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This paper proposes a new coordinated method for preventive generation rescheduling and corrective load shedding to maintain power system transient stability under uncertain wind power variation. A two-step bi-level optimization model is proposed where generation rescheduling and load shedding are coordinated by a risk coordination parameter, which adjusts the total coordination cost in the upper level. Then, based on Extended Equal Area Criterion (EEAC) and trajectory sensitivities, the non-linear risk and stability constraints are converted into the linear form for generation rescheduling cost and load shedding cost optimization in the lower level, respectively. Uncertain wind power output is modeled as a small number of robust test scenarios. Finally, the golden section search is applied to solve the bi-level problem. The proposed method is validated on the New-England 39-bus system by using commercial grade software. The computational efficiency, economic optimality, and stability robustness under random wind power of the method are demonstrated. [ABSTRACT FROM AUTHOR]

The automatic generation control (AGC) system is temporally situated between economic dispatch and synchronous generator dynamics, and its primary role is to regulate frequency within and tie-line flows between control areas. Given appropriate choice of participation factors (feed-forward controller gains that govern the disaggregation of the area-level power requirement to individual generators), the AGC can be engineered to nudge system dynamics toward a steady-state operating point corresponding to economic optimality. This paper establishes necessary and sufficient conditions under which a widely accepted choice of participation factors guarantees the alignment of steady-state synchronous generator outputs with a global minimum of a prototypical economic dispatch problem. In so doing, it resolves several ambiguities and formalizes technical assumptions governing the role of the standard AGC architecture in the context of economic dispatch and steady-state operation. Numerical case studies tailored to a modified version of the New England 39-bus 10-machine test system validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven cooperative method for load frequency control (LFC) of the multi-area power system based on multi-agent deep reinforcement learning (MA-DRL) in continuous action domain. The proposed method can nonlinearly and adaptively derive the optimal coordinated control strategies for multiple LFC controllers through centralized learning and decentralized implementation. The centralized learning is achieved by MA-DRL based on a global action-value function to quantify overall LFC performance of the power system. To solve the MA-DRL problem, multi-agent deep deterministic policy gradient (DDPG) is derived to adjust control agents’ parameters considering the nonlinear generator behaviors. For implementation, each individual controller only needs local information in its control area to deliver optimal control signals. Numerical simulations on a three-area power system and the fully-modeled New-England 39-bus system demonstrate that the proposed method can effectively minimize control errors against stochastic frequency variations caused by load and renewable power fluctuations. [ABSTRACT FROM AUTHOR]

Power flow formulated with a distributed slack bus involves modeling the active-power output of each generator with three elements: a nominal injection modulated by a fraction of the net-load imbalance allocated via a participation factor. This setup acknowledges generator dynamics and system operations, but it has long been plagued by ambiguous and inconsistent interpretations of its constituent elemental quantities. In this paper, we establish that, with the: i) nominal active-power injections set to be the economic dispatch setpoints, ii) participation factors fixed to be the ones used in automatic generation control, and iii) net-load imbalance considered to be the total load and loss unaccounted in economic dispatch, the power flow solution best matches results from a simulation unto steady state of the system differential algebraic equation (DAE) model. Numerical case studies tailored to the New England test system validate the analysis by demonstrating that solutions obtained from a distributed slack formulation offer lower errors (with respect to DAE-model simulations) compared to the exhaustive set of all single slack bus choices. [ABSTRACT FROM AUTHOR]

With increase of practical power system complexity, power system online stability assessment and control is more and more important. Application of the traditional model-driven methods is always limited by contradiction between accuracy and efficiency, while data-driven methods demonstrate strong abilities for the online decision-making support with advancement of various data mining techniques. Instead of direct application of data-driven methods in the power system, this paper first discusses feasible integration approaches for the model-driven and data-driven methods based on the existing achievements, and then, proposes to integrate both methods for the power system online frequency stability assessment and control. The integrated method consists of frequency dynamics prediction and load shedding procedure. In frequency dynamics prediction procedure, integration of system frequency response (SFR) model and the extreme learning machine (ELM)-based learning model is applied, where basic physical causality is kept in the SFR model and ELM is used to fit and correct error of the SFR. The ELM also plays a part in load shedding prediction model construction by digging out mapping relationship from samples. Finally, the proposed prediction and control scheme for the frequency stability is verified by simulations on WSCC 9-bus, New England 39-bus, and NPCC 140-bus system. Results show that the reliability, time efficiency, and accuracy are enhanced with the proposed method. [ABSTRACT FROM AUTHOR]

To analyze the grid integration effect of a virtual synchronous generator (VSG), this paper proposes a simple power system modeling method. It is shown that for a specific disturbance, by simplifying the original network to a radical n generators single-load model, its state-space small-signal model can be obtained using a unified formula, as long as the single generator infinite bus model of each generator is given. Case studies based on the IEEE 9-bus test system as well as the New York New England test system show high efficiency of the proposed modeling to represent slow power and frequency deviations. Modal analyses give insight into how system poles are synthesized by individual generator poles, and how different designs of VSGs affect the system oscillation modes. Potential errors due to the topology simplification and the measures to avoid them are discussed. The time-domain results and modal analyses highlight some important features of VSG, which are overlooked in previous studies. [ABSTRACT FROM AUTHOR]

Frequency dynamics during primary frequency control is closely related to pre-disturbance operating conditions, the disturbance, and equipment characteristics. How to rigorously express such a relation in a frequency stability constrained optimal dispatch problem is still an open question. This paper presents an optimal power flow (OPF) model for generation re-dispatch that considers dynamic frequency response constraints to ensure frequency stability during primary frequency regulation. The distinct feature of the model is that the dynamic frequency response is formulated as a set of differential algebraic equations (DAEs), which allows considering the transient behavior of frequency and mechanical/electromagnetic power for each generator during primary frequency control period. Based on the solution of the optimization problem, a definition of the primary reserve for each unit is proposed according to the maximum of incremental mechanical power. This definition helps meet the adequacy requirement of primary frequency response and achieve partial frequency restoration. Simulation results on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system and the modified IEEE 54-machine 118-bus system validate the effectiveness of the proposed model and reveal the strong coupling between frequency dynamics and the pre-disturbance generation. [ABSTRACT FROM AUTHOR]

System inertia plays a vital role in controlling the angular stability of the system during a disturbance. Due to increased penetration of power electronic interfaced sources, such as Solar Photovoltaic (SPV) source, the overall system inertia reduces and varies depending on their operating conditions. In this paper, an approach for online inertia estimation in the power system network with SPV sources is proposed, using the synchronized measurements from Phasor Measurement Units (PMUs). An equivalent swing equation is used to emulate the network dynamics. A relationship between the inertia constant and the roots of this equation is determined. In order to numerically obtain the roots, the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) method is first used to find the modes present in the frequency signal. A new formulation is proposed to extract an equivalent mode from all the obtained modes. Also, to avoid phase step error, Rate Of Change Of Frequency (ROCOF) is estimated from the equivalent mode of the frequency signal. Results obtained for the 39 bus New England system for various test cases, using Real-Time Digital Simulator (RTDS), prove the efficacy and superiority of the proposed approach over the existing approaches in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to damp interarea oscillations by designing a robust multi-input multioutput supplementary controller for multiterminal dc (MTDC) systems embedded in ac grids. The key idea to achieve robustness lies in explicitly modeling the MTDC current injection as disturbances using an \mathcal H\infty mixed-sensitivity formulation in the linear matrix inequality framework. Control directions are established by selecting wide-area feedback signals and the relative gain array computation. Robustness is assessed through dynamic simulations for scenarios including: first, disturbances on the ac side, second, disturbances on the dc-side such as loss of a converter pole including actuator, third, partial loss of feedback signal, and fourth, communication latencies. The performance of the proposed controller is compared against the conventional \mathcal H\infty based design, using a four-terminal dc grid embedded within the New England–New York test system. The results suggest that the proposed approach demonstrates superior performance following dc-side disturbances, actuator outages, and latency. [ABSTRACT FROM PUBLISHER]

We propose an analytically tractable Bayesian method to infer parameters in power system dynamic models from noisy measurements of bus-voltage magnitudes and frequencies as well as active- and reactive-power injections. The proposed method is computationally appealing as it bypasses the large number of system model simulations typically required in sampling-based Bayesian inference. Instead, it relies on analytical linearization of the nonlinear system differential-algebraic-equation model enabled by trajectory sensitivities. Central to the proposed method is the construction of a linearized model with the maximum probability of being (closest to) the actual nonlinear model that gave rise to the measurement data. The linear model together with Gaussian prior leads to a conjugate family where the parameter posterior, model evidence, and their gradients can be computed in closed form, markedly improving scalability for large-scale power systems. We illustrate the effectiveness and key features of the proposed method with numerical case studies for a three-bus system. Algorithmic scalability is then demonstrated via case studies involving the New England 39-bus test system. [ABSTRACT FROM AUTHOR]

The frequency nadir is a significant indicator for the primary frequency response monitoring and control. It is imperative to predict the maximum frequency deviation and the time at which the maximum occurs with high efficiency and accuracy following a major disturbance. To develop an analytical model for the frequency nadir prediction, the closed-loop is broken and a parabolic frequency deviation is input for decoupling the calculation of governor response and frequency deviation. Following which, the polynomial fitting is adopted to depict the primary frequency response characteristic of each governor. The iterative numerical solution for the frequency nadir prediction model is carried out based on the insight into the features of governor response. Case studies are presented to verify the performance of the analytical model over WSCC 9-bus system, New England 39-bus system and practical provincial power system, where the frequency nadir prediction model demonstrates its advantages of easy implementation, minimum computation, and high accuracy. [ABSTRACT FROM AUTHOR]