Implementing state estimation in low and mediumvoltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty in forecasts can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post-hoc analysis. The method outperforms conventional WLS and is applied to different test feeders and validated on a real test feeder with the utility Alliander in The Netherlands.

Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal dynamics in breast cancer research, we propose a method to efficiently solve an identification problem for a specific class of discrete-time LTV systems, in which the states are fully observed and there is no access to system inputs. In addition, it is assumed that we do not know on which states the inputs act, which can change between time steps, and that the total number of inputs is sparse over all states and over time. The problem is formulated as a compressive sensing problem, which incorporates the effect of measurement noise and which has a solution with a partially sparse support. We derive sufficient conditions for the unique recovery of the system model and input values, which lead to practical conditions on the number of experiments and rank conditions on system outputs. Synthetic experiments analyze the method’s sensitivity to noise for randomly generated models.

State Estimation is an essential technique to provide observability in power systems. Traditionally developed for high-voltage transmission networks, state estimation requires equipping networks with many real-time sensors, which remains a challenge at the scale of distribution networks. This paper proposes a method to complement a limited set of real-time measurements with voltage predictions from forecast models. The method differs from the classical weighted least-squares approach, and instead relies on Bayesian estimation formulated as a linear least squares estimation problem. We integrate recently developed linear models for unbalanced 3-phase power flow to construct voltage predictions as a linear mapping of load predictions. The estimation step is a linear computation allowing high resolution state estimate updates, for instance by exploiting a small set of phasor measurement units. Uncertainties can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post hoc analysis. The method is applied to an IEEE benchmark and on a real network testbed at the Dutch utility Alliander.

Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal dynamics in breast cancer research, we propose a method to efficiently solve an identification problem for a specific class of discrete-time LTV systems, in which the states are fully observed and there is no access to system inputs. In addition, it is assumed that we do not know on which states the inputs act, which can change between time steps, and that the total number of inputs is sparse over all states and over time. The problem is formulated as a compressive sensing problem, which incorporates the effect of measurement noise and which has a solution with a partially sparse support. We derive sufficient conditions for the unique recovery of the system model and input values, which lead to practical conditions on the number of experiments and rank conditions on system outputs. Synthetic experiments analyze the method’s sensitivity to noise for randomly generated models.

High penetration levels of distributed generation (DG) and electric vehicles (EVs) diversify power flow and bring uncertainty to distribution networks, making planning and control more involved for distribution system operators (DSOs). The increased risk of constraint violation triggers the need to augment forecasts with real- time state estimation. This is economically and technically challenging since it requires investing in a large number of sensors and these have to communicate with often older and slower supervisory control and data acquisition (SCADA) systems. We address distribution grid state estimation via combining only a limited set of sensors with load forecast information. It revisits open problems in a recent paper that proposes a Bayesian estimation scheme. We derive the estimator for balanced power networks via rigorous modeling. An off-line analysis of load aggregation, forecast accuracy and number of sensors provides concrete engineering trade-offs to determine the optimal number of sensors for a desired accuracy. This estimation procedure can be used in real time as an observer for control problems or off-line for planning purposes to asses the effect of DG or EVs on specific network components.