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230  Decision Making Applications in Modern Power Systems



                                   Deterministic problem
                       –The input parameters have specific values that are being
                       processed in a few equations resulting in a set of specific
                       outputs.
                       –The output results have the same values regardless of the
                       number of iterations.

                        Inputs                           Outputs

                                      Objective function
                         X 1
                                                            Y 1
                          X 2
                                         F(X)
                          X 3
                                                            Y 2
                          X 4

                                           (A)
                                    Probabilistic problem
                      –The input parameters are not fixed; however, a certain degree
                      of uncertainty is found.
                      –Accordingly, probability distribution functions can be
                      presented to represent the input parameters.
                      –Probabilistic approaches such as MCS are used to determine
                      how the uncertainty of inputs affects the performance of the
                      system being studied.


                        Inputs                            Outputs

                          X 1
                                      Objective function
                                                             Y

                                          F(X)
                          X 2




                                           (B)
            FIGURE 9.2 Deterministic and probabilistic problem formulation. (A) Deterministic problem
            and (B) probabilistic problem.

            3. the uncertainty of DG integration location;
            4. the uncertainty of DG unit rating;
            5. the daily variations in loading profiles;
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