CN109687448A - A kind of active power distribution network flexibility appraisal procedure based on uncertain domain - Google Patents
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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
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
A kind of active power distribution network flexibility appraisal procedure based on uncertain domain, comprising: establish uncertain domain, the uncertain domain is a n-dimensional space;The direction matrix in uncertain domain is established, the direction matrix is diagonal matrix, indicates either direction in hypermatrix;Establish the expression formula of uncertain variables;Establish the mathematical model of flexibility evaluation problem, including primal problem mathematical model and subproblem mathematical model;Establish the constraint condition of flexibility evaluation problem;The primal problem mathematical model and subproblem mathematical model in the mathematical model of flexibility evaluation problem are solved respectively.The present invention can be used for the specific network structure of quantitative analysis and the method for operation for the adaptability of uncertain factor.Flexibility assessment models proposed by the invention are, it can be achieved that the flexibility assessment towards active distribution network operation, the problem of network structure for considering power distribution network compared with having invention, power distribution network are to uncertain variables adaptedness.
Description
Technical field
The present invention relates to a kind of active power distribution network flexibility appraisal procedures.More particularly to a kind of having based on uncertain domain
Source power distribution network flexibility appraisal procedure.
Background technique
The access of high proportion renewable energy is the important means of response environment pollution, is the effective of solution fossil fuel shortages
The development trend and important feature of approach and Future Power System.By taking European Union as an example, European Union's renewable energy in 2016 (is removed
Water power) Analyzing Total Electricity Consumption 29% is accounted for, and propose that the year two thousand fifty realizes the blueprint of 100% type power system of renewable energy.However, with
Conventional power generation unit (such as fired power generating unit) is compared, uncertain, the electric system higher with fluctuation of the power output of renewable energy
It needs to adapt to the above characteristic and there is the ability for maintaining safe and stable operation, the concept of " flexibility " causes respectively in power domain
The attention of state scholar.
The document of related flexibility assessment mostly conducts a research in terms of Power System Planning.Existing research can be divided into following several
Class: the correlativity of electricity is abandoned for flexibility and renewable energy, proposes the probability flexibility towards Power System Planning
Assessment models;The concept of flexibility envelope is proposed to describe the flexible begetting power of electric system;Define electric system flexibility
And calculation method is proposed, construct the Unified frame assessed towards the flexibility of Operation of Electric Systems and planning.Existing research is equal
The matching analysis is carried out to flexibility resource and flexibility demand from the angle of electric system, as being directly facing electricity in electric system
The part of power user, power distribution network have critical role in the realizing route of high proportion type power system of renewable energy.Due to matching
In power grid and do not include conventional thermal power unit, therefore flexibility resource can not match or wrap with flexibility demand from whole system
The angle analysis power distribution network flexibility of network.
The flexibility of power distribution network reflects power distribution network and sufficiently plans as a whole and using schedulable resource in system, successfully manage operation
In multiple uncertain factor disturb (i.e. flexibility demand), the various complicated running environment of flexible adaptation simultaneously maintain high-level fortune
The ability of row realization of goal.
The scene that " active distribution network flexibility " is accessed towards high proportion renewable energy.Probabilistic main source packet
Include: renewable energy power output prediction error, load prediction error etc., the above uncertain source is known as flexibility demand.For master
For dynamic power distribution network, flexibility resource include it is all cope with fluctuation and probabilistic regulating measure, node can be divided into
Flexibility resource and network flexibility resource.On the one hand joint mobility with local uncertain formation in-situ balancing, is gone back simultaneously
Flexibility support and supply will be provided to external system as unit of node, the basic source for becoming power distribution network flexibility is single
Position.
Summary of the invention
The technical problem to be solved by the invention is to provide one kind can be used for the specific network structure of quantitative analysis and operation
Active power distribution network flexibility appraisal procedure based on uncertain domain of the mode for uncertain factor adaptability.
The technical scheme adopted by the invention is that: a kind of active power distribution network flexibility appraisal procedure based on uncertain domain,
Include the following steps:
1) uncertain domain is established, the uncertain domain is a n-dimensional space;
2) direction matrix in uncertain domain is established, the direction matrix is diagonal matrix, indicates either one in hypermatrix
To;
3) expression formula of uncertain variables is established;
4) mathematical model of flexibility evaluation problem, including primal problem mathematical model and subproblem mathematical model are established;
5) constraint condition of flexibility evaluation problem is established;
6) the primal problem mathematical model and subproblem mathematical model in the mathematical model of flexibility evaluation problem are solved respectively.
Direction matrix described in step 2) is expressed as follows:
D=diag (b1,b2,...,bh,...bn) (1)
In formula, D is direction matrix, bhFor the deflected length on the direction dimension h of uncertain variables, n is uncertain becomes
The dimension of amount.
The expression formula of uncertain variables described in step 3) is as follows:
θ=θexp+δDΔθ (2)
In formula, θ is uncertain variables, θexpFor the desired value of uncertain variables, δ is normalized deviation, and Δ θ is not
Determine the difference of variable deviation bound and desired value.
In step 4):
The primal problem, be in the uncertain all directions in domain search seek the smallest direction of single direction flexibility and
Direction flexibility index, the primal problem mathematical model are expressed as follows:
In formula, F is flexibility index, and as F > 1, power distribution network flexibility is abundant, and power distribution network is meeting the institute in uncertain domain
On the basis of having operating condition, wider uncertain variables can be also born;As F=1, power distribution network flexibility is just enough, matches
Power grid is just met for all operating conditions in uncertain domain;As F < 1, power distribution network flexibility is insufficient;δDwFor DwIt is feasible on direction
Maximum deflection difference value;δ is normalized deviation;DwFor the direction matrix on the direction w;
It is D that the subproblem, which is in direction matrix,wWhen, the feasible normalization maximum deviation of the direction is sought, it is described
Subproblem mathematical model is expressed as follows:
In formula, x is the decision variable in optimization process.
Constraint condition described in step 5) includes:
(1) distribution power flow constrains:
In formula, Pi,tAnd Qi,tThe active power and reactive power of load respectively at t period node i;PDGi,tAnd QDGi,tPoint
Not Wei at t period node i distributed generation resource injection active power and reactive power;Gij,tAnd Bij,tRespectively t period node i
Electric conductivity value and susceptance value between node j;ei,tAnd fi,tThe respectively voltage real part and imaginary part of t period node i;ejtAnd fjt
Respectively the voltage real part and imaginary part of t period node j;N is node total number;
(2) node voltage constrains
UI, min≤Ui,t≤UI, max (6)
In formula, Ui,maxAnd Ui,minThe respectively maximum value and minimum value of node i voltage magnitude fluctuation permission;Ui,tWhen for t
Duan Jiediani voltage magnitude;
(3) branch current constrains
Sij,t≤SIj, max (7)
In formula, SijFor the transmission capacity of branch of a network i-j;Sij,maxFor the maximum value of branch of a network i-j transmission capacity.
Step 6) is using particle swarm optimization algorithm primal problem mathematical model, comprising:
(1a) coding: particle is encoded;
(2a) initializes population, determines the position initial value of each particle, the position table of first of particle in kth time iteration
It is shown as a vectorD is the dimension of particle position vector;
(3a) calculates each particle adaptive value;
(4a) finds current first of particle extreme value pld;
(5a) finds the globally optimal solution p of current all particlesgd;
The speed and position of (6a) using following formula more new particle:
Wherein,For speed of first of particle in+1 iteration of kth on dimension d;W is inertial factor, c1With c2For
Studying factors, r1With r2For the random number between [0,1], c1With c2For inertia weight.
Step 6) is to solve subproblem mathematical model using dichotomy, comprising:
(1b) enables y=0, and two endpoints of y wheel iteration are respectivelyWithTwo ends of y wheel iteration are sought simultaneously
Midpoint between point
(2b) seeks two endpoints of y+1 wheel iteration
(2b1) ifIt is feasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns the two of iteration
A endpoint is respectively as follows:
(2b2) ifIt is infeasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns iteration
Two endpoints be respectively as follows:
(3b) returns to (2b) step, loop iteration, until meeting the condition of convergence of setting.
A kind of active power distribution network flexibility appraisal procedure based on uncertain domain of the invention, it is specific to can be used for quantitative analysis
Network structure and the method for operation for uncertain factor adaptability.Flexibility assessment models proposed by the invention, can
It realizes the flexibility assessment run towards active distribution network, network structure, the distribution of power distribution network is considered compared with having invention
The problem of net is to uncertain variables adaptedness.
Detailed description of the invention
Fig. 1 is desired point and critical point schematic diagram in Instable Space;
Fig. 2 is distribution network structure chart;
Fig. 3 is uncertain domain and feasible zone result figure;
Fig. 4 is the node voltage amplitude figure of Critical operating point;
Fig. 5 is the branch power figure of Critical operating point.
Specific embodiment
A kind of active power distribution network flexibility based on uncertain domain of the invention is assessed below with reference to embodiment and attached drawing
Method is described in detail.
A kind of active power distribution network flexibility appraisal procedure based on uncertain domain of the invention, by the spirit based on uncertain domain
Activity Assessment method introduces power distribution network research field, considers the non-convex characteristic of distribution power flow equation, establishes and considers uncertain domain
With the non-convex flexibility assessment models of feasible zone relationship.
A kind of active power distribution network flexibility appraisal procedure based on uncertain domain of the invention, includes the following steps:
1) uncertain domain is established, the uncertain domain is a n-dimensional space;
2) direction matrix in uncertain domain is established, the direction matrix is diagonal matrix, indicates either one in hypermatrix
To;
The direction matrix is expressed as follows:
D=diag (b1,b2,...,bh,...bn) (1)
In formula, D is direction matrix, bhFor the deflected length on the direction dimension h of uncertain variables, n is uncertain becomes
The dimension of amount.
3) expression formula of uncertain variables is established;
The expression formula of the uncertain variables is as follows:
θ=θexp+δDΔθ (2)
In formula, θ is uncertain variables, θexpFor the desired value of uncertain variables, δ is normalized deviation, and Δ θ is not
Determine the difference of variable deviation bound and desired value.
4) mathematical model of flexibility evaluation problem, including primal problem mathematical model and subproblem mathematical model are established;Its
In:
The primal problem, be in the uncertain all directions in domain search seek the smallest direction of single direction flexibility and
Direction flexibility index, the primal problem mathematical model are expressed as follows:
In formula, F is flexibility index, δDwFor DwFeasible maximum deflection difference value on direction, δ are normalized deviation, Dw
For the direction matrix on the direction w;
Flexibility index F is defined as: minimum normalized offset of the feasible zone relative to desired point in uncertain variables space
Amount.As F > 1, power distribution network flexibility is abundant, power distribution network on the basis of meeting all operating conditions in uncertain variables domain,
Wider uncertain variables can also be born;As F=1, power distribution network flexibility is just enough, and power distribution network is just met for not knowing
All operating conditions in scope of a variable;As F < 1, power distribution network flexibility is insufficient.In certain uncertain variables sections, power distribution network
It is out-of-limit to will appear the variables such as node voltage amplitude or branch transimission power.The point of limitation flexibility index is known as critical point, such as Fig. 1
Shown in middle A point;Point corresponding to the predicted value of uncertain variables is known as desired point, as shown in figure 1 shown in O point.
It is D that the subproblem, which is in direction matrix,wWhen, the feasible normalization maximum deviation of the direction is sought, it is described
Subproblem mathematical model is expressed as follows:
In formula, x is the decision variable in optimization process.
5) constraint condition of flexibility evaluation problem is established;The constraint condition includes:
(1) distribution power flow constrains:
In formula, Pi,tAnd Qi,tThe active power and reactive power of load respectively at t period node i;PDGi,tAnd QDGi,tPoint
Not Wei at t period node i distributed generation resource injection active power and reactive power;Gij,tAnd Bij,tRespectively t period node i
Electric conductivity value and susceptance value between node j;ei,tAnd fi,tThe respectively voltage real part and imaginary part of t period node i;ejtAnd fjt
Respectively the voltage real part and imaginary part of t period node j;N is node total number;
(2) node voltage constrains
UI, min≤Ui,t≤UI, max (6)
In formula, Ui,maxAnd Ui,minThe respectively maximum value and minimum value of node i voltage magnitude fluctuation permission;Ui,tWhen for t
Duan Jiediani voltage magnitude;
(3) branch current constrains
Sij,t≤SIj, max (7)
In formula, SijFor the transmission capacity of branch of a network i-j;Sij,maxFor the maximum value of branch of a network i-j transmission capacity.
6) the primal problem mathematical model and subproblem mathematical model in the mathematical model of flexibility evaluation problem are solved respectively;
Wherein
Using particle swarm optimization algorithm primal problem mathematical model, comprising:
(1a) coding: particle is encoded;
(2a) initializes population, determines the position initial value of each particle, the position table of first of particle in kth time iteration
It is shown as a vectorD is the dimension of particle position vector;
(3a) calculates each particle adaptive value;
(4a) finds current first of particle extreme value pld;
(5a) finds the globally optimal solution p of current all particlesgd;
The speed and position of (6a) using following formula more new particle:
Wherein,For speed of first of particle in+1 iteration of kth on dimension d;W is inertial factor, c1With c2For
Studying factors, r1With r2For the random number between [0,1], c1With c2For inertia weight.
Subproblem mathematical model is solved using dichotomy, comprising:
(1b) enables y=0, and two endpoints of y wheel iteration are respectivelyWithTwo ends of y wheel iteration are sought simultaneously
Midpoint between point
(2b) seeks two endpoints of y+1 wheel iteration
(2b1) ifIt is feasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns iteration
Two endpoints are respectively as follows:
(2b2) ifIt is infeasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns iteration
Two endpoints be respectively as follows:
(3b) returns to (2b) step, loop iteration, until meeting the condition of convergence of setting.
An example is given below:
(1) flexibility assessment result
Theoretical calculation is carried out using IEEE33 node example, example topological structure is as shown in Figure 2.The example reference voltage is set
It is set to 12.66kV, photovoltaic access node is 6,7,13,18,29,33, and the analysis period of installed capacity 1MW, this example are 12:
00, the uncertain domain of the period is as shown in the table.
Table 2 does not know domain
It is the idle power output of photovoltaic DC-to-AC converter, the as decision variable of subproblem that resource settings are adjusted in power distribution network.Using
Active power distribution network flexibility appraisal procedure based on uncertain domain of the invention carries out flexibility assessment, acquires critical direction position
In (- 0.261,1), flexibility index is 0.5216.The result illustrates current distribution net work structure and resource, in reply 12:00
Occurs the situation of flexibility deficiency when the uncertain variables at moment, the main corresponding load of the situation is lower than desired value and photovoltaic goes out
Power reaches the indeterminacy section upper bound.
On this basis, feasible zone and schematic diagram of the uncertain domain in Instable Space are depicted, as shown in Figure 3.Figure
Middle abscissa is each node total load of example, and ordinate is the sum of each photovoltaic plant power output.Black line area defined pair in figure
The uncertain domain of load and photovoltaic in table 2 is answered, the surrounded region of blue line is feasible zone in Instable Space.It is in figure as it can be seen that feasible
The main reason for domain presentation ellipse is cut by upper right to lower-left, generated this kind of shape is the constraint of constraint condition interior joint voltage
It is constrained with Branch Power Flow.
Critical point for assessment result carries out the analysis in terms of operative constraint, acquires the voltage per unit value of 33 nodes as schemed
Shown in 4, the transimission power of 32 branches is as shown in Figure 5.By Fig. 4 and Fig. 5 it is found that the restrictive condition of flexibility index is node
18 voltage magnitude.Accordingly, the devices such as corresponding energy storage can be configured at node 18, or electricity is carried out by the variation of network structure
Pressure adjustment.In addition, it can also be seen that the voltage magnitude of node 33 is also close to the upper limit in Fig. 4, this point be restrict flexibility index into
Another factor that one step increases.
Claims (7)
1. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain, which comprises the steps of:
1) uncertain domain is established, the uncertain domain is a n-dimensional space;
2) direction matrix in uncertain domain is established, the direction matrix is diagonal matrix, indicates either direction in hypermatrix;
3) expression formula of uncertain variables is established;
4) mathematical model of flexibility evaluation problem, including primal problem mathematical model and subproblem mathematical model are established;
5) constraint condition of flexibility evaluation problem is established;
6) the primal problem mathematical model and subproblem mathematical model in the mathematical model of flexibility evaluation problem are solved respectively.
2. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In direction matrix described in step 2) is expressed as follows:
D=diag (b1,b2,...,bh,...bn) (1)
In formula, D is direction matrix, bhFor the deflected length on the direction dimension h of uncertain variables, n is the dimension of uncertain variables
Degree.
3. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In the expression formula of uncertain variables described in step 3) is as follows:
θ=θexp+δDΔθ (2)
In formula, θ is uncertain variables, θexpFor the desired value of uncertain variables, δ is normalized deviation, and Δ θ is uncertain
The difference of variable deviation bound and desired value.
4. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In in step 4):
The primal problem is that the smallest direction of single direction flexibility and the party are sought in search in the uncertain all directions in domain
To flexibility index, the primal problem mathematical model is expressed as follows:
In formula, F is flexibility index, and as F > 1, power distribution network flexibility is abundant, and power distribution network is meeting all fortune in uncertain domain
On the basis of market condition, wider uncertain variables can be also born;As F=1, power distribution network flexibility is just enough, power distribution network
All operating conditions being just met in uncertain domain;As F < 1, power distribution network flexibility is insufficient;δDwFor DwOn direction it is feasible most
Large deviation value;δ is normalized deviation;DwFor the direction matrix on the direction w;
It is D that the subproblem, which is in direction matrix,wWhen, the feasible normalization maximum deviation of the direction is sought, the son is asked
Topic mathematical model is expressed as follows:
In formula, x is the decision variable in optimization process.
5. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In constraint condition described in step 5) includes:
(1) distribution power flow constrains:
In formula, Pi,tAnd Qi,tThe active power and reactive power of load respectively at t period node i;PDGi,tAnd QDGi,tRespectively t
The active power and reactive power that distributed generation resource injects at period node i;Gij,tAnd Bij,tRespectively t period node i and node
Electric conductivity value and susceptance value between j;ei,tAnd fi,tThe respectively voltage real part and imaginary part of t period node i;ejtAnd fjtRespectively t
The voltage real part and imaginary part of period node j;N is node total number;
(2) node voltage constrains
UI, min≤Ui,t≤UI, max (6)
In formula, Ui,maxAnd Ui,minThe respectively maximum value and minimum value of node i voltage magnitude fluctuation permission;Ui,tFor t period node
I voltage magnitude;
(3) branch current constrains
Sij,t≤SIj, max (7)
In formula, SijFor the transmission capacity of branch of a network i-j;Sij,maxFor the maximum value of branch of a network i-j transmission capacity.
6. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In step 6) is using particle swarm optimization algorithm primal problem mathematical model, comprising:
(1a) coding: particle is encoded;
(2a) initializes population, determines the position initial value of each particle, the position of first of particle is expressed as in kth time iteration
One vectorD is the dimension of particle position vector;
(3a) calculates each particle adaptive value;
(4a) finds current first of particle extreme value pld;
(5a) finds the globally optimal solution p of current all particlesgd;
The speed and position of (6a) using following formula more new particle:
Wherein,For speed of first of particle in+1 iteration of kth on dimension d;W is inertial factor, c1With c2For study
The factor, r1With r2For the random number between [0,1], c1With c2For inertia weight.
7. a kind of active power distribution network flexibility appraisal procedure based on uncertain domain according to claim 1, feature exist
In step 6) is to solve subproblem mathematical model using dichotomy, comprising:
(1b) enables y=0, and two endpoints of y wheel iteration are respectivelyWithSimultaneously seek y wheel iteration two endpoints it
Between midpoint
(2b) seeks two endpoints of y+1 wheel iteration
(2b1) ifIt is feasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns two ends of iteration
Point is respectively as follows:
(2b2) ifIt is infeasible, then it is D in direction matrixwWhen critical point be located atWithBetween, y+1 takes turns the two of iteration
A endpoint is respectively as follows:
(3b) returns to (2b) step, loop iteration, until meeting the condition of convergence of setting.
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