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Traditional load shedding schemes can be inadequate in grids with high renewable penetration, leading to unstable events and unnecessary grid islanding. Although for both manual and automatic operating modes load shedding areas have been predefined by grid operators, they have remained fixed, and may be sub-optimal due to dynamic operating conditions. In this work, a distributed tri-level linear programming model for automatic load shedding to avoid system islanding is presented. Preventing islanding is preferred because it reduces the need for additional load shedding besides the disconnection of transmission lines between islands. This is crucial as maintaining the local generation-demand balance is necessary to preserve frequency stability. Furthermore, uneven distribution of generation resources among islands can lead to increased load shedding, causing economic and reliability challenges. This issue is further compounded in modern power systems heavily dependent on non-dispatchable resources like wind and solar. The upper-level model uses complex power flow measurements to determine the system areas to shed load depending on actual operating conditions using a spectral clustering approach. The mid-level model estimates the area system state, while the lower-level model determines the locations and load values to be shed. The solution is practical and promising for real-world applications. 

We have all heard that there is growing need to secure resources to obtain supply-demand balance in a power grid facing increasing volatility from renewable sources of energy. There are mandates for utility scale battery systems in regions all over the world, and there is a growing science of “demand dispatch” to obtain virtual energy storage from flexible electric loads such as water heaters, air conditioning, and pumps for irrigation. The question addressed in this tutorial is how to manage a large number of assets for balancing the grid. The focus is on variants of the economic dispatch problem, which may be regarded as the “feed-forward” component in an overall control architecture. 1) The resource allocation problem is identical to a finite horizon optimal control problem with degenerate cost—so called “cheap control”. This implies a form of state space collapse, whose form is identified: the marginal cost for each load class evolves in a two-dimensional subspace, spanned by a scalar co-state process and its derivative. 2) The implication to distributed control is remarkable. Once the co-state process is synthesized, this common signal may be broadcast to each asset for optimal control. However, the optimal solution is extremely fragile, in a sense made clear through results from numerical studies. 3) Several remedies are proposed to address fragility. One is described through “robust training” in a particular Q-learning architecture (one approach to reinforcement learning). In numerical studies it is found that specialized training leads to more robust control solutions. 

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure. This paper explores algorithm design in the continuous time domain, with a finite-horizon optimal control objective. The main contributions are (i) The new Q-ODE: a model-free characterization of the Hamilton-Jacobi-Bellman equation. (ii) A formulation of Convex Q-learning that avoids approximations appearing in prior work. The Bellman error used in the algorithm is defined by filtered measurements, which is necessary in the presence of measurement noise. (iii) Convex Q-learning with linear function approximation is a convex program. It is shown that the constraint region is bounded, subject to an exploration condition on the training input. (iv) The theory is illustrated in application to resource allocation for distributed energy resources, for which the theory is ideally suited. 

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piece-wise quadratic approach, then the error distribution is in the order of 10^-3 

Much has been written on the rooftop solar photovoltaic (PV) adoption in the U.S., but granular economic assessment at large scale is missing. We provide household level PV economic assessment for a medium size city in North Central Florida, and analyze the economic viability of these installations. Results show that a large number of households will not benefit from solar installations. Further, economic viability is heavily reliant on incentives whose future is uncertain at best. Our analysis did not reveal significant variations in economic viability across different household values --- a proxy we used to differentiate household wealth. Yet, building permits and installation locations indicate economically disadvantaged communities have much lower installation rates as has been the main conclusion in the earlier literature. We argue economic assessment for PV should extend beyond simple benefit--cost analysis. A more nuanced approach should be taken in PV feasibility assessment, and structuring incentive schemes. 

We present an open-source wireless network and data management system for collecting and storing indoor environmental measurements and perceived comfort via participatory sensing in commercial buildings. The system, called a personal comfort and indoor environment measurement (PCIEM) platform, consists of several devices placed in office occupants’ work areas, a wireless network, and a remote database to store the data. Each device, called a PCFN (personal comfort feedback node), contains a touchscreen through which the occupant can provide feedback on their perceived comfort on-demand, and several sensors to collect environmental data. The platform is designed to be part of an indoor climate control system that can enable personalized comfort control in real-time. We describe the design, prototyping, and initial deployment of a small number of PCFNs in a commercial building. We also provide lessons learned from these steps. Application of the data collected from the PCFNs for modeling and real-time control will be reported in future work. We use hardware components that are commercial and off-the-shelf, and our software design is based on open-source tools that are freely and publicly available to enable repeatability.