Search

Electrical networks contain thousands of interconnected nodes and edges, which leads to computational challenges in some power system studies. To address these challenges, we contend that network reductions can serve as a framework to enable scalable computing in power systems. By building upon a prior AC "Opti-KRON" formulation, this paper presents a DC power flow formulation for finding network reductions that are optimal within the context of large transmission analysis. Opti-KRON previously formulated optimal Kron-based network reductions as a mixed integer linear program (MILP), where the number of binary variables scaled with the number of nodes. To improve the scalability of the Opti-KRON approach, we augment the MILP formulation with a community detection (CD) technique that segments a large network into smaller, disjoint, but contiguous sub-graphs (i.e., communities). For each sub-graph, we then (in parallel) apply MILP-based along with a new cutting plane constraint, thus, enhancing scalability. Ultimately, the new DC-based Opti-KRON method can achieve a 80-95\% reduction of networks (in terms of nodes) while statistically outperforming other CD- and Kron-based methods. We present simulation results for the IEEE RTS-96 and the 2383-bus Polish networks.

Generalized energy storage (GES), encompassing both physical and virtual energy storage, can provide remarkable but uncertain adequacy flexibility. When assessing GES's contribution to resource adequacy, the literature typically considers exogenous uncertainties (e.g., failures and stochastic response) but overlooks endogenous uncertainties, such as self-scheduling in liberal markets and decision-dependent uncertainty (DDU). In this regard, this paper proposes a novel capacity credit evaluation framework to accurately quantify GES's contribution to resource adequacy, where a sequential coordinated dispatch method is proposed to capture realistic GES operations by coordinating self-scheduling in the day-ahead energy market and real-time adequacy-oriented dispatch in the capacity market. To incorporate DDU of GES (i.e., responsiveness affected by dispatch decisions and prices in capacity market), we present a chance-constrained optimization approach and tractable solution methodologies for real-time dispatch. We propose a practical adequacy assessment method to quantify the impact of DDU on capacity credit by evaluating the consequence of ignoring DDU. Additionally, a novel capacity credit index called equivalent storage capacity substitution is introduced to quantify the equivalent deterministic storage capacity of the uncertain virtual energy storage. Simulations show that the proposed method yields reliable and accurate capacity credit values by accounting for self-scheduling of GES and managing the risk from DDU. Finally, key impact factors of GES's capacity credit are thoroughly discussed, offering valuable insights for the decision-making of capacity market operators., Comment: This is a manuscript submitted to IEEE Transcations on Power Systems

Thermostatically controlled loads (TCLs) have the potential to be flexible and responsive loads to be used in demand response (DR) schemes. With increasing renewable penetration, DR is playing an increasingly important role in enhancing power grid reliability. The aggregate demand of a population of TCLs can be modulated by changing their temperature setpoint. When and/or what proportion of the population sees the setpoint change determines the change in aggregate demand. However, since the TCL population is finite, not all changes in aggregate demand can be maintained for arbitrarily long periods of time. In this paper, the dynamic behavior of a TCL fleet is modeled and used to characterize the set possible changes in aggregate demand that can be reached and the corresponding time for which the demand change can be held, for a given change in setpoint. This set is referred to, in this paper, as the reach and hold set of a TCL fleet. Furthermore, the effect of the setpoint change and ambient temperature on the reach and hold are analyzed. The characterized set is then validated through simulation using both the population TCL models and individual TCL micro-models.

Scenario reduction (SR) aims to identify a small yet representative scenario set to depict the underlying uncertainty, which is critical to scenario-based stochastic optimization (SBSO) of power systems. Existing SR techniques commonly aim to achieve statistical approximation to the original scenario set. However, SR and SBSO are commonly considered into two distinct and decoupled processes, which cannot guarantee a superior approximation of the original optimality. Instead, this paper incorporates the SBSO problem structure into the SR process and introduces a novel problem-driven scenario reduction framework. Specifically, we transform the original scenario set in distribution space into the decision applicability between scenarios in problem space. Subsequently, the SR process, embedded by a distinctive problem-driven distance metric, is rendered as a mixed-integer linear programming formulation to obtain the representative scenario set while minimizing the optimality gap. Furthermore, ex-ante and ex-post problem-driven evaluation indices are proposed to evaluate the performance of SR. A two-stage stochastic economic dispatch problem with renewable generation and energy storage validates the effectiveness of the proposed framework. Numerical experiments demonstrate that the proposed framework significantly outperforms existing SR methods by identifying salient (e.g., worst-case) scenarios, and achieving an optimality gap of less than 0.1% within acceptable computation time., Comment: This is a manuscript submitted to IEEE Transactions on Power Systems. This manuscript contains 10 pages, 5 figures

High penetration of renewable resources results in a power system with lower inertia and higher frequency sensitivity to power imbalances. Such systems are becoming increasingly susceptible to frequency collapse during extreme disturbances. Under-Frequency Load Shedding (UFLS) is a last-resort protection scheme and acts as an emergency brake by shedding load to arrest frequency decline. Current and emerging efforts to optimize UFLS settings and frequency thresholds are mostly network agnostic, ignoring network spatial information. With the prevalence of Distributed Energy Resources (DERs) in the high-renewable paradigm, the power grid is becoming more bidirectional, making some locations in the network less effective for UFLS action than others. This work proposes a Mixed Integer Linear Program that optimizes the UFLS setpoints (prioritizing one location over another) to minimize frequency deviation and load-shed for a given disturbance. The formulation considers system information and DER generation mix at different network locations, increasing model fidelity. The formulation also captures the discrete nature and practical time delays and deadbands associated with UFLS using a minimal set of binary variables, reducing problem complexity. We empirically validate the optimization approach on the dynamic IEEE 39-bus system for performance metrics, including frequency nadir, steady-state frequency and total load shed.

There is growing interest in understanding how interactions between system-wide objectives and local community decision-making will impact the clean energy transition. The concept of energysheds has gained traction in the areas of public policy and social science as a way to study these relationships. However, development of technical definitions of energysheds that permit system analysis are still largely missing. In this work, we propose a mathematical definition for energysheds, and introduce an analytical framework for studying energyshed concepts within the context of future electric power system operations. This framework is used to develop insights into the factors that impact a community's ability to achieve energyshed policy incentives within a larger connected power grid, as well as the tradeoffs associated with different spatial policy requirements. We also propose an optimization-based energyshed policy design problem, and show that it can be solved to global optimality within arbitrary precision by employing concepts from quasi-convex optimization. Finally, we investigate how interconnected energysheds can cooperatively achieve their objectives in bulk power system operations.

Hybrid Energy Systems (HES), amalgamating renewable sources, energy storage, and conventional generation, have emerged as a responsive resource for providing valuable grid services. Subsequently, modeling and analysis of HES has become critical, and the quality of grid services hedges on it. Currently, most HES models are temperature-agnostic. However, the temperature-dependent factors can significantly impact HES performance, necessitating advanced modeling and optimization techniques. With the inclusion of temperature-dependent models, the challenges and complexity of solving optimization problem increases. In this paper, the electro-thermal modeling of HES is discussed. Based on this model, a nonlinear predictive optimization framework is formulated. A simplified model is developed to address the challenges associated with solving nonlinear problems. Further, projection and homotopy approaches are proposed. In the homotopy method, the NLP is solved by incrementally changing the C-rating of the battery. Simulation-based analysis of the algorithms highlights the effects of different battery ratings, ambient temperatures, and energy price variations. Finally, comparative assessments with a temperature-agnostic approach illustrates the effectiveness of electro-thermal methods in optimizing HES.

This paper uses convex inner approximations (CIA) of the AC power flow to tackle the optimization problem of quantifying a three-phase distribution feeder's capacity to host distributed energy resources (DERs). This is often connoted hosting capacity (HC), but herein we consider separative bounds for each node on positive and negative DER injections, which ensures that injections within these nodal limits satisfy feeder voltage and current limits and across nodes sum up to the feeder HC. The methodology decomposes a three-phase feeder into separate phases and applies CIA-based techniques to each phase. An analysis is developed to determine the technical condition under which this per-phase approach can still guarantee three-phase constraints. New approaches are then presented that modify the per-phase optimization problems to overcome conservativeness inherent to CIA methods and increase HC, including selectively modifying the per-phase impedances and iteratively relaxing per-phase voltage bounds. Discussion is included on trade-offs and feasibility. To validate the methodology simulation-based analysis is conducted with the IEEE 37-node test feeder and a real 534-node unbalanced radial distribution feeder., Comment: 9 pages, submitted to PSCC 2024 conference

With the increasing use of renewable generation in power systems, responsive resources will be necessary to support primary frequency control in future low-inertia/under-damped power systems. Flexible loads can provide fast-frequency response services if coordinated effectively. However, practical implementations of such synthetic damping services require both effective local sensing and control at the device level and an ability to accurately estimate online and predict the available synthetic damping from a fleet. In addition, the inherent trade-off between a fleet being available for fast frequency response while providing other ancillary services needs to be characterized. In this context, the manuscript presents a novel, fully decentralized, packet-based controller for diverse flexible loads that dynamically prioritizes and interrupts loads to engender synthetic damping suitable for primary frequency control. Moreover, the packet-based control methodology is shown to accurately characterize the available synthetic damping in real-time, which is useful to aggregators and system operators. Furthermore, spectral analysis of historical frequency regulation data is used to produce a probabilistic bound on the expected available synthetic damping for primary frequency control from a fleet and the trade-off from concurrently providing secondary frequency control services. Finally, numerical simulation on IEEE test networks demonstrates the effectiveness of the proposed methodology., Comment: Submitted to IEEE Transactions on Power systems

This paper presents a market-based optimization framework wherein Aggregators can compete for nodal capacity across a distribution feeder and guarantee that allocated flexible capacity cannot cause overloads or congestion. This mechanism, thus, allows Aggregators with allocated capacity to pursue a number of services at the whole-sale market level to maximize revenue of flexible resources. Based on Aggregator bids of capacity (MW) and network access price ($/MW), the distribution system operator (DSO) formulates an optimization problem that prioritizes capacity to the different Aggregators across the network while implicitly considering AC network constraints. This grid-aware allocation is obtained by incorporating a convex inner approximation into the optimization framework that prioritizes hosting capacity to different Aggregators. We adapt concepts from transmission-level capacity market clearing, utility demand charges, and Internet-like bandwidth allocation rules to distribution system operations by incorporating nodal voltage and transformer constraints into the optimization framework. Simulation based results on IEEE distribution networks showcase the effectiveness of the approach., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

A wind farm can provide reactive power at sub-transmission and transmission buses in order to support and improve voltage profiles. It is common for the reactive power capability of a wind farm to be evaluated as the sum of the individual turbine ratings. However, such an assessment does not take into account losses over the collector network, nor the voltage constraints imposed by the turbines and network. In contrast, the paper presents a method for determining the range of reactive power support that each turbine can provide whilst guaranteeing satisfaction of voltage constraints. This is achieved by constructing convex inner approximations of the non-convex set of admissible reactive power injections. We present theoretical analysis that supports the constraint satisfaction guarantees. An example illustrates the effectiveness of the algorithm and provides a comparison with a fully decentralized approach to controlling wind farm reactive power. Such approaches have the potential to improve the design and operation of wind farm collector networks, reducing the need for additional costly reactive power resources., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

The performance of frequency regulating units for automatic generation control (AGC) of power systems depends on their ability to track the AGC signal accurately. In addition, representative models and advanced analysis and analytics can yield forecasts of the AGC signal that aids in controller design. In this paper, time-series analyses are conducted on an AGC signal, specifically the PJM Reg-D, and using the results, a statistical model is derived that fairly accurately captures its second moments and saturated nature, as well as a time-series-based predictive model to provide forecasts. As an application, the predictive model is used in a model predictive control framework to ensure optimal tracking performance of a down ramp-limited distributed energy resource coordination scheme. The results provide valuable insight into the properties of the AGC signal and indicate the effectiveness of these models in replicating its behavior., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

For fast timescales or long prediction horizons, the AC optimal power flow (OPF) problem becomes a computational challenge for large-scale, realistic AC networks. To overcome this challenge, this paper presents a novel network reduction methodology that leverages an efficient mixed-integer linear programming (MILP) formulation of a Kron-based reduction that is optimal in the sense that it balances the degree of the reduction with resulting modeling errors in the reduced network. The method takes as inputs the full AC network and a pre-computed library of AC load flow data and uses the graph Laplacian to constraint nodal reductions to only be feasible for neighbors of non-reduced nodes. This results in a highly effective MILP formulation which is embedded within an iterative scheme to successively improve the Kron-based network reduction until convergence. The resulting optimal network reduction is, thus, grounded in the physics of the full network. The accuracy of the network reduction methodology is then explored for a 100+ node medium-voltage radial distribution feeder example across a wide range of operating conditions. It is finally shown that a network reduction of 25-85% can be achieved within seconds and with worst-case voltage magnitude deviation errors within any super node cluster of less than 0.01pu. These results illustrate that the proposed optimization-based approach to Kron reduction of networks is viable for larger networks and suitable for use within various power system applications.

Compared with large-scale physical batteries, aggregated and coordinated generic energy storage (GES) resources provide low-cost, but uncertain, flexibility for power grid operations. While GES can be characterized by different types of uncertainty, the literature mostly focuses on decision-independent uncertainties (DIUs), such as exogenous stochastic disturbances caused by weather conditions. Instead, this manuscript focuses on newly-introduced decision-dependent uncertainties (DDUs) and considers an optimal GES dispatch that accounts for uncertain available state-of-charge (SoC) bounds that are affected by incentive signals and discomfort levels. To incorporate DDUs, we present a novel chance-constrained optimization (CCO) approach for the day-ahead economic dispatch of GES units. Two tractable methods are presented to solve the proposed CCO problem with DDUs: (i) a robust reformulation for general but incomplete distributions of DDUs, and (ii) an iterative algorithm for specific and known distributions of DDUs. Furthermore, reliability indices are introduced to verify the applicability of the proposed approach with respect to the reliability of the response of GES units. Simulation-based analysis shows that the proposed methods yield conservative, but credible, GES dispatch strategies and reduced penalty cost by incorporating DDUs in the constraints and leveraging data-driven parameter identification. This results in improved availability and performance of coordinated GES units., Comment: Decision-dependent uncertainty; Generic Energy Storage

Packetized energy management (PEM) is a demand dispatch scheme that can be used to provide ancillary services such as frequency regulation. In PEM, distributed energy resources (DERs) are granted uninterruptible access to the grid for a pre-specified time interval called the packet length. This results in a down ramp-limited response in PEM for DERs that can only consume power from the grid. In this work, a linearized virtual battery model of PEM is provided that is capable of predicting the down-ramp limited output of PEM and is used in a model predictive control (MPC) framework to improve the performance of PEM in tracking an automatic generation control (AGC) signal. By performing statistical analysis on the AGC regulation signal, PJM Reg-D, an ARMA model is derived as a predictor for the MPC-based precompensator. Finally, as an alternative to MPC, it is shown that by varying the packet length as a function of time, for example through packet randomization, frequency regulation can be improved under PEM., Comment: 11 pages, 21 figures

Distributed energy resources (DERs) such as responsive loads and energy storage systems are valuable resources available to grid operators for balancing supply-demand mismatches via load coordination. However, consumer acceptance of load coordination schemes depends on ensuring quality of service (QoS), which embodies device-level constraints. Since each device has its own internal energy state, the effect of QoS on the fleet can be cast as fleet-wide energy limits within which the aggregate "state of charge" (SoC) must be actively maintained. This requires coordination of DERs that is cognizant of the SoC, responsive to grid conditions, and depends on fast communication networks. To that effect, this paper presents a novel real-time grid-and-DER co-simulation platform for validating advanced DER coordination schemes and characterizing the capability of such a DER fleet. In particular, we present how the co-simulation platform is suitable for: i) testing real-time performance of a large fleet of DERs in delivering advanced grid services, including frequency regulation; ii) online state estimation to characterize the corresponding SoC of a large fleet of DERs; and iii) incorporating practical limitations of DERs and communications and analyzing the effects on fleet-wide performance. To illustrate these benefits of the presented grid-DER co-simulation platform, we employ the advanced DER coordination scheme called packetized energy management (PEM), which is a novel device-driven, asynchronous, and randomizing control paradigm for DERs. A fleet of thousands of PEM-enabled DERs are then added to a realistic and dynamical model of the Vermont transmission system to complete validation of the co-simulation platform.

The non-convex complementarity constraints present a fundamental computational challenge in energy constrained optimization problems. In this work, we present a new, linear, and robust battery optimization formulation that sidesteps the need for battery complementarity constraints and integers and prove analytically that the formulation guarantees that all energy constraints are satisfied which ensures that the optimized battery dispatch is physically realizable. In addition, we bound the worst-case model mismatch and discuss conservativeness. Simulation results further illustrate the effectiveness of this approach.

This paper addresses the question: how many distributed energy resources (DERs) are needed to provide $\pm1$MW of flexibility over a number of hours? For this purpose, a metric based on an ISO's own performance score is proposed. Then, a systematic procedure is presented and validated that makes use of either a simulator or the solution to an optimization problem based on a nominal analytical formulation to get flexibility in terms of kW-per-device. Furthermore, simulation-based analysis indicates that flexibility from different DER fleets adds linearly, that is, the total flexibility provided by a mixture of different DER types can be obtained as a convex combination of their individual kW-per-device flexibility. The proposed methodology is validated on ($i$) a centralized coordinator and ($ii$) a device driven DER coordination scheme called packetized energy management (PEM). Furthermore, the effect of heterogeneity as well as PEM specific parameters such as packet length and mean time-to-request on flexibility is also quantified.

This paper presents a novel hierarchical framework for real-time, network-admissible coordination of responsive grid resources aggregated into virtual batteries (VBs). In this context, a VB represents a local aggregation of directly controlled loads, such as smart inverters, electric water heaters, and air-conditioners. The coordination is achieved by solving an optimization problem to disaggregate a feeder's desired reference trajectory into constraint-aware set-points for the VBs. Specifically, a novel, provably-tight, convex relaxation of the AC optimal power flow (OPF) problem is presented to optimally dispatch the VBs to track the feeder's desired power trajectory. In addition to the optimal VB dispatch scheme, a real-time, corrective control scheme is designed, which is based on optimal proportional-integral (PI) control with anti-windup, to reject intra-feeder and inter-feeder disturbances that arise during operation of the power system. Simulation results conducted on a modified IEEE test system demonstrate the effectiveness of the proposed multi-layer VB coordination framework.

Due to their large power draws and increasing adoption rates, electric vehicles (EVs) will become a significant challenge for electric distribution grids. However, with proper charging control strategies, the challenge can be mitigated without the need for expensive grid reinforcements. This manuscript presents and analyzes new distributed charging control methods to coordinate EV charging under nonlinear transformer temperature ratings. Specifically, we assess the trade-offs between required data communications, computational efficiency, and optimality guarantees for different control strategies based on a convex relaxation of the underlying nonlinear transformer temperature dynamics. Classical distributed control methods such as those based on dual decomposition and alternating direction method of multipliers (ADMM) are compared against the new Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) method and a novel low-information, look-ahead version of packetized energy management (PEM). These algorithms are implemented and analyzed for two case studies on residential and commercial EV fleets. Simulation results validate the new methods and provide insights into key trade-offs., Comment: 15 pages, 9 figures, journal

This paper presents a novel frequency-responsive control scheme for demand-side resources, such as electric water heaters. A frequency-dependent control law is designed to provide damping from distributed energy resources (DERs) in a fully decentralized fashion. This local control policy represents a frequency-dependent threshold for each DER that ensures that the aggregate response provides damping during frequency deviations. The proposed decentralized policy is based on an adaptation of a packet-based DER coordination scheme where each device send requests for energy access (also called an "energy packet") to an aggregator. The number of previously accepted active packets can then be used a-priori to form an online estimate of the aggregate damping capability of the DER fleet in a dynamic power system. A simple two-area power system is used to illustrate and validate performance of the decentralized control policy and the accuracy of the online damping estimating for a fleet of 400,000 DERs., Comment: 7 pages, 6 figures, 3 tables, submitted to IEEE smart grid conference 2020

This paper presents a convex, multi-period, AC-feasible Optimal Power Flow (OPF) framework that robustly dispatches flexible demand-side resources in unbalanced distribution feeders against uncertainty in very-short timescale solar Photo-Voltaic (PV) forecasts. This is valuable for power systems with significant behind-the-meter solar PV generation as their operation is affected by uncertainty from forecasts of demand and solar PV generation. The aim of this work is then to ensure the feasibility and reliability of distribution system operation under high solar PV penetration. We develop and present a novel, robust OPF formulation that accounts for both the nonlinear power flow constraints and the uncertainty in forecasts. This is achieved by linearizing an optimal trajectory and using first-order methods to systematically tighten voltage bounds. Case studies on a realistic distribution feeder shows the effectiveness of a receding-horizon implementation.

With increasing penetration of solar PV, some distribution feeders are experiencing highly variable net-load flows and even reverse flows. To optimize distribution systems under such conditions, the scheduling of mechanical devices, such as OLTCs and capacitor banks, needs to take into account forecasted solar PV and actual grid conditions. However, these legacy switching assets are operated on a daily or hourly timescale, due to the wear and tear associated with mechanical switching, which makes them unsuitable for real-time control. Therefore, there is a natural timescale-separation between these slower mechanical assets and the responsive nature of inverter-based resources. In this paper, we present a network admissible convex formulation for holistically scheduling controllable grid assets to position voltage optimally against solarPV. An optimal hourly schedule is presented that utilizes mechanical resources to position the predicted voltages close to nominal values, while minimizing the use of inverter-based resources (i.e., DERs),making them available for control at a faster time-scale (after the uncertainty reveals itself). A convex, inner approximation of the OPF problem is adapted to a mixed-integer linear program that minimizes voltage deviations from nominal (i.e., maximizes voltage margins). The resulting OPF solution respects all the network constraints and is, hence, robust against modeling simplifications. Simulation based analysis on IEEE distribution feeders validates the approach., Comment: arXiv admin note: text overlap with arXiv:1907.06709

Dispatching a large fleet of distributed energy resources (DERs) in response to wholesale energy market or regional grid signals requires solving a challenging disaggregation problem when the DERs are located within a distribution network. This manuscript presents a computationally tractable convex inner approximation for the optimal power flow (OPF) problem that characterizes a feeders aggregate DERs hosting capacity and enables a realtime, grid-aware dispatch of DERs for radial distribution networks. The inner approximation is derived by considering convex envelopes on the nonlinear terms in the AC power flow equations. The resulting convex formulation is then used to derive provable nodal injection limits, such that any combination of DER dispatches within their respective nodal limits is guaranteed to be AC admissible. These nodal injection limits are then used to construct a realtime, open-loop control policy for dispatching DERs at each location in the network to collectively deliver grid services. The IEEE-37 distribution network is used to validate the technical results and highlight various use-cases.

This paper develops an efficient algorithm for the multi-period optimal dispatch of deterministic inverter-interfaced energy storage in an unbalanced distribution feeder with significant solar PV penetration. The three-phase, non-convex loss-minimization problem is formulated as a convex second order cone program (SOCP) for the dispatch of batteries in a receding-horizon fashion in order to counter against the variable renewable net-load generation. The solution of the SOCP is used to initialize a nonlinear program (NLP) in order to ensure a physically realizable solution. The phenomenon of simultaneous charging and discharging of batteries is rigorously analyzed and conditions are derived that guarantee it is avoided. Simulation scenarios are implemented with GridLab-D for the IEEE-13 and IEEE-123node test feeders and illustrate not only AC feasibility of the solution, but also near-optimal performance and solve-times within a minute.

This paper presents a method to obtain a convex inner approximation that aims to improve the feasibility of optimal power flow (OPF) models in distribution feeders. For a resistive distribution network, both real and reactive power effect the node voltages and this makes it necessary to consider both when formulating the OPF problem. Inaccuracy in linearized OPF models may lead to under and over voltages when dispatching flexible demand, at scale, in response to whole-sale market or grid conditions. In order to guarantee feasibility, this paper obtains an inner convex set in which the dispatchable resources can operate, based on their real and reactive power capabilities, that guarantees network voltages to be feasible. Test simulations are conducted on a standard IEEE distribution test network to validate the approach.

In this paper, we employ a bi-level control system to react to disturbances and balance power mismatch by coordinating distributed energy resources (DERs) under packetized energy management. Packetized energy management (PEM) is a novel bottom-up asynchronous and randomizing coordination paradigm for DERs that guarantees quality of service, autonomy, and privacy to the end-user. A hardware-in-the-loop (HIL) simulation of a cyber-physical system consisting of PEM enabled DERs, flexible virtual power plants (VPPs) and transmission grid is developed in this work. A predictive, energy-constrained dispatch of aggregated PEM-enabled DERs is formulated, implemented, and validated on the HIL cyber-physical platform. The energy state of VPPs, composed of a fleet of diverse DERs distributed in the grid, depending upon the distinct real-time usage of these devices. The experimental results demonstrate that the existing control schemes, such as AGC, dispatch VPPs without regard to their energy state, which leads to unexpected capacity saturation. By accounting for, the energy states of VPPs, model-predictive control (MPC) can optimally dispatch conventional generators and VPPs to overcome disturbances while avoiding undesired capacity saturation. The results show the improvement in dynamics by using MPC over conventional AGC and droop for a system with energy-constrained resource

High penetrations of intermittent renewable energy resources in the power system require large balancing reserves for reliable operations. Aggregated and coordinated behind-the-meter loads can provide these fast reserves, but represent energy-constrained and uncertain reserves (in their energy state and capacity). To optimally dispatch uncertain, energy-constrained reserves, optimization-based techniques allow one to develop an appropriate trade-off between closed-loop performance and robustness of the dispatch. Therefore, this paper investigates the uncertainty associated with energy-constrained aggregations of flexible, behind-the-meter distributed energy resources (DERs). The uncertainty studied herein is associated with estimating the state of charge and the capacity of an aggregation of DERs (i.e., a virtual energy storage system or VESS). To that effect, a risk-based chance-constrained control strategy is developed that optimizes the operational risk of unexpectedly saturating the VESS against deviating generators from their scheduled set-points. The controller coordinates energy-constrained VESSs to minimize unscheduled participation of and overcome ramp-rate limited generators for balancing variability from renewable generation, while taking into account grid conditions. To illustrate the effectiveness of the proposed method, simulation-based analysis is carried out on an augmented IEEE RTS-96 network with uncertain energy resources and temperature-based dynamic line ratings.