## 5 Case Studies
Nevertheless, the situation changes with the continuous growth of solar capacity. When \(C_{PV}=C_{STC}=400\) MW, an EES with 1292 MWh capacity and a TES with 949 MWh capacity are need to take full use of solar energy, and the 26.8% cost reduction is mainly attributed to the EES unit, which can be observed from Figure 3c. Finally, we consider sizing the components in the energy hub. The unit capacity costs of PV panel, STC, EES and TES are \(c_{PV}=6\) million CNY/MW, \(c_{STC}=1\) million CNY/MW, \(c_{EES}=1.25\) million CNY/MWh, and \(c_{TES}=0.2\) million CNY/MWh. We change the available budget from 0 to 5 billion CNY. The optimal sizing strategy and optimal daily operation cost are retrieved from model (23). The results under different budgets are provided in Figure 4 and Table 3. When the budget is rare, all investment will be spent on PV panels and STC; storage is needed only if electricity or heat produced by solar energy is larger than the demand. When the budget is greater than 1.5 billion CNY, the marginal cost reduction brought by per unit investment decreases, because EES and TES should be invested in accompanying PV panels and STC. The efficiency of investment is also examined. For a fixed budget \(\Gamma\), let the corresponding optimal sizing strategy be \(\theta^{*}(\Gamma)\), then the cost recovery time can be calculated from \(\Gamma/365(v(0)-v(\theta^{*}(\Gamma)))\) (in years). When the budget \(\Gamma\leq 1.3\) billion CNY, the cost recovery time is 8.8 years, and grows at a constant rate with the increase of budget \(\Gamma\). Suppose the lifespan of the facility is 10 years, the net profit under an available budget \(\Gamma\) and the corresponding optimal sizing strategy \(\theta^{*}(\Gamma)\) is \(365(v(0)-v(\theta^{*}(\Gamma)))-\Gamma\). The results are given in Figure 5, from which we can see that from an optimal net profit perspective, the optimal investment seems to be \(\Gamma=1.3\) billion CNY. If the lifespan of the facility can reach 20 years, then the optimal investment is \(\Gamma=2.0\) billion CNY. Results in Table 4 show that most of the investment on storage will be spent on the TES unit, because of its low cost, and hence the saved capacity of the CHP unit can be used to produce electricity. In the future, the costs of battery and solar panel are expected to drop continuously. Investment on renewable energy and storage will become more rewarding. We test the impact of \(c_{PV}\) and \(c_{EES}\) on the sizing strategy and net profit. The lifespan of the facility is assumed to be 10 years, and the budget is fixed at 1.5 billion CNY. The optimal sizing strategy and optimal daily operation cost are retrieved from (23), and the results are summarized in Table 4. At the beginning, with the decrease of \(c_{PV}\) and \(c_{EES}\), the saved cost will be spent on solar panel, STC, and especially TES, which is verified by the rapidly increased capacity. With the help of EES, the CHP can have more capacity in producing electricity, so EES is not invested in. However, with the continuous decline of \(c_{PV}\) and \(c_{EES}\), EES becomes more favorable, as its cost reduction potential shown in Figure 3c can be fully unleashed; at the same time, the investment in STC and TES reduces. Figure 3: OVF and critical regions with different solar capacities.