CN105095999A - Distributed power station planning method based on improved light robust model - Google Patents
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Abstract
The invention relates to a distributed power station planning method based on an improved light robust model. The method comprises the following steps: 1) acquiring a target function and a constraint condition of a distributed power station to be planned; 2) establishing a distributed power station planning model according to the target function and the constraint condition of the distributed power station to be planned, and converting the distributed power station planning model into the improved light robust model; and 3) solving the improved light robust model to acquire an optimal distributed power station capacity planning layout with lowest cost. Compared with the prior art, the method has the advantages of fastness in solving, small calculation amount and the like.
Description
Technical field
The present invention relates to power scheduling field, especially relating to a kind of distributed power generation station planing method based on improving light robust Model.
Background technology
Scheduling, the planning of electric system contain the various uncertain factors such as the intermittence of the generations of electricity by new energy such as the fluctuation of load, the burst of fault and wind-powered electricity generation photovoltaic, mathematically belong to the planning problem with uncertain parameter.
Take into account the mathematic programming methods of Parameter uncertainties for determinacy mathematic programming methods, all contain the uncertain wave process of parameter because of the development of the many problems of reality itself and operating process and describe and reflect the real process of objective reality problem more truly, make its solution have more practical feasibility, thus be more and more subject to the attention of theory and engineering technical personnel.Uncertainty optimization method mainly contains randomized optimization process and robust Optimal methods.
In electric system, randomized optimization process is most widely used, and covers the every field such as scheduling, planning.But there are the following problems in actual applications for random optimization: first, carry out the probability distribution function that scene simulation must know uncertain parameters in advance, but maybe cannot realize very greatly the usual difficulty of the estimation of probability distribution function in practical problems, even if there are enough historical datas, and statistical analysis matching obtains, also cannot ensure with reality completely the same, therefore its solution can only be an approximate solution; Secondly, the scene of random optimization emulation is discrete, and the parameter uncertainty in reality is mostly continually varying, for obtaining higher simulation accuracy, have to simulate abundant scene, this makes the scale of model abnormal huge, solve difficulty much larger than determinacy planning problem, necessarily simplify although can do, to sacrifice certain precision for cost, nonetheless, its calculated amount still has the difference of the order of magnitude compared with certain problem.How to overcome the problems referred to above, be the problem that randomized optimization process need overcome further.
In recent years, robust optimum theory obtains greater advance, robust is linear, secondary, semidefinite, discrete, adjustable, adaptive optimization is theoretical in succession perfect, the multiple uncertain collection such as interval, ellipsoid, budget are successively set up, the conservative property of model is significantly improved, substantially, close to practical engineering application, for Practical Project problem provides a kind of FA candidate's method for solving.Compared with Stochastic Optimization Model, the outstanding advantages of Robust Optimization Model is the probability distribution not needing prior given uncertain parameter, but the fluctuation of characterising parameter is carried out by a uncertain collection, as long as parameter fluctuation is within uncertain collection scope, its optimum solution is necessarily feasible; Its basic ideas are the extreme cases by finding out uncertain collection, it is changed into deterministic models solve, relative randomized optimization process, its calculated amount significantly reduces, property requirements for uncertain parameter also obviously reduces, thus is more convenient for engineer applied.Because classical robust optimization will meet the complete immunity to uncertain collection, therefore be easy to produce excessively conservative solution, make objective function substantial deviation initial value, therefore how problem is improved around the conservative property of separating, all kinds of document proposes various strategy: it is uncertain that the uncertain collection of document ellipsoid describes " in lines ", improves " apportion " probabilistic conservative property that the interval uncertain collection of document describes; Document proposes the uncertain collection of budget (BudgetedUncertainty), improves conservative property by the constraint of controlling fluctuation total amount to uncertain collection increase by; Document in multi-stage optimization according to the uncertain parameter that earlier stage has realized, by residue decision variable compensation improve conservative property; Document with forward backward skew estimates to set up new uncertain collection, the asymmetry of uncertain parameter distribution can be obtained, thus the probability that is met of the constraint made is higher and improve conservative property; The concept of document utilization Risk Measurement proposes a kind of soft robust Model, with the probability of sacrificing certain constraint satisfaction for cost makes the conservative property of separating obtain improvement to a certain extent.
Current robust optimization has been used to the various practical problemss solving electric system, such as, consider power plant's planning of cost of electricity-generating and load fluctuation, the wind energy turbine set installed capacity considering wind-powered electricity generation fluctuation and idle planning, consider probabilistic economic load dispatching and the Optimization of Unit Commitment By Improveds etc. such as wind-powered electricity generation.
Document proposes a kind of light robust optimization (LightRobust, LR) model of novelty, here " gently " refer to model no longer require as classical Robust Optimization Model constraint completely immune to parameter fluctuation, allow to occur that constraint is run counter to.This article first proposed basic light robust Model, runs counter to that to ensure that desired value departs from not out-of-limit with minimum constraint, thus avoids conservative property excessive; This article also proposed a kind of heuristic light robust Model simultaneously, and under first finding out worst case, each constraint is lax than minimum value, and then under ensureing that desired value departs from not out-of-limit prerequisite, the lax ratio of balanced each constraint, runs counter to degree inequality to avoid constraint.Light robust Model improves the conservative property of robust optimization problem solution to a certain extent.No matter but basic light robust Model or heuristic light robust Model, all existence (1) cannot independently solve, and calculated amount is larger; (2) can not ensure that conservative property one is improved surely; (3) problems such as may excessively running counter to is retrained.And whether overcoming of these problems directly affects the applications well of light robust optimum theory in Practical Project problem.
Summary of the invention
Object of the present invention is exactly provide a kind of to overcome defect that above-mentioned prior art exists to solve the light robust Model of improvement quick, calculated amount is little and application thereof.
Object of the present invention can be achieved through the following technical solutions:
Based on the distributed power generation station method for planning capacity improving light robust Model, comprise the following steps:
1) objective function and the constraint condition at distributed power generation station to be planned is obtained;
2) set up distributed power generation station plan model according to the objective function at distributed power generation station to be planned and constraint condition, and distributed power generation station plan model is converted to improves light robust Model;
3) the minimum Optimal Distribution formula station capacity programming and distribution of acquisition construction cost are solved to improving light robust Model.
Described step 2) in distributed power generation station plan model be:
Objective function:
Demand constraint:
Wherein,
for the installed capacity of power house i,
be respectively installed capacity
lower limit and the upper limit, c
ifor unit cost of investment, N
gfor the power house sum of planning, P
difor the workload demand of node i, n is distributed power generation station arrangement network node sum.
Described step 2) in, distributed power generation station plan model is converted to the light robust Model of improvement and specifically comprises the following steps:
21) keep the installed capacity of distributed power generation station plan model constraint constant, introduce slack and objective function is become:
Wherein, w is weight, and γ is the slack of Robust Constrained;
22) demand constraint is transformed to that right side is uncertain to be constrained to by the slack γ introducing uncertain collection and Robust Constrained:
Wherein, b
ifor maximum fluctuation amplitude, ζ
ifor fluctuation ratio;
23) transferring uncertain for right side constraint to improve light robust Model linear corresponding by sequence intercept method is:
Wherein, b'
jfor sequence after sorting | b'
1|, | b'
2| ..., | b'
n| in element, Γ controls the fluctuation estimated value of total amount and 0 < Γ≤n,
for rounding downwards of estimated value Γ.
The light robust Model of described improvement is:
Described step 3) in solve the method improving light robust Model and comprise simplicial method, dual simplex method and interior point method.
Described step 23) in the sequence concrete steps of intercept method under the uncertain collection condition of budget be:
231) sort: to by maximum fluctuation amplitude b
i(i=1,2 ..., the set that n) forms | b
1|, | b
2| ..., | b
n| in the descending sequence of element, the set after sequence be | b'
1|, | b'
2| ..., | b'
n|;
232) estimated value Γ is rounded downwards into
its fraction part is
233) block: choose | b'
1|, | b'
2| ..., | b'
n| in before
individual element is sued for peace and is got negative, as the right side Section 2 of Robust Constrained conversion type, the
individual element is multiplied by coefficient after then getting and bearing
as the right side Section 3 of Robust Constrained conversion type, the linear corresponding of the light robust Model that is namely improved:
Inequality two ends are transformed to after removing negative sign:
Compared with prior art, the present invention has the following advantages:
One, the impact of uncertain factor has been taken into full account: using workload demand as uncertain factor, the introducing uncertain collection of budget and slack process the constraint condition containing uncertain factor, consider the uncertain of actual load compared with determinacy planing method, model is more realistic;
Two, solve quick, calculated amount is little: when uncertain parameter is right side polynomial expression, and when the uncertain set of its obedience budget, Robust Optimization Model can be directly converted to MILP corresponding by the sequence intercept method proposed, useable linear method solves, and traditional dualistic transformation need not be adopted, also therefore nonlinear terms can not be there are, solve more quick, compared with light robust Model, the light robust Model of improvement that the present invention proposes can independently solve, can ensure the improvement of conservative property, constraint can not excessively be run counter to, and calculated amount is less.
Accompanying drawing explanation
Fig. 1 is method flow diagram of the present invention.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.
Embodiment:
As shown in Figure 1, a kind of distributed power generation station planing method based on improving light robust Model, comprises the following steps:
1) objective function and the constraint condition at distributed power generation station to be planned is obtained;
2) set up distributed power generation station plan model according to the objective function at distributed power generation station to be planned and constraint condition, and distributed power generation station plan model is converted to improves light robust Model;
3) the minimum Optimal Distribution formula station capacity programming and distribution of acquisition construction cost are solved to improving light robust Model.
The electrical network installation planning problem that the present invention adopts one to simplify is to verify the validity of ILR model (improving light robust Model) proposed by the invention, this problem is: three the generating plant costs of investment having completed addressing are respectively 120,720,9,800,000 yuan/MW, the installed capacity upper limit is respectively 190,70,40MW, lower limit is 140 respectively, 40,5MW, generating plant is prepared as three place's loads and powers, the expectation value of load is respectively 75,80,120MW, load fluctuation is expressed as amplitude and the product of fluctuation uncertain variables, is respectively 13.5 ζ
1, 14.4 ζ
2, 21.6 ζ
3mW, ζ
1, ζ
2and ζ
3obey the uncertain set of budget: | ζ
1|≤1, | ζ
2|≤1, | ζ
3|≤1 He | ζ
1|+| ζ
2|+| ζ
3|≤1.1, ignore network constraint, ask the installed capacity of three power plant
and
make construction cost minimum.
Linear programming model (LinearProgramming is set up respectively below for this problem, LP), robust optimization (RobustOptimization, RO), light robust Model (LightRobust, LR) and ILR tetra-kinds of models contrast.Portion's load of wherein not demanding perfection in LR and ILR model meets, and LR model allows to abandon sub-load, but to abandoning the unbounded size system of part, the duty ratio that ILR model needs is abandoned is no more than 0.03, abandons load for avoiding as far as possible, and weight coefficient gets several greatly 50000.
First LP plan model is set up such as formula (1), objective function is minimum construction cost, for RO model, due to load fluctuation, workload demand constraint becomes such as formula the uncertain constraint in right side shown in (2), it is write as such as formula the canonical form shown in (3), then is tried to achieve fluctuation item by sequence intercept method:
1) will be { 21.6,14.4,13.5} after the descending sort of load fluctuation sequence;
2) the uncertain concentrated estimated value Γ of budget load fluctuation obeyed is write as 1+0.1;
3) fluctuation item-21.6-0.1 × 14.4=-23.04 are calculated, the linear corresponding of final formation (4) with first 2 of the rear sequence that sorts.
The Robust Constrained linear corresponding derivation of LR, ILR model is identical with it, and final RO, LR and ILR model is respectively such as formula shown in (5), (6) and (7).
For each model performance under comparing different situations, load expectation value and fluctuation are multiplied by a loading coefficient by this example respectively, form multiple load scenarios, the problem of Δ must be specified for LR model simultaneously, also calculate Δ to each scene and get 0.05,0.1,0.2 and 0.3 3 kind of situation, result of calculation is in table 1.
Table 1 comparison of computational results
In conservative property (see table 1 total cost and with LP cost ratio), at that time, the optimal value of RO model increases 26% than LP model, LR model in conservative property improvement but with value relevant, bigger than normal when getting 0.3, its optimal value than LP model increase 28%, even higher than RO model, conservative property strengthens on the contrary, and only when getting 0.05,0.1 and 0.2, its conservative property is just effectively improved.As can be seen here, value only make the optimal value of LR between the optimal value of LP and RO model, could conservative property be improved.LP model and RO model have thoroughly been broken away from solving of ILR model, can independently calculate, no longer by the puzzlement of value, therefore best optimal value can be obtained, and optimal value than the increment of LP model more than 10%, comparatively increase by the RO model of 37%, significantly improve conservative property.
(see table 1 power shortage ratio in risk, namely degree is run counter in constraint), because LR model runs counter to constraint the system of not limiting, therefore the slack variable value occurred is maximum, when loading coefficient rises to 1.09, the model constrained degree of running counter to of LR reaches 7.65%, and the constraint of ILR model runs counter to degree all the time not more than 5%, shows reliable security.
In contrary relation between risk (constraint is run counter to) and conservative property (total cost).When loading coefficient is 1, the optimal value of robust class model is ascending is followed successively by LR (Δ=0.05), ILR, LR (Δ=0.1), LR (Δ=0.2), RO, LR (Δ=0.3), and constraint is run counter to and is ascendingly followed successively by LR (Δ=0.3), RO, LR (Δ=0.2), LR (Δ=0.1), ILR, LR (Δ=0.05).As can be seen here, when constraint, to run counter to degree larger, and optimal value is less.
In solvability, the present invention is by two kinds and the number of times separated in load growth process, and LP model cannot immunity to the fluctuation of the growth property of load, and therefore robustness is very poor, but it is more to separate number of times in load expectation value increase process gradually; RO model can carry out 100% immunity to load fluctuation, requires the highest, therefore can separate least number of times in load increase process to solution conditions; LR model exchanges solvability for loose constraint, and constraint relax level does not limit, and therefore can separate all the time; The relax level of ILR model to constraint is restricted, therefore can separate number of times more than RO model but lower than LP model in load increase process.
The Performance comparision of each model solution
For the performance of more each model solution, the present invention is when loading coefficient is 1, in the uncertain collection restriction range of budget, stochastic generation 100 groups of loads, to simulate different fluctuation scenes, then verify the residue installed capacity of each model solution under different scene and power shortage situation respectively, statistics is in table 2.Obviously, LP solution to model is maximum to the power shortage occurrence number of each scene, and vacancy ratio average is 4.05%, maximal value 7.57%, and therefore its solution risk is the highest; RO solution to model then always occurs that installed capacity is superfluous, superfluous ratio average 8.7%, maximal value 16.88%, and the conservative property of therefore separating is very large; The performance of LR solution to model is selected relevant with Δ, Δ and residue installed capacity direct proportionality, be inversely prroportional relationship with power shortage, as too high in value (Δ=0.3) superfluous installed capacity, even higher than RO solution to model, cannot ensure the improvement of conservative property; The solution of ILR is then between LP and RO model solution, comparatively LP solution to model is lower for power shortage number of times, vacancy ratio average and maximal value, effectively reduce the risk of power shortage, and the superfluous number of times of installed capacity, comparatively RO solution to model is lower for superfluous installed capacity ratio and maximal value, ensure that conservative property is effectively improved.
The each solution to model of table 2 is to 100 groups of scenes verification index contrast (when loading coefficient is 1)
Instant invention overcomes light robust Model independently to solve, can not ensure that conservative property necessarily improves, retrain shortcomings such as may excessively running counter to, calculated amount is larger.The linear corresponding derived because maintaining the linear feature of model, and can directly adopt linear solution method to carry out solving and improve solution efficiency.While research work of the present invention facilitates the development of robust optimum theory itself, also for having established theoretical foundation based on the development and application of the Power System Unit Commitment improving light robust optimum theory.
Claims (6)
1., based on the distributed power generation station method for planning capacity improving light robust Model, it is characterized in that, comprise the following steps:
1) objective function and the constraint condition at distributed power generation station to be planned is obtained;
2) set up distributed power generation station plan model according to the objective function at distributed power generation station to be planned and constraint condition, and distributed power generation station plan model is converted to improves light robust Model;
3) the minimum Optimal Distribution formula station capacity programming and distribution of acquisition construction cost are solved to improving light robust Model.
2. according to claim 1 a kind of based on improving the distributed power generation station method for planning capacity of light robust Model, to it is characterized in that, described step 2) in distributed power generation station plan model be:
Objective function:
Demand constraint:
Wherein,
for the installed capacity of power house i,
be respectively installed capacity
lower limit and the upper limit, c
ifor unit cost of investment, N
gfor the power house sum of planning, P
difor the workload demand of node i, n is distributed power generation station arrangement network node sum.
3. a kind of distributed power generation station method for planning capacity based on improving light robust Model according to claim 2, it is characterized in that, described step 2) in, distributed power generation station plan model is converted to the light robust Model of improvement and specifically comprises the following steps:
21) keep the installed capacity of distributed power generation station plan model constraint constant, introduce slack and objective function is become:
Wherein, w is weight, and γ is the slack of Robust Constrained;
22) demand constraint is transformed to that right side is uncertain to be constrained to by the slack γ introducing uncertain collection and Robust Constrained:
Wherein, b
ifor maximum fluctuation amplitude, ζ
ifor fluctuation ratio;
23) transferring uncertain for right side constraint to improve light robust Model linear corresponding by sequence intercept method is:
Wherein, b'
jfor sequence after sorting | b '
e|, | b'
2| ..., | b'
n| in element, Γ controls the fluctuation estimated value of total amount and 0 < Γ≤n,
for rounding downwards of estimated value Γ.
4. a kind of distributed power generation station method for planning capacity based on improving light robust Model according to claim 3, it is characterized in that, the light robust Model of described improvement is:
5. according to claim 3 a kind of based on improving the distributed power generation station method for planning capacity of light robust Model, to it is characterized in that, described step 3) in solve the method improving light robust Model and comprise simplicial method, dual simplex method and interior point method.
6. according to claim 3 a kind of based on improving the distributed power generation station method for planning capacity of light robust Model, to it is characterized in that, described step 23) in the concrete steps of sequence intercept method under the uncertain collection condition of budget be:
231) sort: to by maximum fluctuation amplitude b
i(i=1,2 ..., the set that n) forms | b
1|, | b
2| ..., | b
n| in the descending sequence of element, the set after sequence be | b '
1|, | b'
2| ..., | b'
n|;
232) estimated value Γ is rounded downwards into
its fraction part is
233) block: choose | b '
1|, | b'
2| ..., | b'
n| in before
individual element is sued for peace and is got negative, as the right side Section 2 of Robust Constrained conversion type, the
individual element is multiplied by coefficient after then getting and bearing
as the right side Section 3 of Robust Constrained conversion type, the linear corresponding of the light robust Model that is namely improved:
inequality two ends are transformed to after removing negative sign:
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