The study of electrical power flow in interconnected systems is of great significance in power engineering. It uses simple notations like per-unit systems and majorly focuses on important power parameters such as the voltages, real and reactive powers and voltage angles. Power flow analysis allows engineers to determine the best operating procedures for the existing systems as well as the expansion of the power systems.
Presently, power flow analysis involves specifying loads and sources in terms of power constants to determine the steady state of the power networks which forms the basis of other analysis and tools. Unfortunately, enforcing control limits in power flow analysis which is deemed as the ideal way of enhancing the accuracy of the analysis has been very difficult.
Among the features considered during the analysis, voltage regulation by synchronous generators is very vital. Consequently, the bus voltage problems are represented by nonlinear algebraic equations. Furthermore, control devices are utilized to restrict the regulated magnitudes and addition of new variables to the system. The variables help in balancing the equations and the unknowns. However, all the controls have limits, therefore, the control behavior change when the limits are reached must be taken into consideration. It also consists of a switching behavior where the regulated magnitudes can be varied from the given setpoints thus resulting in more complex network modules that consumes a lot of time to analyses.
Several methods for enforcing the limits have been developed. For instance, the type switching and feedback adjustments methods are associated with rebounds due to nonlinear interactions of the controls that lead to slow or prevention of convergence. Therefore, researches have been looking for alternatives for preventing interactions and convergence problems and have identified the rigorous solution of control limits problem as a promising solution.
Dr. Antoni Trias and Dr. Jose Luis Marín at Aplicaciones en Informática Avanzada developed a new general-purpose power method for the rigorous solution of the control limits based on the Lagrangian equations. The method takes into consideration the Mvar limits in regulating generator voltages which are based on the Holomorphic Embedded Loadflow Method. They purposed to achieve a direct, deterministic and constructive method for efficient and precision analysis of power flow in various systems. The work is published in the journal, International Journal of Electrical Power and Energy Systems.
The authors observed that the developed method directly avoided the convergence problems emanating from mutual interactions of the controls as opposed to the initial traditional approaches. Consequently, it resulted in more accurate results with enhanced numerical stability. This was attributed to the possibility of using several steps to calculate the analytic continuation of the power series using the Padé-Weierstrass technique.
The development of a Padé-Weierstrass technique was very significant in the research as it enables exploration of the nature of power flow equations under variable. This allowed for high numerical precision because it can be used even if no limits are being enforced. According to the authors, the method can be extended to other types of regulating devices with limits such as the sequential shunt unit. Therefore, the study will help advance analysis of power flows in electrical systems which will further lead to better use of electrical systems to enhance efficiency and conserve energy.
Trias, A., & Marín, J. (2018). A Padé-Weierstrass technique for the rigorous enforcement of control limits in power flow studies. International Journal of Electrical Power & Energy Systems, 99, 404-418.Go To International Journal of Electrical Power & Energy Systems