## 5 Results and Discussion  
In this section, the results of the optimal sizing of PV-battery systems are presented. Additionally, the TCO, VD, and energy management technique that are used to enable B2G and G2B services during the optimization process are discussed. Moreover, the payback time and profitability of the proposed system are presented and discussed. Subsequently, a sensitivity analysis for different ESS costs is conducted to assess the effect on the profitability, since there is no direct subsidy for BESSs in Europe. The model has been run on a core i-7 computer with 12G DRR4 RAM and CPU 2.70 GHz in MATLAB(r) (academic license). The time of simulation from the start to end was 111 seconds for one day with fixed step time of one second. Table 1 provides the details of the economical parameters that have been used in the PV-battery system optimization. In Belgium, there are several national taxes and levies, such as the electricity excise tax, also called contribution on electricity, and the VAT rate on electricity, which is fixed at 21% since August 2015. Moreover, federal levies are imposed to finance the federal regulator, nuclear decommissioning, social tariffs, RESs, and Combined Heat and Power High Performance (CHP) support [50]. In addition, the regional levies and their rates for renewable energy are set by the respective regional governments in Flanders, Wallonia, and Brussels to fund various components, including compensation for municipalities, support for energy efficiency, and the regional budget for actions in the energy field [50]. In this study, the purchase and sell prices per kWh are based on Luminus [48], which is a producer and supplier of energy (electricity and natural gas) in Belgium. These prices include levies surcharge with a VAT rate of 21% and they consider the day and night prices for on-peak and off-peak times. Moreover, the annual inflation rate of electricity is assumed to be 2% over a year [51]. Besides that, Belgium has a sensitive array of incentives, with the main two being a Feed-In Tariff (FIT) and some regions have adopted a Green Certificate (GC) Scheme. In this regard, the FIT is widely used as a policy mechanism in the world that is designed to accelerate investment in renewable energy technologies, which accounts for a greater share of RE development than either tax incentives or renewable portfolio standard (RPS) policies [52]. In the meanwhile, Belgium opted for investment grants, VAT reductions, and beneficial credit terms. In this study, the sell and purchase prices per kWh are considered as same prices, being based on the Brussels energy market [49; 53]. The voltage stability analysis is critical in the operation of electric power systems. In this regard, [PERSON] et al. [14] used the Multi-Objective Genetic Algorithm (MOGA) for multi-purpose operation plan to achieve an improved voltage stability and reduce the PV output prediction error and it showed a 6% improvement in the voltage stability index. Moreover, [PERSON] et al. [54] used a multi-objective Particle Swarm Optimization (PSO) algorithm for optimal penetration of PV, while maintaining the system stability, and it showed an 11% improvement for the novel line stability index. In addition, [PERSON] et al. [55] used a combination of PSO and Newton Raphson Power Flow (NRPF) methods for the optimal allocation of DG to minimize VD and it showed a 16% reduction in VD. Besides that, the results that were obtained in the present study (see Table 2) demonstrate that the used method