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Matlb| economic scheduling with energy storage, opportunity constraints and robust optimization
2022-07-07 02:38:00 【Power system code】
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The author studies : Bachelor degree in computer science , Master degree in Electrical Engineering . The main research direction is power system and intelligent algorithm 、 Machine learning and deep learning . Currently familiar with python Web crawler 、 machine learning 、 Swarm intelligence algorithm 、 Relevant contents of in-depth learning . It is hoped that computers and power grids can be effectively combined !️️️
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The contents of this article are as follows :️️️:
2 Opportunity constraint method
1 summary
IT Is a universal belief , That is, global warming is advancing . therefore , Urgent and effective carbon emission reduction policies must be adopted , Carbon tax 、 Total amount control and trading . In the new theory , These policies can reduce dependence on carbon intensive energy , Encourage renewable energy , So as to correct the negative environmental externalities . But in practice , The current carbon emission reduction policy may increase the regional electricity price , It leads to inefficiency 、 Economic problems such as unfair distribution . therefore , They are not universally implemented . However , After the outbreak of the novel coronavirus crisis , Opportunities have emerged to implement such policies in practice . Although the coronavirus crisis led to the stagnation of manufacturing , But it also slows down the trend of global warming , Because in the energy sector ,2020 In the first quarter of, carbon emissions decreased year-on-year 3.8% . One side , Low carbon emission levels make the costs associated with carbon reduction policies lower when implemented . In order to maintain this level of cost while resuming normal production , This stagnation period is an excellent period for carbon intensive industries to transform for their own economic interests . On the other hand , This transformation can increase employment , So as to solve their social problems . therefore , There is an urgent need to take advantage of this precious period , Enhance the practicality of carbon reduction policies .
In the power sector , Carbon tax is a common environmental policy aimed at reducing carbon dioxide emissions , But it is usually considered to be economically unfriendly , Especially in areas that rely on coal and other carbon intensive generators . The power grid using energy storage system may be a promising solution to alleviate the regional economic pressure of power grid implementing carbon tax . With clean energy ( For example, solar energy and wind energy ) The increasing development of , In this work , We use two frameworks ( Opportunity constrained framework and robust optimization framework ) To describe stochastic emission aware economic scheduling with storage systems . We study the trade-off between robustness and overall cost to highlight their differences and connections . say concretely , We link these two frameworks with a novel distributed robust optimization framework , The framework considers the actual boundary to estimate the best system performance under reliability requirements . Yes IEEE-6 Node model and IEEE-118 The numerical study of nodes further proves .
2 Opportunity constraint method
The two most widely used optimization methods that can deal with uncertainty are stochastic optimization (SO), These include CC Methods and RO Method . Conventional SO Methods are usually scenario based . in order to
CC Method by Charnes It is proposed that . Use CC The motivation for this approach is to avoid excessive system redundancy , This shows that some constraints can be violated in a limited time . Optimization problems under uncertainty usually take the following form :
among It's the objective function ;u Is the vector of state variables ( for example SOC、);x Is the vector of decision variables ( for example , Power output of each generator );ζ Is a vector of random variables ( for example , Renewable output ). equation (2 b) and (2 d) Indicates a deterministic constraint . stay (2 c) in , A bar indicating the level of risk , Indicates that the embedded constraint should have at least a probability . In this section , We initially used general routines to describe CC optimization problem , Then use the concept of prevention and control to simplify , This is a common practice in power systems .
3 Examples and Matlab Code implementation
3.1 Numerical example
By improving 6 Node system and IEEE 118 The nodal system is studied numerically to evaluate the proposed method . In the first test case , Focus on numerical comparison CC、DRO And perspective scene , This scenario believes that renewable energy power generation is perfect . In this paper, renewable energy data is extracted from the data set , The data set is represented by 5 Minute resolution provides information about predicted and actual wind energy data . chart 1 The histogram of error samples is drawn . about CC problem , We need to estimate the distribution model of prediction error . say concretely , Two unimodal distributions are used to fit the original sample , Gaussian distribution and Laplace distribution , Separately shown 1(a) Sum graph 1(b) The curve shows . as for RO, We need to determine the upper limit of the expected absolute prediction error ( namely Mn). In order to prevent the influence of outliers , Let's just think about 0.1-quantile To 0.9-quantile Samples in the range , And take the average of all absolute values to approach the upper limit . In practice , If we are allowed to reduce excess wind power or unfulfilled load when wind power generation exceeds the selected interval , The estimate is still valid .
chart 1 Gauss and Laplace estimation of wind prediction error
chart 3 IIIE6 chart
chart 3 IEEE118 chart
3.2 Matlab Code
This article only shows part of the code , See : We are shipping your work details
%% Gaussian distribution
function [x,fval]=gen_performance_CC_Gaussian(T,N,M,bb,d_f,p,q,H,fmax,gmin,gmax,ramp_rate,epsilon,gamma,error_data,w_loc,w_num,DR,UR)
virtual_bb=[bb bb bb];
real_bb=zeros(N,1);
if sum(bb)~=0
for flag=1:1
for k=1:w_num
i=w_loc(k);
virtual_bb(i,flag)= gen_virtual_storage_capacity(bb(i),epsilon,T,gamma,error_data,flag);
end
[standard_delta,real_bb(:,flag)]= gen_standard_delta(bb,virtual_bb(:,flag),w_loc);
end
end
x=zeros(T*N*4,1);
fval=zeros(1,1);
for flag=1:1
umin=-ramp_rate*real_bb(:,flag);
umax=ramp_rate*real_bb(:,flag);
[x(:,flag),fval(:,flag)]=MinC(T,N,M,real_bb(:,flag),d_f,p,q,H,fmax,gmin,gmax,umin,umax,DR,UR);
end
end
3.3 result
4 At the end
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