The inclusion of higher-order terms in small-signal (modal) analysis augments the information provided by linear analysis and enables better dynamic characteristic studies on the power system. This can be done by applying Normal Form theory to simplify the higher order terms. However, it requires the preliminary expansion of the nonlinear system on the normal mode basis, which is impracticable with standard methods when considering large scale systems. In this paper, we present an efficient numerical method for accelerating those computations, by avoiding the usual Taylor expansion. Our computations are based on prescribing the linear eigenvectors as unknown field in the initial nonlinear system, which leads to solving linear-only equations to obtain the coefficients of the nonlinear modal model. In this way, actual Taylor expansion and associated higher order Hessian matrices are avoided, making the computation of the nonlinear model up to third order and nonlinear modal analysis fast and achievable in a convenient computational time. The proposed method is demonstrated on a single-machine-infinite-bus (SMIB) system and applied to IEEE 3-Machine, IEEE 16- Machine and IEEE 50-Machine systems.

The impact of SPV integration on grid performance is a topic of ongoing debate, with conflicting reports on its effects. This study employs modal analysis, Newton-Raphson power flow, and time-domain simulations to assess the effects of SPV integration on voltage profiles, active power loss, and system stability in the IEEE 4-machine and Nigerian 50-bus power systems. The findings reveal that SPV integration impacts power systems differently, emphasizing the need for a comprehensive approach that considers voltage stability, power losses, and stability constraints. While SPV integration can improve voltage levels and reduce power losses, it may also compromise transient stability, highlighting the importance of careful planning and grid reinforcement. For the IEEE 4-machine system, SPV integration is feasible up to 25% based on power loss, but transient stability constraints limit it to 0%. For the Nigerian grid, optimal SPV integration is achieved at 10% based on power loss and voltage profile, while transient stability constraints limit integration to 5%. This study underscores the necessity of a multi-metric approach to defining SPV penetration limits, considering the trade-offs between voltage performance, power loss, and system stability.

Increasing nonlinearity in today’s grid challenges the conventional small-signal (modal) analysis (SSA) tools. For instance, the interactions among modes, which are not captured by SSA, may play significant roles in a stressed power system. Consequently, alternative nonlinear modal analysis tools, notably Normal Form (NF) and Modal Series (MS) methods are being explored. However, they are computation-intensive due to numerous polynomial coefficients required. This paper proposes a fast NF technique for power system modal interaction investigation, which uses characteristics of system modes to carefully select relevant terms to be considered in the analysis. The Coefficients related to these terms are selectively computed and the resulting approximate model is computationally reduced compared to the one in which all the coefficients are computed. This leads to a very rapid nonlinear modal analysis of the power systems. The reduced model is used to study interactions of modes in a two-area power system where the tested scenarios give same results as the full model, with about 70% reduction in computation time.

Integrating renewable energy sources into existing power grids presents considerable challenges, especially with the intermittency of wind and solar power. This issue is particularly acute in developing countries like Nigeria, where grid infrastructure is often weak, significantly limiting the potential for RE penetration. This study explores strategies to enhance RE integration in Nigeria by employing Flexible Alternating Current Transmission System (FACTS) devices. By leveraging the reactive-power sensitivity index through modal analysis, the optimal location for the FACTS device can be determined. Analysis of the Nigerian power grid demonstrates that the deployment of FACTS devices, specifically Static Synchronous Compensators (STATCOMs), can increase the penetration limit of RE by 40%. This enhancement allows for the integration of an additional 152 MW of wind energy without compromising system stability. The findings underscore the potential of FACTS devices to improve voltage profiles and overall grid stability, thereby facilitating a higher integration of renewable energy sources into weak grids without necessitating substantial changes to the existing power system architecture. This solution can help Nigeria and other countries with similar infrastructure challenges to overcome their renewable energy integration hurdles and transition towards a more sustainable, reliable, and resilient energy mix, paving the way for a cleaner and greener future.

The global electricity demand is growing rapidly and is expected to double by 2050. This growth requires significantly expanding the current high-voltage transmission lines, which is a long-term and costly solution. As an alternative, utilities use advanced technologies like Flexible Alternating Current Transmission System (FACTS) devices as a temporary measure, postponing the expansion. However, it is necessary to locate these devices in the network properly to avoid negative outcomes. Traditional methods for FACTS placement focus on voltage profile improvement and power loss reduction, neglecting rotor angle stability. This can lead to oscillatory instability, especially in weak power grids. To address this issue, the paper proposes a simple approach to optimize the placement of shunt FACTS devices in power systems . The method improves both voltage and rotor angle stability without compromising power loss. The proposed approach considers rotor angle stability constraints, which is essential for system stability during transient events. The study was demonstrated on Nigeria’s 50-bus 330 kV power system, with results indicating a 31% improvement in angle stability with an enhanced voltage profile. The method is straightforward, non-iterative, and provides a cost-effective solution for FACTS device placement in power systems.