Intelligent Renewable Energy Systems. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Программы
Год издания: 0
isbn: 9781119786283
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of certain equality and inequality constraints as stated below [68],

      (a) Equality Constraints

      At any time instant t, the active and the reactive power balance for the distribution network should be maintained by the equation as follows

      (1.23)image

      This equality constraint is fulfilled by the load flow solution of the distribution networks. Putility, Qutility are the active and reactive power taken from the utility, respectively, PDG, QDG are the active and reactive power supplied by the RDGs, in order, and shunt capacitors, and images is the percentage load level expressed in per unit.

      (b) Inequality Constraints

       (i) The bus voltages of the distribution networks at any time instant must be within the minimum (Vmin) and maximum (Vmax) voltage level as in(1.24)The placement of RDGs and the shunt capacitors may increase the bus voltage beyond the limit at low voltage level and decrease the bus voltage at high load level. Therefore, bus voltages are kept within the prescribed limit by introducing the penalty function defined as(1.25)

       (ii) The active and reactive power generation of the DGs should be within the specified limit given as(1.26)where are the minimum and the maximum limit of the active power injection of the DGs and are the minimum and the maximum limit of the reactive power injection of the DGs which are to be maintained at any time instant. These inequalities are maintained by introducing the penalty function as below(1.27)

       (iii) The total active and reactive power injections by the RDGs and shunt capacitors at any time instant should be less than the total active and reactive power load demand of the distribution network at the same instant. This inequality constraint is defined as(1.28)These inequality constraints are considered by introducing the two penalty functions as(1.29)

       (iv) Branch currents, after the placement of DGs and shunt capacitors, should be within the maximum allowable level to maintain the feeder thermal limit. The branch current limit should be(1.30)This limit is considered in the objective function with the help of a penalty function described as(1.31)After considering all the penalty functions, the objective function, to be minimized, is(1.32)The values of the penalty factors τfeed are to be selected as very high value for a minimization problem. In this book chapter, the penalty values are selected as 1016 [68]. If any of the inequality constraints violates then the corresponding penalty function adds a very high value to the objective function.

images

      An entry “NA” means not applicable.

      So, it may be inferred that the proposed novel SPBO method works fine to solve ten CEC-2005 benchmark functions considered in this book chapter.

Functions Attributes PSO TLBO CS SOS SPBO
F1 Best FF -450.0000 4.3423×103 285.0288 -450.0000 -450.0000
Worst FF -450.0000 1.2868×104 2.6304×104 -450.0000 -450.0000
Mean -450.0000 6.1561×103 9.2000×103 -450.0000 -450.0000
Std. Dev 0 2.4294×103 8.1507×103 0 0
Rank 3

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