# Optimization of DC Energy Storage in Tokamak Poloidal Coils
## 4 Possible Optimization Parameters with Their Constraints
Nevertheless, a verification is presented in [38] for two SC cells and in [46] for four cells with balancing. Therefore, the parameters to be considered for the optimization are as follows:  
* Base SC cell or module. This is important to identify the unitary voltage and capacitance, but also the ESR intrinsic to it [47]. * Number of series \(N_{\rm s}\) and/or parallel \(N_{\rm P}\) cells/modules. * Maximum current requested to supply the load coils in the desired scenario \(I_{\rm Lmax}\). As the peak current of the SC cells is extremely high (on the order of 1000 A), this parameter is normally well satisfied when the other ones are optimized. * Maximum voltage \(V_{\rm max}\) across the DC link. This is not a trivial parameter, because the voltage of the DC link can change during the operation to fully exploit the stored energy. Of course, it cannot exceed the maximum rated values of the SC cells and of the rest of the hardware. Normally, the voltage limitations are not due to the number of SC cells that can be placed in series (what is reported in the datasheets for modules is due to the insulation of the diagnostic systems), but to the other components as the IGBTs. It is a design choice whether to select as \(V_{\rm max}\) the maximum value requested by the load coils during the scenario or the maximum value allowed by the hardware. The energy is higher with the latter choice. * Minimum voltage \(V_{\rm min}\) necessary to drive the currents in the desired scenario(s). In fact, a PS converter can operate only if the voltages across the semiconductor switches exceed their turn-on values. These minimum voltages are not trivial parameters, because the voltage of the DC link can change during the operation to fully exploit the stored energy. As explained in the next section, SC manufacturers usually provide characteristics for cycles not discharging below \(V_{\rm max}/2\). * Peak power requested to supply the load coils in the desired scenario(s). For the properties of the Ragone plot, using SCs, this parameter normally is also well satisfied when the other ones are optimized. Figure 5: General topology of the PF coil PS used for the design and optimization. * Maximum energy stored or storable in the DC link \(E_{\text{DC}}\). It seems an immediate parameter given by the time integral of the power during the scenario, but it is not the optimal operating mode for pulses longer than some seconds. The actual value must be selected in compliance with the maximum input power demand from the grid. * Maximum input power demand from the grid \(P_{\text{gridmax}}\) (and related charger rating). In principle, this power can even be zero if the scenario is completely driven by the energy in the DC storage. This can lead to a simplification for very short operations [17]. However, as some form of charger must be present, it generally makes sense to exploit its contribution. All these parameters are discussed in the next section. Here, it is worth noticing that they are not independent. The most important relationship is that between \(V_{\text{max}}\) and \(E_{\text{DC}}\), established by the well-known formula  
\[E_{\text{DC}}=\frac{1}{2}{C}{V_{\text{max}}}^{2} \tag{1}\]  
Better optimization performance could be achieved by releasing or relaxing the constraints among parameters. A higher energy density can be obtained if the DC storage is based on LICs [21] or hybridized with batteries [35; 36]. A separated charger can provide a higher \(V_{\text{max}}\) specifically for short ramps [17]. A deeper SC discharge can be obtained by inserting a further stage with a boost converter between the SC bank and the H-bridge. An offset to \(V_{\text{max}}\) not depending on (1) can be added by an H-bridge fed by standard capacitors in cascade with the H-bridge fed by the SCs [22]. Further ideas to reduce the interdependence among parameters are proposed in the next sections. However, none of these solutions appears so advantageous in general cases as to justify its additional costs or complications.