Page 259 - Hybrid-Renewable Energy Systems in Microgrids

236 Hybrid-Renewable Energy Systems in Microgrids

a given load and the desired LPSP, the optimum configuration or number of batteries
and PV modules was calculated based on the minimum cost of the system.
More studies have been reported literature, where the authors optimally designed
the sizes of the components of a PV- battery system for SA mode using Graphic con-
struction techniques [41,94]. In their study [94], the authors presented a technique to
find the optimum combination of PV wind system using the existing meteorological
data, based on the solution of supply-demand energy balance using graphical con-
struction techniques.
The graphical construction method can be explained using one example. One can
determine the combination of PV panels and wind turbines that satisfy a given LPSP.
Fig. 12.5 can be a plot representing the number of PV modules versus the number of
wind turbines for a given LPSP. To determine a PV/wind turbine combination to mini-
mize the cost of the system one can use the cost function given below:

=
C=α⋅NPV+β⋅NWIND+C 0 C α • N PV + β • N WIND + C o (12.8)

where: C is the capital cost of the hybrid system, α is the cost of a PV module, β is
the cost of one wind turbine, and C 0 is the total constant costs including the cost of
design.
For optimum system combination,

δ N PV β
δNPVδNWIND = − βα δ N WIND =− α (12.9)

The solution can be illustrated using the graph shown in Fig. 12.6. Point R represents
 β 
− βα the optimum system configuration where the inclination of the line equal to  −  .
 α 
4.2.5 Multi-objective design

In the engineering field, to carry out any design, often the designer has to consider
several objectives simultaneously. It is not uncommon that some of the objectives
may conflict with another [95]. While designing the components of HRES optimally,
generally the designer carries out the design process considering at least two objec-
tives—to minimise the system cost and emission of pollutants [65]. However, these
two objectives create a conflict, since a reduction in design costs infers a rise in pollut-
ant emissions and vice versa. Hence, the task of getting a satisfactory result in design
problems with multiple objectives is complex. Due to the involvement of a large num-
ber of variables that are considered and of the mathematical models applied, this kind
of design process becomes extremely complicated. Classic optimization techniques
may consume extreme computational time or even being incompetent of considering
all the characteristics associated with the design problem.
Some researchers have presented the methodology to [35,69,96] design these kinds
of systems. In their works, this is usually done by searching the configuration and/