• Energy Research
• Closed Access close

The frequency–amplitude (F-A) curve has been proposed to characterize the electromechanical oscillation frequency of a single-machine-infinite-bus (SMIB) system considering nonlinearity of the swing equation. For a multi-machine system, the F-A curve regarding one oscillation mode is a projection of the system trajectory between the stable equilibrium point and the stability boundary onto the F-A plane. This letter provides rigorous proofs of six general properties of the F-A curve.

This paper proposes a measurement-based voltage stability monitoring method for a load area fed by N tie lines. Compared to a traditional Thevenin equivalent based method, the new method adopts an N $+1$ buses equivalent system so as to model and monitor individual tie lines. For each tie line, the method solves the power transfer limit against voltage instability analytically as a function of all parameters of that equivalent, which are online identified from real-time synchronized measurements on boundary buses of the load area. Thus, this new method can directly calculate the real-time power transfer limit on each tie line. The method is first compared with a Thevenin equivalent based method using a 4-bus test system and then demonstrated by case studies on the Northeast Power Coordinating Council (NPCC) 48-machine, 140-bus power system.

This paper develops an analytical method for assessing the safety margins of a generation rejection scheme (GRS) reliably. It also presents a practical framework for implementing the proposed method integrated with energy management system and synchrophasor data in power grid operations. By employing a concept of virtual load connected to the critical generation bus of the single machine equivalent of the real-time operations case, we calculate, similar to transfer analysis, the allowable power to the virtual load in MW after tripping the pre-planned number of generation units and thus determine the required rejected power for the GRS initiating scenario. This virtual loading can be interpreted as the safety margin of the designed GRS to ensure its stabilizing operation. This research further develops a computationally efficient technique for refining the safety margin potentially with the measured synchrophasor data to improve the robustness of the GRS in practice. Understanding the safety margin is envisioned to help investigate and identify other practical options than tripping generators for protecting the system integrity. Accuracy and efficacy are demonstrated for real Korea power system cases.

This paper proposes a direct damping feedback control method. By real-time changing the power output of power electronics-interfaced resources, this method aims to control the damping ratio of a targeted oscillation mode to a desired value. It adopts a proportional-integral controller tuned for a nonlinear single-input-single-output model. The model approximates the re-al-time dynamic process of damping estimation and control for the targeted mode represented by a single-oscillator power system equivalent. The paper also proposes utilizing the zero-th order parametric resonance phenomenon to simplify the design of this new control method. The parameters of the controller are optimized considering both robustness and time performance of damping control. Tests on a single-machine-infinite-bus system and a 140-bus 48-machine Northeast Power Coordinating Council system validate the effectiveness of the proposed damping controller utilizing battery-based energy storage systems.

When generators of a power system are subject to a large disturbance, their electromechanical oscillations (EOs) are essentially nonlinear as observed from their rotor angle waveforms due to the nonlinear power network. However, traditional modal analysis has not given enough considerations to nonlinearities in EOs. This paper analytically formulates the accurate oscillation frequency (OF) of an EO mode addressing nonlinearities. It is revealed that when the system model and condition are fixed, the OF of any EO mode is energy-dependent as a function of the oscillation amplitude (OA). That is characterized by a new tool named Frequency-Amplitude (F-A) curve regarding each mode, from which the frequency decreases from the natural frequency toward zero when the amplitude grows to a critical threshold. The paper proves that an F-A curve is actually a projection of the system trajectory between the stable equilibrium and the stability boundary onto the OF-OA plane regarding one mode. Based on the concept of F-A curve, a stability index is defined and estimated from measurements for online angle stability analysis. The proposed methodology is presented in detail using an SMIB system and then demonstrated on the IEEE 9-bus system and WECC 179-bus system having multiple EO modes.

This paper develops a computationally efficient method to bound the impact of multiple uncertain parameters in a dynamic load model. Load model trajectory sensitivity is first conducted on regional dynamics only (e.g., a large industrial load bus and its model for adequately representing the bus voltage dynamics) to identify critical and correlated load parameters. Systemwide trajectory sensitivity on the entire power system model is then evaluated for this reduced set of parameters, and finally, the impact of multiple uncertain parameters on the representation of power system dynamics is bounded. To reinforce this reasoning, we elaborate on the conceptual meaning of the load model trajectory sensitivity, its implication, and its applicability to the entire power grid analysis. This research also develops a fluctuation index of trajectory sensitivity (FI-TS) to effectively rank and select the model parameters based on the impact of their perturbations on the system's dynamic performance. Case studies for the Korean power system demonstrate the validity and efficacy of the developed methods for adequately bounding the uncertainty impacts with reference to the comprehensive time-domain dynamic simulation approach.

An efficient splitting strategy is important for the islanding operation of power systems. In this paper, a mixed-integer linear programming (MILP)-based splitting method is proposed. First, the graph theory is employed to transform the splitting problem into a graph partition problem. Then, the graph partition problem is modeled as an MILP optimization problem with consideration to the network connectivity of all subgraphs. The MILP-based splitting strategy can be efficiently computed with existing commercial solvers, and the multiple optimal solutions can be captured with the recursive process. Compared with the splitting methods in the literature, the proposed method is more flexible and efficient, such that the users can select the optimal solution from multiple solutions with different interests and heuristic splitting rules (e.g., with the minimum amount of switched lines). Finally, the effectiveness of the proposed method has been verified with IEEE 30-, 118-, and 300-bus test systems.

This paper studies real-time estimation of stability margin of a power system under disturbances by continuous measurement data. The paper presents a Ball-On-Concave-Surface (BOCS) mechanics system as a power system's adaptive equivalent representing its real-time status and the stability region about a monitored variable. The parameters of the equivalent are adaptive to the operating condition and can online be identified from the phase-plane trajectories of the monitored variable. Accordingly, the stability margin and risk of instability can be estimated. Case studies on a two-generator system and a 179-bus system show that the BOCS system can be applied either locally or for wide-area stability monitoring in real-time calculation of stability margin. This paper proposes a new idea for using real-time measurements to develop and identify a power system's adaptive equivalent as a basis for online prediction of instability.

Real-time damping estimation for a dominant inter-area mode is important for situational awareness of potential angular instability in power systems. Electromechanical oscillations energized by large disturbances often manifest obvious nonlinearities in measurements on first several swings. Traditional methods based on linear system theory often discard first several swings intentionally to avoid nonlinearity; if not, the estimated damping ratios often vary with the length and starting point of the measuring window. By identifying a nonlinear oscillator to fit a dominant mode, this paper proposes a new measurement-based approach utilizing complete post-disturbance data for robust damping estimation independent of the measuring window. Case studies on the IEEE 9-bus system and a 48-machine Northeast Power Coordinating Council system validate the proposed approach for providing accurate and robust damping estimation compared with existing methods including the Prony's method. Meanwhile, three factors influencing damping estimation in practical applications are also addressed, including measurement noises, limited coverage of PMU measurements, and existence of multiple dominant modes.