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This paper proposes an approach to obtain dynamic versions of static distribution factors, such as power-transfer, line-outage, and outage-transfer distribution factors. With the proposed dynamic distribution factors (DDFs), one can predict line flows over the post-contingency transient period with the same computational effort as obtaining static distribution factors. Our development centers on deriving closed-form expressions that approximate generator outputs through the post-contingency transient period with a reduced-order aggregate dynamical model to recover dynamic generator participation factors. The full suite of DDFs can then be derived by combining these dynamic generator participation factors with injection shift factors, i.e., static linear sensitivities of line active-power flows with respect to nodal active-power injections, computed at the pre-disturbance steady-state operating point. We illustrate the accuracy and computational benefits of the proposed DDFs via numerical case studies involving the New England test system. [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]

This paper examines multi-interval real-time markets in the context of U.S. independent system operators (ISOs). We show that current ISO implementations that settle only the upcoming interval of the multi-interval solution can create incentive problems. Fundamentally, this is the result of each successive optimization problem treating historical losses as sunk costs. To solve the incentive issues, we present an existing proposal and a new multi-interval pricing method. Both methods incorporate historical losses and produce prices that appropriately incentivize generators to follow multi-interval dispatch instructions when implemented with a fixed finite horizon and perfect foresight. In practice, the fixed horizon requirement necessary for this result is not satisfied because new information about the future is constantly being revealed to the ISO as time proceeds. Realistic rolling horizon implementations for an ISO New England-based system suggest that the new method results in lower out-of-market payments than both current ISO implementations and the existing proposal. [ABSTRACT FROM AUTHOR]

Appropriately designed renewable support policies can play a leading role in promoting renewable expansions and contribute to low emission goals. Meanwhile, ill-designed policies may distort electricity markets, put power utilities and generation companies on an unlevel playing field and, in turn, cause inefficiencies. This paper proposes a framework to optimize policymaking for renewable energy sources, while incorporating conflicting interests and objectives of different stakeholders. We formulate a tri-level optimization problem where each level represents a different entity: a state regulator, a power utility and a wholesale electricity market. To solve this tri-level problem, we exploit optimality conditions and develop a modification of the Column-and-Cut Generation (C&CG) algorithm that generates cuts for bilinear terms. The case study based on the ISO New England 8-zone test system reveals different policy trade-offs that policymakers face under different decarbonization goals and implementation scenarios. [ABSTRACT FROM AUTHOR]

Distance relays are quite vulnerable to maloperation during dynamic stressed situations. The apparent impedance seen by the relay encroaches the zone-3 resulting in distance relay maloperation that can initiate cascading failures. This paper presents an enhanced scheme for wide area backup protection which implements improved protection algorithms to decide final relaying status. A machine learning tool namely Deep Neural Network is utilized to build those protective relaying decision logics: RDL-1 and RDL-2. Wide area information retrieved from phasor measurement units (PMU) is used to take real time decisions. RDL-1 is designed to detect if the system is operating in normal or stressed condition. During normal state, traditional zone-3 relay undertakes the relaying decision. However, under stressed situations, RDL-1 switches the decision-taking to RDL-2. RDL-1 also predicts whether the system is progressing towards an out-of-step situation so that appropriate remedial action can be undertaken. Proposed scheme was studied on IEEE-39 bus New England system using MATLAB/SIMULINK and validated on Real Time Digital Simulator platform and third zone mal-tripping are avoided. Performance of the proposed algorithm was compared with the conventional blinder and other data-mining techniques which show considerably high classification accuracy. [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]

US transmission systems and wholesale electricity markets, albeit federally regulated, often span across multiple state jurisdictions. In this environment, state regulators can strategically exploit this techno-economic coupling to advance their clean energy policy goals at the expense of neighboring jurisdictions. This paper investigates strategic regulatory competition to understand its effect on achieving Renewable Portfolio Standards (RPS). We formulate a chance-constrained equilibrium problem with equilibrium constraints (CC-EPEC), which considers multiple state regulators, acting in coordination with in-state power companies, to implement RPS goals in the least-cost manner. To solve this CC-EPEC, we customize a Progressive Hedging (PH) algorithm. The case study uses the CC-EPEC and PH algorithm to analyze the effects of state regulatory competition in the ISO New England system. [ABSTRACT FROM AUTHOR]

This paper presents a power swing detection algorithm in multi-machine power systems, which uses wide-area synchrophasor measurements and is based on Zubov’s stability boundaries. Zubov’s boundary method, an approximation of the famous Lyapunov function, is very common for numerical analyses of power system stability. This work extends the concept of Zubov’s approximation boundaries to online protection applications. First, the proposed protection algorithm constructs a series of Zubov’s stability boundaries on power angle–frequency ($\delta$ – $\omega$) plane for generators based on real-time measurements from phasor measurement units/merging units. Then, it tracks the trajectory of each generator in the $\delta$ – $\omega$ plane after the disturbance to differentiate out-of-step (OOS) conditions from stable swings. The proposed approach is suitable for online applications, which is a significant improvement over the existing methods for swing detection since it does not require offline studies and network reduction. Effectiveness of the proposed method is shown using a single-machine infinite bus and New-England 10-machine 39-bus systems. The proposed method is also implemented in a hardware-in-the-loop setup with a customized IEC 61850-based OOS relay, and performance is compared with a commercially available relay. [ABSTRACT FROM AUTHOR]

Poorly damped inter-area modes of oscillations represent a major concern to power system operation since they detain the power transfer capability of transmission networks. This situation becomes more stringent as the tie-lines are heavily stressed and/or large amounts of renewable energy resources are installed. To overcome this issue, a detailed mathematical model is proposed in this paper to reduce the linearized model of a large power system using the cross-Gramian technique. The presented approach divides the system into a study area which contains one generation unit with installed power system stabilizer (PSS) and an external one which comprises the rest of generation units in the system. Model order reduction is only applied to the external area with the objective of maintaining the characteristics of the original model. Meanwhile, the dynamics of the study area are preserved to provide the required damping through the designed PSS. In addition, an online tuning methodology is also presented to provide robust damping performance in response to changes in the system operating conditions. The deployed cross-Gramian model order reduction alleviates the computational burden and time associated with the online PSS tuning when original power system models are used. The effectiveness of the proposed approach is tested using the New-England 39-bus system in addition to another practical system which resembles the Northern Regional Power Grid India test system. [ABSTRACT FROM AUTHOR]

Power system transient stability control is gaining huge attention in present time. Inspired by the consistency theory of multi-agent system, a distributed finite-time frequency control framework is presented to improve the frequency dynamic of the transient process by adjusting the steam valving. The stability of the proposed distributed frequency control scheme is ensured by including the Lyapunov-based constraints. The communication delay is fully considered in the deigned distributed frequency control framework which has no limitations on communication delay by fully utilizing the local information. Meanwhile, the proposed cyber-physical topology divides the power system into several clusters according to the physical coupling between generators. The designed distributed control scheme based on the proposed cyber-physical topology owns the capability to defend denial-of-service (DoS) attacks which may influence the performance of distributed control scheme, which is also presented in theoretical proof. The designed voltage control based on the direct feedback linearization method can be applied to coordinate all existing frequency controls, in the premise of the system stability. The performance of the proposed control scheme is evaluated under the cases of different communication delays and DoS attacks through the simulation on New England 39-bus 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]

Efficiently accommodating uncertain renewable resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize the uncertainty and their scenario-based stochastic extensions are limited in their ability to simultaneously maximize social welfare and guarantee non-confiscatory market outcomes in expectation and per each scenario. This article proposes a chance-constrained stochastic market design, which is capable of producing a robust competitive equilibrium and internalizing uncertainty of the renewable resources in the price formation process. The equilibrium and resulting prices are obtained for different uncertainty assumptions, which requires using either linear (restrictive assumptions) or second-order conic (more general assumptions) duality in the price formation process. The usefulness of the proposed stochastic market design is demonstrated via the case study carried out on the 8-zone ISO New England testbed. [ABSTRACT FROM AUTHOR]

An identification algorithm is proposed for generator outages in external systems given tie-line flow measurements and pre-outage linear sensitivity factors. The problem is challenging due to limited information available to operators in interconnected systems. To overcome the underdetermined nature of the problem (the number of tie-line measurements is smaller than the number of generators), a clustering method based on pivoted QR decomposition is implemented so that the outage location can be identified to the area of origination. Two test systems, the 68-bus New England system and the 500-bus synthetic system, were used for validation. The results demonstrate that with limited knowledge of the external system, the algorithm is able to identify the correct generator cluster in all cases. Another advantage of the proposed algorithm is its high efficiency, which enables detection within sub-milliseconds. In addition, an estimation of the cluster injection change is also provided by the algorithm. [ABSTRACT FROM AUTHOR]

This study develops an open-source 8-zone test system for teaching, training, and research purposes that is based on ISO New England structural attributes and data. The test system models an ISO-managed wholesale power market populated by a mix of generating companies and load-serving entities that operates through time over an 8-zone AC transmission grid. The modular extensible architecture of the test system permits a wide range of sensitivity studies to be conducted. To illustrate the capabilities of the test system, we report energy cost-savings outcomes for a comparative study of stochastic versus deterministic DAM security constrained unit commitment (SCUC) formulations under systematically varied reserve requirement levels for the deterministic formulation. [ABSTRACT FROM AUTHOR]