Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, ...because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. Facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.
This paper provides an extension of the observability rank condition to nonlinear systems driven by both known and unknown inputs. In particular, the systems here considered are characterized by ...dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input (or disturbance) and multiple known inputs. Additionally, it is assumed that the unknown input is a differentiable function of time (up to a given order). The goal of the paper is not to design new observers for these systems but to provide the analytic condition in order to check the weak local observability of the state. This condition is simple and can be easily and automatically applied to the nonlinear systems mentioned above, independently of their complexity and type of nonlinearity. In particular, the complexity of the analytic condition is comparable to the complexity of the standard method to check the state observability in the case without unknown inputs (i.e., the observability rank condition). This is a fundamental practical (and unexpected) advantage. As for the observability rank condition, the proposed analytic condition is based on the computation of the observable codistribution. Similarly to the case of only known inputs, the observable codistribution is obtained by recursively computing the Lie derivatives of the outputs along the vector fields that characterize the dynamics. However, in correspondence of the unknown input, the corresponding vector field must be suitably rescaled. Additionally, the Lie derivatives of the outputs must also be computed along a new set of vector fields that are obtained by recursively performing suitable Lie bracketing of the vector fields that define the dynamics. In practice, the entire observable codistribution is obtained by a very simple recursive algorithm. Finally, it is shown that the recursive algorithm converges in a finite number of steps, and the criterion to establish that the convergence has been reached is provided. The proposed analytic extension of the observability rank condition is illustrated by checking the weak local observability of several nonlinear systems driven by known inputs and a single disturbance.
A prerequisite to dynamic state estimation of a stochastic nonlinear dynamic model of a power system is its observability analysis. However, due to the model nonlinearity, the traditional methods ...either suffer from a poor estimation accuracy if a linear approximation is performed or yield an extremely complicated procedure if the Lie-derivative method is applied to a large-scale power system. To address these weaknesses, we propose a new data-driven Koopman-based observability method by revealing the link that exists between the Koopman operator and the Lie-derivative in the Koopman canonical coordinates. This enables the proposed data-driven method not only to be fully derivative-free , which alleviates its implementation complexity but also overcomes the model nonlinearity and inaccuracy of the system. Furthermore, as an important byproduct, the proposed observability analysis scheme provides a valuable guide for the selection of the observables of the Koopman operator, which is a major difficulty for the application of this operator. Finally, we demonstrate the excellent performance of the proposed method on several IEEE standard test systems.
In this paper, we first establish a definition of strong structural controllability and observability for a single state node (i.e., SSC and SSO state nodes), based on the conditions of strong ...structural controllability and observability outlined in existing works. Secondly, we provide a necessary and sufficient condition for SSC and SSO state nodes in acyclic graphs. Thirdly, we provide the relationship between the conditions for SSC and SSO state nodes with the fixed controllable and observable nodes used in the existing literature. As a practical application of SSC and SSO state nodes, we introduce Structural Kalman Decomposition (SKD), an innovative technique that utilizes the information from these state nodes for robust system dynamics analysis under parameter uncertainties.
Due to limited instrumentation, distribution grids are currently challenged by observability issues. On the other hand, smart meter data are communicated to utility operators from nodes with ...renewable generation and elastic demand. This paper employs grid data from metered buses toward inferring the underlying grid state. System nodes are partitioned into buses with time-varying injections that are assumed metered, and buses with relatively stationary conventional loads that are non-metered. Exploiting the variability at metered buses and the stationarity of conventional loads, the novel idea here is to solve the non-linear power flow (PF) equations jointly over consecutive time instants. By putting forth a coupled formulation of the PF problem (CPF), grid states can be recovered by metering fewer buses. An intuitive and easily verifiable rule pertaining to the locations of (non-)metered buses on the physical grid is shown to be a necessary and sufficient criterion for local observability in radial networks. To account for noisy smart meter readings, a coupled power system state estimation (CPSSE) problem is further devised. Both CPF and CPSSE tasks are tackled via augmented semi-definite program relaxations. The observability criterion along with the CPF and CPSSE solvers are numerically corroborated using randomly generated and actual solar and load data on the IEEE 34-bus benchmark feeder.
In this paper, the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor ...measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The implementation, validation, and the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.
In order to control a discrete-event system (DES), the supervisory controller observes event sequences. Observability, together with controllability, is required for obtaining the exact specification ...language via supervisory control. By extending observability, relative observability was recently investigated. In this article, relative network observability, which accommodates observation incompleteness and delay in relative observability, is defined. An algorithm is proposed to transform relative network observability to network observability. This leverages existing solutions to problems concerning network observability to solve problems concerning relative network observability. In particular, we propose techniques for checking relative network observability and calculating supremal controllable and relatively network observable sublanguage.
Reinforcement learning (RL) algorithms have been around for decades and employed to solve various sequential decision-making problems. These algorithms, however, have faced great challenges when ...dealing with high-dimensional environments. The recent development of deep learning has enabled RL methods to drive optimal policies for sophisticated and capable agents, which can perform efficiently in these challenging environments. This article addresses an important aspect of deep RL related to situations that require multiple agents to communicate and cooperate to solve complex tasks. A survey of different approaches to problems related to multiagent deep RL (MADRL) is presented, including nonstationarity, partial observability, continuous state and action spaces, multiagent training schemes, and multiagent transfer learning. The merits and demerits of the reviewed methods will be analyzed and discussed with their corresponding applications explored. It is envisaged that this review provides insights about various MADRL methods and can lead to the future development of more robust and highly useful multiagent learning methods for solving real-world problems.
The objective of traditional phasor measurement unit (PMU) placement approaches is to find the minimal number of PMUs to achieve full system observability. Very few consider the probability and the ...consequence severity of observability loss. For example, following cascading failures, lines are tripped, and the topology of the grid changes, which may result in observability loss for parts of the grid. With limited number of PMUs, it is desired that the PMUs should still sustain observability for the power grid after top-severe cascading failures, other than after those cascading failures of low severity. To address the above issues related with the consequence severity of observability loss, this study proposes a risk-oriented PMU placement approach. The proposed approach uses two indices, namely the probability of observability loss and the severity of its corresponding consequence to design the optimal PMU placement strategy. The authors show that the proposed approach is able to capture the critical events, while traditional approaches fail to do so. Extensive simulation results carried out on the IEEE 39-bus and 118-bus systems demonstrate the effectiveness of the proposed risk-oriented approach.
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