## 2 System Layout
### Bi-Directional Current Flow
Through the applications of the first and second laws of thermodynamics and knowing the total current entering a node is equal to that of the sum of currents departing from it, and noting that the voltage is regulated at a constant value, the linear combination  
Figure 7.8  
where \(\text{\theta}\) is the participation matrix contain values varying between 0 and 1, it also accounts for the efficiency of the converters. Each source contributes a percentage of the power to the system. The efficiency of the power electronics involved in high power application usually sits above 90% but as the power drops so do the yield, hence, an effective voltage regulation will require a robust control method to account for both uncertainties in the model and the nonlinearity of the efficiency. The schematics of the power electronics configuration is illustrated in Figure 7.9 This configuration is also referred to as a multi-input single output converter (MISO) [23]. As stated earlier, DC MGs offers an intuitive platform to conduct both a theoretical study and deploy experimental tests [24], since the voltage is regulated at a constant value,  
\[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]0 Microgrid multi current sources model. \[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]1 Microgrid multisource power electronics schematics. all energy related analysis is done on the inner current control loop, in other words the problem of stability is decoupled from the problem of energy management which in turn can be formulated into an optimization problem. Figure 10, showcases the general structure of control; the output of the voltage regulation is considered an index of the energy required (denoted \(\Gamma_{\text{ref}}^{*}\)) to maintain the stability of the system. The index \(\Gamma_{\text{ref}}^{*}\) is used as a hard maximum limit for renewable energy management block in the production of energy with two modes of operations, Equations (51) and (52);  
\[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]2  
\[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]3  
In the case where the renewables are able to supply 100% of the required energy the energy management block simply forwards the desired set point to the resources dispatching. Else, when the required energy of the system exceeds that of the current renewable capacity, the maximum power point tracking (MPPT) algorithm is triggered, outputting the maximum current possible as disclosed in \[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]4  
\[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]5 Output renewables current at different maximums. \[R_{\text{bat}}=f(\int_{t_{0}}^{t}I_{\text{charging}}(\tau)d\tau) \tag{39}\]6 Control structure of the multi-source microgrid. In addition to enforcing strict system limits, the Energy Storage System (EESS) management block is responsible for overseeing protective mechanisms in the event of a fault. Moreover, depending on various scenarios, the EESS may be prompted to discharge and compensate for power imbalances. The storage capacity of the microgrid is directly correlated with the effectiveness of optimization methods, for this reason it is essential to manage the charging and discharging cycles properly. During the time of the day when energy is most inexpensive or free, the system initiates the charging process. In the subsequent provided illustration, a negative sign indicates charging, whereas a positive value indicates discharging. The state of charge (SOC) of the battery is maintained within an appropriate range to prevent premature degradation, Equation (53). Numerous other constraints can be specified, such as the number of charge/discharge cycles per day, the rate of consumption change, and voltage range. \[\left\{