CN109829560B - Renewable energy power generation cluster access planning method for power distribution network - Google Patents
Renewable energy power generation cluster access planning method for power distribution network Download PDFInfo
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Abstract
The invention relates to a renewable energy power generation cluster access planning method of a power distribution network, which adopts an upper planning model and a lower scheduling model, wherein the upper planning model aims at the maximum income of renewable energy power generation investors; the objective function of the lower scheduling model comprises a power balance index, the adjustment cost of a distribution company and the active reduction amount of renewable energy power generation, adjustment measures comprise the action of a tie switch, the tap action of an on-load voltage regulating transformer, the active reduction and reactive compensation of renewable energy power generation, the time sequence correlation among loads and renewable energy resources is modeled by adopting a C-Vine Copula model, and a typical planning scene considering the load and resource correlation is generated by combining a Latin hypercube sampling method.
Description
Technical Field
The invention relates to a power distribution network renewable energy power generation cluster access planning method considering load and resource time sequence correlation.
Background
Renewable energy power generation is connected into the power distribution network, and has positive effects on saving energy and reducing carbon emission. However, when the generated energy of the renewable energy source is 20% -30% of the total generated energy of various power sources, the intermittent and random output of the renewable energy source can cause the problems of overvoltage, power dumping and the like of the system. Therefore, in order to increase the acceptance of the power distribution network for renewable energy generation, it is necessary to consider the impact of renewable energy generation on the system operation during the planning phase.
Aiming at the renewable energy power generation planning problem of a power distribution network, the existing researches are mainly to perform site selection and volume setting of renewable energy power generation under a single transformer substation. The method considers that the power distribution networks under different substations are independent of each other, the relation and influence of operation among a plurality of substations in the system are not considered, and the complementary supporting capability of power among the plurality of substations is ignored. Because the same objective function and constraint conditions are used when planning is carried out on each transformer substation, the output characteristics of a plurality of transformer substations are possibly similar after renewable energy power generation planning is carried out, and if the power of the plurality of transformer substations in the same area is simultaneously dumped and transferred to a previous power grid, the normal operation of a high-voltage power distribution network can be influenced. The active power distribution network can realize active management of renewable energy power generation and other equipment accessed to the power distribution network by utilizing advanced new technologies such as automation, communication, power electronics and the like. The distribution network is widely provided with the interconnection switch and the sectionalizing switch, and the active distribution network can realize dynamic reconfiguration of the network by controlling the on-off of the switch, thereby being beneficial to reducing network loss and balancing load. Therefore, when the access and the digestion problem of renewable energy power generation are studied in the power distribution network, the influence of the connection of output power among a plurality of substations after the access of renewable energy power generation and the influence of network reconstruction on the change of power supply supporting capacity among the multiple substations are considered, the cluster access planning of renewable energy power generation of the multiple substations of the power distribution network is developed, and the cluster access capacity of renewable energy power generation under each substation is determined.
In the planning stage, intermittent renewable energy power generation is connected into the power distribution network, so that the uncertainty of the operation of the power distribution network is improved, and the difficulty of scene selection in the power distribution network planning process is increased. The random characteristics of the load and the resource are accurately depicted by a small number of representative scenes, so that the calculated amount can be effectively reduced and the precision of the planning result can be improved. The renewable energy power generation planning method considering uncertainty mainly comprises planning based on a multi-scene technology, planning based on an opportunity constraint theory and planning based on a fuzzy theory, wherein a scene analysis method enumerates possible values of uncertain factors according to rules, and combines the possible values into a series of planning scenes, and each scene has corresponding probability, so that an uncertainty problem is converted into a deterministic problem, and modeling and solving difficulty is reduced. In addition to the uncertainty of the load and the resource, there is some correlation between the variables. However, current methods can only represent linear correlations between variables, and modeling between variables with nonlinear correlations is not accurate enough. The Copula function does not require that the variables have the same edge distribution, and can describe the characteristics of nonlinearity, asymmetry, tail correlation and the like among the variables. The PairCopula method is a branch in a Copula function, can represent the correlation between multidimensional variables, has flexible structure, and can better capture the correlation between any two variables, however, the method is less applied to power system planning at present.
In summary, the drawbacks and deficiencies of the prior art methods can be summarized as follows:
(1) Aiming at the planning problem of renewable energy power generation in a power distribution network, the existing researches are mostly to perform site selection and volume setting of renewable energy power generation under a single transformer substation. The method considers that the power distribution networks under different substations are independent of each other, and the relation and influence of operation among a plurality of substations in the system are not considered.
(2) In the renewable energy power generation planning process, the influence of various regulation measures in an active power distribution network, especially network reconstruction, on the change of power supply supporting capacity among multiple power stations is not fully considered.
(3) The prior art method only can describe linear correlation between load and resource, and modeling between variables with asymmetric and nonlinear correlation is not accurate enough.
Disclosure of Invention
Aiming at the problems, the invention provides a renewable energy power generation cluster access double-layer planning method considering the time sequence correlation of load and renewable energy resources. The technical proposal is as follows:
an access planning method for renewable energy power generation clusters of a power distribution network adopts an upper planning model and a lower scheduling model, wherein the upper planning model aims at the maximum income of renewable energy power generation investors, and a used planning scene considers nonlinear and asymmetric correlations among loads and resources; the objective function of the lower scheduling model comprises a power balance index, the adjustment cost of a distribution company and the active reduction amount of renewable energy power generation, adjustment measures comprise the action of a tie switch, the tap action of an on-load voltage regulating transformer, the active reduction and reactive compensation of renewable energy power generation, the time sequence correlation among loads and renewable energy resources is modeled by adopting a C-Vine Copula model, and a typical planning scene considering the load and resource correlation is generated by combining a Latin hypercube sampling method.
Wherein, the lower scheduling model includes:
(1) Objective function 1: operating costs of distribution company
f 1 ＝C loss +C reg
Wherein C is loss And C reg The net loss cost and the regulation cost of the distribution company respectively, wherein the regulation cost comprises the tap regulation cost of the on-load voltage regulating transformer and the action cost of a tie switch, c l To have power price, P ij 、Q ij For active and reactive power flowing from upstream node i to node j, V i For the voltage value of node i, i→j represents that node i is connected with node j, R ij The resistance value of the line between the node i and the node j is given, and N is the node set of the power distribution network; c tap In order to adjust the cost of the tap at a time,and->Tap position, c, for time t and time t-1 swi Cost for single action of tie switch, < >>And->The state of the tie line switch at the time t and the time t-1;
(2) Objective function 2: block power balance index
The active balance index and the reactive balance index are provided by taking a high-voltage/medium-voltage transformer substation and a network connected below the transformer substation as a block, and are defined as follows:
wherein, in the formula, N block P is the total number of clusters block,i For the active demand or active output of the ith block, Q block,i Reactive demand or reactive output for the ith cluster;
the smaller the active balance index or reactive balance index is, the smaller the active power or reactive power exchanged between the block and the outside is, the more the active power or reactive power in the block is balanced, the power balance index is optimized through the operation of the tie switch, the power flowing through the upper-level transformer station due to power unbalance is reduced, and the power balance of the system is improved;
the power balance index objective function is:
f 2 ＝ω 1 f P_Bal +ω 2 f Q_Bal
wherein omega is 1 And omega 2 The percentage is the weight of the active balance index and the reactive balance index, can be determined according to the difference of the importance of the indexes, andneeds to satisfy omega 1 +ω 2 ＝1；
(3) Objective function 3: renewable energy source reduction
Renewable energy reduction is taken as one of lower-layer scheduling targets:
in the method, in the process of the invention,and->Respectively the ith PV Individual photovoltaics or ith WTG The active cutting amount of each fan;
and (3) normalizing 3 objective functions:
in the method, in the process of the invention,for the normalized objective function, +.>f imin Is the minimum value of the ith objective function, f imax Maximum value of ith objective function;
the overall objective function of the lower layer scheduling model is:
wherein lambda is 1 、λ 2 、λ 3 Respectively, the objective functions after planningThe weight coefficient of the system can be comprehensively determined according to factors such as importance degree of each target in the scheduling process, actual running condition and the like, and lambda needs to be satisfied 1 +λ 2 +λ 3 ＝1；
The constraint conditions of the lower layer scheduling model comprise:
(1) Constraint of tide equation
Wherein P is j ＝P Lj -P total,PV,j -P total,WTG,j +P cut,PV,j +P cut,WTG,j ，Q j ＝Q Lj -Q PV,j -Q WTG,j ；
Wherein R is ij 、X ij Respectively representing the resistance value and the reactance value of the line between the node i and the node j, P j And Q j Active and reactive power for node j payload, P Lj And Q Lj Active and reactive power for node j load, P total,PV,j And P cut,PV,j Active power and active curtailment, P, of node j photovoltaic respectively total,WTG,j And P cut,WTG,j Respectively carrying out active power and active reduction on a fan of the node j;
(2) System security constraints
In the method, in the process of the invention,and->The upper and lower voltage limits at the node j are respectively;
(3) Distributed photovoltaic operation constraints
Q PV，j ＝(P total,PV,j -P cut,PV,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing photovoltaic output power min Limiting;
(4) Fan operation constraint
Q WTG，j ＝(P total,WTG,j -P cut,WTG,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing fan output power min Limiting;
(5) On-load tap changer constraints
U i ＝k ij,t U j
k ij,t ＝1+K ij,t Δk ij
In U i And U j The voltages at the high-voltage side and the low-voltage side of the transformer are respectively, ij Kandrespectively the lower limit and the upper limit of the tap gear of the transformer, K ij,t For tap position at time t of transformer, deltak ij The gear ratio, k, is adjusted for adjacent taps of the transformer ij,t The voltage transformation ratio of the high-low voltage side of the transformer at the moment t;
(6) Tie switch constraint
The state of the tie switch is such that the load on the tie is continuously supplied and not operated in a closed loop, so that for a tie having N tie switches only one tie switch should be operated in an open mode
In the method, in the process of the invention,the switching state of the tie line switch on the line at the moment i-j is 1 if the tie line switch is closed, and 0 if the tie line switch is opened; o is a set of branches along the line forming a ring network;
(7) 220kV transformer substation power constraint
In order to ensure safe operation of the system, the reverse power is prevented from being transmitted to the power transmission network, and the power of the 220kV transformer substation is required to be not returned:
0≤P sub,220kV ≤P rated,220kV
g) Power constraint of distribution substation with 220kV or below level
The distribution company has the right to cut down the active output of renewable energy power generation so as to limit the reverse power to be less than or equal to 60% of the rated capacity of the transformer substation:
-0.6×P rated,＜220kV ≤P sub ≤P rated,＜220kV 。
the upper planning model comprises:
determining the cluster access capacity of photovoltaic and fans under each 35kV transformer substation:
maxF upper ＝max(C cell -C inv -C main )
obtaining the electricity selling income of a renewable energy power generation user according to the electricity selling quantity of the photovoltaic and the fan:
wherein r is the discount rate, ny, N PV 、N WTG The planning years, the number of photovoltaics and the number of fans respectively, c sell,PV And c sell,WTG The online electricity prices of the photovoltaic and the blower fan are respectively,and->Respectively, the ith scene in the y year and the s scene PV Individual photovoltaics or ith WTG The actual on-line electric quantity of each fan;
and (3) solving the construction cost according to the installation capacity of the fan and the photovoltaic:
wherein, c ins,PV And c ins,WTG The construction cost of the photovoltaic and the fan unit capacity is respectively,and->Mounting capacities for photovoltaic and fan respectively
And obtaining the operation and maintenance cost of renewable energy power generation according to the installation capacity of the absolute photovoltaic and the total power generation capacity of the fan:
wherein, c om,PV Annual operating maintenance costs for photovoltaic unit installation capacity c om,WTG The operation and maintenance cost for the unit power generation amount of the fan,is the ith in the ith scene of the y year WTG The actual power generation of each fan;
renewable energy power generation planning is limited by geographical factors of installation sites and total investment cost factors, and installation capacity limitation needs to be met:
and->
In the method, in the process of the invention,and->Respectively represent the ith PV Individual photovoltaic mounting points or ith WTG The upper limit of the installation capacity of the installation points of the fans.
The planning scene generation steps are as follows:
(1) Reading historical data X of wind resource, light resource, industrial load, agricultural load, commercial load and residential load ori ＝(x 1,ori ,x 2,ori ,x 3,ori ,x 4,ori ,x 5,ori ,x 6,ori ) Each type of data is subjected to per unit to obtain:
wherein x is i,ori I=1,..6 represents raw data of wind resource, light resource, industrial load, agricultural load, commercial load, and residential load, x i,ori,max I=1,..6 represents a peak value of a corresponding resource or a device installation capacity of a corresponding type of load, x i I=1, &..6 is the raw per-unit data of the wind resource, the light resource, the industrial load, the agricultural load, the commercial load and the residential load obtained;
(2) Using cumulative distribution function u i ＝F i (x i ),u i ∈[0,1]I=1,..6, converting the original data X to [0,1]Uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 )；
(3) For uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 ) Carrying out parameter estimation and fitting goodness test by using a maximum likelihood function and an Anderson Darling method, and solving parameters and structures of a C-Vine Copula function corresponding to the data U;
(4) Generating [0,1 ] using Latin hypercube sampling method]Upper independent uniformly distributed variables (w 1 ,w 2 ,w 3 ,w 4 ,w 5 ,w 6 ) The following conditional distribution formula can be obtained according to the obtained C-Vine Copula structure:
wherein z= (Z) 1 ,z 2 ,z 3 ,z 4 ,z 5 ,z 6 ) Corresponding scenes in a uniform domain for six types of data;
(5) Inverse function using raw data edge distribution functionu i ∈[0,1]I=1,..6, finding a typical per-unit scene of six types of data in the actual domain;
(6) And multiplying the obtained typical per-unit scene of the four types of loads with the installation capacity of the four types of load equipment corresponding to each transformer substation in the planning area, summing the obtained typical per-unit scene of the four types of loads, and obtaining the typical scene of the total load of each transformer substation, wherein the typical scene of the resources is obtained by multiplying the typical per-unit scene of the resources with the peak value of the resources.
Compared with the prior art, the method for planning the access of the renewable energy power generation clusters of the power distribution network by considering the load and the time sequence correlation of the resources has the following advantages:
(1) The invention develops renewable energy power generation planning aiming at a power distribution network comprising a plurality of substations, and considers the influence of power complementary supporting capacity and network reconstruction among the substations on the planning. The method determines the total installation capacity of the photovoltaic and the fan under each transformer substation, and guides and determines the specific installation position and capacity of the photovoltaic and the fan under each transformer substation in the follow-up planning work.
(2) In order to improve the power generation capacity of renewable energy sources and improve the power balance degree of a system, the invention provides a power balance degree index. The active balance index can be optimized through network reconstruction, so that the influence of the reverse power on the upper power grid is reduced, and the installation capacity of renewable energy power generation is increased.
(3) The invention models the correlation between the load and the resource based on the C-Vine Copula method, and can accurately represent the nonlinear and asymmetric correlation between the variables. And then a Latin hypercube sampling method is used for generating a smaller number of typical scenes for planning renewable energy power generation, so that the calculation speed is improved while the calculation accuracy is ensured.
Drawings
FIG. 1 is a flow chart of a two-layer planning model
FIG. 2 is a schematic diagram of the structure of C-Vine Copula
FIG. 3 is a schematic electrical wiring diagram of a programming embodiment
FIG. 4 is a C-Vine Copula result between load and resources in an embodiment
Detailed Description
The invention will now be described with reference to the accompanying drawings and tables.
The renewable energy power generation cluster access planning method comprises an upper layer planning model and a lower layer scheduling model. The upper planning model aims at the maximum income of renewable energy power generation investors, and determines the cluster access capacity of photovoltaic and fans under each 35kV transformer substation:
maxF upper ＝max(C cell -C inv -C main )
obtaining the electricity selling income of a renewable energy power generation user according to the electricity selling quantity of the photovoltaic and the fan:
wherein r is the discount rate, ny, N PV 、N WTG The planning years, the number of photovoltaics and the number of fans respectively, c sell,PV And c sell,WTG The online electricity prices of the photovoltaic and the blower fan are respectively,and->Respectively, the ith scene in the y year and the s scene PV Individual photovoltaics or ith WTG The actual net power of each fan.
And (3) solving the construction cost according to the installation capacity of the fan and the photovoltaic:
wherein, c ins,PV And c ins,WTG The construction cost of the photovoltaic and the fan unit capacity is respectively,and->Mounting capacities for photovoltaic and fan respectively
And obtaining the operation and maintenance cost of renewable energy power generation according to the installation capacity of the absolute photovoltaic and the total power generation capacity of the fan:
wherein, c om,PV Annual operating maintenance costs for photovoltaic unit installation capacity c om,WTG The operation and maintenance cost for the unit power generation amount of the fan,is the ith in the ith scene of the y year WTG The actual power generation of each fan.
Renewable energy power generation planning is limited by geographical factors of installation places, total investment cost and other factors, and installation capacity limitation needs to be met:
and->
In the method, in the process of the invention,and->Respectively represent the ith PV Individual photovoltaic mounting points or ith WTG The upper limit of the installation capacity of the installation points of the fans.
The objective functions of the lower scheduling model include a power balance index, a regulating cost of a distribution company and an active reduction amount of renewable energy power generation. The regulation measures comprise the action of a tie switch, the tap action of an on-load regulating transformer, the active reduction and reactive compensation of renewable energy power generation.
(1) Objective function 1: operating costs of distribution company
f 1 ＝C loss +C reg
Wherein C is loss And C reg The method comprises the steps of respectively obtaining the network loss cost and the regulation cost of a distribution company, wherein the regulation cost comprises the tap regulation cost of the on-load voltage regulating transformer and the action cost of a tie switch. c l For the price of active power, P ij 、Q ij For active and reactive power flowing from upstream node i to node j, V i For the voltage value of node i, i→j represents that node i is connected with node j, R ij For node i and nodeAnd the line resistance value between the points j, N is a power distribution network node set. c tap In order to adjust the cost of the tap at a time,and->Tap position, c, for time t and time t-1 swi Cost for single action of tie switch, < >>And->The tie line switch state at time t and time t-1.
(2) Objective function 2: block power balance index
The invention uses a high-voltage/medium-voltage transformer substation and the network connected below the transformer substation as a block. The high-permeability distributed renewable energy source power generation is connected into the power distribution network to generate power for reversing, so that the system network loss is increased, and the service life of the transformer substation is shortened. In order to improve the capacity of the blocks for generating power of renewable energy sources, reduce power dumping and improve the power complementarity between distribution networks in a cluster, the invention provides an active balance degree index and a reactive balance degree index, which are defined as follows:
wherein, in the formula, N block P is the total number of clusters block,i For the active demand or active output of the ith block, Q block,i Reactive demand or reactive output for the i-th cluster.
The smaller the active balance index or reactive balance index, the smaller the active power or reactive power exchanged between the block and the outside, and the more the active or reactive power in the block is balanced. Through the operation of the tie switch, the power balance index can be optimized, the power flowing through the upper-level substation due to power unbalance is reduced, and the power balance of the system is improved.
The power balance index objective function is:
f 2 ＝ω 1 f P_Bal +ω 2 f Q_Bal
wherein omega is 1 And omega 2 The weight of the percentage which is an active balance index and a reactive balance index can be determined according to the difference of index importance, and omega needs to be satisfied 1 +ω 2 ＝1。
(3) Objective function 3: renewable energy source reduction
In order to improve the level of the distributed power supply, reduce the amount of abandoned wind and abandoned light and improve the utilization efficiency of renewable energy sources, the invention takes the renewable energy source reduction amount as one of lower-layer scheduling targets.
In the method, in the process of the invention,and->Respectively the ith PV Individual photovoltaics or ith WTG The active cutting amount of each fan.
Since three objective functions are different in dimension, it is necessary to normalize them.
In the method, in the process of the invention,for the normalized objective function, +.>f imin Is the minimum value of the ith objective function, f imax Is the maximum of the ith objective function.
The objective function of the lower layer scheduling model is:
wherein lambda is 1 、λ 2 、λ 3 Respectively, the objective functions after planningThe weight coefficient of the system can be comprehensively determined according to factors such as importance degree of each target in the scheduling process, actual running condition and the like, and lambda needs to be satisfied 1 +λ 2 +λ 3 ＝1。
The lower layer scheduling model objective function includes:
(1) Constraint of tide equation
Wherein P is j ＝P Lj -P total,PV,j -P total,WTG,j +P cut,PV,j +P cut,WTG,j ，Q j ＝Q Lj -Q PV,j -Q WTG,j 。
Wherein R is ij 、X ij Respectively are provided withRepresenting the resistance and reactance values of the line between node i and node j, P j And Q j Active and reactive power for node j payload, P Lj And Q Lj Active and reactive power for node j load, P total,PV,j And P cut,PV,j Active power and active curtailment, P, of node j photovoltaic respectively total,WTG,j And P cut,WTG,j And respectively reducing the active power and the active power of the node j fan.
(2) System security constraints
In the method, in the process of the invention,and->The upper and lower voltage limits at node j, respectively.
(3) Distributed photovoltaic operation constraints
Q PV，j ＝(P total,PV,j -P cut,PV,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing photovoltaic output power min And (5) limiting.
(4) Fan operation constraint
Q WTG，j ＝(P total,WTG,j -P cut,WTG,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing fan output power min And (5) limiting.
(5) On-load tap changer constraints
U i ＝k ij,t U j
k ij,t ＝1+K ij,t Δk ij
In U i And U j The voltages at the high-voltage side and the low-voltage side of the transformer are respectively, ij Kandrespectively the lower limit and the upper limit of the tap gear of the transformer, K ij,t For tap position at time t of transformer, deltak ij The gear ratio, k, is adjusted for adjacent taps of the transformer ij,t The voltage transformation ratio of the high-voltage side and the low-voltage side of the transformer at the moment t.
(6) Tie switch constraint
The state of the tie switch is such that the load on the tie is continuously supplied and not operated in a closed loop, so that for a tie having N tie switches only one tie switch should be operated in an open mode
In the method, in the process of the invention,the switching state of the tie line switch on the line at the moment i-j is 1 if the tie line switch is closed, and 0 if the tie line switch is opened; o is a set of branches along the line forming a ring network.
(7) 220kV transformer substation power constraint
In order to ensure safe operation of the system, the reverse power is prevented from being transmitted to the power transmission network, and the power of the 220kV transformer substation is required to be not returned:
0≤P sub,220kV ≤P rated,220kV
g) Power constraint of distribution substation with 220kV or below level
Because the high-permeability distributed renewable energy sources in the power distribution network are connected, the reverse power can cause the increase of network loss and the overcurrent of lines, a power distribution company has the right to cut down the active output of the renewable energy source power generation so as to limit the reverse power to be less than or equal to 60% of the rated capacity of a transformer substation.
-0.6×P rated,＜220kV ≤P sub ≤P rated,＜220kV
And solving the upper planning model by adopting a genetic algorithm, and transmitting the obtained fan and photovoltaic installation capacity to the lower scheduling model. The lower layer scheduling model is a mixed integer nonlinear programming problem, the original NP difficult nonlinear problem is converted into a mixed integer second order cone programming model through linearization and cone relaxation, cutting constraint is added for solving in order to ensure the cone relaxation accuracy, the cone relaxation error is reduced to a preset range, and finally the scheduling result is transmitted to the upper layer programming model. The upper layer model and the lower layer model are alternately and iteratively solved until the calculation termination condition is triggered, and the REG planning result is output. The algorithm flow of the two-layer planning model is shown in fig. 1.
According to the invention, historical data obtained from a planning area are divided into wind speed, illumination, industrial load, agricultural load, commercial load and resident load data, the historical data are subjected to per unit processing according to resource peaks corresponding to the six types of data and the installation capacity of various load devices, and then a C-Vine Copula method is adopted to perform correlation modeling on the six types of per unit data, so that a C-Vine Copula structure considering nonlinear and asymmetric correlations among variables is obtained. Then, an independent and uniformly distributed sample is generated by using a Lating hypercube sampling method, and a typical per unit scene considering multi-variable correlation is generated by combining the obtained C-Vine Copula structure. And finally, multiplying the obtained per-unit scene of the four types of loads with the installation capacity of the four types of load equipment corresponding to each transformer substation and summing the multiplied per-unit scene, so that a typical scene of the total load of each transformer substation can be obtained, and multiplying the resource per-unit scene by a resource peak value to obtain the typical scene of the resource.
The Copula function is a powerful tool for researching the correlation among random variables, and can connect the joint distribution of multiple random variables with each unitary marginal distribution to describe the characteristics of nonlinearity, asymmetry, tail correlation and the like among the variables. Let F be a function F with edge distribution according to Sklar's theorem 1 (x 1 ),...,F n (x n ) An n-dimensional Copula function C exists for the n-element joint probability distribution function of (2) so that forHas the following components
F(x 1 ,x 2 ,···,x n )＝C(F 1 (x 1 ),F 2 (x 2 ),···,F n (x n ))
If F 1 (x 1 ),...,F n (x n ) And C is a Copula function corresponding to F only.
Let u i ＝F i (x i ),u i ∈[0,1]I=1,..n is uniformly distributed, then
C(u 1 ,...,u n )＝P(U 1 ≤u 1 ,...,U n ≤u n )＝F(F 1 -1 (u 1 ),...,F n -1 (u n ))
Wherein F is i -1 (u i ) Is the inverse of the edge distribution function.
The probability density function of the Copula function is defined as follows:
wherein f i (x i ) As a probability density function, f (x 1 ,x 2 ,···,x n ) As a joint probability density function, c (F 1 (x 1 ),F 2 (x 2 ),···,F n (x n ) A Copula probability density function.
The Pair Copula structure decomposes the multi-element Copula function into a plurality of pairs of binary Copula functions, has flexible structure and can better capture the dependency relationship between any two variables.
Random variable x= (X) 1 ,...,X n ) Can be divided into (a) joint probability density functionsSolution to
f(x 1 ,x 2 ,···,x n )＝f n (x n )·f(x n-1 |x n )·f(x n-2 |x n-1 ,x n )...f(x 1 |x 2 ,...,x n )
The above equation can be decomposed into the product of a suitable Pair Copula function and a conditional probability density function:
where v is a d-dimensional vector, v j Is any element in v -j Representing removal of v j The subsequent vector v. Thus, the multiple probability density function may be represented by a plurality of Pair Copula functions.
The Pair copula structure involves the edge condition distribution function F (x|v) of the variables:
wherein C is i,j|k Is a binary Copula distribution function. When v comprises only a single variable,
the Pair Copula structure mainly comprises two forms, namely D-Vine and Canonical Vine (C-Vine), and the C-Vine form is used in the invention. The structure of C-Vine can be expressed as
Where j represents the number of layers of C-Vine, i represents the edges of each layer, and in the j-th layer, there is always one node connected to n-j edges. The n-dimensional C-VineCopula structure is shown in FIG. 2.
And estimating the Pair Copula parameters by adopting a maximum likelihood method. Assuming n-dimensional variables, each with T observations, each variable can be represented by:
x i ＝(x i,1 ,...,x i,T )
for a binary Copula density function c j,j+i|1,...,j-1 Obtaining the parameter theta of the C-Vine by solving a logarithmic maximum likelihood function:
since there are many types of binary Copula functions that can be used to fit the correlation between the raw data, it is important to select the most appropriate Copula function in the C-Vine Copula function structure. Therefore, a goodness-of-fit test is needed to verify that the selected Copula function type accurately characterizes the correlation between variables and to select the most appropriate Copula function. And carrying out fitting goodness test by adopting an Anderson Darling method.
Let X and Y represent two random variables, respectively, with their respective marginal distribution functions u=f X (x) =p (x+.x) and v=f Y (Y) =p (y.ltoreq.y) with a joint distribution function of F X,Y (x,y)＝P(X≤x,Y≤y)，Suppose F X And F Y Are all continuous functions, there is a unique Copula function C: [0,1 ]] 2 →[0,1]：
F X,Y (x,y)＝C(F X (x),F Y (y))＝C(u,v)＝P(U≤u,V≤v)
When u=u, the conditional distribution function between U and V is:
wherein D is 1 Represents the partial derivative of C (u, v) with respect to u.
Random variable Z 1 ＝U＝F X (x) And Z 2 ＝C(V|U)＝C(F Y (y)|F X (x) At [0,1 ]]Are independently and uniformly distributed. Thus, the random variable S (X, Y) = [ Φ ] -1 (F X (X))] 2 +[Φ -1 C(F Y (Y)|F X (X))] 2 Is χ with 2 degrees of freedom 2 Distribution. If (X) 1 ,Y 1 )，...,(X n ,Y n ) Is a random sample from the population (X, Y), then S (X 1 ,Y 1 )，...,S(X n ,Y n ) Is χ from a degree of freedom of 2 2 A random sample of the distribution. Thus, the test is assumed to be
H 0 (X, Y) there is a Copula function C (u, v)
Wherein the marginal distribution function F X And F Y Is known. By calculating S (X 1 ,Y 1 )，...,S(X n ,Y n ) The test hypothesis H can be 0 Transition to test auxiliary hypothesis:
is->Distribution of
If it isIf true H 0 Hold true if reject%>Reject H 0 。
Because the Anderson Darling test has relatively good characteristics for a large number of different situations, the present invention uses the Anderson Darling method pairIt is assumed that the test is performed. The test statistic of the Anderson Darling method is:
wherein S is j ＝S(X j ,Y j ) J=1,.. (1) ≤…≤S (n) 。F 0 X subject to degree of freedom 2 2 Distribution.
However, in practical application F X And F Y Is generally unknown, so an empirical distribution function is used instead of an edge distribution function:
and->
UsingInstead of S (X) j ,Y j ):
In addition, in the case of the optical fiber,
it should be noted that if the edge distribution function of the variable is unknown, the substitution with an empirical distribution function affects the threshold of the goodness-of-fit test. The invention uses a Bootstrap method to determine the critical value of which the confidence level is 1-alpha, and comprises the following steps:
(1) From the initial observations (x 1 ,y 1 )，...,(x n ,y n ) Estimating Copula function C (u, v; θ) estimation of the parameter θValue of
(2) From Copula functionGenerating n independent observations +.>
(3) From the following componentsi=1.. n estimates Copula function C (u, v; θ) estimation of the parameter θ +.>From the following componentsAnd->Calculate->Calculating the value AD of the Anderson Darling test statistic using the calculated values * ；
(4) Repeating the step (2) and the step (3) for N times to obtain the value AD of the test statistic *(1) ,...,AD *(N) The value of the test statistic corresponding to the 1-alpha quantile is the required critical value.
If from the initial observation (x 1 ,y 1 )，...,(x n ,y n ) And rejecting zero assumption if the calculated value of the test statistic is larger than the calculated critical value, wherein the Copula function is considered unsuitable for describing the observation value dependent structure, otherwise, accepting the zero assumption.
The scene generation method considering the load and the time sequence correlation between resources based on the C-Vine Copula method comprises the following specific steps:
(1) Reading historical data X of wind resource, light resource, industrial load, agricultural load, commercial load and residential load ori ＝(x 1,ori ,x 2,ori ,x 3,ori ,x 4,ori ,x 5,ori ,x 6,ori ) Each type of data is subjected to per unit to obtain:
wherein x is i,ori I=1,..6 represents raw data of wind resource, light resource, industrial load, agricultural load, commercial load, and residential load, x i,ori,max I=1,..6 represents a peak value of a corresponding resource or a device installation capacity of a corresponding type of load, x i I=1,..6 is the raw per-unit data of the wind resource, the light resource, the industrial load, the agricultural load, the commercial load, and the residential load obtained.
(2) Using cumulative distribution function u i ＝F i (x i ),u i ∈[0,1]I=1,..6, converting the original data X to [0,1]Uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 )。
(3) For uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 ) And carrying out parameter estimation and fitting goodness test by using a maximum likelihood function and an Anderson Darling method, and solving the parameters and the structure of the C-Vine Copula function corresponding to the data U.
(4) Generating [0,1 ] using Latin hypercube sampling method]Upper independent uniformly distributed variables (w 1 ,w 2 ,w 3 ,w 4 ,w 5 ,w 6 ). From the C-Vine Copula structure that has been obtained, the following conditional distribution formula can be obtained:
wherein z= (Z) 1 ,z 2 ,z 3 ,z 4 ,z 5 ,z 6 ) For a scene where six types of data correspond in the homogeneous domain.
(5) Inverse function x using raw data edge distribution function i ＝F i -1 (z i ),u i ∈[0,1]I=1,..6 finds a typical per-unit scene of six classes of data in the actual domain.
(6) And multiplying the obtained typical per-unit scene of the four types of loads with the installation capacity of the four types of load equipment corresponding to each transformer substation in the planning area, summing the obtained typical per-unit scene of the four types of loads, and obtaining the typical scene of the total load of each transformer substation, wherein the typical scene of the resources is obtained by multiplying the typical per-unit scene of the resources with the peak value of the resources.
The present invention will be described with reference to fig. 3 to 4 and tables 1 to 5.
An embodiment of a medium-high voltage distribution network in a certain part of China is selected, and fig. 3 is an electrical wiring diagram of the embodiment. This embodiment includes 8 substations including 1 220kV/110kV substation, 2 110kV/35kV substation, 5 35kV/10kV substation. In addition, the embodiment also comprises 8 lines, wherein 2 lines are 110kV lines, 6 lines are 35kV lines, and breaking switches are arranged on the 35kV lines.
The load under each 35kV substation is equivalent to its low-voltage side without considering the specific grid parameters under the 35kV substation. The method comprises the steps of acquiring 8760 hours of illumination intensity, wind speed and load historical data in the past year in a planning area, dividing the load into industrial load, agricultural load, commercial load and residential load, and counting the peak value of resources and the equipment installation capacity corresponding to various load historical data. The capacity of each transformer substation and the installation capacity of various load devices connected with each transformer substation are shown in the attached table 1. According to the invention, the cluster access planning of the photovoltaic and the fans is carried out on each 35kV transformer substation, the planning period is 15 years, and the annual load increase rate is set to be 3%. The single fan capacity is 2MW. The planning economy and scheduling parameters are shown in the accompanying table 2.
The structure of the C-Vine Copula among a plurality of variables obtained by the scene generation method provided by the invention is shown in the figure 3. And generating a typical planning scene by combining a Latin hypercube sampling method, and obtaining average load and peak load of each transformer substation, wherein the average load and the peak load are shown in an attached table 3.
The planning results obtained by using the double-layer planning method provided by the invention are shown in the attached table 4, and other results are shown in the attached table 5.
Table 1 shows the transformer capacity of each 35kV substation and the installation capacity of each type of load equipment in the planned area
Table 2 is parameters of the planning embodiment
Table 3 shows the average and peak load conditions for each 35kV substation
Table 4 shows the planning results for each substation fan and photovoltaic
Table 5 is other results of the planning calculation
Claims (1)
1. An access planning method for a renewable energy power generation cluster of a power distribution network adopts an upper planning model and a lower scheduling model, wherein the upper planning model aims at the maximum income of renewable energy power generation investors; the objective function of the lower scheduling model comprises the running cost of a distribution company, a block power balance index and renewable energy source reduction, and the adjustment measures comprise the action of a tie switch, the tap action of an on-load voltage regulating transformer, the active reduction and reactive compensation of renewable energy source power generation; modeling by adopting a C-Vine Copula model aiming at time sequence correlation between load and renewable energy resources, and generating a typical planning scene considering the load and resource correlation by combining a Latin hypercube sampling method, wherein,
the lower layer scheduling model comprises:
(1) Objective function 1: operating costs of distribution company
f 1 ＝C loss +C reg
Wherein C is loss And C reg The net loss cost and the regulation cost of the distribution company respectively, wherein the regulation cost comprises the tap regulation cost of the on-load voltage regulating transformer and the action cost of a tie switch, c l To have power price, P ij 、Q ij For active and reactive power flowing from upstream node i to node j, V i For the voltage value of node i, i→j represents that node i is connected with node j, R ij The resistance value of the line between the node i and the node j is given, and N is the node set of the power distribution network; c tap In order to adjust the cost of the tap at a time,and->Tap position, c, for time t and time t-1 swi Cost for single action of tie switch, < >>And->The state of the tie line switch at the time t and the time t-1;
(2) Objective function 2: block power balance index
The active balance index and the reactive balance index are provided by taking a high-voltage/medium-voltage transformer substation and a network connected below the transformer substation as a block, and are defined as follows:
wherein, in the formula, N block P is the total number of clusters block,i For the active demand or active output of the ith block, Q block,i Reactive demand or reactive output for the ith cluster;
the smaller the active balance index or reactive balance index is, the smaller the active power or reactive power exchanged between the block and the outside is, the more the active power or reactive power in the block is balanced, the power balance index is optimized through the operation of the tie switch, the power flowing through the upper-level transformer station due to power unbalance is reduced, and the power balance of the system is improved;
the power balance index objective function is:
f 2 ＝ω 1 f P_Bal +ω 2 f Q_Bal
wherein omega is 1 And omega 2 The percentages are weights of active balance degree index and reactive balance degree index, are determined according to different importance of the indexes, and are required to meet omega 1 +ω 2 ＝1；
(3) Objective function 3: renewable energy source reduction
Renewable energy reduction is taken as one of lower-layer scheduling targets:
in the method, in the process of the invention,and->Respectively the ith PV Individual photovoltaics or ith WTG The active cutting amount of each fan;
and (3) normalizing 3 objective functions:
wherein f i * As normalized objective function, f i * ∈[0,1]，f imin Is the minimum value of the ith objective function, f imax Maximum value of ith objective function;
the overall objective function of the lower layer scheduling model is:
wherein lambda is 1 、λ 2 、λ 3 Respectively the planned objective functions f 1 * 、The weight coefficient of the system can be comprehensively determined according to factors such as importance degree of each target in the scheduling process, actual running condition and the like, and lambda needs to be satisfied 1 +λ 2 +λ 3 ＝1；
The constraint conditions of the lower layer scheduling model comprise:
(1) Constraint of tide equation
Wherein P is j ＝P Lj -P total,PV,j -P total,WTG,j +P cut,PV,j +P cut,WTG,j ，Q j ＝Q Lj -Q PV,j -Q WTG,j ；
Wherein R is ij 、X ij Respectively representing the resistance value and the reactance value of the line between the node i and the node j, P j And Q j Active and reactive power for node j payload, P Lj And Q Lj Active and reactive power for node j load, P total,PV,j And P cut,PV,j Active power and active curtailment, P, of node j photovoltaic respectively total,WTG,j And P cut,WTG,j Respectively carrying out active power and active reduction on a fan of the node j;
(2) System security constraints
In the method, in the process of the invention,and->The upper and lower voltage limits at the node j are respectively;
(3) Distributed photovoltaic operation constraints
Q PV，j ＝(P total,PV,j -P cut,PV,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing photovoltaic output power min Limiting;
(4) Fan operation constraint
Q WTG，j ＝(P total,WTG,j -P cut,WTG,j )tanθ
Where θ=cos -1 PF min Minimum power factor PF representing fan output power min Limiting;
(5) On-load tap changer constraints
U i ＝k ij,t U j
k ij,t ＝1+K ij,t Δk ij
In U i And U j The voltages at the high-voltage side and the low-voltage side of the transformer are respectively, ij Kandrespectively the lower limit and the upper limit of the tap gear of the transformer, K ij,t For tap position at time t of transformer, deltak ij The gear ratio, k, is adjusted for adjacent taps of the transformer ij,t The voltage transformation ratio of the high-low voltage side of the transformer at the moment t;
(6) Tie switch constraint
The state of the tie switch is such that the load on the tie is continuously supplied and not operated in a closed loop, so that for a tie having N tie switches only one tie switch should be operated in an open mode
In the method, in the process of the invention,the switching state of the tie line switch on the line at the moment i-j is 1 if the tie line switch is closed, and 0 if the tie line switch is opened; o is a set of branches along the line forming a ring network;
(7) 220kV transformer substation power constraint
In order to ensure safe operation of the system, the reverse power is prevented from being transmitted to the power transmission network, and the power of the 220kV transformer substation is required to be not returned:
0≤P sub,220kV ≤P rated,220kV
g) Power constraint of distribution substation with 220kV or below level
The distribution company has the right to cut down the active output of renewable energy power generation so as to limit the reverse power to be less than or equal to 60% of the rated capacity of the transformer substation:
-0.6×P rated,＜220kV ≤P sub ≤P rated,＜220kV ；
the upper planning model comprises:
determining the cluster access capacity of photovoltaic and fans under each 35kV transformer substation:
maxF upper ＝max(C cell -C inv -C main )
obtaining the electricity selling income of a renewable energy power generation user according to the electricity selling quantity of the photovoltaic and the fan:
wherein r is the discount rate, ny, N PV 、N WTG The planning years, the number of photovoltaics and the number of fans respectively, c sell,PV And c sell,WTG The online electricity prices of the photovoltaic and the blower fan are respectively,and->Respectively, the ith scene in the y year and the s scene PV Individual photovoltaics or ith WTG The actual on-line electric quantity of each fan;
and (3) solving the construction cost according to the installation capacity of the fan and the photovoltaic:
wherein, c ins,PV And c ins,WTG The construction cost of the photovoltaic and the fan unit capacity is respectively,and->Mounting capacities for photovoltaic and fan respectively
And obtaining the operation and maintenance cost of renewable energy power generation according to the installation capacity of the absolute photovoltaic and the total power generation capacity of the fan:
wherein, c om,PV Annual operating maintenance costs for photovoltaic unit installation capacity c om,WTG The operation and maintenance cost for the unit power generation amount of the fan,is the ith in the ith scene of the y year WTG The actual power generation of each fan;
renewable energy power generation planning is limited by geographical factors of installation sites and total investment cost factors, and installation capacity limitation needs to be met:
in the method, in the process of the invention,and->Respectively represent the ith PV Individual photovoltaic mounting points or ith WTG The upper limit of the installation capacity of the installation points of the fans;
the planning scene generation steps are as follows:
(1) Reading historical data X of wind resource, light resource, industrial load, agricultural load, commercial load and residential load ori ＝(x 1,ori ,x 2,ori ,x 3,ori ,x 4,ori ,x 5,ori ,x 6,ori ) Each type of data is subjected to per unit to obtain:
wherein x is i,ori I=1,..6 represents raw data of wind resource, light resource, industrial load, agricultural load, commercial load, and residential load, x i,ori,max I=1,..6 represents a peak value of a corresponding resource or a device installation capacity of a corresponding type of load, x i I=1, &..6 is the raw per-unit data of the wind resource, the light resource, the industrial load, the agricultural load, the commercial load and the residential load obtained;
(2) Using cumulative distribution function u i ＝F i (x i ),u i ∈[0,1]I=1,..6, converting the original data X to [0,1]Uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 )；
(3) For uniformly distributed data u= (U) 1 ,u 2 ,u 3 ,u 4 ,u 5 ,u 6 ) Carrying out parameter estimation and fitting goodness test by using a maximum likelihood function and an Anderson Darling method, and solving parameters and structures of a C-Vine Copula function corresponding to the data U;
(4) A Latin hypercube sampling method is used to generate [0 ], with independent uniformly distributed variables (w 1 ,w 2 ,w 3 ,w 4 ,w 5 ,w 6 ) The following conditional distribution formula is obtained according to the obtained C-Vine Copula structure:
wherein z= (Z) 1 ,z 2 ,z 3 ,z 4 ,z 5 ,z 6 ) Corresponding scenes in a uniform domain for six types of data;
(5) Inverse function x using raw data edge distribution function i ＝F i -1 (z i ),u i ∈[0,1]I=1,..6, finding a typical per-unit scene of six types of data in the actual domain;
(6) Multiplying the obtained typical per-unit scene of the four types of loads with the installation capacity of the four types of load equipment corresponding to each transformer substation in the planning area, summing the obtained typical scene of the total load of each transformer substation, and multiplying the resource per-unit scene with the resource peak value to obtain the typical scene of the resource.
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