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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]

Load aggregators can use demand response programs to motivate residential users toward reducing electricity demand during peak time periods. This article proposes a demand response algorithm for residential users, while accounting for uncertainties in the load demand and electricity price, users’ privacy concerns, and power flow constraints imposed by the distribution network. To address the uncertainty issues, we develop a deep reinforcement learning (DRL) algorithm using an actor-critic method. We apply federated learning to enable users to determine the neural network parameters in a decentralized fashion without sharing private information (e.g., load demand, users’ potential discomfort due to load scheduling). To tackle the nonconvex power flow constraints, we apply convex relaxation and transform the problem of updating the neural network parameters into a sequence of semidefinite programs (SDPs). Simulations on an IEEE 33-bus test feeder with 32 households show that the proposed demand response algorithm can reduce the peak load by 33% and the expected cost of each user by 13%. Also, we demonstrate the scalability of the proposed algorithm in 330-bus and 1650-bus feeders with real-time pricing scheme. [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]

Power tracing is the task of disaggregating the power injection of a generator (or a load) into a sum of constituent components that can unambiguously be attributed to loads (generators) and losses. Applications of power tracing range the broad spectrum of: transmission services pricing, loss allocation in distribution networks, fixed-cost allocation, modelling bilateral transactions, and financial storage rights. This paper develops an analytical approach to power tracing leveraging elementary circuit laws. The method is rigorous from a system-theoretic vantage point, and it yields unambiguous results that are consistent with constitutive principles that describe the steady-state behaviour of power networks. Moreover, it can be implemented with limited computational burden, applies to networks with arbitrary topologies, and preserves the coupling between active- and reactive-power injections. Numerical experiments indicate that given a solved power-flow solution, disaggregations can be computed for a test system with 2383 buses, 327 generators, and 2056 loads in 4.34 s on a personal computer, hence establishing computational scalability. Furthermore, applications are demonstrated in distribution and transmission networks with case studies focused on quantifying the impact of distributed generation on loss allocation and extracting nodal contributions to bilateral transactions, respectively. [ABSTRACT FROM AUTHOR]

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]

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real-time. The method does not rely on the system power flow model. Instead, it uses only high-frequency synchronized data collected from phasor measurement units to estimate the injection shift factors through linear least-squares estimation, after which other DFs can be easily computed. Such a measurement-based approach is desirable since it is adaptive to changes in system operating point and topology. We further improve the adaptability of the proposed approach to such changes by using weighted and recursive least-squares estimation. Through numerical examples, we illustrate the advantages of our proposed DF estimation approach over the conventional model-based one in the context of contingency analysis and generation re-dispatch. [ABSTRACT FROM PUBLISHER]