Publications
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Journal Papers
Ning Qi, Pierre Pinson, Mads R. Almassalkhi, Yingrui Zhuang, Yifan Su, Feng Liu, "Capacity Credit Evaluation of Generalized Energy Storage Considering Endogenous Uncertainty," IEEE Trans. on Power Systems (in review: Rev01).
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.
Yingrui Zhuang, Lin Cheng, Ning Qi, Mads R. Almassalkhi, Feng Liu, "Problem-Driven Scenario Reduction Framework for Power System Stochastic Operation," IEEE Trans. on Power Systems (in review: Rev01).
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.
Conference Proceedings
Journal Papers
Tanmay Mishra, Amrit Pandey, and Mads R. Almassalkhi, "Predictive Optimization of Hybrid Energy Systems with Temperature Dependency" Electric Power Systems Research, vol. 235, p. 110 767, 2024, (Presented at the 2024 Power Systems Computations Conference - PSCC).
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 bat- tery. 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.
Hani Mavalizadeh and Mads R. Almassalkhi, "Decomposed Phase Analysis using Convex Inner Approximations: a Methodology for DER Hosting Capacity in Distribution Systems" Electric Power Systems Research, vol. 235, p. 110 652, 2024, (Presented at the 2024 Power Systems Computation Conference - PSCC).
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 host- ing 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 iterative method has been proposed to modify the 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.
Mohsen Banaei, Francesco D'Ettorre, Razgar Ebrahimy, Mads R. Almassalkhi, and Henrik Madsen, "Procuring Flexibility in Power Systems with Incentive-based Grid Access Requests," International Journal of Electric Power & Energy Systems, Vol. 156, 109745, 2024.
Demand-side flexibility is an important tool for enhancing the interaction of renewable energy resources and reducing the need for grid upgrades. To employ this flexibility as a market product, it is necessary to aggregate and coordinate by coordinating responsive loads. In this regard, designing effective load coordination mechanisms that consider the preferences of aggregators, end-users, and network operators is critical for the successful implementation of demand response (DR) programs. This paper proposes an incentive- based method for coordinating a group of controllable devices that is practical, does not require complex, high-order models of the entire system, respects end-users privacy and quality of service (QoS), and can readily incorporate network conditions to ensure grid reliability. The proposed method includes algorithms at both the end-user level for con- trollable device operation and the aggregator level for managing the grid access requests. These algorithms are fast and with low computational burden which makes them suitable for the designed framework, reduces the implementation cost and increases the chance of scalability. The method is illustrated with a realistic test system consisting of a set of controllable heat pumps used in pool heating systems and uncontrollable loads placed in a distribution feeder and supplied by a distribution substation transformer. Simulation results highlight the effectiveness of the proposed method in satisfying the controllable device, end-users, and grid constraints. Comparing the results with similar existing meth- ods shows that the method is 11% more cost-effective than traditional ON/OFF methods while reducing the number of rejected grid access requests from the devices, significantly.
Conference Proceedings
Dakota Hamilton, Samuel Chevalier, Amrit Pandey, and Mads R. Almassalkhi, "Towards Energysheds: A Technical Definition and Cooperative Framework for Future Power System Operations", IEEE Conference on Decision and Control (CDC)), accepted (to appear).
There is growing interest in understanding how in- teractions 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.
Journal Papers
Mads R. Almassalkhi and Soumya Kundu, "Intelligent Electrification as an enabler of Clean Energy and Decarbonization," Current Sustainable/Renewable Energy Reports, September 2023 (Invited paper).
Electrification efforts will change electric demand pat- terns, but must be made beneficial to the deployment of renewable generation. To ensure this, we need intelligent coordination of millions of resulting dis- tributed energy resources (DERs). We provide an overview of challenges and opportunities associated with intelligent electrification as a means to enable decarbonization and clean energy.
Hani Mavalizadeh, Luis D. A. Espinosa, and Mads R. Almassalkhi, "Improving frequency response with synthetic damping available from fleets of distributed energy resources," IEEE Transactions on Power Systems, 2023.
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.
Amrit Pandey, Mads R. Almassalkhi, and Samuel Chevalier, "Large-scale Grid Optimization: The Workhorse of Future Grid Computations," Curr Sustainable Renewable Energy Rep, July 2023 (Invited paper).
The computation methods for modeling, controlling, and optimizing the transforming grid are evolving rapidly. We review and systemize knowledge for a special class of computation methods that solve large-scale power grid optimization problems. Recent Findings: We find that while mechanistic physics-based methods are leading the science in solving large-scale grid optimizations, data-driven techniques, especially physics constrained ones, are emerging as an alternative to solve otherwise intractable problems. We also find observable gaps in the field and ascertain these gaps from the paper’s literature review and by collecting and synthesizing feedback from industry experts. Summary: Large-scale grid optimizations are pertinent for, among other things, hedging against risk due to resource stochasticity, evaluating aggregated DERs’ impact on grid operation and design, and improving the overall efficiency of grid operation in terms of cost, reliability, and carbon footprint. We attribute the continual growth in scale and complexity of grid optimizations to a large influx of new spatial and temporal features in both transmission (T) and distribution (D) networks. Therefore, to systemize knowledge in the field, we discuss the recent advancements in T and D systems from the viewpoint of mechanistic physics-based and emerging data-driven methods.
Mustafa Matar, Hani Mavalizadeh, Sarnaduti Brahma, Mads R. Almassalkhi, and Safwan Wshah, "Learning the state-of-charge of heterogeneous fleets of distributed energy resources with temporal residual networks," Journal of Energy Storage, Volume 70, 2023.
With increased use of renewable energy such as wind and solar, electric power generation is experiencing increased variability and uncertainty, which drives larger imbalances between the electric demand and supply. To mitigate this challenge, one can use distributed energy resources to beget flexible demand from coordinating fleets of smart electric water heaters (EWH) and residential (kW-scale) batteries. To effectively coordinate and characterize such a large and heterogeneous fleet of distributed energy resources (DERs), a common abstraction is denoted a virtual battery (VB). While the state of charge (SoC) of individual DERs (e.g., EWHs's water temperature) can be easily measured, determining the SoC of a controlled virtual battery aggregation is a technically challenging task due to the fleet's heterogeneous nature, characterized by nonlinear, stochastic, partial differential equations with time-varying parameters. In this paper, a data-driven approach is presented that utilizes a deep-learning-based Temporal Residual Causal Network to determine the SoC for a heterogeneous fleet of DERs, updated using only available end-use measurements. Unlike existing literature that generally relies on complex physics-based models, our deep learning (DL) model is trained using practical input-output data. The simulation results demonstrate that accurate estimation can be achieved with a low computational burden, considering a range of parametric variations at the device and fleet levels, such as fleet population size, background demand, DER device parameters, and coordinator communication losses. The results suggest that the proposed approach has appropriate generalization and robustness properties for practical, real-time control settings
Himadri Basu, Yasaman Pedari, Mads R. Almassalkhi, and Hamid R. Ossareh, "Computationally Efficient Collision-Free Trajectory Planning of Satellite Swarms Under Unmodeled Orbital Perturbations," AIAA Journal of Guidance, Control, and Dynamics, May 2023.
This paper studies the problem of collision-free trajectory planning for a satellite swarm reconfiguration under perturbations and modeling uncertainties in a low Earth orbit (LEO). Determining exact trajectory planning solutions is computationally heavy as they require solving a mixed-integer nonlinear program owing to i) nonlinear relative dynamic models of satellites, ii) fuel-optimal assignment of satellites on the final formation, and iii) nonconvex collision avoidance constraints. To address these, first, a suitable linear model for trajectory planning is identified by quantifying modeling accuracy associated with various models capturing LEO perturbations. The effects of any residual modeling errors in the path prediction are mitigated by shrinking-horizon model-predictive feedback control, which updates the control command based on the latest satellite measurements. Secondly, an optimal swarm configuration is efficiently computed by decoupling the target-assignment algorithm from the trajectory optimization problem. Based on the estimated fuel expenditure for each satellite–target pairing, the target-assignment algorithm selects a configuration with minimal fuel consumption. Lastly, to determine collision-free, fuel-optimal maneuvers, two novel trajectory planning approaches, namely, distributed and decentralized trajectory optimization, are presented. While the former iteratively searches for collision-free feasible paths to optimal terminal configuration, the latter computes a near-optimal configuration with collision-free paths.
N. Qi, P. Pinson, M. R. Almassalkhi, L. Cheng, and Y. Zhuang, "Chance Constrained Economic Dispatch of Generic Energy Storage under Decision-Dependent Uncertainty," IEEE Transactions on Sustainable Energy, 2023.
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.
Conference Proceedings
Hani Mavalizadeh and Mads R. Almassalkhi "Methodology for comparing the performance of DER coordination schemes in providing frequency regulation," IEEE PES General Meeting, 2023.
In this paper, we illustrate a novel methodology
for comparing and quantifying the performance of
different distributed energy resources (DER)
schemes’ ability to deliver frequency regulation
services across a number of salient criteria. The
schemes considered include (bottom-up) packetized
energy management, fitness-based methods, and
(direct load control) optimization-based methods.
The criteria of interest include tracking
performance, scalability of communication,
scalability of computation, device availability,
ability to maintain consumer quality of service
(CQoS) relative to delivered hot water
temperatures, and impact on the device quality of
service (DQoS) such as average cycling rates.
Moreover, we augment the fitness-based method with
an ability to estimate the fitness values
dynamically which significantly reduces the
communication burden while maintaining the tracking
capability. Finally, the simulations and
corresponding comparisons are based on a
representative subset of PJM’s historical Reg-D
data.
Mazen Elsaadany and Mads R. Almassalkhi, "Battery Optimization for Power Systems: Feasibility and Optimality," IEEE Conference on Decision and Control, pp. 562-569, Singapore, 2023.
The deployment of battery energy storage systems (BESS) is necessary to integrate terawatts of renewable generation while supporting grid resilience and reliability efforts. Optimizing battery dispatch requires predictive battery models that accurately characterize the battery state of charge (SOC) to ensure that the battery operates within the energy and power limits and avoids unexpected saturation effects. Furthermore, most BESS are unable to simultaneously charge and discharge, which begets an additional, non-convex complementary constraint. This paper presents and compares recently developed predictive battery models that side-step the non-convexity while providing supporting analysis on modeling error and optimal parameter selection. Specifically, insights for four different predictive BESS formulations are presented, including non-linear, mixed-integer, linear convex relaxation, and linear robust formulations. Additionally, two two-stage approaches are also considered. Analysis is conducted on optimal parameter selection for two of the methods, as well, as providing a new and improved SOC error bound on the relaxed formulation and the role of sustainability constraints on the robust formulation. Through the lens of relevant BESS use-cases, the paper discusses optimality and feasibility guarantees between the different models and provides extensive simulation-based analysis.
Technical Report
Mads R. Almassalkhi, et al, "Packetized energy management: coordination transmission and distribution" United States Department of Energy - Advanced Research Projects Agency - Energy (ARPA-E), March, 2023.
This is the final technical report (FTR) for the project Packetized Energy Management (PEM): Coordinating Transmission and Distribution, which was part of the ARPA-E NODES program from 2015 to 2023. The high-level goal of the project was to develop and demonstrate novel, scalable, and impactful technologies related to the coordination of networked distributed energy resources (DERs). By demonstrating responsive means by which fleets of DERs could be coordinated to enhance grid operation and reliability, the U.S. could accelerate renewable integration and electrification efforts and meet decarbonization goals.
Journal Papers
S. Brahma, A. Khurram, H. Ossareh, and M. Almassalkhi, "Optimal Frequency Regulation using Packetized Energy Management," IEEE Transactions on Power Systems, 2022 (Early access).
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.
A. Khurram, M. Amini, L. Duffaut Espinosa, P. H. Hines, and M. Almassalkhi, "Real-time Grid and DER Co-simulation Platform for Validating Large-scale DER Control Schemes," IEEE Transactions on Smart Grid, (Early Access)).
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.
Conference Proceedings
S. Chevalier and M. Almassalkhi, "Towards Optimal Kron-based Reduction Of Networks (Opti-KRON) for the Electric Power Grid," IEEE Conference on Decision and Control, 2022 (to appear).
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 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.
N. Nazir, I. A. Hiskens, and M. R. Almassalkhi, "Exploring reactive power limits on wind farm collector networks with convex inner approximations." IREP Bulk Power System Dynamics and Control Symposium, 2022.
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. The predictive model is used in a model predictive control framework to ensure optimal tracking performance of down ramp-limited DER 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.
N. Nazir and M. Almassalkhi, "Market mechanism to enable grid-aware dispatch of Aggregators in radial distribution networks,". IREP Bulk Power System Dynamics and Control Symposium, 2022.
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.
S. Brahma, H. Ossareh, and M. R. Almassalkhi, "Statistical Modeling and Forecasting of Automatic Generation Control Signals,". IREP Bulk Power System Dynamics and Control Symposium, 2022.
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. The predictive model is used in a model predictive control framework to ensure optimal tracking performance of down ramp-limited DER 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.
A. Khan, S. Paudyal, and M. Almassalkhi, "Performance Evaluation of Network-Admissible Demand Dispatch in Multi-Phase Distribution Grids,". IREP Bulk Power System Dynamics and Control Symposium, 2022.
As the penetration of flexible loads increases in distribution networks, demand dispatch schemes need to consider the effects of large-scale load control on distribution grid reliability. More specifically, we need demand dispatch schemes that actively ensure that distribution grid operational constraints are not violated (i.e., network-admissible) and still deliver valuable market services. For network-admissible demand dispatch schemes that depend on live 3-phase grid measurements, their overall performance and ability to manage constraints depends on the number, update rate, and multi-phase nature of the available measurements. In this context, the manuscript develops and evaluates the performance of a new network-admissible version of the device-driven demand dispatch scheme called Packetized Energy Management (PEM) within a large multi-phase distribution feeder. Specifically, this work investigates the effects of different levels and rates of grid measurements for a practical-sized, 2,522-node, unbalanced distribution test feeder with a 3000 flexible kW-scale loads operating under the network- admissible PEM scheme. The results demonstrate the value of live grid measurements in managing distribution grid operational constraints while PEM is able to effectively deliver frequency regulation services.
A. Khurram, M. Almassalkhi, and L. Duffaut Espinosa, "A Group-based Approach for Heterogeneity in Packetized Energy Management,". IEEE Conference on Control Technology and Applications, CCTA 2022.
In practice, fleets of DERs are inherently heterogeneous due to manufacturers' specifications and the effects of wear and tear. Accounting for heterogeneity is critical in the design of control policies for DER aggregations, otherwise, the system response may be inaccurate and performance can be degraded. This paper presents a group-based approach to characterize parametric heterogeneity in a fleet of aggregated DERs by grouping into homogeneous fleets. The proposed group-based approach borrows concepts from quantization in the area of signal processing and the paper particularly highlights the effect of rated power heterogeneity due to its relevance to the control policy design in packetized energy management (PEM). The reason for this is that the effective control mechanism in PEM is a function of the aggregate DER demand and the rated power of devices that are switched on. As a result, the PEM system is susceptible to tracking errors that may degrade performance in a heterogeneous fleet. Therefore, the proposed quantization based approach provides a systematic approach to group DERs in the fleet so that the desired performance is achieved.
O. Oyefeso, G. Ledva, I. Hiskens, M. Almassalkhi, and J. Mathieu, "Control of Aggregate Air-Conditioning Load using Packetized Energy Concepts,". IEEE Conference on Control Technology and Applications, CCTA 2022.
This paper extends the packetized energy management (PEM) control strategy to enable coordination of compressor-based thermostatically controlled loads (TCLs), such as air conditioners, thus providing a new method to harness the flexibility of this ubiquitous resource. This flexibility can be used to provide a variety of grid services such as frequency regulation. While in traditional PEM, resources request energy packets and turn on if their request is approved, here we modify the PEM scheme by introducing the concept of turn-off requests. We find that this increases flexibility and improves load tracking performance. Through a case study, we evaluate the performance of a population of air conditioners providing frequency regulation under PEM, highlighting both the capabilities and performance limitations. Simulations indicate our controller extensions increase resource availability by at least 150% and improve tracking performance by up to 61%. Specifically, we show that it is possible for a population of about 1000 TCLs to achieve power tracking RMS errors below 1% when providing more than 0.2 MW of frequency regulation.
H. Basu, M. Almassalkhi, and H. Ossareh, "Comparative Analysis of Satellite Relative Dynamics and Fuel-Optimal Trajectory Planning of Satellites Using Minimum Distance Assignment," American Control Conference (ACC), 2022.
In this paper, we present a fuel-optimal trajectory optimization (TO) problem for satellite formation flying (SFF) in near-circular low-earth orbits (LEO) under perturbations and modeling uncertainties. Non-spherical gravity (J2) of the earth and air drag are two dominant perturbing forces in LEO which cause significant orbital measurement errors and eventually sub-optimal actuation and trajectory prediction by the TO algorithm. By quantifying uncertainties and modeling errors associated with various relative dynamical models of satellites, we identify a model that is suitable for the TO problem. However, one of the key challenges to design of a computationally efficient TO algorithm for satellite swarms pertains to the assignment of each satellite to a location in a given final formation. To address this, we first decouple the final configuration assignment problem from the TO, derive minimum distance assignment between initial and final formation pairs, and then by using this minimum distance assignment in the TO algorithm, we efficiently compute near-optimal trajectories and actuation under given mission specifications. Our proposed formulation is scalable to large swarm sizes and it allows the computation load to be distributed over the satellite swarm at the expense of small loss in fuel-optimality.
Popular Magazines
M. Almassalkhi, J. Frolik, and P. Hines, "How To Prevent Blackouts By Packetizing The Power Grid" IEEE Spectrum, February, 2022.
The rules of the Internet can also balance electricity supply and demand. Packetized energy management (PEM) is a way to balance the power grid and make it more reliable while also maximizing the use of renewable energy and avoiding the installation of massive amounts of energy storage or other expensive infrastructure.
Journal Papers
N. Nazir and M. Almassalkhi, "Grid-aware aggregation and realtime disaggregation of distributed energy resources in radial networks," IEEE Transactions on Power Systems, 2021 (Early Access).
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.
M. Botkin-Levy, A. Engelmann, T. Mühlpfordt, T. Faulwasser, and M. Almassalkhi, "Distributed control of charging for electric vehicle fleets under dynamic transformer ratings," IEEE Transactions on Control Systems Technology, vol. 30, no. 4, pp. 1578-1594, July 2022.
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 with fixed and variable populations, respectively. The latter motivates a novel EV hub charging model that captures arrivals and departures. Simulation results validate the new methods and provide insights into key trade-offs.
N. Nazir and M. Almassalkhi, "Guaranteeing a physically realizable battery dispatch without charge-discharge complementarity constraints," IEEE Transactions on Smart Grid, 2021 (Early Access).
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.
L. Duffaut Espinosa, A. Khurram, and M. Almassalkhi, "Reference-Tracking Control Policies for Packetized Coordination of Heterogeneous DER Populations," IEEE Transactions on Control Systems Technology, vol. 29, no. 6, pp. 2427-2443, Nov. 2021.
This manuscript presents design and analysis of a set of reference-tracking control policies for large-scale coordination of distributed energy resources (DERs) and quantifies tracking errors that arise due to heterogeneity in the power ratings for a fleet of DERs. In particular, the relay-based, reference-tracking control strategy that underpins much of packetized energy management (PEM) is augmented to uniquely leverage PEM's energy packet request mechanism to optimize the number of accepted requests and to explicitly consider the quality of service (QoS). In addition, tracking errors from modeling a heterogeneous fleet of packetized DERs with a group of homogeneous macromodels are analytically derived for relevant PEM information scenarios. Finally, simulation-based analysis validates the results and shows that PEM is suitable for providing load balancing and ramping services for the grid.
N. Nazir and M. Almassalkhi, "Voltage positioning using co-optimization of controllable grid assets," IEEE Transactions on Power Systems vol. 36, no. 4, pp. 2761-2770, July 2021.
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.
S. Brahma, N. Nazir, H. Ossareh, and M. Almassalkhi, "Optimal and resilient coordination of virtual batteries in distribution feeders," IEEE Transactions on Power Systems vol. 36, no. 4, pp. 2841-2854, July 2021.
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.
Conference Proceedings
S. Brahma, M. Almassalkhi, and H. Ossareh, "Optimal Control of Virtual Batteries using Stochastic Linearization," IEEE Conference on Control Technology and Applications (CCTA) , August 8-11, 2021.
Stochastic Linearization (SL) is a method of linearizing a nonlinearity that, unlike traditional Jacobian linearization that is valid only close to the operating point, uses statistical properties of the input to render the linearization fairly accurate over a wide range of inputs. In this paper, the method of SL is applied to optimally design controllers for an aggregation of distributed energy resources (DERs), called a virtual battery (VB), by taking into account the solar penetration levels, grid parameters, and the VB power limits. Analysis and simulation results show that VB performance can be greatly improved over a baseline design that ignores VB power limits, and that the controllers can be adaptively designed to effectively respond to changes in system parameters. This proves to be a new method for designing controllers to improve the participation of power-constrained VBs.
A. Khurram, L. Duffaut Espinosa, and M. Almassalkhi, "A Methodology for Quantifying Flexibility in a fleet of Diverse DERs," IEEE PES PowerTech , June 28 - July 2, 2021.
This paper addresses the question: how many distributed energy resources (DERs) are needed to provide ±1MW 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.
Journal Papers
M. Almassalkhi, S. Brahma, N. Nazir, H. Ossareh, P. Racherla, S. Kundu, S. P. Nandanoori, T. Ramachandran, A. Singhal, D. Gayme, C. Ji, E. Mallada, Y. Shen, P. You, and D. Anand, "Hierarchical, grid-aware, and economically optimal coordination of distributed energy resources in realistic distribution systems," Energies (Special issue: Building-to- Grid Integration through Intelligent Optimization and Control), vol. 13, no. 23, p. 6399, 2020.
Renewable portfolio standards are targeting high levels of variable solar photovoltaics (PV) in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliably manage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimizes the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.
L. L. Duffaut Espinosa and M. Almassalkhi, "A packetized energy management macromodel with quality of service guarantees for demand-side resources," IEEE Transactions on Power Systems, vol. 35, no. 5, pp. 3660-3670, 2020.
Using distributed energy resources (DERs), such as thermostatically controlled loads (TCLs), electric vehicles (EVs), and energy storage systems (ESSs) as a way to manage demand has been known for decades. A demand management scheme that explicitly considers the individual DER's local quality of service (QoS) is known as demand dispatch. Packetized energy management (PEM) is a demand dispatch paradigm that borrows packet-based concepts from wireless communications to dynamically manage fleets of DER at-scale and in realtime via small, discrete fixed-duration/fixed-power energy packets. PEM addresses QoS in a bottom-up fashion by having a coordinator authorize/deny incoming requests from DERs to consume energy packets. This manuscript extends prior work on modeling a large-scale population (i.e., macro-model) of homogeneous TCLs and ESSs operating under the PEM paradigm. In particular, we extend the macro-model methodology to include deferrable loads (DLs), such as EVs, together with analysis of QoS guarantees. Comparisons between an agent-based (micro-model) simulation and the proposed macro-model are presented to validate modeling accuracy and QoS guarantees.
A. Khurram, L. Duffaut Espinosa, R. Malhame, and M. Almassalkhi, "Identification of Hot Water End-use Process of Electric Water Heaters from Energy Measurements," Electric Power Systems Research, vol. 189 (106625), 2020. Presented at 21st Power Systems Computation Conference (PSCC), June 29 - July 3, 2020.
This paper presents an algorithm for the identification of parameters for a stochastic hot water end-use process that drives a homogeneous population of thermostatically controlled electric water heaters (EWH). Usually, only metered interval consumption data (kWh) is collected and the hot water end-use process is unobservable to utility and aggregators. However, the availability of EWHs for demand response (DR) is closely coupled with the hot water end-use process. In this context, the hot water end-use process is modeled as a two-state Markov chain (Use / No use), which causes the thermostatic ON-OFF switching process to behave as a Markov renewal process (MRP). A set of first passage-time problems is developed to obtain the moments of the transition probability densities of the MRP. These problems are addressed by establishing a system of coupled partial differential equations characterizing the temperature evolution of the EWH population. A key quantity in the methodology for estimating the parameters is the total time an EWH is ON within a period of interest. It is referred to as the total busy time. Total busy time in this approach is a random variable for which analytical expressions of the moments are developed as a function of the metered window length. The latter expressions become the basis of a hot water demand model identification algorithm which is validated using agent-based simulations of EWHs.
N. Nazir and M. Almassalkhi, "Stochastic multi-period optimal dispatch of energy storage in unbalanced distribution feeders," Electric Power Systems Research, vol. 189 (106783), 2020. Presented at 21st Power Systems Computation Conference (PSCC), June 29 - July 3, 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.
M. Amini and M. Almassalkhi, "Optimal Corrective Dispatch of Uncertain Virtual Energy Storage Systems," IEEE Transactions on Smart Grid, vol. 11, no. 5, pp. 4155 - 4166, 2020.
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.
N. Nazir, P. Racherla, and M. Almassalkhi, "Optimal multi-period dispatch of distributed energy resources in unbalanced distribution feeders," IEEE Transactions on Power Systems, vol. 35, no. 4, pp. 2683-2692, 2020.
This paper presents 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 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-123 node test feeders and illustrate not only AC feasibility of the solution, but also near-optimal performance and solve-times within a minute.
Z. Hurwitz, Y. Dubief, and M. Almassalkhi, "Economic effciency and carbon emissions in multi-energy systems with flexible buildings," International Journal of Electrical Power and Energy Systems , vol. 123 (106114), 2020.
Multi-energy systems (MES) offer an opportunity to leverage energy conversion processes and temporary energy storage mechanisms to reduce costs and emissions during operation of buildings, campuses, and cities. With increasing options for flexibility in demand-side resources, it is possible to temporarily defer thermal and electrical demand of (flexible) buildings without sacrificing comfort and convenience of its occupants, which can improve overall MES economic efficiency and reduce emissions.
To that effect, this paper develops a linear optimization formulation of a MES with flexible (thermal and electric) building demands that capture nonlinearities in the efficiencies of energy conversion processes. The optimization formulation accounts for multiple time-steps to capture the (first-order) dynamics of large thermal building loads. The flexible buildings are parameterized, in part, based on historical data from a college campus in Vermont, USA. The idea of the MES model is to investigate the role that flexible building loads play in reducing costs and emissions for a small campus relative to that of a possible carbon tax. The operation of the MES is optimized to reduce costs based on representative seasons and carbon tax scenarios. Interestingly, it is found that when utilized optimally, flexible buildings can offer an effective method to improve economic efficiency while also reducing carbon emissions close to the levels that a carbon tax would realize, though without carbon price's large cost increases. That is, we present evidence that flexible buildings in Vermont may offer another route to achieve the emission goals close to that of a carbon tax policy.
Conference Proceedings
L. Duffaut Espinosa, A. Khurram, and M. Almassalkhi, "A Virtual Battery Model for Packetized Energy Management," IEEE Conference on Decision and Control, 14-18 Dec., 2020.
The goal of this paper is to develop a low-order model to represent the coordination of distributed energy resources based on concepts that make the internet work and is known as packetized energy management (PEM). The low-order model includes energy as a state variable together with dynamic opt-out constraints and internal packet request feedback, which in principle turns the model into a PEM virtual battery (PEM-VB) model. The paper focuses on a homogeneous aggregation of electric water heaters (EWHs) under PEM. It is shown that the bottom-up logic of the PEM-VB makes the system observable mainly due to the convenient feeding back of the number of packet requests through the communication channel established between the PEM coordinator and devices enrolled in the scheme. Without such extra information, the system loses the ability to observe the system's stored energy state. A procedure for computing the maximum and minimum energy bounds for the PEM-VB is developed. Moreover, the PEM-VB is explicitly used as the underlying model for an extended Kalman filter observer formulation with the purpose of estimating the energy stored in a simulated ensemble of agent-based EWHs under PEM. The use of PEM-VB is demonstrated in pre-positioning of flexible resources depending upon load forecasts. Finally, conclusions and future directions are provided.
H. Mavalizadeh, L. Duffaut Espinosa, and M. Almassalkhi, "Decentralized Frequency Control using Packet-based Energy Coordination," IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), December, 2020.
Distributed algorithms provide attractive features for solving Optimal Power Flow (OPF) problems in interconnected power systems compared to traditional centralized algorithms. Distributed algorithms help to maintain the control autonomy and data privacy of subsystems, which is particularly relevant in competitive markets and practical control system implementations. This paper analyzes a distributed optimization algorithm known as the "Auxiliary Principle Problem" to solve multiperiod distributed DCOPF problems with energy storage systems. The proposed approach enables multiple interconnected systems with their own sub-objectives to share their resources and to participate in an electricity market without implicitly sharing information about their local generators or internal network parameters. The paper also shows how the proposed approach can enable future microgrids to coordinate their operation, reduce the total operational cost, and avoid internal constraint violations caused by unscheduled flows (USF) while maintaining the subsystems' autonomy. We used an 11-bus test system consisting of two interconnected subsystems to evaluate the proposed approach and analyze the impact of USF.
Technical Reports
M. Almassalkhi et al, "Robust and resilient coordination of feeders with uncertain distributed energy resources: from real-time control to long-term planning," United States Department of Energy (SETO), 2020.
In this project, we bring together state-of-the-art optimization and control tools to provide a pragmatic, yet innovative hierarchical scheme for coordinating DERs at scale
Journal Papers
S. R. Shukla, S. Paudyal, and M. R. Almassalkhi, "Efficient distribution system optimal power flow with discrete control of load tap changers," IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 2970-2979, 2019.
Load tap changers (LTCs) are commonly used for voltage control in distribution systems. The mechanical relays on LTCs are controlled in discrete steps; hence, distribution optimal power flow (DOPF) formulations require LTCs to be modeled with integer variables. Integer variables are generally ignored or relaxed and rounded off to reduce the computational burden in DOPF models. However, in this paper, we highlight and overcome complex infeasibility issues caused by rounding methods. Moreover, recent advances in convex optimization have improved the computational tractability of the DOPF problem. In this paper, we develop and analyze numerical efficiency of different but exact formulations for incorporating LTCs as integer control assets in a relaxed second-order cone program (SOCP) version of the DOPF model. The resulting formulation becomes a mixed-integer SOCP (MISOCP), which is computationally tractable compared to mixed-integer non-linear program (MINLP). To recover the exact optimal solution in the proposed MISOCP-DOPF model, a McCormick relaxation is employed within a sequential bound-tightening algorithm. We show that solutions obtained from MISOCP-DOPF are always ac feasible. Thus, the MISOCP-DOPF yields optimal and realistic ac solutions, and is validated in large distribution feeders and is compared to MINLP counterpart.
Conference Proceedings
K. Desrochers, V. Hines, F. Wallace, J. Slinkman, A. Giroux, A. Khurram, M. Amini, M. Almassalkhi, and P.D.H. Hines, "Real-world, full-scale validation of power balancing services from packetized virtual batteries," EEE PES Conference on Innovative Smart Grid Technologies (ISGT), 18-21 Feb, 2019.
There is increasing consensus that flexible demand is critical to solve challenges associated with the rapid growth of variable renewable generation and aging transmission, distribution and generation infrastructure. Conventional direct load control programs are largely insufficient to address these issues. This paper presents results from validation tests of a new approach to demand side management, in which an aggregated fleet of devices is managed as a virtual battery, using principles that are found in communication networks: packetization and randomization. Validation results from a cyber-physical testbed with 5000 devices and a field-trial with 82 customer-owned water heaters show that the packetized virtual battery system can effectively solve a number of different problems. Customer satisfaction survey results illustrate that the system is able to maintain a high level of service quality.
M. Amini, A. Khurram, A. Klem, M. Almassalkhi, and P. Hines, "A Model-Predictive Control Method for Coordinating Virtual Power Plants and Packetized Resources, with Hardware-in-the-Loop Validation," IEEE PES General Meeting (PESGM), 4-8 Aug., 2019.
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, depend 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 resources.
N. Nazir and M. Almassalkhi, "Convex inner approximation of the feeder hosting capacity limits on dispatchable demand," IEEE Conference on Decision and Control (CDC), 11-13 Dec. 2019.
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.
Conference Proceedings
L. D. Espinosa, M. Almassalkhi, P. D. H. Hines, and J. Frolik, "System Properties of Packetized Energy Management for Aggregated Diverse Resources," Power Systems Computation Conference (PSCC), 11-15 June 2018.
This paper presents the systematic analysis of a population of diverse distributed energy resources (DERs) coordinated using a bottom-up approach known as packetized energy management (PEM). Particularly, for the aggregation of DERs modeled as a bilinear system, a simple discrete-time control law is provided that maximizes the number of accepted requests while tracking a regulation signal provided by a regional transmission operator. Moreover, the mechanics of energy packet completion rates under persistent inputs and the definition of a nominal quality of service (QoS) controller for PEM are provided. Finally, the observability of the PEM system is addressed including an implementation of the extended Kalman filter (EKF) for state estimation of the dynamic state of a diverse DER population.
[ abstract ] [ pdf ] [ link ]
M. Amini and M. Almassalkhi, "Trading off robustness and performance in receding horizon control with uncertain energy resources," Power Systems Computation Conference (PSCC), 11-15 June 2018.
Increased utilization of residential and small commercial distributed energy resources (DERs) has led DER aggregators to develop concepts such as the virtual power plants (VPP). VPPs aggregate the energy resources and dispatch them akin to a conventional power plant or grid-scale battery to provide flexibility to the system operator. Since the level of flexibility from aggregated DERs is uncertain and time varying, the VPPs' dispatch can be challenging. To improve the system operation, flexible VPPs can be formulated probabilistically and can be realized with chance-constrained model predictive control (CCMPC). This can be solved using scenario-based methodology, which provides a-priori probabilistic guarantees on constraint satisfaction. This paper focuses on understanding the robustness and performance trade offs in receding horizon control with uncertain energy resources. The CCMPC dispatches robustly the uncertain VPPs and conventional generators while taking into account economically optimal, secure reference trajectory for generating assets. Closed-loop performance is with respect to minimizing the deviation of conventional generators from their reference trajectory. To evaluate the trade off between robustness and system performance with uncertain energy resources, a simulation-based analysis is carried out on the modified IEEE 30-bus system.
[ abstract ] [ pdf ] [ link ]
N. Nazir and M. Almassalkhi, "Receding-horizon optimization of unbalanced distribution systems with time-scale separation for discrete and continuous control devices," Power Systems Computation Conference (PSCC), 11-15 June 2018.
This paper presents a method for the optimal control of discrete and continuous devices in an unbalanced three-phase distribution network with significant renewable generation. A hierarchical control scheme is presented where the discrete mechanical assets are dispatched at a slow time-scale as a mixed-integer program (MIP) and the continuous DERs are controlled at a fast time-scale as a convex program. The optimization programs are operated at two time scales as they manage controllable grid resources with different levels of responsiveness and flexibility. The MIP optimizes slow mechanical assets to position voltage robustly against uncertain net-load and a three-phase SOCP program is used to solve the fast loss-minimization optimization for the continuously operated DERs while providing corrective control against the intermittent and variable renewable net-load generation. The scheme is presented on the IEEE-13 node test feeder.
[ abstract ] [ pdf ] [ link ]
S. Brahma, M. Almassalkhi, and H. Ossareh, "A Stochastic Linearization Approach to Optimal Primary Control of Power Systems with Generator Saturation," IEEE Conference on Control Technology and Applications (CCTA), 21-24 Aug. 2018.
Quasilinear Control (QLC) is a set of methods used for analysis and design of systems with nonlinear actuators and sensors. It is based on the method of stochastic linearization, which replaces a nonlinearity by an equivalent gain and bias. Here, we leverage QLC to systematically design an optimal droop controller for primary frequency control of power systems with asymmetric generator saturation and renewable penetration. The droop parameters are found by solving an optimization problem wherein the cost function is a combination of the change in frequency and the actuator input. Simulation studies show that the combined output and control cost is improved compared to a baseline design, and that the systematic design process provides an appropriate response to any change in input or system parameters.
[ abstract ] [ pdf ] [ link ]
Book Chapter
Mads Almassalkhi, Luis Duffaut Espinosa, Paul D. H. Hines, Jeff Frolik, Sumit Paudyal, and Mahraz Amini, "Asynchronous Coordination of Distributed Energy Resources with Packetized Energy Management," 20th In: Meyn S., Samad T., Hiskens I., Stoustrup J. (eds) Energy Markets and Responsive Grids. The IMA Volumes in Mathematics and its Applications,, pp 333-361, vol 162. Springer, 2018.
To enable greater penetration of renewable energy, there is a need to move away from the traditional form of ensuring electric grid reliability through fast-ramping generators and instead consider an active role for flexible and controllable distributed energy resources (DERs), e.g., plug-in electric vehicles (PEVs), thermostatically controlled loads (TCLs), and energy storage systems (ESSs) at the consumer level. However, in order to facilitate consumer acceptance of this type of load coordination, DERs need to be managed in a way that avoids degrading the consumers' quality of service (QoS), autonomy, and privacy. This work leverages a probabilistic packetized approach to energy delivery that draws inspiration from random access, digital communications. Packetized energy management (PEM) is an asynchronous, bottom-up coordination scheme for DERs that both abides by the constraints of the transmission and distribution grids and does not require explicit knowledge of specific DER's local states or schedules. We present a novel macro-model that approximates the aggregate behavior of packetized DERs and is suitable for estimation and control of available flexible DERs to closely track a time-varying regulation signal. PEM is then implemented in a transmission/distribution system setting, validated with realistic numerical simulations, and compared against state-of-the-art load coordination schemes from industry.
Conference Proceedings
M. Almassalkhi, J. Frolik, and P. Hines, "Packetized energy management: asynchronous and anonymous coordination of thermostatically controlled loads," American Control Conference (ACC), May 24-26, 2017.
Because of their internal energy storage, electrically powered, distributed thermostatically controlled loads (TCLs) have the potential to be dynamically managed to match their aggregate load to the available supply. However, in order to facilitate consumer acceptance of this type of load management, TCLs need to be managed in a way that avoids degrading perceived quality of service (QoS), autonomy, and privacy. This paper presents a real-time, adaptable approach to managing TCLs that both meets the requirements of the grid and does not require explicit knowledge of a specific TCL's state. The method leverages a packetized, probabilistic approach to energy delivery that draws inspiration from digital communications. We demonstrate the packetized approach using a case-study of 1000 simulated water heaters and show that the method can closely track a time-varying reference signal without noticeably degrading the QoS. In addition, we illustrate how placing a simple ramp-rate limit on the aggregate response overcomes synchronization effects that arise under prolonged peak curtailment scenarios.
L. D. Espinosa, M. Almassalkhi, P. D. H. Hines, and J. Frolik, "Aggregate Modeling and Coordination of Diverse Energy Resources Under Packetized Energy Management," IEEE Conference on Decision and Control (CDC), Dec. 12-15, 2017.
Transmitting a large file across the internet requires breaking up the file into smaller packets of data. Packetized energy management (PEM) leverages similar concepts from communication theory to coordinate distributed energy resources by breaking up deferrable residential consumer demands into smaller fixed-duration/fixed-power packets of energy. Each individual load is managed by a probabilistic automaton that stochastically requests energy packets as a function of its local dynamic state (e.g., temperature or state-of-charge). Based on the aggregate request rate from packetized loads and grid conditions, the PEM coordinator will modulate the rate of accepting requests, which permits tight tracking of a reference (load-shaping or market) signal. This paper presents a state bin transition (macro) model suitable for characterizing a diverse population of electric water heaters (EWHs) and energy storage systems (ESSs) under a single PEM coordinator that is validated against an agent-based simulation of the diverse loads. The resulting model illustrates how diversity of packetized load types enhances the level of flexibility offered by the coordinator.
L. Duffaut Espinosa and Mads Almassalkhi and Paul Hines and S. Heydari and Jeff Frolik, "Towards a Macromodel for Packetized Energy Management of Resistive Water Heaters," IEEE Conference on Information Sciences and Systems (CISS) , Dec. 12-15, 2017.
This paper presents a state bin transition (macro)model for a large homogeneous population of thermostatically controlled loads (TCLs). The energy use of these TCLs is coordinated with a novel bottom-up asynchronous, anonymous, and randomizing control paradigm called Packetized Energy Management (PEM). A macro-model for a population of TCLs is developed and then augmented with a timer to capture the duration and consumption of energy packets and with exit-ON/OFF dynamics to ensure consumer quality of service. PEM permits a virtual power plant (VPP) operator to interact with TCLs through a packet request mechanism. The VPP regulates the proportion of accepted packet requests to allow tight tracking of balancing signals. The developed macro-model compares well with (agent-based) micro-simulations of TCLs under PEM and can be represented by a controlled Markov chain.
Conference Proceedings
Mads Almassalkhi, Yury Dvorkin, Jennifer Marley, Ricardo Fernandez-Blanco, Ian Hiskens, Daniel Kirschen, Jonathon Martin, Hrvoje Pandzic, Ting Qiu, Mushfiqur Sarker, Maria Vrakopoulou, Yishen Wang, Mengran Xue, "Incorporating Storage as a Flexible Transmission Asset in Power System Operation Procedure," Power Systems Computation Conference (PSCC) , June 20-24, 2016.
Managing uncertainty caused by the large-scale integration of wind power is a challenge in both the day-ahead planning and real-time operation of a power system. Increasing system flexibility is the key factor in preserving operational reliability. While distributed energy storage is a promising way to increase system flexibility, its benefits have to be optimally exploited to justify its high installation cost. Optimally operating distributed energy storage in an uncertain environment requires decisions on multiple time scales. Additionally, storage operation needs to be coordinated with the scheduling and dispatching of conventional generators. This paper proposes and demonstrates a three-level framework for coordinating day-ahead, near real-time and minute-by-minute control actions of conventional generating units and distributed energy storage. A case study illustrates the interactions between the three levels and the effectiveness of this approach both in terms of economics and operational reliability.
Mads Almassalkhi and Anna Towle, "Enabling city-scale multi-energy optimal dispatch with energy hubs," Power Systems Computation Conference (PSCC) , June 20-24, 2016.
This paper further extends the class of energy hubs that can be modeled with a concise system description and in a computationally efficient optimization framework to permit rapid analysis of multi-energy systems. The new hub models are then embedded in the multi-energy system analysis tool Hubert and solves the multi-period optimal dispatch (MPOD) problem for a broad class of energy hub systems. Specifically, this paper presents recent improvements developed for Hubert, including the use of piece-wise linear modeling to capture nonlinear converter efficiencies, limits on hub component outputs to reflect physical limits of converters, and hub emission limits. These developments enable appropriate modeling of multi-energy micro-grids and cities and are illustrated with a multi-energy model of The University of Vermont's campus under different capital planning scenarios and modeling assumptions. Interestingly, the shortcomings of using a traditional constant-efficiency hub converter model are illustrated with an energy storage sizing application for multi-energy systems. It is shown that the traditional hub models can significantly undersize energy storage as compared to the more accurate piece-wise linear energy hub formulation.
Mahraz Amini and M. Almassalkhi, "Investigating delays in frequency-dependent load control," IEEE Innovative Smart Grid Technologies (ISGT) Asia , Nov/Dec 28-01, 2016.
Increased penetration of renewables will require significant regulating reserves, so there is a need to re-think the traditional operating paradigm: supply follows demand. Recent work has expanded the role of flexible and controllable energy resources, such as energy storage and dispatchable demand, to regulate power imbalances and stabilize grid frequency. However, as shown in this paper, the large-scale deployment of dispatchable (i.e., controllable) loads needs to carefully consider the existing regulation schemes in power systems, i.e., generator droop control. That is, this paper illustrates with a standard linearized model, the complex nature of system-wide frequency stability from time-delays in actuation of dispatchable loads and the effect of different network topologies. Interestingly, we show that delay-induced instability can be stabilized by injecting additional delay into load controller.
Journal Papers
M. Almassalkhi and I. Hiskens, "Model-Predictive Cascade Mitigation in Electric Power Systems with Storage and Renewables Part I: Theory and implementation," IEEE Transactions on Power Systems, vol. 30, no. 1, pp. 67-77, 2015.
A novel model predictive control (MPC) scheme is developed for mitigating the effects of severe line-overload disturbances in electrical power systems. A piece-wise linear convex approximation of line losses is employed to model the effect of transmission line power flow on conductor temperatures. Control is achieved through a receding-horizon model predictive control (MPC) strategy which alleviates line temperature overloads and thereby prevents the propagation of outages. The MPC strategy adjusts line flows by rescheduling generation, energy storage and controllable load, while taking into account ramp-rate limits and network limitations. In Part II of this paper, the MPC strategy is illustrated through simulation of the IEEE RTS-96 network, augmented to incorporate energy storage and renewable generation.
M. Almassalkhi and I. Hiskens, "Model-Predictive Cascade Mitigation in Electric Power Systems With Storage and Renewables Part II: Case-Study," IEEE Transactions on Power Systems, vol. 30, no. 1, pp. 78 - 87, 2015.
The novel cascade-mitigation scheme developed in Part I of this paper is implemented within a receding-horizon model predictive control (MPC) scheme with a linear controller model. This present paper illustrates the MPC strategy with a case-study that is based on the IEEE RTS-96 network, though with energy storage and renewable generation added. It is shown that the MPC strategy alleviates temperature overloads on transmission lines by rescheduling generation, energy storage, and other network elements, while taking into account ramp-rate limits and network limitations. Resilient performance is achieved despite the use of a simplified linear controller model. The MPC scheme is compared against a base-case that seeks to emulate human operator behavior.
Book Chapter
M. Almassalkhi and I. Hiskens, "Impact of energy storage on cascade mitigation in multi-energy systems," in Energy Storage for Smart Grids: Planning and Operation for Renewable and Variable Energy Resources, P. Du and N. Lu, Eds., Pages 115-169, Elsevier, 2015.
The methods described in this chapter examine a bilevel cascade mitigation scheme that considers both the economic and security objectives in operation of the energy system. The rst level operates on a slow timescale (i.e., hourly) and determines a trajectory of optimal economical set points for generation, storage, load control, and wind curtailment. The second level operates in the background and responds to contingencies (i.e., line outages) on a much faster minute-by-minute timescale to ensure that the system is driven back to a secure and economically optimal operating regime and line overloads are alleviated. The eect of energy storage on the performance of cascade mitigation is investigated through storage scenarios within a multienergy\energy hub" framework. Finally, a temperature-based cascade mitigation is described for the electric bulk power system where the role of energy storage is highlighted with a case-study.
Conference Proceedings
M. Almassalkhi, B. Simon, and A. Gupta, "A Novel Online Energy Management Solution for Energy Plants," IEEE Power Systems Conference (PSC), March 11-14, 2014.
Energy plants represent large energy consumers with a wide array of energy needs, assets (e.g. boilers, chillers, storage, on-site generation), and constraints on operations. An innovative energy management system for energy plants is presented in this paper. Through predictive optimization of plant assets, energy analytics, pricing signals, and historical and real-time data, the online energy management system supplies energy plants with salient hourly, real-time recommendations and enables “what-if” analysis to achieve improved economic efficiency. Within a systems context, the paper draws upon ideas from power systems and highlights technical issues related to plant optimization. The paper also describes actual implementations of the energy management solution at two energy plants in the US, providing economic details and an analysis of the savings achieved.
Conference Proceedings
M. Almassalkhi and I. Hiskens, "Temperature-based Model-Predictive Cascade Mitigation in Electric Power Systems," IEEE Conference on Decision and Control (CDC), Dec. 10-13, 2013.
This paper proposes a novel model-predictive control scheme which combines both economic and security objectives to mitigate the effects of severe disturbances in electrical power systems. A linear convex relaxation of the AC power flow is employed to model transmission line losses and conductor temperatures. Then, a receding-horizon model predictive control (MPC) strategy is developed to alleviate line temperature overloads and prevent the propagation of outages. The MPC strategy seeks to alleviate temperature overloads by rescheduling generation, energy storage and other network elements, subject to ramp-rate limits and network limitations. The MPC strategy is illustrated with simulations of the IEEE RTS-96 network augmented with energy storage and renewable generation.
Ph.D. Dissertation
Mads R. Almassalkhi, "Optimization & Model-Predictive Control for Overload Mitigation in Resilient Power Systems," Ph.D. Dissertation, University of Michigan Department of Electrical Engineering and Computer Science, May 2013.
The National Academy of Engineering named the electric power grid the greatest engineering achievement of the 20th century. However, as recent large-scale power grid failures illustrate, the (electro-mechanical) electric grid is being operated closer and closer to its limits. Specifically, the electric grid of the 20th century is aging and congested. Due to the protracted and cost-intensive nature of upgrading energy infrastructures, major research initiatives are now underway to improve the utility of the existing infrastructure. One important topic is contingency management. Accordingly, this dissertation comprises of practical, yet rigorously justified, feedback control algorithms that are suitable for power system contingency management. The main goals of the algorithms are to prevent or mitigate overloads on network elements (e.g. lines and transformers).
In this dissertation, a coupling of energy infrastructures is examined as a method for improving system reliability and a simple cascade mitigation approach highlights the role of model-predictive control and energy storage in improving system response to severe disturbances (e.g. line outages). The ideas of balancing economic and safety criteria are developed and implemented with a receding-horizon model-predictive controller (RHMPC) for electric transmission systems with energy storage and renewables. The novel RHMPC scheme employs a lossy “DC” power flow model and is proven to alleviate conductor temperature overloads and returns the system to an economically optimal state. Finally, an incentive-based distributed predictive-control algorithm is developed to prevent overloads in the distribution network caused by overnight charging of PEVs. In addition, Matlab-based simulations are included to illustrate the performance and behavior of all proposed overload mitigation schemes. The automatic schemes presented in this dissertation are, essentially, “closing the loop” in contingency management, and will help bring the electric power grid into the 21st century.
Conference Proceedings
M. Almassalkhi and I. Hiskens, "Impact of Energy Storage on Cascade Mitigation in Multi-energy Systems," IEEE Power and Energy Society General Meeting, July 22-26, 2012.
In this paper, we establish energy-hub networks as multi-energy systems and present a relevant model-predictive cascade mitigation control (MPC) scheme within the framework of energy hubs. The performance of both open- and closed-loop mitigation schemes is investigated for various energy storage scenarios. The results are illustrated using a small 11-hub network and a larger 69-hub network and show that sizing and performance ratings of energy storage devices have significant effect on cascade mitigation control in multi-energy systems. Specifically, we conclude that increasing energy storage capacity and limiting the rate of energy delivery improves long-term performance of our closed-loop MPC scheme.
R. Hermans, M. Almassalkhi, and I. Hiskens, "Incentive-based Coordinated Charging Control of Plug-in Electric Vehicles at the Distribution-transformer Level," American Control Conference, June 27-29, 2012.
Distribution utilities are becoming increasingly aware that their networks may struggle to accommodate large numbers of plug-in electric vehicles (PEVs). In particular, uncoordinated overnight charging is expected to be problematic, as the corresponding aggregated power demand exceeds the capacity of most distribution substation transformers. In this paper, a dynamical model of PEVs served by a single temperature-constrained substation transformer is presented and a centralized scheduling scheme is formulated to coordinate charging of a heterogeneous PEV fleet. We employ the dual-ascent method to derive an iterative, incentive-based and non-centralized implementation of the PEV charging algorithm, which is optimal upon convergence. Then, the distributed open-loop problem is embedded in a predictive control scheme to introduce robustness against disturbances. Simulations of an overnight charging scenario illustrate the effectiveness of the so-obtained incentive-based coordinated PEV control scheme in terms of performance and enforcing the transformer's thermal constraint.
Conference Proceedings
M. Almassalkhi and I. Hiskens, "Cascade mitigation in energy hub networks," IEEE Conference on Decision and Control, Dec 12-15, 2011.
The paper establishes a formulation for energy hub networks that is consistent with mixed-integer quadratic programming problems. Line outages and cascading failures can be considered within this framework. Power flows across transmission lines and pipelines are compared with flow bounds, and tripped when violations occur. The outaging of lines is achieved using a mixed-integer disjunctive model. A model predictive control (MPC) strategy is developed to mitigate cascading failures, and prevent propagation of outages from one energy-carrier network to another. The MPC strategy seeks to alleviate overloads by adjusting generation and storage schedules, subject to ramp-rate limits and governor action. If overloads cannot be eliminated by rescheduling alone, MPC determines the minimum amount of load that must be shed to restore system integrity. The MPC strategy is illustrated using a small 12 hub network and a much larger network that includes 132 energy hubs.
M. Almassalkhi and I. Hisken, "Optimization framework for the analysis of large-scale networks of energy hubs," Power Systems Computation Conference, June 27-29, 2011.
Through a reformulation of energy hubs, this paper presents a novel format for describing general energy hub networks. This format underpins the development of tools for analyzing large-scale interconnected energy hub networks. The tools are developed in MATLAB and seamlessly interface with CPLEX optimization libraries to allow users to quickly implement and solve optimal scheduling problems. Our application takes a concise network description file as input, uses MATLAB to build the matrices for the entire system, and outputs the requested results from CPLEX. The work presented herein supports electrical and natural gas networks, wind generating capacity, district heat loads, and the main elements of energy hubs (converters and energy storage). Addition of other energy types and hub elements is straightforward.
