CN107145707B - Distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost - Google Patents
Distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost Download PDFInfo
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Abstract
The invention provides a distribution transformer planning method considering distributed energy output uncertainty and life cycle cost, and belongs to the field of power distribution network planning. Firstly, considering the output uncertainty of distributed photovoltaic power generation, providing a distribution transformer risk constant volume method based on an opportunity constraint theory; on the basis, a three-point estimation method is used for calculating the distribution network probability power flow after the distributed photovoltaic power generation is accessed, meanwhile, a target function based on the life cycle cost is constructed, and finally, a distribution transformer uncertainty planning model based on the life cycle theory is provided. The example simulation result shows that compared with the traditional deterministic distribution transformer planning method, the method provided by the invention not only can finely measure all the costs in the whole life cycle of the equipment, but also can accurately calculate the influence of the uncertainty of the distributed power supply on the constant volume model selection of the equipment, and makes up the boundary between the constant volume and the model selection of the distribution transformer, thereby effectively improving the economical efficiency of the distribution transformer planning.
Description
Technical Field
The invention relates to a power distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost, and belongs to the field of power distribution network planning including Distributed Generation (DG).
Background
In recent years, distributed power generation technology has been increasingly emphasized with the increasing problems of environmental pollution and energy shortage. In a power distribution network, the permeability of a distributed power source, especially a distributed Photovoltaic Generation (PVG), is rapidly increasing, and under this background, how to make scientific power equipment investment decisions and building a reliable and economic power distribution network is a research hotspot in the current planning field.
Distribution transformers (distribution transformers) are important power equipment in a power distribution network, and have the advantages of large use amount, wide application range, long operation time and huge energy-saving potential. For a long time, distribution transformer investment planning focuses on initial investment or stage cost, and neglects potential cost of equipment in the whole service cycle such as later-stage operation and retirement disposal, so that the selection of capacity and model of the equipment lacks the whole view angle throughout the whole service life cycle of the equipment, and an over-conservative or aggressive planning scheme is easily formed, and large investment waste is caused. In view of this, a distribution transformer investment decision method based on a Life Cost Cycle (LCC) theory has been gradually recognized and applied, and it is mainly to realize constant volume selection for power distribution science by accurately calculating a value characteristic change rule of a distribution transformer in a whole service Cycle (i.e., a Life Cycle) from purchase, operation, maintenance and retirement recovery on the basis of ensuring planning reliability. Meanwhile, researches find that although accurate assessment of the distribution transformation LCC cost is realized in the distribution transformation planning, certain problems still exist: on one hand, the influence of uncertain factors in the power distribution network is not considered during planning, and the uncertain factors in the power distribution network planning process are further increased along with the access of a large number of distributed power supplies to the power distribution network, so that the distribution transformation planning based on the deterministic LCC cost cannot accurately evaluate the influence of the uncertain factors, and the actual requirements of the existing power distribution network planning containing the distributed power supplies are difficult to meet; on the other hand, most of the conventional distribution and transformation model selection problems only aim at the distribution and transformation model selection problem under the fixed capacity, the distribution and transformation volume and the model selection are divided into two independent problems to be calculated respectively in the planning process, and the inherent influence of the distribution and transformation model selection on the distribution and transformation model selection is possibly ignored, so that the calculation accuracy of a planning model is influenced.
At present, a planning method accurately considering uncertainty factors is applied to a certain extent in the fields of power supply planning and circuit grid planning. The planning model considering the influence of uncertainty factors is constructed by using uncertainty modeling methods such as opportunity constraint, robust optimization and the like, so that a series of planning problems of the power grid after the distributed power supply is connected are solved, and good reference and reference are provided for the distribution transformer planning problem research.
Disclosure of Invention
The invention provides a distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost after distributed photovoltaic power generation access, which comprises the steps of firstly, constructing a risk model for distribution capacity calculation based on an opportunity constraint theory, determining the optimal distribution capacity in different confidence intervals, then, providing a distribution network probability load flow calculation method based on a three-point estimation method, taking the probability load flow calculation method as a constraint condition to be included in a planning model, then, considering the influence of distribution capacity selection on investment cost and operation cost, providing a mathematical expression mode of distribution transformation LCC cost, and finally, establishing an uncertainty distribution planning model aiming at minimizing the LCC cost.
The technical scheme adopted by the invention is as follows:
a power distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost comprises the following steps:
step 1: and (4) planning the distribution capacity based on the opportunity constraint theory.
Step 1.1: determining a photovoltaic output probability model and a load fluctuation probability model of a planning region according to actual conditions;
step 1.2: and establishing a distribution transformation capacity planning model based on opportunity constraint according to the actual load data of the distribution area.
Step 2: and modeling the uncertainty distribution transformation selection based on the life cycle theory.
Step 2.1: establishing a distribution transformation selection type objective function based on a full life cycle theory;
step 2.2: and (4) carrying out fine analysis on the operation cost of the distribution transformer by considering the uncertainty of photovoltaic output and load fluctuation.
And step 3: a probability power flow model solving method based on a three-point estimation method.
Through the steps, the planning of the distribution network transformer considering the photovoltaic output uncertainty and the whole life cycle cost is completed.
The invention provides a power distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost, which has the following technical effects:
1): compared with the traditional constant-volume type selection method for the distribution transformer, the influence of the photovoltaic power generation output uncertainty and the total life cycle cost of the distribution transformer are considered at the same time, the uncertain LCC planning method is provided, a conservative or impersonable planning scheme is effectively avoided, and the refinement level of the planning is improved.
2): compared with the traditional distribution transformer constant volume model selection method, the influence of distribution transformer capacity selection on investment cost and operation cost in distribution transformer model selection is fully considered, the unification of distribution transformer constant volume and model selection problems is realized, and the planning refinement level is improved.
Drawings
FIG. 1 is a flow chart of solving a probability power flow model based on a three-point estimation method.
FIG. 2 is a graph illustrating iterative convergence according to an embodiment of the present invention.
FIG. 3 is a comparison of the prediction error probability density versus the fitting curve for different prediction models of the present invention.
Fig. 4 is a distribution transformation LCC cost diagram under different comprehensive model selection modes under the method 1.
Detailed Description
A power distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost is specifically implemented as follows
Step 1: and (3) planning the distribution transformer capacity based on the opportunity constraint theory:
step 1.1: and determining a photovoltaic output probability model and a load fluctuation probability model of the planning region according to the actual situation.
The illumination intensity over a certain period of time is generally described using a Beta distribution:
in the formula: i is the intensity of light, IrRepresenting a maximum illumination intensity during the time period; alpha and Beta are two parameters of Beta distribution; Γ (·) is a gamma function.
The relationship between PVG contribution and illumination intensity can be approximated as:
in the formula: pPVGThe magnitude of the photovoltaic output active power is obtained;the rated capacity of the photovoltaic unit.
According to the function distribution theorem of random variables, the probability density function of the output of the photovoltaic generator set is deduced by combining the formula (1) and the formula (2) as follows:
in the formula: qPVGIs the reactive component of the light output power;and the power factor of the photovoltaic unit is shown.
The load fluctuation characteristic is generally described approximately using a normal distribution:
in the formula: pLIs the active component of the load; mu.sP、σPThe expectation and standard deviation of the load active component; qLIs the reactive component of the load; theta is expressed as the power factor angle of the load.
Step 1.2: establishing a distribution transformation capacity planning model of the transformer area based on opportunity constraint:
the uncertainty of the output of the photovoltaic power grid connected to the load side and the active power P provided by the superior power grid of the transformer area are processed by using the opportunity constraint theoryNAnd photovoltaic active power output PPVGThe sum of the active power P is less than the active power P required by the transformer areaLShould not exceed a given confidence e:
f{PN+λPPVG≤PL}≤e(5)
in the formula: f {. denotes the probability that the event holds in {. is }; lambda represents the proportion of the photovoltaic direct supply user output to the total output; the confidence e is given artificially according to the actual economic and social development conditions of the region.
Simultaneous equations (3) and (5) can be obtained:
active power P required by known platform loadLFrom the above equation, the net supply load P at a given confidence level can be determinedNThe increase of the load of the set area is totally increased by PNTo undertake, the distribution transformer attachment capacity can be determined according to equation (7):
in the formula:representing the active power provided by the superior power grid in the t year; delta is the annual average load growth rate; t planning the maximum service life of the distribution transformer;representing the distribution capacity of the jth branch upper platform area of the distribution network in the life cycle T; eta is the economic load rate of the distribution transformer; n is a radical ofbranchRepresenting the total number of the branch circuits of the power distribution network; xijRepresents the proportion of the load of the distribution network distribution area on the jth branch, kjThe load synchronization rate of the j-th branch road is the load synchronization rate of the j-th branch road.
Step 2: modeling of uncertainty distribution transformation selection based on a life cycle theory:
step 2.1: establishing a type selection objective function:
the objective function of the distribution transform selection planning model is as follows:
minCT＝CI+CW+CO+CF+CR (8)
in the formula: cTThe LCC cost is distributed and changed in the period T; cIInitial investment cost for distribution transformer; cWThe operating cost for the distribution transformer; cOThe maintenance cost for the distribution transformer; cFFailure cost for distribution transformer; cRThe decommissioning costs for the distribution transformer.
Step 2.2: detailed model of cost of each stage in distribution transformer whole life cycle considering photovoltaic output and load fluctuation uncertainty
1) Initial investment cost C of distribution transformerI：
The initial investment cost of the distribution transformer mainly comprises the purchase cost C of the distribution transformerGZAnd installation and commissioning cost CAZIt is mainly influenced by the size of the transformer capacity and the type selection:
in the formula: the distribution transformer installation and debugging cost is generally 6.2% of the purchase cost;the distribution type of the jth branch upper platform area of the power distribution network in the life cycle T is shown; g (-) is a function of the change of the initial investment cost along with the distribution transformation capacity and the model, the larger the selection of the distribution transformation capacity is, the better the model selection is, the larger the initial investment cost is, and the specific change refers to the relevant distribution transformation parameters, see appendix.
2) Distribution transformer operating cost C considering photovoltaic output and load fluctuation uncertaintyWAnd (3) analysis:
the operation cost of the distribution transformer mainly comprises the operation energy consumption cost C of the distribution transformerNHAnd cost of daily routing inspection CCS。
In the formula:the energy consumption cost of the year t is changed;for the annual inspection cost of the distribution transformer, the daily inspection expense of the distribution transformer is about 5 ten thousand yuan per year; r is the inflation rate of the currency, and is usually taken to be 3.5%; r is social discount rate, and is usually 10%; p is the comprehensive electricity price; delta StFor the unit running loss of the distribution transformer in the t year, the detailed mathematical expression is as follows:
in the formula:andrespectively unit no-load loss and unit load loss in the t year of the distribution transformer;andrespectively represents unit no-load active loss and unit no-load reactive loss in the t year of the distribution transformer, and M (-) and N (-) respectively representThe function changing along with the distribution transformer model and the capacity can be directly calculated and obtained by referring to related distribution transformer technical parameters;andrespectively representing unit load active loss and unit load reactive loss in the t year of the distribution transformer; f (-) and S (-) respectively representA function which changes with distribution type, capacity, photovoltaic output and load fluctuation; k is the reactive economic equivalent, i.e. the active power loss caused in the transformer per kW of reactive power loss, and is usually 0.1 kW/kvar.
Considering the uncertainty of photovoltaic output and load fluctuation, the distribution transformer operation load loss can not be accurately measured directly according to the nameplate parameters, therefore, the invention researches and introduces the probability power flow model to accurately solve the distribution transformer load loss of the distribution network transformer branch, and the probability power flow model is as follows:
in the formula: paAnd QaRespectively representing the active power and reactive power injection quantity of the node a; w represents the number of distribution network nodes; vaAnd VbRespectively representing the voltage amplitudes of the node a and the node b; r iszAnd xzRespectively a platform area branch circuit resistor and a reactor; r isbAnd xbRespectively a distribution resistance and a reactance; gabAnd BabRespectively representing the real part and the imaginary part of the node admittance matrix; deltaabRepresenting the phase angle difference between node a and node b.
3) Maintenance cost C for distribution transformerO：
The overhaul and maintenance cost of the distribution transformer mainly comprises the overhaul cost C of the operation life cycle of the distribution transformerDXAnd minor repair cost CXXThe service life of the distribution transformer is 20 to 25 years in a normal condition, and the distribution transformer is subjected to minor repair every year, major repair every 5 years and major repair every 10 years after being put into operation. The cost is irrelevant to the size and the model of the distribution transformation capacity, and the calculation formula is as follows:
in the formula: cdxRepresents a single overhaul cost; cxxRepresenting the single minor repair cost, and U representing the major repair times; floor (. cndot.) indicates decimal rounding down.
4) Distribution transformer fault cost CCF：
The distribution transformer fault cost mainly comprises distribution transformer fault overhaul cost and fault loss cost. This cost is related to the distribution capacity and model selection. Can be represented by the following formula:
in the formula: ccfAnnual fault costs; kdFor conversion multiple of electricity price, generally take Kd＝15；tgMean time of year accident power off time, tg＝ε×24；ψiRepresenting the average load rate of the distribution transformer in the t year; epsilon is the annual distribution transformer accident rate, the better the distribution transformer model, the lower the accident rate; cjxThe failure overhaul cost is 3% of the equipment purchase cost generally; and epsilon is the annual fault rate of the distribution transformer.
5) Distribution transformer retirement disposal cost CCD：
The decommissioning disposal cost of the distribution transformer mainly comprises the scrapping cost of the distribution transformer and the residual value fee of the equipment. The residual charge of the equipment is positively correlated with the distribution variable capacity and the model. Is represented as follows:
in the formula: cbfThe equipment scrapping cost is 32 percent of the equipment installation cost generally; cczThe residual value fee of the equipment is generally 5 percent of the purchase fee.
Step 2.3: constraint conditions are as follows:
1) node voltage and branch current constraints
In the formula: viminAnd VmaxRespectively is the minimum value and the maximum value of the voltage amplitude of the ith node; i isjAndthe actual value and the maximum allowable value of the jth branch current are obtained; n is a radical ofbusAnd the total number of the nodes of the power distribution network.
2) And DG access node installation capacity constraint:
in the formula: si.DGInstalling capacity for the access node of the ith node DG;it is allowed to install an upper capacity limit for the ith node DG.
3) Distribution and transformation model and capacity discreteness constraint:
the set A is set as a distribution transformer design capacity grade, the set B is a model of a distribution transformer to be selected, and the following constraint conditions exist:
and step 3: a three-point estimation method-based probabilistic power flow model solving method comprises the following steps:
distribution transformer unit load loss Delta S of set areaFThe functional relationship with photovoltaic output and platform load is as follows:
in the formula: delta SWDistributing the loss of the branch where the transformer is located for the transformer area;andrespectively representing the photovoltaic output and the load of the ith node; ζ represents the ratio of the distribution impedance to the impedance of the branch in which it is located.
Make unit load loss Delta SFThe random variable Y is used for expressing, the photovoltaic output and the platform area load are expressed by the random variable X, and the formula (12) is simplified as follows:
Y＝ζ×f(X)＝ζ×f(X1,X2…,Xn) (20)
in the formula: n represents the total number of random variables X.
Assume X for each random variablekThe expected and standard deviations (k ═ 1,2,3 … n) are μkAnd σkAnd selecting a random variable XkDesired μ ofkAnd three sampling values at each point in the left and right fields, denoted as xk.i(i ═ 1,2,3), the expression for which is as follows:
xk.i＝μk+ξk.iσk(i＝1,2,3) (21)
in the formula: xik.iThe position coefficient of the ith sample value is the kth random variable. Xik.iCan be expressed as:
in the formula: lambda [ alpha ]k.3Expressed as a random variable XkThe greater the absolute value of the skewness coefficient (b) is, the more the random variable X iskThe distribution of (a) deviates greatly from the standard plus-minus distribution; lambda [ alpha ]k.4For measuring random variable XkThe smaller the absolute value of the kurtosis coefficient of the steepness degree of the probability density of (A) in the vicinity of the expected value, the more concentrated the value of the random variable in the vicinity of the expected value, and λk.4If 0, the random variable X is describedkHas the same steepness as the standard normal distribution. XkCoefficient of skewness of (lambda)k.3And a kurtosis coefficient lambdak.4Are respectively:
in the formula: e [ (X)k-μk)3]、E[(Xk-μk)4]Is a random variable XkThird and fourth central moments.
Sampling value xk.i(i-1, 2,3) each corresponding weight coefficient pk.iComprises the following steps:
as shown in the formulas (23) to (24), the three-point estimation method essentially determines the sample value x according to the first four moments of the input random variablek.i(i is 1,2,3), and each sample value is evaluated deterministically using a deterministic functional relationship as shown in equation (25).
Yk.i＝ζ×f(μ1…，μk-1，xk.i,μk+1…，μn)i＝1,2,3 (25)
It is noteworthy that each random variable sample time contains its expected value mukTherefore, since n deterministic evaluations are repeated, only 2n +1 evaluations of Y are required. According to the above conclusion, in combination with the weight coefficients corresponding to the sampling points, the z-order origin moment of Y can be expressed as:
after each moment of the output variable Y is obtained, the expected mu can be obtainedYAnd standard deviation σYNamely, the unit load loss expectation and variance of the distribution transformation of the transformer area.
The detailed solving calculation flow chart is shown in the attached figure 1.
Example (b):
the invention takes a modified IEEE33 power distribution network node system as an example to verify the effectiveness and the correctness of the distribution transformation selection type constant volume method provided by the invention. The simulation test is realized by programming in Matlab environment.
1) Modified IEEE33 node system:
assuming that a newly added platform area A, B, C, D in an area corresponds to the load nodes 34, 35, 36 and 37, the load reference values of the newly added platform areas are respectively 50kVA, 70kVA, 90kVA and 110kVA and are all subject to normal distribution (expected to be the load reference value of the corresponding node, the variance is 1), and the impedance of the distribution transformation of each platform area is respectively converted into the corresponding branch impedance parameters. And the nodes 5, 14, 21 and 37 are respectively accessed by 100kW, 150kW, 200kW and 250kW photovoltaic units, the power output of each photovoltaic unit is taken as 0.85, and the power output of each photovoltaic unit is subjected to Beta distribution of parameters. A modified IEEE33 distribution network node system is shown in fig. 1. The voltage class is 12.66kV, the reference power is 100MVA, and the tie switch is disconnected.
The annual average load growth rate of the area is set to be 0.05, the models of novel transformers to be selected comprise dry 10kV transformers of SCB10 series, SCB11 series and SCB13 series, detailed technical parameters of the transformers are shown in an appendix, the life cycle of the distribution transformer is designed to be 20 years, and comprehensive distribution transformer constant volume and type selection planning needs to be carried out aiming at a transformer area A, B, C, D.
A modified IEEE33 node distribution network is shown in fig. 2.
2) Example simulation results and analysis:
the correctness and the effectiveness of the method are verified, and three methods are respectively utilized to carry out the distribution transformation planning decision on the calculation example of the invention:
the method comprises the following steps: according to the distribution transformer planning method considering the photovoltaic output uncertainty and the whole life cycle cost, the confidence coefficient is 0.01, and the annual average load growth rate is 0.05.
The method 2 comprises the following steps: and the deterministic distribution transformer planning method considers the distribution transformer operation condition and the whole life cycle cost. At the moment, the uncertain influences of DG output and load fluctuation are ignored, so that when the distribution transformer capacity is selected, the confidence coefficient is 0; and when the distribution transformation selection is carried out, the photovoltaic output and newly added load point parameters take expected values according to respective probability density functions to carry out conventional deterministic load flow calculation, and the other parameter settings are the same as the method 1.
The method 3 comprises the following steps: a distribution fuzzy planning method considering the cost of the whole life cycle. At the moment, fuzzification processing is carried out on the operation condition of the distribution transformer, DG output and load fluctuation are ignored, and when the distribution transformer capacity is selected, the confidence coefficient is 0; when the distribution transformer selection is carried out, the distribution transformer LCC is roughly estimated only according to the parameters of the distribution transformer nameplate without referring to the load flow calculation result; and meanwhile, the influence of the constant volume model selection result of each station area on the power flow is not considered, and each station area carries out independent constant volume and model selection.
The method comprises the following steps: simulation results and analysis of method 1:
the variation of the distribution capacity of A, B, C, D four zones in the solution calculation example under different confidence intervals is shown in figure 3.
Considering the actual distribution of the SCB10 series, SCB11 series and SCB13 series to the factory design capacity, the results of selecting the distribution capacity of each station under different confidence intervals can be shown in table 1 according to fig. 3.
TABLE 1 constant volume results of distribution and transformation under different confidence of each zone
As shown in fig. 3 and table 1, the distribution transformer planning capacity is negatively correlated with the confidence probability, and the reason is that in an uncertain environment, the lower the confidence value is, which means that the risk in the system planning process is smaller, and thus the selected distribution transformer capacity is larger, so that the method of the present invention can realize the fine measurement of the system operation risk in the distribution transformer capacity selection process; the selection of the distribution transformer capacity is also influenced by the system load, and the larger the system load is, the larger the distribution transformer planning capacity is.
Assuming that the confidence coefficient is 0.01, it can be determined from table 1 that the distribution capacity of the transformer area A, B, C, D is 250kVA, 315kVA, 400kVA, and 500kVA, respectively. Based on this, the total LCC cost of the distribution area A, B, C, D corresponding to 81 different comprehensive distribution and transformation model selection modes can be obtained by the distribution and transformation model selection planning method (method 1) of the present invention as shown in fig. 4.
From fig. 4 it can be found that: the 42 th distribution transformation integrated selection mode (zone A: SCB11, zone B: SCB11, zone C: SCB11 and zone D: SCB13) will minimize the LCC total cost of the 20 years in the future of the zone A, B, C, D, and the integrated selection result is optimal.
In order to further study the influence of the confidence coefficient on the distribution transformation selection result, according to the method, the confidence coefficient value interval is 0.01-0.2, the step length is 0.01, the four distribution areas are subjected to comprehensive distribution transformation constant volume and selection under the same condition, and A, B, C, D comprehensive distribution transformation constant volume and selection results of the four distribution areas under different confidence intervals are obtained and are shown in table 2:
TABLE 2 comprehensive constant volume model selection result of distribution transformer under different confidence coefficients
From table 2, it can be found that the capacity selection and model selection results of the distribution transformer of the station areas under different confidence coefficients are changed continuously, and the optimal LCC cost is characterized by decreasing first and then increasing with the gradual increase of the confidence coefficient. In a confidence interval [ 0.01-0.06 ], the total cost of the LCC of the four distribution transformer areas is reduced along with the integral increase of the confidence; in the interval of the confidence coefficient [ 0.07-0.2 ], the LCC cost increases with the increase of the confidence coefficient, and the increase speed is faster and faster. In the calculation example of the invention, when the confidence coefficient is 0.07, the distribution transformer LCC cost is minimum, and the comprehensive constant volume and model selection of the distribution transformer of each station area are optimal.
The main reasons for this phenomenon are: in a confidence interval [ 0.01-0.06 ], the selection of the capacity of the distribution transformer is relatively large, the selection of the model is relatively good, the running loss of the distribution transformer is low, and the investment cost saved by the distribution transformer on the selection of the capacity and the model is more than the increased running cost along with the increase of the risk; in the confidence factor range of [ 0.07-0.2 ], along with the selection of the capacity of the distribution transformer is smaller and smaller, the selection of the model is poorer and poorer, the impedance of the distribution transformer is gradually increased, the increasing speed is larger and the running loss of the distribution transformer is larger, so that the saved investment cost is difficult to offset the running cost of the distribution transformer which is increased sharply.
Simulation results and comparative analysis in the mode 2 and the mode 3:
under the same conditions, the distribution transformation integrated constant volume and selection were performed on A, B, C, D four zones in the inventive example by means of the mode 2 and the mode 3, and the results are shown in table 3 by comparing with the method 1.
Table 3 distribution transformation constant volume model selection results under different planning methods
From table 3 it can be found that: in the method 2, the distribution transformation models selected by the station area B and the station area D are better, and the total cost of the LCC is increased by 6.1647 ten thousand yuan. The main reasons are as follows: the confidence coefficient of the distribution transformer planning under the method 2 is 0, which means that no risk is given during the constant volume type selection of the distribution transformer, so that the capacity of the distribution transformer is larger than that of the distribution transformer selected under the method 1, the model selection is better, the initial investment cost of the distribution transformer is further influenced, and meanwhile, the advantage of the planning scheme under the method 2 in the operation cost cannot make up the disadvantage of the initial investment in the whole life cycle of the distribution transformer, so that the total LCC cost is larger than that of the method 1. Secondly, the distribution transformation capacity planning result of each distribution area under the method 3 is the same as that of the method 2, but in the distribution transformation selection mode, the selection of the distribution area A, B, C is more excellent, and the total cost of LCC is increased by 21.2029 ten thousand yuan. The main reasons are as follows: in the aspect of distribution transformer capacity selection, both the method 3 and the method 2 perform deterministic constant volume planning under the condition that the confidence coefficient is 0, so that the capacity selection results are the same, and in the aspect of distribution transformer model selection, the method 3 does not consider the actual power flow operation result of the power distribution network, and directly utilizes the load loss calibrated on a distribution transformer nameplate to perform LCC (best load control) accounting, so that the accounting result is larger than the actual condition, the operation cost of the calculation is high, and the distribution transformer model selection is more conservative than the method 2.
In conclusion, the method provided by the invention can accurately measure the photovoltaic output uncertainty and the load fluctuation, and simultaneously fully considers the influence of the distribution transformation capacity on the model selection, so that the obtained planning scheme has higher economical efficiency compared with the traditional method, and the refinement level of the power distribution network planning is effectively improved.
The present invention has been described in terms of the preferred embodiments, but the above embodiments are not intended to limit the present invention in any way, and all technical solutions obtained by substituting equivalents or equivalent variations fall within the scope of the technical solutions of the present invention.
Claims (1)
1. A power distribution network transformer planning method considering photovoltaic output uncertainty and life cycle cost is characterized by comprising the following steps:
step 1: and (3) planning the distribution transformer capacity based on the opportunity constraint theory:
step 1.1: determining a photovoltaic output probability model and a load fluctuation probability model of a planning region, and generally describing the illumination intensity in a certain time period by adopting Beta distribution in an approximate manner:
in the formula: i is the intensity of light, IrRepresenting a maximum illumination intensity during the time period; alpha and Beta are two parameters of Beta distribution; Γ (·) is a gamma function;
the relationship between PVG contribution and illumination intensity can be approximated as:
in the formula: pPVGThe magnitude of the photovoltaic output active power is obtained;rated capacity of the photovoltaic unit;
according to the function distribution theorem of random variables, the probability density function of the output of the photovoltaic generator set is deduced by combining the formula (1) and the formula (2) as follows:
in the formula: qPVGIs the reactive component of the photovoltaic output;expressing the power factor of the photovoltaic unit;
the load fluctuation characteristics are described approximately using a normal distribution:
in the formula: pLIs the active component of the load; mu.sP、σPThe expectation and standard deviation of the load active component; qLIs the reactive component of the load; θ represents the power factor angle of the load;
step 1.2: the method comprises the steps of establishing a distribution area distribution transformation capacity planning model based on opportunity constraint, processing uncertainty of output after photovoltaic access to a load side and active power P provided by a superior power grid of a distribution area by using an opportunity constraint theoryNAnd photovoltaic active power output PPVGThe sum of the active power P is less than the active power P required by the transformer areaLShould not exceed a given confidence e:
f{PN+λPPVG≤PL}≤e (5)
in the formula: f {. denotes the probability that the event holds in {. is }; lambda represents the proportion of the photovoltaic direct supply user output to the total output; the confidence e is given artificially according to the actual economic and social development conditions of the region;
simultaneous equations (3) and (5) can be obtained:
active power P required by known platform loadLFrom the above equation, the net supply load P at a given confidence level can be determinedNSimultaneously setting a distribution areaThe increase of the load is totally PNTo undertake, the distribution transformer attachment capacity can be determined according to equation (7):
in the formula:representing the active power provided by the superior power grid in the t year; delta is the annual average load growth rate; t planning the maximum service life of the distribution transformer;representing the distribution capacity of the jth branch upper platform area of the distribution network in the life cycle T; eta is the economic load rate of the distribution transformer; n is a radical ofbranchRepresenting the total number of the branch circuits of the power distribution network; xijRepresents the proportion of the load of the distribution network distribution area on the jth branch, kjThe load concurrence rate of the platform area on the jth branch is;
step 2: modeling of uncertainty distribution transformation selection based on a life cycle theory:
step 2.1: and (3) establishing a model selection objective function, wherein the objective function of the distribution transformation model selection planning model is as follows:
minCT＝CI+CW+CO+CF+CR (8)
in the formula: cTThe LCC cost is distributed and changed in the period T; cIInitial investment cost for distribution transformer; cWThe operating cost for the distribution transformer; cOThe maintenance cost for the distribution transformer; cFFailure cost for distribution transformer; cRA decommissioning disposal cost for the distribution transformer;
step 2.2: considering the photovoltaic output and load fluctuation uncertainty, and finely analyzing the distribution transformer operation cost;
the operation cost of the distribution transformer mainly comprises the operation energy consumption cost C of the distribution transformerNHAnd cost of daily routing inspection CCS，
In the formula:the energy consumption cost of the year t is changed;in order to meet the annual inspection cost of distribution transformer, R is the inflation rate of the goods, R is the social discount rate, and p is the comprehensive electricity price; delta StFor the unit running loss of the distribution transformer in the t year, the detailed mathematical expression is as follows:
in the formula:andrespectively unit no-load loss and unit load loss in the t year of the distribution transformer;andrespectively represents unit no-load active loss and unit no-load reactive loss in the t year of the distribution transformer, and M (-) and N (-) respectively representThe function changing along with the distribution transformer model and the capacity can be directly calculated and obtained by referring to related distribution transformer technical parameters;andrespectively representing unit load active loss and unit load reactive loss in the t year of the distribution transformer; f (-) and S (-) respectively representA function which changes with distribution type, capacity, photovoltaic output and load fluctuation; k is reactive economic equivalent, namely active power loss caused by reactive power loss of each kilowatt in the transformer;
a probability power flow model is introduced to accurately solve the distribution transformer load loss of the power distribution network transformer branch, and the probability power flow model is as follows:
in the formula: paAnd QaRespectively representing the active power and reactive power injection quantity of the node a; w represents the number of distribution network nodes; vaAnd VbRespectively representing the voltage amplitudes of the node a and the node b; r iszAnd xzRespectively a platform area branch circuit resistor and a reactor; r isbAnd xbRespectively a distribution resistance and a reactance; gabAnd BabRespectively representing the real part and the imaginary part of the node admittance matrix; deltaabRepresenting the phase angle difference of the node a and the node b;
step 2.3: constraint conditions are as follows:
1) node voltage and branch current constraints:
in the formula: viminAnd VmaxRespectively is the minimum value and the maximum value of the voltage amplitude of the ith node; i isjAndthe actual value and the maximum allowable value of the jth branch current are obtained; n is a radical ofbusThe total number of the nodes of the power distribution network is;
2) and DG access node installation capacity constraint:
in the formula: si.DGInstalling capacity for the access node of the ith node DG;an upper limit of capacity is allowed to be installed for the ith node DG;
3) distribution and transformation model and capacity discreteness constraint:
the set A is set as a distribution transformer design capacity grade, the set B is a model of a distribution transformer to be selected, and the following constraint conditions exist:
and step 3: a three-point estimation method-based probabilistic power flow model solving method comprises the following steps:
distribution transformer unit load loss Delta S of set areaFThe functional relationship with photovoltaic output and platform load is as follows:
in the formula: delta SWDistributing the loss of the branch where the transformer is located for the transformer area;andrespectively representing the photovoltaic output and the load of the ith node; ζ represents the proportion of the distribution impedance to the impedance of the branch in which the distribution impedance is positioned;
make unit load loss Delta SFThe random variable Y is used for expressing, the photovoltaic output and the platform area load are expressed by the random variable X, and the formula (15) is simplified as follows:
Y＝ζ×f(X)＝ζ×f(X1,X2…,Xn) (16)
in the formula: n represents the total number of random variables X;
according to the steps of the traditional three-point estimation method, the unit load loss expectation and the variance of the distribution transformer in the transformer area can be obtained by solving:
in the formula: mu.sYAnd σYIs the expected and standard deviation of the output variable Y;
through the steps, the planning of the distribution network transformer considering the photovoltaic output uncertainty and the whole life cycle cost is completed.
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| CN109299869B (en) * | 2018-09-14 | 2021-03-16 | 广东电网有限责任公司 | Cost calculation method and device for distribution transformer |
| CN109617054B (en) * | 2018-12-13 | 2022-03-29 | 华南理工大学 | Constant volume type selection method for distribution transformer considering access of optical storage system |
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| CN110334964B (en) * | 2019-07-11 | 2023-12-05 | 南京工业大学 | Comprehensive energy system planning method based on life cycle and energy theory |
| CN112036611B (en) * | 2020-08-12 | 2022-06-07 | 国网山东省电力公司经济技术研究院 | Power grid optimization planning method considering risks |
| CN112000914B (en) * | 2020-08-14 | 2023-05-26 | 长江勘测规划设计研究有限责任公司 | Quick simulation calculation method for optimal super-distribution ratio of grid-connected photovoltaic project |
| CN112310959A (en) * | 2020-10-13 | 2021-02-02 | 国网湖北省电力有限公司宜昌供电公司 | Power distribution network low voltage comprehensive treatment method considering uncertainty factors and correlation thereof |
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Application publication date: 20170908 Assignee: Hubei Yunzhihang Drone Technology Co.,Ltd. Assignor: CHINA THREE GORGES University Contract record no.: X2023980044730 Denomination of invention: A Transformer Planning Method for Distribution Networks Considering the Uncertainty of Photovoltaic Output and Total Life Cycle Cost Granted publication date: 20191227 License type: Common License Record date: 20231027 |
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