# Optimization of DC Energy Storage in Tokamak Poloidal Coils
## 4 Possible Optimization Parameters with Their Constraints  
Having assessed that PF PSs would benefit from an energy storage based on SCs, the design challenge consists of optimizing its dimensions and costs together with its power demand from the grid. In fact, the SC banks may be the most expensive and largest part of the PS system. A simple design based on peak requirements would cancel any potential advantage in terms of cost and performance. In practice, it is necessary to solve an optimization problem under strongly variable and complex loads. In typical commercial technologies for energy storage applications, a single SC cell has a capacitance on the order of thousands of farads but can sustain a voltage on the order 2-3 V. Therefore, the practical implementations are always based on the series (and parallel) of multiple cells. For this reason, manufacturers usually provide assembled modules with voltages on the order of tens or hundreds of volts (for example, 16; 48; 54; 64, or 160 V). For the specific case of PF PSs, these voltages are still insufficient and, in addition, the required current (power) and energy can be attained only by packs (banks) of SC cells or modules. Some manufacturers propose racks of modules including some management, control, and cooling systems. Racks are useful for specific applications such as grid storage, but their fixed voltage does not allow a flexible design optimization. The first step in PS design consists of the choice of a topology. For the purpose of this paper, a single H-bridge based on IGBTs with a single SC DC link can be considered. Figure 5 shows a block scheme of the PS topology for a single PF coil that will be used for the optimization and for the circuital simulations. In the final design, more IGBTs/bridges in series/parallel, or the split of the DC link in more SC banks connected to a portion of the necessary H-bridges, could have practical benefits [44]. However, these details would not affect the dimensions of the SC-DC link to be optimized and the following analysis. A slightly different situation occurs when an SC module and a small converter are combined in a basic unit to be connected in series/parallel to reach any value of voltage/current [14]. This has the advantage of focusing on the design of a single unit [14] but is constrained to discrete values, resulting in fewer degrees of freedom in achievable optimizations. For this reason, the adoption of a large DC link, not related to any particular SC model, is preferred for the analysis. To have a good balance, the banks must consist of cells/modules from the same family and must contain the same number, \(N_{\rm s}\), of SCs in series in each of the \(N_{\rm P}\) parallel branches, thus resulting in being fully defined by the dimensions \(N_{\rm s}\times N_{\rm P}\). It is commonly accepted in all the references that the model of a group of series/parallel cells can be extended from the model of a single cell. This is not strictly sound according to the circuit theory for more complex models, but it is, rather, applicable to a simplified model equivalent capacitance plus ESR. In particular, this simplification is valid if all the assembled cells/modules are identical. This is not valid in real cases due to the component tolerances. Another aspect to be considered is that the application of the standard formulas for linear circuits is not applicable under the non-ideal phenomena observed in SCs [40]. However, manufacturers usually include in the commercial modules/cabinets specific systems to balance the tolerances [45; 46]. This supports the simplification, but, on the other hand, slightly modifies the SC equivalent circuit. Therefore, the tolerances are expected to be compensated in the estimation of the bank size, and they could be covered in the assumed safety margins. The absence of direct characterization of modules and packs is probably related to the difficulty of finding a specific instrument to perform it.