CN107591844B - Active power distribution network robust reconstruction method considering node injection power uncertainty - Google Patents
Active power distribution network robust reconstruction method considering node injection power uncertainty Download PDFInfo
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Abstract
The invention discloses an active power distribution network robust reconstruction method considering node injection power uncertainty, which is characterized in that an active power distribution network robust reconstruction model considering the minimum times of network switching actions and the minimum network active loss as objective functions and considering network safe operation as constraint conditions is established on the basis of reasonably analyzing and modeling distributed power output and load demand uncertainty by using affine numbers. The method makes up the defects of neglecting the intermittent output of the distributed power supply and the charging of the electric automobile in the current power distribution network reconstruction scheme, and can provide support for the next safety evaluation of the active power distribution network.
Description
Technical Field
The invention relates to an active power distribution network robust reconstruction method considering node injection power uncertainty, and belongs to the technical field of active power distribution network optimized operation and control.
Background
The power generation grid connection of distributed power Supplies (DGs) such as high-permeability photovoltaic power stations and fans and the large-scale access and application of active loads such as Electric Vehicles (EVs) enable a traditional one-way radial power distribution network to be gradually changed into a multi-energy-source-containing power supply system, and if necessary, an Active Distribution Network (ADN) running in a weak annular topological structure is assisted. Meanwhile, the distributed power supply and the active load easily cause strong uncertainty of the injection power of the power distribution network, the traditional power distribution network reconstruction technology faces huge challenges, and the problem of researching the influence of the uncertainty on the network reconstruction is a difficult problem to be solved urgently. Therefore, the uncertainty of the injection power of the multi-type distributed power supply and the load needs to be reasonably analyzed and modeled, and is considered in a network reconstruction model, so that the reliability of the safe and economic operation of the active power distribution network is further improved.
In general, uncertainty problems of distributed power output and load demand are reflected in uncertainty of a specific power distribution network reconstruction model calculation, namely, line power flow. At present, probability load flow, fuzzy load flow and interval load flow are mainly calculated for uncertain load flow of a power distribution network, a power distribution network reconstruction optimization model based on uncertain load flow calculation is mainly divided into a probability model, a fuzzy number model and a robust model, wherein compared with the probability model and the fuzzy number model, the uncertainty problem of injection power of the power distribution network is described in the power distribution network robust reconstruction optimization model by an interval method, the prior specific distribution condition of parameters does not need to be obtained, only upper and lower boundary information of each uncertain variable needs to be concerned, and therefore the power distribution network reconstruction optimization model has a higher engineering application value.
At present, many research works have been carried out on the aspect of active power distribution network robust reconstruction technology considering node injection power uncertainty at home and abroad, but in most of the research works, the selection of the number of injected power intervals in the network has certain subjective initiative, reasonable modeling analysis is not carried out on the upper limit and the lower limit, and the established active power distribution network robust reconstruction model does not consider the problem of important load-charging load modeling of electric vehicles. In addition, the piecewise linear method adopted when the nonlinear variable in the model is subjected to the linear relaxation operation has low precision.
Disclosure of Invention
In order to overcome the defects of the traditional power distribution network reconstruction technology and the existing active power distribution network robust reconstruction technology, the active power distribution network robust reconstruction model is analyzed and expressed more precisely, the upper limit and the lower limit of uncertain physical quantities such as photovoltaic power generation, fan power generation, electric vehicle charging and the like in the model are reasonably selected and added into the active power distribution network robust model in the form of affine numbers, and in order to enable the mathematical model after linear relaxation to be as accurate as possible, a piecewise linear approximation method based on the optimal equidistant thought is introduced to linearly relax the original target function. The method can be used for making up the defects of neglecting the intermittent output of the distributed power supply and the charging of the electric automobile in the current power distribution network reconstruction scheme, and can provide support for the next safety evaluation of the active power distribution network.
In order to solve the technical problem, the invention provides an active power distribution network robust reconstruction method considering uncertainty of node injection power, which comprises the following steps:
(1) reasonably modeling and analyzing the uncertainty problem of the node injection power by adopting affine numbers, wherein the uncertainty problem of the node injection power comprises photovoltaic power generation, wind power generation and random charging of an electric automobile;
(2) on the basis of the step (1), establishing an active power distribution network robust reconstruction model taking the minimum number of network switching actions and the minimum network active loss as objective functions and comprehensively considering network safe operation as constraint conditions, wherein the constraint conditions comprise node injection power balance constraint, branch maximum capacity constraint and radial network topology constraint;
(3) a piecewise linear approximation method based on the optimal isometric thought is introduced to relax the target function of the robust reconstruction model of the active power distribution network into a linear solvable form, and the robust reconstruction model of the active power distribution network is further equivalently converted into a double-layer mixed integer linear programming problem according to a dual theorem;
(4) and decomposing and solving the converted robust reconstruction model of the active power distribution network by adopting a column constraint generation algorithm to obtain an optimal reconstruction scheme of the active power distribution network.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. the method can be used for making up the defects of neglecting the intermittent output of the distributed power supply and the charging of the electric automobile in the current power distribution network reconstruction scheme, and can provide support for the next safety evaluation of the active power distribution network;
2. compared with the existing active power distribution network robust reconstruction model, the method focuses on accurately expressing the active power distribution network robust reconstruction model, reasonably selects the upper limit and the lower limit of uncertain physical quantities such as photovoltaic power generation, fan power generation, electric vehicle charging and the like in the model, and adds the uncertain physical quantities into the active power distribution network robust model in the form of affine numbers, so that the active power distribution network robust reconstruction model established by the method is more accurate and has higher practical application value;
3. the column-and-constraints generation (C & CG) algorithm adopted in the invention is a relatively high-efficiency method, and the calculation efficiency and the solving performance of the C & CG algorithm are superior to those of the existing Benders and derivative algorithms thereof, so that the active power distribution network robust reconstruction mathematical model can be effectively solved, and the online application of the active power distribution network robust reconstruction technology can be further accelerated.
Drawings
FIG. 1 is a flow chart of a photovoltaic power generation system interval prediction algorithm employed in an embodiment;
FIG. 2 is a flow chart of a wind power system interval prediction algorithm employed in the embodiment;
FIG. 3 is a flowchart of an electric vehicle charging load interval prediction algorithm employed in the embodiment;
fig. 4 is a schematic diagram of a simple active power distribution network including multiple types of DG and loads according to an embodiment;
FIG. 5 is a flowchart of solving an active power distribution network robust reconstruction mathematical model with network node injection power uncertainty using C & CG algorithm according to an embodiment;
FIG. 6 is a flow chart of the present invention.
Detailed Description
On the basis of the existing theoretical research, reasonable analysis and modeling are carried out on uncertainty of distributed power supply output and load demand by using affine numbers, and an active power distribution network robust reconstruction model taking the minimum number of times of network switching actions and the minimum network active loss as objective functions and considering network safe operation as constraint conditions is established. In order to accurately solve the mathematical model, firstly, a piecewise linear approximation method based on the optimal equidistance thought is introduced to relax the original objective function into a linear solvable form; secondly, further equivalently converting the model into a double-layer mixed integer linear programming problem according to a dual theorem; and finally, solving the model by adopting an efficient decomposition algorithm, so that the calculation efficiency of the algorithm can be further improved. The method makes up the defects of neglecting the intermittent output of the distributed power supply and the charging of the electric automobile in the current power distribution network reconstruction scheme, and can provide theoretical support for the next safety evaluation of the active power distribution network.
Referring to fig. 1, most of the existing short-term power prediction models of photovoltaic power generation systems adopt deterministic point prediction, that is, a power value determined by photovoltaic output at a certain time in the future is given, and obviously, the uncertainty of the photovoltaic output is ignored by the point value power prediction method, and meanwhile, the prediction error is large. In order to improve a prediction result, students at home and abroad successively provide a novel interval prediction method for a photovoltaic power generation system in recent years, the method does not need to construct a complex mathematical relational expression between photovoltaic output and factors such as illumination intensity, external environment temperature and the like, namely, a prediction result interval of the photovoltaic output at a certain confidence coefficient at a certain moment in the future is provided through a large amount of statistical data of historical power generation, corresponding weather and the like and by combining a mathematical statistical prediction theory. Considering that the complexity of the interval state estimation model of the active power distribution network has a certain influence on the estimation result, the interval prediction of the photovoltaic power generation system output is performed by establishing a dual-output neural network model by using an upper and lower limit estimation method in the embodiment, and the algorithm mainly comprises the following implementation steps:
1) setting an input value of a neural network training system; photovoltaic output is related to a number of factors, such as illumination radiation intensity, photovoltaic array area, and ambient temperature. And collecting historical photovoltaic output data and meteorological data at corresponding moments according to a certain sampling interval, and taking the processed data as the input of a neural network.
2) An interval prediction evaluation function is determined. Important factors for measuring the interval prediction performance are interval coverage (PICP) and interval width (PINAW), and the calculation formulas are respectively shown in formula (1):
where λ is the number of deterministic predictions made, cκ′The evaluation index is the predicted value of the k' th time; suppose there is some predicted value yκ′When is coming into contact with
When c is greater thanκ′＝1；Otherwise, cκ′＝0；
AndP PVΛ is the difference between the minimum value and the maximum value of the target predicted value;
because the output interval prediction value of the photovoltaic power generation system is related to a plurality of influence factors, an ideal interval prediction result is high in coverage rate and small in width, but the coverage rate and the interval width are in contradiction, and an optimization function needs to be established by comprehensively evaluating the coverage rate and the interval width of the interval, so that multi-objective optimization is converted into single-objective optimization. The interval prediction comprehensive evaluation index function selected in this embodiment is as follows:
f＝PINAW(1+γ(PICP)e-η(PICP-Ψ))
where Ψ is the confidence value and is also the tuning parameter for f, η is also the tuning parameter for f, and η∈ [50,100] in actual engineering.
3) The optimal photovoltaic output interval prediction is given by combining a particle swarm optimization algorithm, and the optimal photovoltaic output interval prediction is specifically obtained by the steps of ① initializing and setting parameters such as the scale and the inertia constant of a particle swarm to generate an initial particle swarm (namely, an initial interval value of the photovoltaic output prediction), ② randomly initializing the position and the speed of each particle in a search space, setting the individual optimal position of each particle as the current particle position, obtaining the optimal position of the swarm, ③ continuously updating the position and the speed of the particle, ④ calculating the adaptive value of each particle, updating the individual optimal position of each particle and the optimal position of the whole swarm, ⑤ stopping the search if the stopping condition is met, otherwise returning to the step ③ to continue the search, and outputting the optimal photovoltaic output interval prediction by continuously optimizing until the global optimal solution is found.
In order to analyze the influence of different fluctuation scenes of photovoltaic output on the active power distribution network reconstruction scheme, the uncertainty of the photovoltaic output can be expressed as an affine number form as follows:
in the formula (I), the compound is shown in the specification,PVto influence the uncertainty disturbance factor of the photovoltaic output, andPV＝[-1,+1]。
the method for predicting wind power output by using an information association analysis means such as a neural network method is adopted in the embodiment, a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine (OS-E L M) structure is adopted on the basis of the existing research, wind speed is corrected by an E L M model, and then wind power generation power is predicted by a second layer E L M, and the method is mainly implemented as follows:
1) the method comprises the following steps of (1) carrying out data preprocessing, wherein historical generated power data of a wind power system and corresponding meteorological forecast data such as wind speed, wind direction, temperature and the like are included, and a vector theta in an equation (4) is considered as a network input of E L M:
Θ＝[v vsinvcosρ]T(4)
wherein v is the wind speed; v. ofsin、vcosThe positive and cosine values of the wind direction, respectively, rho is the air density, which can be calculated from the temperature, air pressure and relative air humidity, all the input data in the E L M network need to be normalized to [0,1 ]]An interval.
2) And a wind speed correction step, namely, according to a common wind turbine power output characteristic curve, the fact that a small wind speed change can cause an obvious wind turbine output power change in the process of cutting-in wind speed to rated wind speed is easily known, so that wind speed forecast data needs to be corrected to a certain degree, and a first layer E L M network can be adopted to simulate and correct the nonlinear relation between the forecast wind speed and the actually measured wind speed.
3) Adopting a second-layer E L M network to predict the wind turbine output interval, selecting the corrected wind speed value, the wind direction correction, the cosine value and the air density value at the current moment as the input values of the second-layer E L M network, and taking the upper and lower interval values of the wind turbine output at the current moment
Is output by the network.
The uncertainty in fan output can also be expressed as an affine number form as shown below:
in the formula (I), the compound is shown in the specification,WT＝[-1,+1]is an uncertainty disturbance factor influencing the output of the fan.
Referring to fig. 3, because charging of the electric vehicle is a strong uncertainty process, factors affecting the charging load of the electric vehicle include the driving characteristics of the vehicle owner, the selection mode of charging, the charging duration, the battery characteristics, the grid electricity price at the current time, and the like, it is difficult to perform modeling analysis on the prediction of the charging load demand of the electric vehicle from the mechanism direction. In order to improve the rationality and accuracy of the electric vehicle charging load interval prediction model, on the basis of the existing relevant research, the embodiment predicts the electric vehicle charging load demand by adopting a monte carlo sampling method based on statistical data rules and a mode of combining the interval number. The user behavior is mainly determined by the daily driving mileage d of the electric vehicle and the starting time t (assuming that the charging is started immediately after the last trip of the user is finished) in the charging process, and according to national household trip Survey item (NHTS 2009) Survey data, the probability statistical rules of d and t can be roughly obtained by combining a maximum likelihood estimation method, and are respectively shown as the following formulas (6) and (7):
in the formula, mud＝3.2，σd＝0.88，μt＝17.6，σt＝3.4。
In addition, the battery SOC of the electric automobile and the daily driving distance d thereof also approximately satisfy a linear relation, and then the charging time length T of the electric automobileCCan be estimated as
In the formula, W100The average power consumption of the electric automobile is hundred kilometers (unit: kW.h/100 km); pCThe charging power (unit: kW) of the EV.
In the optimized peak-valley electricity price time period, the electric automobile generally adopts an orderly charging mode, and then a single electric automobile is in t0The charging power demand at a time may be expressed as
In the formula: p (t)0) Is t0Power requirements of a single electric vehicle on a time section; pC(t0) Is t0Charging power of a single EV on a time section; zetaC(t0) Is t0The probability of the charging power of a single electric vehicle on the time section, psi (·), is a probability density function of the initial charging time of the electric vehicle, i.e. equation (7).
Assuming that a certain region has M electric vehicles, and the total charging load of the electric vehicles can be obtained by accumulating the single electric vehicles one by one in one day, the tth0The total electric vehicle charging load in this region of time section is:
it should be noted that, because the analytic solution of equation (9) is difficult to derive, the total charging demand of EV on each time slice in a certain day needs to be sampled by using the monte carlo method based on a large amount of historical statistical data, and the total charging demand is approximately in accordance with the normal distribution, and the expected value and the standard deviation are μEVAnd σEVFrom this, EV charging demand is expressed in terms of the number of available sections:
in the above equation, the radius adjustment parameter with ν being a number of intervals can be set in accordance with actual circumstances, and generally, ν is 3, whereby equation (11) can be converted into an affine form as shown in the following equation:
in the formula (I), the compound is shown in the specification,EV＝[-1,+1]is an uncertainty perturbation factor that affects EV charging demand.
For the conventional load in the active power distribution network, the fluctuation characteristics of the conventional power load have certain regularity, so the accuracy of load prediction is often very high, particularly the accuracy of a short-term prediction method for 24 hours before the day is as high as more than 90%, and therefore the uncertainty of the conventional load can be expressed by affine numbers as follows:
in the formula, PLIn order to be predictive of the normal load demand,L＝[-1,+1]the perturbation factor is its uncertainty.
Referring to fig. 4, a schematic diagram of a simple active power distribution network including a DG such as a photovoltaic power generation system and a wind turbine power generation system, and an electric vehicle and a conventional load is shown. In order to better reflect the influence of uncertainty of DG and load injection power in a system on a network reconstruction result and further improve the practical engineering application value of the power distribution network reconstruction result, all node injection power in an active power distribution network robust reconstruction model is not fuzzy represented by a certain determined predicted value, but is respectively depicted by affine numbers, a worst fluctuation scene (a second stage) is searched in a given DG and load uncertainty range, and a network reconstruction scheme (a first stage) under the worst fluctuation scene is formulated, so that the active power distribution network two-stage robust reconstruction model shown as the following formula can be built on the basis of the existing power distribution network robust reconstruction research:
1) objective function
In the formula: c1Cost factor, C, required for one branch switching action2Cost coefficient (C) corresponding to active loss during network reconfiguration1、C2The value of (b) can be set according to actual conditions); ik is a branch in the network with i as a head-end node and k as a tail-end node; omegan、ΩbRespectively are node and branch number sets in the network; lambda [ alpha ]ikFor the state information (binary nominal variables) of the switches on the branch ik, λik0/1 denotes that the switch on branch ik is in open/closed state, and
then is the initial state information of the switch on the branch ik; rikIs the resistance value of the branch; pik、QikRespectively the active power and the reactive power flowing through the branch circuit; viThe voltage amplitude of the branch head end node i can be approximately regarded as V in a static reconstruction model of the power distribution networki＝1.0(p.u.)。
The strong non-convex form presented by equation (14) will inevitably cause the network reconstruction model to be subject to the NP-hard problem and not easy to solve efficiently. From the mathematical point of view, the quadratic function with the shape of y ═ f (x) can be infinitely approximated by a straight line by introducing the piecewise linear approximation idea, so that the quadratic function is subjected to first orderAnd (5) linear approximation processing. The reasonable segmentation method is selected from the linear relaxation idea and is a key problem, in order to improve the accuracy of linear approximation as much as possible, the invention adopts the optimal equidistant piecewise linear approximation method commonly used in the mathematical field to carry out pair formula (14)
Respectively performing first-order linear approximate expression, and expressing the relaxed objective function as:
in the formula, l and j are respectively PikAnd QikNumber of cross section after piecewise linearization, and omegal、ΩjRespectively collecting the number of the sections; pik_l、Qik_jAre respectively PikAnd QikCorresponding linear function on each cross section, and αik_l、βik_jThen the slope of its linear function, respectively, and the following derived constraints:
2) constraint conditions
① power balance constraints
In the formula (I), the compound is shown in the specification,
load active and reactive demands at node i expressed in the form of affine numbers,
active and reactive power outputs of the distributed power supply at the node i expressed in the form of affine numbers respectively, it needs to be mentioned that most of conventional loads and DGs are currently used in the steady-state analysis process of the active power distribution networkThe method adopts an active power-reactive power control mode, namely the reactive power of the conventional load, the photovoltaic output and the fan output can be correspondingly calculated according to a given power factor, and the reactive power of the electric automobile is controlled by a unit power factor, and the reactive power requirement of the electric automobile for charging is zero; for convenience of description, the affine numerical forms shown in the formulae (3), (5), (12) and (13) are uniformly equivalent to the affine numerical forms shown in the formulae
Wherein W is a rated value, and delta W is a maximum fluctuation value and is a disturbance factor; psi、QsiRespectively the active and reactive powers, omega, of the outlet terminal of the transformer installed at the node iSIs a collection of nodes in the network where the transformer is installed.
② branch capacity constraints
In the formula (I), the compound is shown in the specification,
the maximum active and reactive power allowed to flow on branch ik, respectively.
③ radial network topology constraints
In the formula, N is the total action times of switches or breakers on all branches in the network; mu.sikLikewise a binary nominal variable, mu ik1 represents that the node i on the branch ik is a parent node (root node) of the node k; omegamThe node is a collection of other nodes except the node provided with the transformer in the network. In actual engineering, in order to protect and set and reduce short-circuit current, a power distribution network is generally required to run radially as much as possible.
In summary, the two-stage robust reconstruction mathematical model of the active power distribution network, which is established in this embodiment and takes the multi-type DG and the load uncertainty into consideration, takes (15) as an objective function and takes equations (16) to (19) as constraint conditions, and it can be known by the model that the first stage takes the load demand and the uncertain disturbance of the distributed power supply output as decision variables, and the second stage takes the switch state as the decision variables.
Referring to fig. 5, in this embodiment, a flowchart for solving an active power distribution network robust reconstruction mathematical model with uncertainty of network node injection power by using a C & CG algorithm is specifically analyzed as follows:
the method for solving the two-stage robust reconstruction model of the active power distribution network established for the research institute is characterized in that firstly, the model is expressed as a matrix form:
in the formula, phi is an uncertainty set of injection power of each node; lambda and x are decision variables of the first stage and the second stage respectively; c. CTλ represents the number of switching actions during the network reconfiguration, and bTx represents the active loss of the network; the three constraints represent a radial network topology constraint, a branch capacity constraint, and a node injection power balance constraint, respectively.
Since Φ is an unknown but bounded discrete set, let Φ be { Φ ═ Φ1,φ2,…,φwThe purpose of two-stage robust reconstruction is to optimize the decision variable λ of the first stage, while the decision variable x of the second stage is actually a function of the uncertain bounded set Φ, which can mean x ═ x1,x2,…,xt}. Therefore, the decision variables in the first stage are discrete variables, the decision variables in the second stage are continuous variables, and the robust reconstruction model is analyzed in a mathematical form and is known to be a large-scale combinatorial optimization problem, and generally, a decomposition algorithm can be adopted for solving, wherein column-and-constraint generation (C) is generated&CG) algorithm is a relatively high-efficiency method, and the calculation efficiency and the solving performance of the CG algorithm are superior to those of Benders and derivative algorithms thereof, so that the CG algorithm is widely applied to the fields of large-scale unit combination, economic dispatching and the like in recent years, and therefore C is adopted in the invention&CG algorithm based two-stage robust static reconstruction model for established active power distribution networkAnd (6) solving.
The principle of the C & CG algorithm can be used to transform equation (20) into a master-problem (MP) as shown in equation (21) and a sub-problem (SP) as shown in equation (22):
the main problem is that the states of all switches in the network are decided under the constraint conditions of radial operation, node injection power balance, branch capacity and the like so as to minimize the network operation cost (including the cost caused by switch action cost and network loss), and the uncertain set phi in the constraint conditions of the main problem is replaced by a partial enumeration scene with an superscript r' by enumerating a limited number of possible fluctuation scenes in each node injection power uncertain set phi, so that the main problem is known to be a mixed integer linear programming problem in a single optimization target form, and the target value after optimization is a lower limit value of an original target function (20). And the subproblems are used for generating new enumeration scenarios and are added to the main problem shown in the formula (21) in the form of constraints. For any given λ*All subproblems solve a corresponding optimal solution xi (lambda)*) Or to give decisions that determine some uncertain disturbance sets are not feasible for the second stage. The sub-problem is to generate for a certain λ*Of the worst fluctuating scenario, i.e. cTλ*+Ξ(λ*) Can be used as the upper limit value of the original objective function formula (20). C&The CG algorithm carries out iterative solution on the subproblems, so that new column constraint conditions can be continuously generated and added into the main problem to carry out iterative solution again until the upper limit and the lower limit are converged to the optimal solution.
It should be mentioned that the objective function in the sub-problem is in the form of "max-min" double-layer optimization, and is difficult to be directly converted into a single-layer optimization objective function, so that it is not easy to solve numerically. For such problems, a strong dual theorem can be considered, and a lagrange multiplier is introduced to express the inner layer model by using the dual model thereof to obtain a 'max' model, so that the 'max' model is converted into a single 'max' optimization target form, as shown in formula (23):
in the formula, both pi and theta are Lagrange multipliers. Meanwhile, in order to avoid the situation that the algorithm is difficult to converge due to multiplication of a plurality of variables of pi, theta and phi in the operation process, the worst fluctuation scene of the uncertainty of the injection power of each node is set at the extreme value point of the uncertainty interval range in the actual algorithm design process.
Based on the analysis, given the convergence accuracy of the algorithm, the approximate solving process of the active power distribution network two-stage robust reconstruction model based on the C & CG algorithm is shown in FIG. 5.
Claims (8)
1. The active power distribution network robust reconstruction method considering the uncertainty of the node injection power is characterized by comprising the following steps: the method comprises the following steps:
(1) reasonably modeling and analyzing the uncertainty problem of the node injection power by adopting affine numbers, wherein the uncertainty problem of the node injection power comprises photovoltaic power generation, wind power generation and random charging of an electric automobile;
(2) on the basis of the step (1), establishing an active power distribution network robust reconstruction model taking the minimum number of network switching actions and the minimum network active loss as objective functions and comprehensively considering network safe operation as constraint conditions, wherein the constraint conditions comprise node injection power balance constraint, branch maximum capacity constraint and radial network topology constraint;
(3) a piecewise linear approximation method based on the optimal isometric thought is introduced to relax the target function of the robust reconstruction model of the active power distribution network into a linear solvable form, and the robust reconstruction model of the active power distribution network is further equivalently converted into a double-layer mixed integer linear programming problem according to a dual theorem;
(4) decomposing and solving the converted active power distribution network robust reconstruction model by adopting a column constraint generation algorithm to obtain an optimal reconstruction scheme of the active power distribution network;
in the step (1), when the uncertainty of the output of the photovoltaic power generation system is characterized by the affine number, performing interval modeling on the output of the photovoltaic power generation system by establishing a double-output neural network model by adopting an upper and lower limit estimation method, converting the interval number into an affine number form and adding the affine number form to the established robust reconstruction model;
when the output uncertainty of the wind power generation system is characterized by the interval number, a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine structure is adopted, the wind speed is corrected through the model, the wind power generation power is predicted by a second layer, the output uncertainty of the fan expressed by the interval number is obtained, and the interval number is converted into an affine number form and added into an established robust reconstruction model;
when the interval modeling analysis is carried out on the electric vehicle random charging, the interval prediction is carried out on the electric vehicle charging load demand in a mode of combining a Monte Carlo sampling method based on statistical data rules with the interval number, and the interval number is converted into an affine number form and added into the established robust reconstruction model.
2. The active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 1, characterized in that: the method for estimating the upper and lower limits is adopted to predict the interval of the output of the photovoltaic power generation system by establishing a dual-output neural network model, and comprises the following steps:
1) setting input values of a neural network training system: collecting historical photovoltaic output data and meteorological data at corresponding moments according to a certain sampling interval, and taking the processed data as input of a neural network;
2) determining an interval prediction evaluation function: important factors for measuring the interval prediction performance comprise interval coverage rate and interval width, and the calculation formulas are respectively shown as formula (1):
where PICP is the interval coverage, PINAW is the interval width, λ is the number of deterministic predictions, cκ′The evaluation index is the predicted value of the k' th time; suppose there is some predicted value yκ′When is coming into contact with
When c is greater thanκ′1 is ═ 1; otherwise, cκ′＝0；
AndP PVΛ is the difference between the minimum value and the maximum value of the target predicted value;
an optimization function needs to be established through comprehensive assessment of the interval coverage rate and the interval width, multi-objective optimization is converted into single-objective optimization, and an interval prediction comprehensive assessment index function f is as follows:
wherein psi is a confidence value, η is an adjusting parameter of an interval prediction comprehensive evaluation index function f;
3) and (3) providing the optimal photovoltaic output interval prediction by combining a particle swarm optimization algorithm, wherein the optimization method comprises the following specific steps:
① initializing particle swarm parameters to generate an initial particle swarm, namely an initial interval value predicted by photovoltaic output;
② randomly initializing the position and speed of each particle in the search space, setting the individual optimal position of each particle as the current particle position, and obtaining the group optimal position;
③ continuously updating the position and velocity of the particle;
④ calculating the adaptive value of each particle, updating the individual optimal position of each particle and the optimal position of the whole population;
⑤ if the stop condition is satisfied, stopping the search, otherwise returning to step ③ to continue the search.
3. The robust reconstruction method for the active distribution network considering uncertainty of node injection power according to claim 1 or 2, characterized by: the uncertainty of the photovoltaic contribution is expressed in the form of affine numbers:
in the formula (I), the compound is shown in the specification,PVto influence the uncertainty perturbation factor of the photovoltaic contribution, andPV＝[-1,+1]。
4. the active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 1, characterized in that: the method adopts a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine structure to obtain the uncertainty of the output of the wind power generation system represented by the interval number, and comprises the following steps:
1) data preprocessing: taking the vector theta in the formula (4) as the input of the neural network:
Θ＝[v vsinvcosρ]T(4)
wherein v is the wind speed; v. ofsin、vcosRespectively are the sine and cosine values of the wind direction; ρ is the air density; all input data in the neural network are normalized to [0,1 ]]An interval;
2) and a wind speed correction link: a first layer of neural network is adopted to simulate and correct the nonlinear relation between the forecast wind speed and the actually measured wind speed;
3) predicting the output interval of the wind power generation system: adopting a second layer of neural network to predict the interval of the output of the wind power generation system, selecting a corrected wind speed value, a wind direction correction value, a cosine value and an air density value at the current moment as input values of the second layer of neural network, and taking values of upper and lower intervals of the output of the wind power generation system at the current moment
Outputting for the network;
the uncertainty of the wind power system contribution is represented in the form of affine numbers as follows:
in the formula (I), the compound is shown in the specification,WT＝[-1,+1]is an uncertainty disturbance factor influencing the output of the fan.
5. The active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 1, characterized in that: the method is characterized in that a Monte Carlo sampling method based on statistical data rules is combined with interval numbers to predict the charging load demand of the electric automobile: according to survey data of family trip survey items in the United states, a maximum likelihood estimation method is combined to obtain the daily driving mileage d of the electric vehicle and the probability statistical law of the initial time t of the charging process, wherein the probability statistical laws are respectively shown as the following formulas (6) and (7):
charging is started immediately after the last trip of the user is finished;
charging duration T of electric automobileCComprises the following steps:
in the formula, W100The unit is the hundred kilometers average power consumption of the electric automobile: kW.h/100 km; pCCharging power for EV, unit: kW;
a single electric vehicle at t0The charging power demand at a time may be expressed as
In the formula: p (t)0) Is t0Power requirements of a single electric vehicle on a time section; pC(t0) Is t0Charging power of a single EV on a time section; zetaC(t0) Is t0The probability of the charging power of a single electric vehicle on a time section, psi (·), is a probability density function of the initial charging moment of the electric vehicle;
t th day0The total charging load of the electric automobile in the region on the time section is as follows:
wherein M is the total quantity of electric vehicles in the region;
based on historical statistical data, total charging demands of the EV on each time section in a certain day are respectively sampled by using a Monte Carlo method, the charging demands are subjected to normal distribution, and the expected values and standard deviations are respectively muEVAnd σEVFrom this, EV charging demand is expressed in terms of the number of available sections:
in the formula, upsilon is a radius adjusting parameter of interval number;
the charging load requirement of the electric automobile is in the form of affine number as shown in the following formula:
in the formula (I), the compound is shown in the specification,EV＝[-1,+1]an uncertainty perturbation factor affecting EV charging demand;
the uncertainty of the conventional load can be expressed as an affine number:
in the formula (I), the compound is shown in the specification,PLin order to be predictive of the normal load demand,L＝[-1,+1]the perturbation factor is its uncertainty.
6. The active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 1, characterized in that: the objective function in step 2 is expressed as:
in the formula: c1Cost factor, C, required for one branch switching action2A cost coefficient corresponding to active loss during network reconstruction; ik is a branch in the network with i as a head-end node and k as a tail-end node; omegan、ΩbRespectively are node and branch number sets in the network; lambda [ alpha ]ikFor the state information of the switches on the branch ik, λik0/1 indicates that the switch on branch ik is in the open/closed state,
initial state information of the switch on the branch ik; rikIs the resistance value of the branch; pik、QikRespectively the active power and the reactive power flowing through the branch circuit; viThe voltage amplitude of a node i at the head end of the branch circuit is;
in the step 3, the optimal equidistant piecewise linear approximation method is adopted to carry out on the equation (14)
Respectively performing first-order linear approximate expression, and expressing the relaxed objective function as:
in the formula, l and j are respectively PikAnd QikNumber of cross section after piecewise linearization, and omegal、ΩjRespectively collecting the number of the sections;Pik_l、Qik_jare respectively PikAnd QikCorresponding linear function on each cross section, and αik_l、βik_jThen the slope of its linear function, respectively, and the following derived constraints:
7. the active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 6, characterized in that: the power balance constraint is expressed as:
in the formula (I), the compound is shown in the specification,
load active and reactive demands at node i expressed in the form of affine numbers,
respectively representing active and reactive power output, delta P, of the distributed power supply at a node i in the form of affine numberi D、
The fluctuation limits, Δ P, of the active and reactive demand of the load at node i, respectivelyi G、
Respectively setting active and reactive output fluctuation threshold values of the distributed power supply at the node i as disturbance factors; psi、QsiRespectively the active and reactive powers, omega, of the outlet terminal of the transformer installed at the node iSA node set with a transformer installed in the network;
the branch capacity constraint is expressed as:
in the formula (I), the compound is shown in the specification,
the maximum active power and the maximum reactive power allowed to flow through the branch ik are respectively;
the radial network topology constraint is expressed as:
in the formula, N is the total action times of switches or breakers on all branches in the network; mu.sikIs a binary nominal variable, muik1 represents that the node i on the branch ik is a father node of the node k; omegamThe node is a collection of other nodes except the node provided with the transformer in the network.
8. The active power distribution network robust reconstruction method considering node injection power uncertainty according to claim 1, characterized in that: and 4, decomposing and solving the converted robust reconstruction model of the active power distribution network, wherein the method comprises the steps of splitting the original objective function into a main problem and a subproblem, and iteratively solving the subproblem to generate new column constraint conditions, adding the new column constraint conditions into the main problem, and iteratively solving again until the upper limit and the lower limit are converged to an optimal solution.
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