Matlb| economic scheduling with energy storage, opportunity constraints and robust optimization

Welcome to this blog ️️️

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 ！️️️
Blogger advantages ： Try to think carefully about blog content , Clear logic , For the convenience of the reader , Bloggers have created a special column directory , There is only one article in the whole column , It shows that I attach importance to it ： Blogger column directory . Be extremely meticulous , It is convenient for everyone to learn ！ populist ！！！ And I opened a column for my girlfriend , Very romantic , Take a look when you are tired of learning code , Have a look ： A romantic encounter with a girlfriend . If there is a problem, you can privacy bloggers , Bloggers will reply as soon as they see .
Currently updated ： Knowledge of power system , Journal papers , Algorithm , Machine learning and artificial intelligence learning .
Support ： If you think the blogger's article is good or you can use it , You can follow the blogger for free , It would be better if the three collections support ！ This is my greatest support ！

                          

                                    Welcome to

                      Blogger Homepage ： Power System Research Office

                    Column catalog ： The beauty of power system and algorithm

                       

                          

Bloggers' extracurricular interests ： Chinese and Western Philosophy , To readers ：

Do research , It involves a deep ideological system , Researchers need to be logical , Be practical and serious , But you can't just try , Many times, borrowing is more important than trying , Then there should be innovation and inspiration to look up to the stars . When the teacher asks you what science is in philosophy class , What is the time of electricity , Don't think these questions are funny , Philosophy is to pursue the ultimate problem , Look for those self-evident questions that only children will ask, but you can't answer . In this column, I will record some philosophical thinking and scientific research notes when I am free ： Scientific research and philosophy . Readers are advised to browse one by one in the order of the catalogue , Lest you suddenly fall into the dark maze and can't find the way to come , It's not enough to reveal the answers to all your questions , But if you can raise doubts in your chest , It may not lead to a different scene with beautiful sunset , If it actually brings you a bitter rain in the spiritual world , Then take the opportunity to wash the things that were stored there “ truth ” Dust on the .

      Maybe , After the rain, the clouds gather , God Chi's heaven and earth is more clear .......

The contents of this article are as follows ：️️️：

1 summary

2  Opportunity constraint method

3 Examples and Matlab Code implementation

3.1 Numerical example

3.2 Matlab Code

3.3 result  

4 At the end  

 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  

Some theories cite network literature , If there is infringement, please contact the blogger to delete .