 | Optimization method and device for power distribution network interval network reconstruction model |
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