# A Review of Distribution Grid Consumption Strategies Containing Distributed Photovoltaics
## 3 Distribution Grid Consumption Strategy with Distributed PV
#### 3.1.1 Objective Function  
Consumption refers to the process of delivering the electricity generated by distributed PV power systems to the grid and coordinating its operation with other power systems. Distributed PV siting and sizing is the process of determining the size and layout of distributed PV power generation systems by taking into account various factors, such as topography, climate, building shading, and electricity load, in order to select the appropriate  
Figure 6: Photovoltaic power generation system.  
location and capacity for installation [12]. In practical application, distributed PV siting and capacity sizing can effectively solve the problem of consumption. By reasonably selecting the location and capacity size and coordinating the operation with the power grid, it can ensure that the distributed PV power generation system can operate in coordination with the power grid to avoid problems such as voltage fluctuations and frequency changes so as to guarantee the safe and stable operation of the power grid.  
Before determining the appropriate distributed PV siting and capacity model, it is necessary to plan the objective function and constraints to ensure that the final optimization model is more in line with the actual, commonly used objective function as follows.  
(1) Node voltage deviation: reflecting the voltage distribution before and after adaptive reactive power control, the lower the deviation value indicates that the voltage distribution is more reasonable.  
\[f=\sum\limits_{i=1}^{N}{(\frac{U_{i}-U_{ref}}{U_{\text{imax}}-U_{\text{imin}}}) ^{2}} \tag{1}\]  
where \(f\) is the sought voltage deviation, U\({}_{\text{i}}\) and U\({}_{\text{ref}}\) are the actual measured and reference values of voltage at node i, and N is the set of load nodes.  
(2) Power loss: power loss reduction index.  
\[f^{\prime}=P_{Loss}-P^{\prime}_{Loss} \tag{2}\]  
where \(f\) is taken to its minimum value and is the best choice to reduce power loss, the equation represents the total power after access minus the total power before access.  
(3) Minimum active network loss and minimum voltage deviation.  
\[\left\{\begin{array}{l}\text{min}f_{1}=\sum\limits_{i=1}^{N}{R_{i}\frac{P_{ i}^{2}+Q_{\text{f}}^{2}}{U_{i}^{2}}k_{i}}\\ \text{min}f_{2}=\sum\limits_{t=1}^{k}{\frac{(U_{ts}-U_{tN})^{2}}{{U_{tN}}^{2}} }\end{array}\right. \tag{3}\]  
where N is the total number of branches; P\({}_{\text{i}}\) and Q\({}_{\text{i}}\) are the active and reactive power of the ith branch, respectively; U\({}_{\text{i}}\) is the voltage of the terminal node of the ith branch; R\({}_{\text{i}}\) is the resistance of the ith branch; k\({}_{\text{i}}\) is the switching state of the ith branch, with 0 representing the disconnection and 1 representing the closure; \(f\)1 is the total active loss; t is the node number; k is the total number of the nodes; U\({}_{\text{ts}}\) and U\({}_{\text{UN}}\) denote the actual and rated voltage of the ith node, respectively; and f\({}_{2}\) denotes the voltage offset.  
In addition to the above typical objective functions, more objective functions can be added in the subsequent optimization process to make the results more realistic.