**3. DC Flow Analysis**

To perform a current flow analysis of the defined DC network, an electricity-based circuit model is required. The nodal analysis method based on the presented PV circuit was used. In this method, an admittance matrix which includes cable components is adjusted in power flow analysis according to the PV power extraction.

For the general analysis of PV circuits for current estimation, the admittance of the components was divided into two categories (consumption and supply) for simplicity. With these simplifications, the PV current can then be reflected in the matrix representation. In a PV system, a current flows through the cathode for grounding. According to [13], a method was used to eliminate the current leakage in consideration of ground impedance. Since this study examined the impact of computational load with a focus on a previously used method of deriving current expectation based on real-time power output, the detailed resistance component between each PV module is applied to the admittance matrix. A consideration is made of the resistance component of the DC pole of the cathode which is generally considered as the ground section.

In this study, the nodal analysis was applied to formulate the detailed current flow in DC section. With this, the PV system can convert the energy extraction state of each module into a current flow. The output power of the PV module can be changed as a negative admittance component to be included in the matrix. In the case of an ESS, the charging and discharging power can be implemented as equivalent components according to the amount of profile. Based on a single module, each component can be represented by an admittance matrix as follows:

$$\mathbf{g} = \begin{vmatrix} \mathbf{G}\_P & -\mathbf{G}\_{PN} & -\mathbf{G}\_{P0} & 0 \\ -\mathbf{G}\_{PN} & \mathbf{G}\_N & 0 & 0 \\ -\mathbf{G}\_{P0} & 0 & \mathbf{G}\_{PCS} & -\mathbf{G}\_{DC} \\ 0 & 0 & -\mathbf{G}\_{DC} & \mathbf{G}\_{ESS} \end{vmatrix} \tag{1}$$

The diagonals of the admittance matrix for positive/negative node of module and connection points of PCS, ESS ( *GP*, *G N*, *GPCS*, *GESS*) includes power extractions along with connected cable component as follows:

$$G\_P = \mathcal{g}\_{\mathbb{R}} + \mathcal{g}\_{Pm-1} \tag{2}$$

$$\mathcal{G}\mathbb{N} = \mathcal{g}\_n + \mathcal{g}\_{\mathcal{N}m-1} \tag{3}$$

$$G\_{\rm PCS} = \mathcal{g}\_{\rm Nnn-1} + \mathcal{g}\_{\rm PCS} + \mathcal{g}\_{dc-dc} \tag{4}$$

$$G\_{DC} = g\_{dc-dc} + g\_{ESS} \tag{5}$$

The non-diagonals of the admittance matrix for positive/negative section are solely composed with regarded cable (*gPnn*−1, *gNnn*−1) or equivalent admittance of own conversion system (*gdc-dc*, *gESS*). When adding n modules, the size of the admittance matrix adds *n* × 2 columns and rows on the basis of generalized matrix (1). Based on this, it is possible to analyze a mean conversion time for a large PV system and organize a feasibility study whether the expected delay is within a constraint.

In the iterative process, it is necessary to define an input variable with previous state (k) that can reflect the amount of output power to estimate the voltage level of the DC section which is considered as an unknown value. The corresponding input parameter must be converted to an admittance value, and the power extracted from each PV module connected in series can be updated repeatedly as follows:

$$\log\_{n:k} = -\frac{P\_{n:k}}{\left(V\_{Pn:k} - V\_{N:n:k}\right)^2} \tag{6}$$

The admittance component for ESS is able to be expressed as shown in Equation (7) considering grounding.

$$g\_{ESS\,k} = -\frac{P\_{ESS\,k}}{V\_{ESS\,k}^2} \tag{7}$$

The voltage in each section for next state (*k* + 1) is a ffected by the admittance factor due to the modified value until it converges within the available range. The main PCS current is fixed for convergence as a slack element. To perform the iterations considered as the main calculation, the inverse matrix is used to advance the iteration method as described in (8). The generalized control diagram is illustrated in Figure 4.

$$\left[V\_{k+1}\right] = \left[\mathcal{g}\_k\right]^{-1} \times \left[I\_k\right] \tag{8}$$

**Figure 4.** Modified control diagram of iterative method.

The contents of (1) depends on the number of PV modules, hence, a large-scale PV generation system requires further dimensional matrix. If n modules are added, the circuit will be expanded as mentioned earlier which results in a change of the basic equation as given in (9). Based on the

configured sparse matrix, an analysis of the possible computational load and delay effect on main controller was performed using case studies.

