# A Study of Order Modification for Reactive Power Support by Wind Farm during Communication Failure
## 2 System Description
### Based Algorithm for Reative Power Allocation  
Electrical loss minimization is based on a fast optimization method, using a linearization process. In the radial structure of the wind generation system, the central controller is designed to minimize sectional loss by generating suitable references--deciding each proportion in accordance with the electric components of the layout. Therefore, the reactive power allocation coefficient that are expected to supply by each turbine should be continually updated. The proportion of the entire reactive power order can be segmented as shown in the following equation:  
\[Q_{order}=\sum_{l=1}^{L}\sum_{n=1}^{N}Q_{ref}(l,n) \tag{1}\]  
\[Q_{ref}(l,n)=\eta_{ln}Q_{l} \tag{2}\]  
where, \(Q_{order}\) is the entire required reactive power order of the wind farm, \(n\) is the node number in each array, \(Q_{l}\) is the allocated reactive power to array \(l\). The reactive power allocation coefficient of each turbine in Reference [18] can be summarized in the following equation:  
\[\eta_{Int}=\frac{\sqrt{r_{n\cdot n+1}}}{\sqrt{r_{H\cdot n}+\sqrt{r_{n\cdot n+1 }}}}\cdot(1-\eta_{l\cdot n-1}) \tag{3}\]  
\[\eta_{ln}=\frac{\sqrt{r_{n\cdot n+1}}}{\sqrt{r_{H\cdot n}+\sqrt{r_{n\cdot n+1 }}}}\quad(if\ n=1)\]  
where, \(r_{n\cdot n+1}\) is the line resistance between connection points of WT \(n\) and \(n+1\), \(r_{H}\) is the line resistance relative to the connection height of the turbine. The coefficients are affected with the number of WTs and these values were modified with PI controller in this paper. The expected reactive power supply of the array is allocated according to an incremental loss technique. The reference quantity of each array is fixed when the incremental values of the equation below become equal:  
\[\frac{dLoss}{dQ_{1}}=\frac{dLoss}{dQ_{2}}=\cdots=\frac{dLoss}{dQ_{l}}=\lambda \tag{4}\]  
where electrical loss by reactive power is established with a variable composed by the resistance components, as follows:  
\[Loss(Q)=\alpha Q_{1}^{2}+\beta Q_{2}^{2}+\cdots+\gamma Q_{L}^{2} \tag{5}\]  
The value need to be stored as a data form within the designated period until a recalculating process updates it, and this value has uncertainties which could not be considered in emergency situations, such as voltage dips within the grid side. Based on this, several automatic response equations can be designed to cope with the special conditions of the electrical network. A stabilized reactive power supply is obtained through an automatic order modification algorithm, when a state of unavailability for the command deriving process occurs, due to communication failure. To achieve this, the algorithm should be established with its own measurable value, including electric flow and  
Figure 2: Core control flowchart of the proposed method. voltage level. The appropriate reactive requirements for a turbine are derived through the voltage condition of the connected node. The V-Q modal analysis is frequently used to solve issues in reactive power flow and AC voltage [19]. The fast decoupled method can linearize the system value, according to the voltage angle and quantity. The power flow equations are given by:  
\[\left[ \begin{array}{c}\Delta P\\ \Delta Q\end{array} \right]=\left[ \begin{array}{cc}J_{P\delta}&J_{PU}\\ J_{Q\delta}&J_{QU}\end{array} \right]\left[ \begin{array}{c}\Delta\delta\\ \frac{\Delta U}{U}\end{array} \right] \tag{6}\]  
If the power variation is neglected, the change of the required reactive power can be rewritten as:  
\[\Delta Q_{req}=\left(J_{QU}-J_{Q\delta}\frac{J_{PU}}{J_{P\delta}}\right)\cdot \frac{\Delta U}{U} \tag{7}\]  
where, \(Q_{req}\) is the practical required quantity (including mismatches by cables) of a certain array.