## 4 Results
### Second Model  
In this case the model of Equation (20) was made with all the available points (1 to 16 of Table 3) to explore the response surfaces of the four fitted responses. Once again, the models corresponding to \(\gamma_{con}\)-n and \(\gamma_{pow}\)-n have a lower value of R\({}^{2}\) (52.8% and 41.6%, respectively) whereas the other four are acceptable.  
Figure 7 shows the level curves in the experimental domain for the two fitted responses \(\gamma_{switch}\)-d, Figure 7a and \(\gamma_{switch}\)-n in Figure 7b.  
A value equal to or less than 0.03 is considered optimal for these variables (\(\gamma_{switch}\)-d and \(\gamma_{switch}\)-n) and any value over 0.10 is absolutely rejected. The acceptable region is marked in the figure with vertical stripes and the non-acceptable ones with horizontal stripes. It may be observed that the distribution of compressor power has to be completely different according to whether we consider system behaviour in the daytime or in the night-time. It is sufficient to install two compressors of similar power (50, 50, 0) or three compressors with a different distribution (40, 10, 50), to achieve the optimal response during the day, Figure 7a. Alternatively, any configuration in which the first compressor contributes 60% or more of the power, regardless of how the remaining power is distributed between the other two compressors is sufficient for the night-time. In addition, \(\gamma_{switch}\)-n is always maintained below 0.10 whatever the power distribution.  
The other two daytime variables \(\gamma_{conv}\)-d and \(\gamma_{pow}\)-d follow a very similar behaviour in the form of \(\gamma_{switch}\)-d.  
It is therefore necessary to look for a \"compromise\" configuration in the distribution of power between the three compressors.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{\(\gamma_{conv}\)-d} & \multicolumn{3}{c}{\(\gamma_{switch}\)-d} & \multicolumn{3}{c}{\(\gamma_{pow}\)-d} & \multicolumn{3}{c}{\(\gamma_{switch}\)-n} \\ \hline \# & **d(x)** & \(s\begin{pmatrix}\mathbf{\hat{\gamma}(x)}\end{pmatrix}\) & \(\mathbf{\hat{\gamma}(x)}\) & \(\mathbf{\hat{\gamma}(x)}\) & \(\mathbf{\hat{d}f_{n}(x)}\) & \(s\begin{pmatrix}\mathbf{\hat{\gamma}(x)}\end{pmatrix}\) & \(\mathbf{\hat{\gamma}(x)}\) & \(\mathbf{\hat{d}f_{n}(x)}\) & \(s\begin{pmatrix}\mathbf{\hat{\gamma}(x)}\end{pmatrix}\) & \(\mathbf{\hat{\gamma}(x)}\) & \(\mathbf{\hat{d}f_{n}(x)}\) & \(s\begin{pmatrix}\mathbf{\hat{\gamma}(x)}\end{pmatrix}\) & \(\mathbf{\hat{\gamma}(x)}\) & \(\mathbf{\hat{d}f_{n}(x)}\) \\ \hline
11 & 0.306 & 0.0183 & 0.097 & \(-6.36\) & 0.0258 & 0.130 & 0.99 & 74.331 & 1,4092.48 & 0.07 & 0.0016 & 0.034 & 0.57 \\
12 & 0.345 & 0.0185 & 0.052 & 1.44 & 0.0262 & 0.081 & \(-2.42\) & 75.441 & 1,4213.72 & 3.10 & 0.0017 & 0.042 & 0.68 \\
13 & 0.430 & 0.0191 & 0.075 & 1.49 & 0.0270 & 0.077 & \(-2.42\) & 77.794 & 1,4163.14 & 4.37 & 0.0017 & 0.033 & \(-2.13\) \\
14 & 0.306 & 0.0183 & 0.068 & 1.01 & 0.0258 & 0.099 & 1.02 & 74.331 & 1,4165.96 & 0.90 & 0.0016 & 0.030 & \(-2.73\) \\
15 & 0.503 & 0.0196 & 0.075 & 1.78 & 0.0277 & 0.118 & 0.01 & 79.736 & 1,4015.29 & 0.21 & 0.0018 & 0.040 & 0.12 \\
16 & 0.542 & 0.0198 & 0.085 & 2.33 & 0.0280 & 0.111 & \(-0.28\) & 80.767 & 1,4024.90 & 0.95 & 0.0018 & 0.038 & \(-3.98\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of applying the model to the test-points 11–16 in Table 1. The values of \({\it dif}_{n}(\mathbf{x})\) in italics are those which exceed the critical value 3.8 (in absolute value).