The implementation of distributed generation (DG) becomes more common while causing a challenge to maintain the voltage stability in a power system. The optimal placement of multiple DGs in a planning stage can effectively solve this problem. In many cases, the best placement has been determined by the small-signal study like the modal analysis. However, it is acceptable only if the linearization of large-scale nonlinear power system is accurate. To overcome this, this paper proposes the new optimal placement algorithm for multiple DGs based on the model-free Lyapunov exponent estimation to maintain the voltage of system stable. In other words, the individual Lyapunov exponents of all buses are firstly estimated to determine the candidates for optimal placement of DGs. Then, the maximum Lyapunov exponent for each candidate is calculated to decide which bus is the best place to improve the voltage stability of system. Several time-domain simulation studies are carried out to verify the effectiveness of proposed algorithm. In particular, its performance is compared with that of the conventional method. The results show that the optimal placement of multiple DGs determined by the proposed algorithm improves the voltage stability of system much more effectively.INDEX TERMS Distributed generation, model-free Lyapunov exponent estimation, optimal placement, voltage stability. II. PROPOSED OPTIMAL DG PLACEMENT ALGORITHM A. CONVENTIONAL MODAL ANALYSISDONGHEE CHOI (Senior Member, IEEE) received the B.S. and Ph.D. degrees in electrical engineering from the

The high penetration of wind power decreases the system inertia and primary frequency reserve while replacing the conventional synchronous generators (SGs). Therefore, if the system operator does not take appropriate action on the remaining generation units (GUs) operation, high penetration of wind power will aggravate the frequency stability. To solve this problem, wind power plants (WPPs) may provide the inertial response and primary frequency response (PFR) to support the frequency stability. However, due to the variability of renewable energy, WPPs may not provide adequate frequency response whenever it is required. This paper proposes an algorithm to determine the operation of GUs to provide appropriate PFR for a power system with high penetration of wind power. Through the proposed algorithm, it calculates the required PFR to restore the decreased frequency stability caused by the high penetration of wind power. Then, while considering the available PFR from WPPs, it redetermines the droop coefficient of SGs governor to provide the sufficient PFR to recover the frequency stability. Finally, the effectiveness of the proposed algorithm is verified on the practical Korean electric power system.

The energy storage system (ESS) is developing into a very important element for the stable operation of power systems. An ESS is characterized by rapid control, free charging, and discharging. Because of these characteristics, it can efficiently respond to sudden events that affect the power system and can help to resolve congested lines caused by the excessive output of distributed generators (DGs) using renewable energy sources (RESs). In order to efficiently and economically install new ESSs in the power system, the following two factors must be considered: the optimal installation placements and the optimal sizes of ESSs. Many studies have explored the optimal installation placement and the sizing of ESSs by using analytical approaches, mathematical optimization techniques, and artificial intelligence. This paper presents an algorithm to determine the optimal installation placement and sizing of ESSs for a virtual multi-slack (VMS) operation based on a power sensitivity analysis in a stand-alone microgrid. Through the proposed algorithm, the optimal installation placement can be determined by a simple calculation based on a power sensitivity matrix, and the optimal sizing of the ESS for the determined placement can be obtained at the same time. The algorithm is verified through several case studies in a stand-alone microgrid based on practical power system data. The results of the proposed algorithm show that installing ESSs in the optimal placement could improve the voltage stability of the microgrid. The sizing of the newly installed ESS was also properly determined.

Energy storage system (ESS) is developing into a very important element to ensure stable operation of the power system. ESS has features of quick control and free charging and discharging. By using these characteristics, it can efficiently respond to sudden events of the power system and is helpful in resolving congested lines caused by excessive output of the distributed generators (DGs) using renewable energy sources (RESs). In order to install new ESSs efficiently and economically in the power system, the following two things must be considered: optimal installation placements and optimal sizes of ESSs. There are many studies on the optimal installation placement and sizing of ESS through analytical approaches, mathematical optimization techniques, and artificial intelligence. This paper presents an algorithm to determine the optimal installation placement and sizing of ESS for virtual multi-slack (VMS) operation based on power sensitivity analysis in the stand-alone microgrid. Through the proposed algorithm, the optimal installation placement could be determined by simple calculation, and the optimal sizing of ESS www.videleaf.com for the determined placement could be obtained at the same time. The algorithm is verified through several case studies in the stand-alone microgrid where the practical power system data is reflected.