5.1. Second-order polynomial (Quadr

5.1. Second-order polynomial (Quadratic) model fitting and RSM results
The general representation of second order regression model of
the design is shown in Eq. (7):
Y ¼ b0 þ b1x1 þ b2x2 þ b3x3 þ b4x1x2 þ b5x2x3 þ b6x1x3 þ b7x21
þ b8x22
þ b9x23
ð7Þ
where Y is the selected response; b0–b9 are the regression coefficients
and x1–x3 are the factors. This model is used to estimate
the relationship between the cost function, Y, and the three independent
factors, PV size, x1, wind turbine rotor swept area, x2, and
battery capacity, x3. Here, b1, b2, b3 coefficients denote the main effect
of factors x1, x2 and x3, respectively. Besides, b4 denotes the
interaction between factors x1, x2; b5 denotes the interaction between
factors x2, x3, and b6 denotes the interaction between factors
x1, x3. Finally, b7, b8, b9 denote the quadratic effect of factors x1, x2
and x3, respectively.
In order to fit the metamodel given in Eq. (7), 15 experiments
with three independent replications in the middle are utilized as