Differential Evolution Algorithm And Application On Stochastic Optimal Power Flow

Given that Differential Evolution (DE) is an efficient and powerful population-basedstochastic search technique for solving optimization problems over continuous space,non-convex and global, it has been widely applied in many scientific and engineeringfields including Optimal Power Flow (OPF) of electric power system. OPF, a complexnonlinear optimization problem, is used to find the power flow results which realizesthe defined optimization objective under the system security constraints through theregulating the system control and has already been the basic tool in the field ofelectrical system dispatch, economic dispatch and market trade.In fact,severaluncertainties exist in the power system objectively,especially with the access of largeamount of new energy and complicity of the load at present, which leads to moreprominent uncertain characteristics of the short-term load prediction and the OPF.Thus, this thesis makes further study on DE and its application in the StochasticOptimal Power Flow(SOPF) in the electric grids.Considering the load uncertainty andthe engineering characteristics of SOPF, the algorithm study has been set on the fuzzydiscretization and simplified method of fuzzy rough sets(RS) attributes based on thecontinuous attribute of differential evolution rough set decision.This thesis alsodiscusses about the short-term load uncertainty prediction method and the SOPF issueaccording to the DE algorithm to obtain the probability distribution characteristics ofload. Aiming at finding new solution of the short-term load uncertainty prediction andthe SOPF issue for the electric system, this thesis conducts DE algorithm and itsinnovative application study, which have a great sense on science and engineering.The factors which influence the short-term load of electrical system such as powerconsumption, temperature, and wind speed possess the uncertain characteristics,namely, randomness, roughness and fuzziness. The short-term load prediction isusually authentic, continuous, and fuzzy. Although conventional Rough Sets (RS)theory has advantage in dealing with these uncertain issues, it can only solve the issueswith discrete attributes. For this, this thesis conducts the design of continuous fuzzydiscretization algorithm based on DE. This algorithm uses binary code in which theindividuals of population are demonstrated by real string to enforce local searchcapacity.This thesis also proposes a new algorithm to handle the continuous and fuzzyissue in the RS theory based on DE algorithm. This algorithm is pragmatic enough to provide a more reliable discretization method for handling the continuous and fuzzyattributes which influence short-term load.On the basis of the continuous attributes fuzzy discretization according to DE,considering the characteristics of decision attributes in RS, that is the discrepancy intheir importance, dependency and complexity and the actual characteristic of fuzziness,this thesis makes a research on attribute reduction issue in fuzzy RS and proposed anew attribute reduction algorithm. Through binary discrete code and the design offitness function, this algorithm controls the individuals to evolute towards theminimum numbers of attributes and brings in dependence from decision attributes infuzzy positive domain to the condition attributes so as to define the fitness function.The experiment shows that this new algorithm can not only search the minimumattributes reduction rapidly and correctly but also save the calculation time of UCI datasets. Compared with the attributes reduction method of genetic algorithm, the DEalgorithm is rapid and possesses smaller population scale. The example proves that thisnew algorithm is convenient and efficient and reliable to deal with uncertain attributesprediction of the short-term load in the system.Aiming at the uncertain and different attributes of short-term load, this thesisprovides a new uncertainty prediction algorithm based on differential evolution fuzzyrough sets attributes reduction and Least squares support vector machine (LS-SVM),which was the forecast data training entry, to solve short-term load forecasting. On theone hand, this algorithm will be applied in the uncertainty prediction of short-termload--to conduct continuous attributes fuzzy discretization on the historic samples.Through the dynamic attributes reduction of fuzzy RS on historic samples of loadforecast, the simplest attributes sets which is most closed to attributes of load. By theimproved fuzzy c means clustering algorithm, this thesis sorts major attritions obtainedfrom fuzzy RS reduction. Short-term load uncertain forecast is made from Monte Carloand LS-SVM. Examples show that, compared with conventional SVM, the approach inthis thesis possesses several advantages such as, the little average relative error offorecast, short operation time, small numbers of unqualified prediction points. On theother hand, applying this algorithm in the study of uncertainty forecast of bus net loadcontaining the distributed energy, the algorithm is also proved to be effective. From thealgorithm above, the probability distribution characteristics of load is obtained so as toprovide correct load uncertain description model in SOPF.Based on the application of DE to acquire uncertain distribution characteristic ofload and use of on OPF, this theses proposes a new algorithm based on improved DE and Monte Carlo method aiming at the SOPF considering the load uncertainty.Through the self-adaptive proportional factor, the improved DE address theconvergence rate in SOPF. This thesis adds random perturbation and avoids localoptimum, preventing premature convergence. Through the combination of improvedDE algorithm and Monte Carlo method, the objective function in SOPF, output ofgenerator as well as the probability distribution characteristics of power flow isobtained. The proposed methods are illustrated in the standard IEEE30-bus system andthe result proves its effectiveness and robustness compared with improved GA andPSO algorithm. Better average optimal values and faster operation speed are obtainedwith the same sampling frequency using this algorithm.In conclusion, aiming at DE algorithm and its application issue in SOPF, this thesisfirstly proposes the new algorithm on fuzzy RS attributes discretization based on DEalgorithm. Then a new uncertainty forecast method of LS-SVM short-term load and aninnovative method of SOPF considering the load uncertainty based on improved DEalgorithm are provided. The simulation example demonstrates the effectiveness andadvantages of this algorithm. The study of this research meets the demand of powersystem development and has a great science and engineering sense in uncertain powersystem dispatch, optimization decision, etc.