**3. DC Flow Analysis**

To perform the current flow analysis about a target DC network, an electric based circuit model should first be developed. In order to estimate the voltage variation of each section based on the power extraction, an equivalent circuit was developed for power flow analysis.

In case of the general analysis of the PV circuit for current estimation, the resistance in the circuit is divided into two categories (shunt and series) as shown in Figure 4 to advance it in terms of simplification [32]. With this simplification, environmental factors such as irradiation (G) can be reflected in output current expression. On the PV system, however, since a current flows through the negative pole which is for grounding, for detailed current analysis, a method to reflect this circumstance should be derived. In Ref. [33], a method is derived to eliminate the leakage current in consideration of the earth impedance. In this regard, a method of applying the grounding components to the detailed analysis is continually being studied. In addition, although the general method introduces each environmental variable as a constant value to advance the prediction of current flow, it is di fficult for these methods to reflect a real-time environment. In this paper, we focused on the method of deriving the amount of current based on real-time power output, and tried to improve the accuracy by minimizing the variables. Figure 5 shows a simplified circuit which includes PV, ESS and DC/AC inverter to connect the main grid. The resistance components between each PV module were imposed in the circuit for purposes of clearly describing voltage fluctuation on a low-voltage DC network. Reflection of the inner voltage variation condition for large-scale PV generation system is a demanded feature which is also considered in commercialized simulation tool as well. In this paper, the resistance components at the negative DC pole which is usually considered as ground section is utilized to improve the accuracy of voltage calculation.

**Figure 4.** Equivalent circuit of single diode model for PV.

**Figure 5.** Power flow analysis model for DC.

Firstly, the equivalent component of the PV module in the figure is based on a single module; the basic objective of the described circuit is to derive a mathematical expression for voltage level of each section including the front of the inverter device. In the case of the PCS for a PV system, since the AC side is connected to stable grid network, it is capable of converging as an equivalent circuit. To reflect the voltage variation in the DC section, the Norton equivalent method is applied in this study. When DC network analysis is imposed into the PV system, there is a need to imply the power extracting condition for each module in current flow form. The output power of the PV module can be modified to obtain an equivalent circuit with negative values if each module is considered as an admittance component. In case of ESS component, both charging and discharging power can be

implemented using an equation that has described modeling processes. Each component in the figure can be transformed using the components mentioned as follows:

$$
\begin{vmatrix}
\mathbf{g}\_1 + \mathbf{g}\_{u10} & -\mathbf{g}\_1 & -\mathbf{g}\_{u10} & 0 & 0 \\
0 & 0 & -\mathbf{g}\_{cq} & \mathbf{g}\_{cq} + \mathbf{g}\_{ESS} & V\_{ESS}
\end{vmatrix}
\begin{vmatrix}
V\_{u1} \\
V\_{d1} \\
V\_{dc} \\
V\_{ESS}
\end{vmatrix} = 
\begin{vmatrix}
0 \\ 0 \\ \mathbf{i}\_{dc} \\ 0
\end{vmatrix}
\tag{7}
$$

The DC section of single array would consist directly connected PV module, main PCS for subsystem, and DC/DC convertor for introduced storage devices. The three basic models could be transferred as an electrical component in order to proceed as an iterative calculation process. The iteration requires input parameters including a known quantity to derive each section's voltage levels which are considered as unknown values in the circuit elements. The system input parameters include admittance values, which are repeatedly updated with extracted power from series-connected PV modules, and derived based on Equation (8).

$$\mathcal{g}\_{\rm dl} = -\frac{P\_{\rm n}}{\left(V\_{\rm un} - V\_{\rm dn}\right)^2} \tag{8}$$

The voltage for PV modules considers both the upper and lower side and are continuously modified throughout the iteration process as unknown values. The admittance component of ESS are as follows in Equation (9) by assuming shared grounding option.

$$g\_{ESS} = -\frac{P\_{ESS}}{V\_{ESS}^2} \tag{9}$$

Since the voltage level of each section is dependent on electrical current via power flows, the modified values would continuously a ffect the admittance component until every input parameter is converged. The corresponding current of PCS would hold the relevant DC power flow as a strict component in the system matrix. To perform the iteration, which is considered as a main calculation, an inverse matrix is utilized to progress the iteration as described in Equation (10).

$$[V] = [\mathcal{g}]^{-1} \times [I] \tag{10}$$

The contents of Figure 5 are based on single PV module; hence, large-scaled PV generation system requires further dimensional matrix. If n modules are added, the circuit will be expanded as mentioned above, which results in a change in the basic equation as follows in (11).

When adding *n* modules, an *n* × 2 matrix size expansion is progressed on an existing equation. If this equation is analyzed in detail, it is possible to consider a di fference of production by large modules and organize an equation about the profile of each module with the required data.

