# A Novel Higher-Order Numerical Scheme for System of Nonlinear Load Flow Equations
###### Abstract
* Disadvantages: Less accurate than Newton-Raphson, may not converge for highly nonlinear systems, requires assumptions to decouple real and reactive power calculations. 4. Modified Newton Method: * Advantages: Combines advantages of Newton-Raphson and fast decoupled methods, faster convergence than traditional Newton-Raphson. * Disadvantages: May require more computational resources than fast decoupled method, convergence issues still possible for highly nonlinear systems. 5. DC Load Flow Method: * Advantages: Extremely fast convergence, suitable for initial approximations or preliminary studies, computationally efficient. \begin{table}
\begin{tabular}{c c c} \hline
**Types of Bus** & **Specified Quantities** & **Unspecified Quantities** \\ \hline Slack bus & \(|V|,\delta\) & \(P,Q\) \\ \hline Generator/\(PV\) bus & \(P,|V|\) & \(Q,\delta\) \\ \hline Load/\(PQ\) bus & \(P,Q\) & \(|V|,\delta\) \\ \hline \end{tabular}
\end{table} 
Table 1: Classification of buses. * Disadvantages: Limited accuracy due to linearization of power flow equations, not suitable for highly nonlinear systems or systems with voltage deviations. * Sparse Matrix Techniques:
* Advantages: Memory-efficient for large systems, reduces computational burden by exploiting network sparsity. * Disadvantages: Requires additional implementation complexity, may not significantly improve computational speed for small to medium-sized systems. Each technique has its own trade-offs in terms of convergence speed, accuracy, computational complexity, and suitability for different system sizes and nonlinearities. The choice of method depends on the specific requirements and characteristics of the power system being analyzed. Thus, development of new algorithms is required to meet the needs, including those related to speed, storage, dependability, calculation time, convergence characteristics, etc. On the other hand, Newton-Raphson and its higher-order variants are reliable and give robust solutions. Higher-order Jarratt methods offer several merits for solving load flow equations in power system analysis. These methods exhibit faster convergence compared to traditional methods like Gauss-Seidel or Newton-Raphson, especially for power systems with highly nonlinear characteristics, improved stability properties, making them more robust in handling systems with large mismatches between generation and consumption or systems with voltage stability issues, enhanced robustness against initial guess selection and system parameter variations, reducing the likelihood of convergence failures and improving overall solution reliability. Higher-order Jarratt methods offer higher-order accuracy in approximating the solutions to load flow equations, leading to more accurate results compared to lower-order methods. Jarratt methods, particularly higher-order variants, are efficient for solving load flow equations in large-scale power systems, where traditional methods may suffer from slow convergence or computational inefficiencies. These methods typically require fewer iterations to converge compared to lower-order methods, resulting in reduced computational burden and faster solution times, which is crucial for real-time and large-scale power system analysis. With the increasing complexity and nonlinearity of modern power systems, higher-order Jarratt methods offer a viable solution approach that can effectively handle the intricacies of these systems, ensuring accurate and efficient load flow analysis. The nonlinear power flow equations are influenced by voltages \(|V|\) and phase angle \(\delta\). Newton-Raphson type methods are widely used for the power flow analysis which comprises the bus admittance matrix. In order to solve the power system, the derivative of a function is expressed by a matrix, and the Jacobian is computed. Furthermore, we obtain the partial derivatives of power flow equations containing active and reactive powers.