CN109861232A - A kind of power distribution network dynamic restructuring decreasing loss method based on second order cone relaxation method - Google Patents
A kind of power distribution network dynamic restructuring decreasing loss method based on second order cone relaxation method Download PDFInfo
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Abstract
The present invention relates to Operation Technique of Electric Systems, more particularly to a kind of power distribution network dynamic restructuring decreasing loss method based on second order cone relaxation method, this method considers the part throttle characteristics in different function region in power distribution network, to reduce network loss as target, establish power distribution network Dynamic Reconfiguration Model of Multi, and convex optimization form is converted for power flow equation by second order cone relaxation, quickly acquire globally optimal solution, change to lead to too small amount of switch, the network loss of reduction power distribution network that can be very considerable and the quality of voltage that can be improved power distribution network.This method is also overcomed since there is spatial and temporal distributions differences for load in power distribution network operational process, may result in the problems such as trend is unevenly distributed weighing apparatus, node voltage collapses, network loss is excessively high.
Description
Technical field
The invention belongs to Operation Technique of Electric Systems field more particularly to a kind of power distribution networks based on second order cone relaxation method
Dynamic restructuring decreasing loss method.
Background technique
Line loss per unit is to reflect an important indicator of power distribution network power supply economics, in the operational process of power grid enterprises, line
Path loss consumption accounts for operating cost a part.With the continuous propulsion of new round power system reform, power grid becomes strong Controlling line loss
The important means of enterprise getting profit.Since power distribution network generallys use closed loop design, the mode of open loop operation, have in power distribution network a large amount of
Normally closed switch and a small amount of interconnection switch, the grid structure of power distribution network is fixed under normal conditions.However due in power distribution network
Load have space and time difference characteristic, if the network topology of power distribution network remain unchanged will will lead to different periods trend distribution
Unevenly, lead to that the network loss of power distribution network is excessively high, part of nodes voltage collapse is serious.With the development of smart grid, in power distribution network
Switch can be controlled by power electronic equipment, also known as flexible switch, therefore pass through the dynamic restructuring side of research power distribution network
Method is of great significance to reduction line loss, economy operation of power grid.
The dynamic restructuring of power distribution network, which refers to, considers time and the spatially change procedure of trend, puts Mobile state by split
The Nonlinear Dynamic combinatorial optimization problem of opening and closing operations realization power distribution network the safe and economic operation.It is ground at present in power distribution network dynamic restructuring
Study carefully that field is mainly based upon traditional optimization and intelligent optimization algorithm is solved, can only obtain approximate suboptimal solution and nothing
Method theoretically proves that solution obtained is globally optimal solution, therefore carries out dynamic restructuring reduction route using convex optimization method and damage
Consumption still has the space of promotion.
Summary of the invention
Lead to too small amount of switch the object of the present invention is to provide one kind to change, the network loss for reducing power distribution network improves power distribution network
The method of quality of voltage.
To achieve the above object, the technical solution adopted by the present invention is that: a kind of power distribution network based on second order cone relaxation method
Dynamic restructuring decreasing loss method, comprising the following steps:
Step 1, the mathematical model of power distribution network reconfiguration；
Step 1.1, objective function:
In formula: T indicates the scheduling instance in 24 hours；The load bus quantity of N expression power distribution network；GijIndicate branch ij's
Conductance；Vi,tIndicate node i in the voltage of t period；θij,tIndicate that branch ij is poor in the generator rotor angle of t period, C (i) is indicated and node j
The node being connected；αij,tIndicate connected state of the branch ij in the t period, αij,t=1 indicates branch ij connection, αij,t=0 indicates
Branch ij is disconnected；Δ t indicates a scheduling slot；
Step 1.2, constraint condition:
Following constraint condition need to be met when power distribution network reconfiguration:
I, node active balance constrains
In formula:Indicate node i in the active size of load of t moment；
II, the constraint of node reactive balance
In formula:Indicate node i in the reactive load size of t moment；
III, node voltage bound
Vimin≤Vi,t≤Vimax (4)
In formula: ViminWith VimaxRespectively indicate the voltage magnitude bound of node i；
The radial topological tree constraint of IV, power distribution network
In formula: β indicates the hierarchical relationship between node i and node j, βij=1 illustrates that i is the father node of j, βij=0 explanation
I is not the father node of j, β0j=0 indicates that balance nodes are not centainly father nodes；
V, line power transmission capacity constrains
In formula: PlineIndicate line security capacity；
VI, the limitation of switch motion quantity
In formula: L indicates all line sets, NmIndicate that maximum actuation switchs number；
Step 2, second order cone Relaxation method；
Step 2.1, with trend relaxation method, equivalencing is carried out to former power flow equation by formula (8):
Then the active injection power of node is converted into formula (9):
The idle injecting power of node is converted into formula (10):
Formula (4) is converted into the form of formula (11):
Step 2.2 introduces virtual voltage relevant to route connection variableWithIf αη=1 Shi ZeyouWithIf αη=0 Shi ZeyouGuarantee its establishment by formula (12)~(15)；
Objective function is indicated by formula (16):
Formula (17) indicates the constraint of node active balance:
Formula (18) indicates the constraint of node reactive balance:
Formula (19) indicates line security capacity-constrained:
|GijRij,t+BijTij-Gijui,t|≤Pline(19)；
Step 2.3 constrains former variable by formula (20)~(21)；
Step 2.4, when objective function is formula (16), solution space can be relaxed as cone by formula (22)~(23),
And when objective function has enough gradients to return to optimal solution on the conical surface, to convert MIXED INTEGER second order for reconstruction
Cone planning MISOCP, acquires globally optimal solution in finite time；
The step of step 3, dynamic restructuring, is as follows:
Step 3.1, initialization data, the original state of network parameter, distribution net topology including power distribution network, load space-time
Distribution curve；
One day is divided into 24 periods by step 3.2, optimizes respectively to each hour, obtains 24 hours one day
Dynamic topology；
Step 3.3 merges the result with phase homeomorphism and Time Continuous, to 24 hours one day are divided into more
A typical time period；
Step 3.4 optimizes the distribution net topology in different time sections, and updates switch state and trend change
Amount；
Step 3.5 judges whether the switch state between different time sections meets switch motion count constraint condition, if full
Foot, then export dynamic restructuring strategy at times, otherwise merges two periods and optimizes and add switch changed position number constraint.
Beneficial effects of the present invention: considering the part throttle characteristics in different function region in power distribution network, to reduce network loss as mesh
Mark establishes power distribution network Dynamic Reconfiguration Model of Multi, and converts convex optimization form for power flow equation by second order cone relaxation, quickly asks
Globally optimal solution is obtained, by merging similar switch state, the action frequency of switch is reduced, to avoid the frequent of grid structure
Change, realizes the target for reducing network loss, improving quality of voltage.
Detailed description of the invention
Fig. 1 is one embodiment of the invention dynamic restructuring flow chart.
Specific embodiment
Embodiments of the present invention are described in detail with reference to the accompanying drawing.
An important indicator of the network loss of power distribution network as power distribution network performance driving economy, research reduce distribution network loss rate
Strategy has a very important significance.Since load may result in there is spatial and temporal distributions difference in power distribution network operational process
The problems such as trend is unevenly distributed weighing apparatus, node voltage collapses, network loss is excessively high.
The present embodiment is considered not by the way that power distribution network is divided into industrial area, shopping centre, the functional area of residential quarter three
With the load curve difference in region.In order to which the trend of balanced power distribution network is distributed, for the present embodiment to reduce network loss as target, optimization is every
Switch state in a period converts convex optimization form for power flow equation by second order cone relaxation method, and passes through solution
MIXED INTEGER Second-order cone programming problem obtains the optimal dynamic topology of power distribution network.Finally by similar switch state is merged, reduce
The action frequency of switch realizes the target for reducing network loss, improving quality of voltage to avoid the frequent change of grid structure.
The present embodiment is achieved through the following technical solutions, a kind of power distribution network dynamic restructuring based on second order cone relaxation method
Decreasing loss method, comprising:
One, the mathematical model of power distribution network reconfiguration
The target of power distribution network reconfiguration is usually the network loss of reduction system, therefore the present embodiment is by optimizing in each period
Switch state to reduce the active power loss of power distribution network whole day.
[1] objective function
In formula: T indicates the scheduling instance in 24 hours；The load bus quantity of N expression power distribution network；GijIndicate branch ij's
Conductance；Vi,tIndicate node i in the voltage of t period；θij,tIndicate that branch ij is poor in the generator rotor angle of t period, C (i) is indicated and node j
The node being connected；αij,tIndicate connected state of the branch ij in the t period, αij,t=1 indicates branch ij connection, αij,t=0 indicates
Branch ij is disconnected；Δ t indicates that a scheduling slot, the present embodiment are 15 minutes.
[2] constraint condition
Following constraint condition need to be met when power distribution network reconfiguration:
I, node active balance constrains
In formula:Indicate node i in the active size of load of t moment.
II, the constraint of node reactive balance
In formula:Indicate node i in the reactive load size of t moment.
III, node voltage bound
Vimin≤Vi,t≤Vimax (4)
In formula: ViminWith VimaxRespectively indicate the voltage magnitude bound of node i.
The radial topological tree constraint of IV, power distribution network
In formula: β indicates the hierarchical relationship between node i and node j, βij=1 illustrates that i is the father node of j, βij=0 explanation
I is not the father node of j, β0j=0 indicates that balance nodes are not centainly father nodes.
V, line power transmission capacity constrains
In formula: PlineIndicate line security capacity.
VI, the limitation of switch motion quantity
In formula: L indicates all line sets, NmIndicate that maximum actuation switchs number.
Two, second order cone Relaxation method
It is 01 variable since power flow equation has nonlinear feature and switch state, power distribution network reconfiguration problem is one
A mixed integer nonlinear programming problem (Mixed Integer Nonlinear Programming Problem, MINLP),
Simultaneously because power flow equation is non-convex, power distribution network reconfiguration problem is caused to be difficult to pass through Analytic Method.With trend relaxation method, lead to
It crosses formula (8) and equivalencing is carried out to former power flow equation:
Then the active injection power of node is converted into formula (9):
The idle injecting power of node is converted into formula (10):
Formula (4) is converted into the form of formula (11):
In order to consider power distribution network reconfiguration problem, virtual voltage relevant to route connection variable is introducedWithIf αη=
1 Shi ZeyouWithIf αη=0 Shi ZeyouGuarantee its establishment by formula (12-15).
Then objective function is indicated by formula (16):
Formula (17) indicates the constraint of node active balance:
Formula (18) indicates the constraint of node reactive balance:
Formula (19) indicates line security capacity-constrained:
|GijRij,t+BijTij-Gijui,t|≤Pline (19)
So far power flow equation is converted into linear representation, but due to introducing nuisance variable in formula (8), it is necessary to pass through formula
(20-21) constrains former variable to guarantee the accuracy of variable replacement.
However the corresponding solution space of formula (20-21) is the conical surface, again such that problem is non-convex.When objective function is formula (16)
When, solution space can be relaxed as cone by formula (22-23), and when objective function there are enough gradients to return to optimal solution
On the conical surface, to convert MIXED INTEGER Second-order cone programming (Mixed Integer Second-Order for reconstruction
Conic Programming, MISOCP), globally optimal solution can be acquired in finite time.
Three, dynamic restructuring strategy
Since the distribution of load has certain period characteristic, such as morning peak, evening peak and night electricity consumption situation.Therefore
The present embodiment optimizes the switch state of each period, by dividing to the dynamic restructuring period to keep away
Exempt to switch frequent movement.The specific steps of algorithm are as shown in Figure 1.
Algorithm comprises the concrete steps that:
(i) initialization data, original state, the load spatial and temporal distributions of network parameter, distribution net topology including power distribution network
Curve.
(ii) it was divided into 24 periods for one day, each hour is optimized respectively, obtains 24 hours one day dynamics
Topology.
(iii) result with phase homeomorphism and Time Continuous is merged, to 24 hours one day are divided into multiple
Typical time period.
(iv) the distribution net topology in different time sections is optimized, and updates switch state and trend variable.
(v) judge whether the switch state between different time sections meets switch motion count constraint condition, if it is satisfied, then
Dynamic restructuring strategy at times is exported, otherwise two periods are merged and optimizes and adds switch changed position number constraint.
It should be understood that the part that this specification does not elaborate belongs to the prior art.
Although being described in conjunction with the accompanying a specific embodiment of the invention above, those of ordinary skill in the art should
Understand, these are merely examples, various deformation or modification can be made to these embodiments, without departing from original of the invention
Reason and essence.The scope of the present invention is only limited by the claims that follow.
Claims (1)
1. a kind of power distribution network dynamic restructuring decreasing loss method based on second order cone relaxation method, characterized in that the following steps are included:
Step 1, the mathematical model of power distribution network reconfiguration；
Step 1.1, objective function:
In formula: T indicates the scheduling instance in 24 hours；The load bus quantity of N expression power distribution network；GijIndicate the electricity of branch ij
It leads；Vi,tIndicate node i in the voltage of t period；θij,tIndicate that branch ij is poor in the generator rotor angle of t period, C (i) is indicated and node j phase
The node of connection；αij,tIndicate connected state of the branch ij in the t period, αij,t=1 indicates branch ij connection, αij,t=0 indicates branch
Road ij is disconnected；Δ t indicates a scheduling slot；
Step 1.2, constraint condition:
Following constraint condition need to be met when power distribution network reconfiguration:
I, node active balance constrains
In formula:Indicate node i in the active size of load of t moment；
II, the constraint of node reactive balance
In formula:Indicate node i in the reactive load size of t moment；
III, node voltage bound
Vimin≤Vi,t≤Vimax (4)
In formula: ViminWith VimaxRespectively indicate the voltage magnitude bound of node i；
The radial topological tree constraint of IV, power distribution network
In formula: β indicates the hierarchical relationship between node i and node j, βij=1 illustrates that i is the father node of j, βij=0 illustrates that i is not
The father node of j, β0j=0 indicates that balance nodes are not centainly father nodes；
V, line power transmission capacity constrains
In formula: PlineIndicate line security capacity；
VI, the limitation of switch motion quantity
In formula: L indicates all line sets, NmIndicate that maximum actuation switchs number；
Step 2, second order cone Relaxation method；
Step 2.1, with trend relaxation method, equivalencing is carried out to former power flow equation by formula (8):
Then the active injection power of node is converted into formula (9):
The idle injecting power of node is converted into formula (10):
Formula (4) is converted into the form of formula (11):
Step 2.2 introduces virtual voltage relevant to route connection variableWithIf αη=1 Shi ZeyouWithIf αη=0 Shi ZeyouGuarantee its establishment by formula (12)~(15)；
Objective function is indicated by formula (16):
Formula (17) indicates the constraint of node active balance:
Formula (18) indicates the constraint of node reactive balance:
Formula (19) indicates line security capacity-constrained:
|GijRij,t+BijTij-Gijui,t|≤Pline(19)；
Step 2.3 constrains former variable by formula (20)~(21)；
Step 2.4, when objective function is formula (16), solution space can be relaxed as cone by formula (22)~(23), and work as
Objective function has enough gradients that optimal solution is returned on the conical surface, to convert MIXED INTEGER second order cone rule for reconstruction
MISOCP is drawn, globally optimal solution is acquired in finite time；
The step of step 3, dynamic restructuring, is as follows:
Step 3.1, initialization data, original state, the load spatial and temporal distributions of network parameter, distribution net topology including power distribution network
Curve；
One day is divided into 24 periods by step 3.2, optimizes respectively to each hour, obtains 24 hours one day dynamics
Topology；
Step 3.3 merges the result with phase homeomorphism and Time Continuous, to be divided into multiple allusion quotations for 24 hours one day
The type period；
Step 3.4 optimizes the distribution net topology in different time sections, and updates switch state and trend variable；
Step 3.5 judges whether the switch state between different time sections meets switch motion count constraint condition, if it is satisfied,
Dynamic restructuring strategy at times is then exported, otherwise two periods are merged and optimizes and adds switch changed position number constraint.
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Application publication date: 20190607 |