# Multi-Objective Configuration Optimization of
## 3 Computation of Reference Power Output of ESS and Power Accommodation for HESS  
As stated in Section 2.2, the actual power output of the ESS is computed via Equation (6) or Equation (7), in which its reference power output is determined taking into account the reference power of wind turbine and the SOC of each ESS device. On the other hand, compensation of the fluctuating wind power is realized through real-time control of the HESS power output. Consequently, suitable power accommodation strategy is important for enhancing the compensation effect. Fuzzy control is widely applied to accommodate the HESS for avoiding SOC limit violation. The process for computing the reference power output of each ESS is described as follows.  
Firstly, estimate the SOC of each ESS using Equation (15) when charging or Equation (16) when discharging, and then apply them as the input of fuzzy control. Essentially, the two equations are used to compute the SOC after compensating the wind power with individual ESS.  
\[SOC^{t}_{pi}=\frac{(1-r_{SDCi})E^{t-1}i+\min(\Delta P^{t}_{WD},P^{t}_{maxi}) \Delta t\eta_{Ci}}{E_{ratedi}},i=SC,B \tag{15}\]  
\[SOC^{t}_{pi}=\frac{(1-r_{SDCi})E^{t-1}i+\max(\Delta P^{t}_{i}-P^{t}_{maxi}) \Delta t/\eta_{D}}{E_{ratedi}},i=SC,B. \tag{16}\]  
Secondly, get the membership value and determine the corresponding rule based on the membership function depicted in Figure 3 and the fuzzy control rules illustrated in Table 1 [8,9].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \multicolumn{4}{c}{\(SOC^{t}_{pSC}\)} \\ \cline{3-9} \(SOC^{t}_{pB}\) & & & & & \(\Delta P_{WD}\geq\textbf{0}\) & & & \\ \cline{2-9}  & **VS** & **S** & **M** & **L** & **S** & **M** & **L** & **VL** \\ \hline VS & ZE & NS & NL & NL & PM & PS & ZE & ZE \\ S & ZE & ZE & NL & NL & PL & PM & ZE & ZE \\ M & ZE & ZE & NL & NL & PL & PL & ZE & ZE \\ L & ZE & ZE & NM & NL & PL & PL & ZE & ZE \\ VL & ZE & ZE & NS & NM & PL & PL & PS & ZE \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fuzzy control rule. SOC: state of charge.  
Figure 3: Membership function: (**a**) battery; (**b**) supercapacitor for \(\Delta P_{WD}\geq 0\); (**c**) supercapacitor for \(\Delta P_{WD}<0\); (**d**) fuzzy control output.  
Thirdly, compute the modification coefficient for the power of ESS based on Equation (17) [9; 13]. Finally, compute the reference power output of each ESS according to Equation (18).  
\[b^{t}=\frac{\sum\limits_{i}\sum\limits_{j}\mu_{i}(SOC^{t}{}_{pSC})\mu_{j}(SOC^{t }{}_{pB})\Delta k_{ij}}{\sum\limits_{i}\sum\limits_{j}\mu_{i}(SOC^{t}{}_{pSC}) \mu_{j}(SOC^{t}{}_{pB})}\;\;i=\left\{\begin{array}{ll}\mathrm{VS},\mathrm{S}, \mathrm{M},\mathrm{L}&\Delta P\geq 0\\ \mathrm{S},\mathrm{M},\mathrm{L},\mathrm{VL}&\Delta P<0\end{array}\right.,\;j= \mathrm{VS},\mathrm{S},\mathrm{M},\mathrm{L},\mathrm{VL} \tag{17}\]  
\[\Delta P^{t}{}_{WD}\geq 0\;P^{t}{}_{refSC}=(1+b^{t})\Delta P^{t}{}_{WD},P^{t}{ }_{refB}=-b^{t}\Delta P^{t}{}_{WD} \tag{18}\]  
\[\Delta P^{t}{}_{WD}<0\;P^{t}{}_{refSC}=(1-b^{t})\Delta P^{t}{}_{WD},P^{t}{}_{ refB}=b^{t}\Delta P^{t}{}_{WD}\quad.\]  
Once the reference power output of each ESS is obtained, its real-time power output can be derived according to Equation (6) or Equation (7). Investigation from Figure 3 and Table 2, it is clear that the remaining energy in the supercapacitor is regarded to be adequate only when \(SOC_{pSC}\leq 0.5\) for \(\Delta P_{WD}\geq 0\) and \(SOC_{pSC}>0.7\) for \(\Delta P_{WD}<0\). And only in the two cases, the fluctuating wind power is compensated by the supercapacitor. The fluctuation is compensated by the battery and the supercapacitor when the remaining energy in the supercapacitor is insufficient.