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A Distributionally Robust Resilience Enhancement Strategy for Distribution Networks Considering Decision-Dependent Contingencies
When performing the resilience enhancement for distribution networks, there are two obstacles to reliably model the uncertain contingencies: 1) decision-dependent uncertainty (DDU) due to various line hardening decisions, and 2) distributional ambiguity due to limited outage information during extreme weather events (EWEs). Here, to address these two challenges, this paper develops scenario-wise decision-dependent ambiguity sets (SWDD-ASs), where the DDU and distributional ambiguity inherent in EWE-induced contingencies are simultaneously captured for each possible EWE scenario. Then, a two-stage tri-level decision-dependent distributionally robust resilient enhancement (DD-DRRE) model is formulated, whose outputs include the optimal line hardening, distributed generation (DG) allocation, and proactive network reconfiguration strategy under the worst-case distributions in SWDD-ASs. Subsequently, the DD-DRRE model is equivalently recast to a mixed-integer linear programming (MILP)-based master problem and multiple scenario-wise subproblems, facilitating the adoption of a customized column-and-constraint generation (C&CG) algorithm. Finally, case studies demonstrate a remarkable improvement in the out-of-sample performance of our model, compared to its prevailing stochastic and robust counterparts. Moreover, the potential values of incorporating the ambiguity and distributional information are quantitatively estimated, providing a useful reference for planners with different budgets and risk-aversion levels.
Distributionally Robust Bilevel Optimization Model for Distribution Network With Demand Response Under Uncertain Renewables Using Wasserstein Metrics
Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.
PDPTW-DB: MILP-Based Offline Route Planning for PDPTW with Driver Breaks
The Pickup and Delivery Problem with Time Windows (PDPTW) involves optimizing routes for vehicles to meet pickup and delivery requests within specific time constraints, a challenge commonly faced in logistics and transportation. Microtransit, a flexible and demand-responsive service using smaller vehicles within defined zones, can be effectively modeled as a PDPTW. Yet, the need for driver breaks—a key human constraint—is frequently overlooked in PDPTW solutions, despite being necessary for regulatory compliance. This study presents a novel mixed-integer linear programming formulation for the Pickup and Delivery Problem with Time Windows and Driver Breaks (PDPTW-DB). To the best of our knowledge this formulation is the first to consider mandatory periodic driver breaks within optimized Microtransit routes. The proposed model incorporates regulatory compliant break scheduling directly within the vehicle routing optimization framework. By considering driver break requirements as an integral component of the optimization process, rather than as a post-processing step, the model enables the generation of routes that respect hours of service regulations while minimizing operational costs. This integrated approach facilitates the generation of schedules that are operationally efficient and prioritize driver welfare through driver breaks. We work with a public transit agency from the southern USA, and highlight the specific nuances of driver break optimization, and present a Pickup and Delivery Problem with Time Windows formulation for optimizing Microtransit operations and scheduling driver breaks. We validate our approach using real-world data from the transit agency. Our results validate our formulation in producing cost-effective, and regulation-compliant solutions.
District EnErgy Planner (DEEP) v2
The District EnErgy Planner - DEEP is an Mixed Integer Linear Programming (MILP) optimization software tool to solve district energy system, technology configuration, operation strategies, and energy retail business schemes. DEEP takes user input energy demand on heating, cooling and electricity demand. Energy loss through pipeline is calculated for heating and cooling from central plants. The optimal system configuration to minimize the district energy system life cycle cost or minimize CO2 emission is calculated based on energy balance equations and various constraints. The recent update on DEEP include a feature of waste heat utilization energy balance based optimization to take into accounts of different temperature bands of heat into account to maximize system efficiency. Another feature is to optimize district energy retail by provide optimal pricing scheme for heating, cooling and electricity to end users to incorporate district to grid demand response.
RODeO (Revenue Operation and Device Optimization Model) [SWR 20-67]
The Revenue, Operation, and Device Optimization (RODeO) model explores optimal system design and operation considering different levels of grid integration, equipment cost, operating limitations, financing, and credits and incentives. RODeO is a price-taker model formulated as a mixed-integer linear programming (MILP) model in the GAMS modeling platform. The objective is to maximizes the net revenue for a collection of equipment at a given site. The equipment includes generators (e.g., gas turbine, steam turbine, solar, wind, hydro, fuel cells, etc.), storage systems (batteries, pumped hydro, gas-fired compressed air energy storage, long-duration systems, hydrogen), and flexible loads (e.g., electric vehicles, electrolyzers, flexible building loads). The input data required by RODeO can be classified into three bins: 1) utility service data, which refers to retail utility rate information (meter cost, energy and demand charges), 2) electricity market data, which include energy and reserve prices, 3) other inputs, which refer to additional electrical demand, product output demand, technological assumptions, financial properties, and operational parameters.
Optimal Mitigation Planning For Adversarial Scenarios
We propose a generalized framework which performs an optimal partitioning of a limited budget into various organizational sectors in order to improve the cybersecurity of a smart device or component in the Cyber Physical Energy System (CPS). The framework identifies the adversarial threats and possible attack sequences which can be performed to exploit cyber vulnerabilities of the component. Thereafter, we formulate an Mixed Integer Linear Programming (MILP) optimization problem which aims to evaluate the optimal budget partitions in order to minimize the number of highly likely attack sequences. Though we provide results for using the framework in CPES, the proposed methodology can be extended for multiple domains with a set of known adversarial and mitigation actions.
North Carolina Water Utility Builds Resilience with Distributed Energy Resources
As the frequency and duration of grid outages increase, backup power systems are becoming more important for ensuring that critical infrastructure continues to provide essential services. Most facilities rely on diesel generators, which may be ineffective during long outages owing to limited fuel supplies and high generator failure rates. Distributed energy resources such as solar, storage, and combined-heat-and-power systems, coupled with on-site biofuel production, offer an alternative source of on-site generation that can provide both cost savings and resilience (i.e., the ability to respond to catastrophic events with longer-term consequences). A mixed-integer linear program minimizes costs and maximizes resilience at a wastewater treatment plant in Wilmington, North Carolina. We find that the plant can reduce life-cycle energy costs by 3.1% through the installation of a hybrid combined-heat-and-power, photovoltaic, and storage system. When paired with existing diesel generators, this system can sustain full load for seven days while saving $664,000 over 25 years and reducing diesel fuel use by 48% compared with the diesel-only solution. This analysis informed a decision by the Cape Fear Public Utility Authority to allocate funds for the implementation of a combined-heat-and-power system at the wastewater treatment plant in fiscal year 2023. Finally, the benefits of deploying hybrid combined-heat-and-power technologies and the utilization of on-site biofuel production extend, on a national scale, to thousands of wastewater treatment facilities and other types of critical infrastructure.
Machine-learning-aided cognitive reconfiguration for flexible-bandwidth HPC and data center networks [Invited]
This paper proposes a machine-learning (ML)-aided cognitive approach for effective bandwidth reconfiguration in optically interconnected datacenter/high-performance computing (HPC) systems. The proposed approach relies on a Hyper-X-like architecture augmented with flexible-bandwidth photonic interconnections at large scales using a hierarchical intra/inter-POD photonic switching layout. We first formulate the problem of the connectivity graph and routing scheme optimization as a mixed-integer linear programming model. A two-phase heuristic algorithm and a joint optimization approach are devised to solve the problem with low time complexity. Then, we propose an ML-based end-to-end performance estimator design to assist the network control plane with intelligent decision making for bandwidth reconfiguration. Numerical simulations using traffic distribution profiles extracted from HPC applications traces as well as random traffic matrices verify the accuracy performance of the ML design estimator ( < <#comment/> 9 % <#comment/> error) and demonstrate up to 5 × <#comment/> throughput gain from the proposed approach compared with the baseline Hyper-X network using fixed all-to-all intra/inter-portable data center interconnects.
AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Final Report)
The AGGREGATE project team successfully developed and validated various modules for outage management. Brief summaries of each module are provided to showcase their strength for outage management and restoration for a distribution system with a high penetration of connected distribution energy resources (DERs). In recent years, inverter-based DERs have been widely deployed in distribution system. A most of behind-the-meter (BTM) solar power generation is not visible to the utility. The data-driven DER and load estimation modules are using machine learning (ML) and artificial intelligence (AI) to manage this issue, which provides an opportunity for distribution system operators (DSOs) to operate systems and make decisions in real-time for a distribution system with a high penetration of DERs deployed. Also, the estimated DER and true load can be further leveraged in network aggregation and cold-load pick up estimation for reducing the computing complexity and providing for fast restoration. After load demand and DER power generations have been estimated, the information will support topology and state estimation (SE). The topology estimation module demonstrated the viability of mixed integer linear programming (MILP) formulation to estimate the most likely operational radial topology and outage sections using power flow measurements, historical/estimated load and DERs data and smart meter ping measurements. Formulation includes continuous (power flow, load and DERs data) and binary measurements (smart meter ping measurements) in a single formulation. Errors in continuous data and binary data are modeled as normal distribution and Bernoulli distribution, respectively. In the future distribution grid, the power injection from controllable DERs will be essential for efficient and resilient grid operation. However, determining the optimal DER injections and restoration actions is dependent on knowledge of the system states. State estimation (SE), already the cornerstone of transmission energy management systems, will become commonplace in distribution management systems as more measurements become available from deployment of automated metering infrastructure (AMI). Observability analysis is the first step in SE, as it determines the sufficiency of the available measurements for accurately estimating the current system states. A new type of pseudo-measurement called a Correlational Measurement (CM) is introduced in this module, to enhance the observability of the system to enable more accurate SE. CMs encapsulate knowledge of correlation between demand patterns for similar classes of loads as well as injection patterns for same-technology renewable DERs. During grid contingency scenarios, DERs have been traditionally disconnected, without any fault ride-through capabilities. However, with new regulations and better technology, it is feasible for these resources to contribute to the grid’s restoration after an adverse event and hence enhance resilience. The controllability module proposes a two-step restoration scheme for the power system restoration process by leveraging additional degrees of freedom in power electronics interfaced DERs for mitigating voltage problems. In a resilience mode without the utility system, the distribution grid relies on DERs to serve critical load. In such a severe event with multiple faults on the distribution feeders, actuation of various protective devices (PDs) divides the distribution system into electrical islands. The undetected actuated PDs due to fault current contributions from DERs can delay the restoration process, thereby reducing the system resilience. The Advanced Outage Management (AOM) and the Advanced Feeder Restoration (AFR) modules developed in this project provide improved system resilience with multiple DERs. AOM identifies the faulted sections and actuated PDs in a distribution system with DERs by incorporating smart meter data. The most credible outage scenario including fault locations, PD actuations, and fault indicator (FI) failures is identified by a set of binary integer linear programming incorporating hypotheses. The AFR module serves to restore a distribution system with available energy resources taking into consideration the availability of utility sources and DERs. By partitioning the system into islands, critical load will be served with the available generation resources within islands based on the solution of a MILP. When the utility systems become available, the optimal path will be determined by a spanning tree search algorithm that reconnects these islands back to substations and restores the remaining load. The transmission and distribution (T&D) co-simulation module was used to validate the effect of a control action performed on the distribution side assets as it propagates to the transmission side. This ensures that the control action performed results in a feasible operating point on both the transmission and the distribution system. In addition to validation, the team used the T&D co-simulation module to demonstrate how distribution system assets can be used to mitigate issues on the transmission system. Specifically, the team demonstrated that appropriate switching operations on the distribution side can alleviate the line overload condition on the transmission side without causing new operational constraint violations.
Models and Strategies for Optimal Demand Side Management in the Chemical Industries
Deregulation and the increase of renewable electricity generation from wind and solar photovoltaics have transformed the U.S. electricity market. Economic and environmental benefits notwithstanding, the presence of renewables has increased variability and uncertainty on the supply side of the grid. Managing demand, rather than generation – a strategy referred to as “demand response (DR)” – is an attractive approach for mitigating this imbalance. DR efforts aim to reduce electricity usage during peak demand times, lessening stress on the grid. Industrial users are particularly attractive entities for DR participation since they present large, localized loads that can provide significant relief on grid demand and –unlike other large loads, such as buildings – are minimally dependent on human needs and preferences. In this project, we accomplished three main objectives. (1) We developed data-driven low-order DR scheduling-relevant dynamic models of chemical processes. Concurrently, we studied the formulation and solution of the associated optimal DR production scheduling problems. (a) A prototype air separation unit (ASU) model was used to generate simulated operating data for initial modeling efforts, which enabled the later use of industrial data for data-driven modeling. (b) We utilized Hammerstein-Wiener (HW) and Finite Step Response (FSR) models to represent nonlinear plant dynamics. (c) The HW models were linearized using exact linearization so they could potentially be embedded in power system models, which are formulated as mixed integer linear programs (MILPs). (d) We solved DR optimization problems under uncertainty and found that even naïve predictions of electricity price and product demand led to significant cost savings benefits. (2) Our DR scheduling optimization problem formulations are amenable to real-time solution. (a) We utilized Lagrangian Relaxation (LR) to efficiently solve the optimization problem by decoupling subproblems linked by complicating constraints. (b) We have achieved computation times for the 3-day DR scheduling problem of an ASU as low as 1.88 minutes. (3) Our representations of the DR behavior of chemical process as grid-level batteries were embedded in power system models. (a) For a small-scale grid, we found that incorporating the dynamics of the chemical plant in the optimal power flow calculations resulted in better resource management leading to up to 15% and 46% cost reduction for the grid and chemical plant operations, respectively, during periods of power line congestion. We have published several works dedicated to modeling and solving DR optimization problems from the user side. These were published in top peer-reviewed journals and are summarized in this report. The most recent work (and papers in preparation) considers DR scheduling from the grid side. Future efforts will consider networked plants (e.g., air separation units operating on a common pipeline) for DR participation, which is expected to amplify the capabilities of industrial DR participants to perform load-shifting. Our consideration of uncertainty in DR has inspired future directions in this area as well: we plan to develop multistage methods to fully account for the effects of uncertainty in DR scheduling.
Integrating Concentrating Solar Power Technologies into the Hybrid Optimization and Performance Platform (HOPP)
As the world increases renewable energy deployment, there is an increasing interest in hybridizing various generation and storage technologies to maximize net benefit to the developer and/or off-taker. A particularly interesting combination of renewable technologies is concentrating solar power (CSP) with thermal energy storage (TES), photovoltaics (PV), and electrochemical battery energy storage (BESS). Due to the system complexity of CSP technology, it is difficult to evaluate the technological and financial performance of a CSP-PV hybrid system without detailed modeling of annual operations. To address this challenge, we have developed a modeling framework for evaluating the performance and financial viability of CSP systems hybridized with PV and battery technologies. This modeling effort incorporates CSP tower and trough systems into an existing modeling tool recently developed by NREL referred to as the Hybrid Optimization and Performance Platform (HOPP). This report outlines the modeling methodology as well as preliminary results from example case studies conducted using the model. The methodology describes: (i) the integration of CSP tower and troughs into HOPP using python interfaces to access System Advisor Model (SAM) underlining technology models, (ii) the mathematical formulation of the mixed integer linear program dispatch optimization model which optimizes operations of storage asset to either maximize system revenue or minimize operating cost while load following, (iii) the design analysis methods implemented within HOPP, and (iv) simulation clustering for the purposes of reducing computational expense. We exercise the model using a case study of a future scenario where we assume (i) CSP and PV technologies achieve the 2030 cost targets provided by the Solar Energy Technologies Office (SETO), (ii) battery costs reduce to the 2030 mid cost projection presented by NREL. Lastly, (iii) electricity prices for southern California in 2030 are provided by NREL's Cambium database, and (iv) a capacity payment of $150/kW-yr based on the system capacity factor during the to 100 net-load hours.
New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms
While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.
Substation-Level Grid Topology Optimization Using Bus Splitting
Operations of substation circuit breakers are important for maintenance needs and topology reconfiguration in power systems. Bus splitting is one type of topology change where the two bus bars at a substation can become electrically disconnected under certain actions of circuit breakers. Because these events involve detailed substation modeling, they are typically not considered in routine power system operation and control. In this paper, an improved substation-level topology optimization framework is developed by expanding traditional line switching decisions by breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bilinear terms in the resultant optimization problem to linear inequality constraints. Thus, a tractable mixed-integer linear program reformulation is attained that allows for efficient solutions in real-time operations. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the computational performance and economic benefits of the proposed topology optimization approach.
Improved Air-Conditioning Demand Response of Connected Communities over Individually Optimized Buildings
Connected communities potentially offer much greater demand response capabilities over singular building energy management systems (BEMS) through an increase of connectivity. The potential increase in benefits from this next step in connectivity is still under investigation, especially when applied to existing buildings. This work utilizes EnergyPlus simulation results on eight different commercial prototype buildings to estimate the potential savings on peak demand and energy costs using a mixed-integer linear programming model. This model is used in two cases: a fully connected community and eight separate buildings with BEMS. The connected community is optimized using all zones as variables, while the individual buildings are optimized separately and then aggregated. These optimization problems are run for a range of individual zone flexibility values. The results indicate that a connected community offered 60.0% and 24.8% more peak demand savings for low and high flexibility scenarios, relative to individually optimized buildings. Energy cost optimization results show only marginally better savings of 2.9% and 6.1% for low and high flexibility, respectively.
Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage
Variable renewable energy availability has increased the volatility in energy prices in most markets. Nuclear power plants, with a large ratio of capital to variable costs, have historically operated as base load energy suppliers but the need for more flexible operation is increasing. We simulate the techno-economic performance of a 950 MWt nuclear power plant, based on the Westinghouse lead-cooled fast reactor, coupled with molten salt thermal storage as a method for flexible energy dispatch. We use the System Advisor Model to model the nuclear reactor thermal power input and power cycle operating modes. We combine this robust engineering model with a mixed-integer linear program model for optimized dispatch scheduling. We then simulate the coupled nuclear and thermal storage system under different market scenarios with varying price volatility. We find that the coupled plant outperforms the base plant under markets where energy price peaks fluctuate by a factor of two or more about the mean price. We show that a calculated power purchase agreement price for the plant improves by up to 10% when operating under California energy market conditions. Sensitivity analysis on the thermal storage cost shows that the optimal design remains unchanged even when doubling costs.
Series FACTS Devices for Increasing Resiliency in Severe Weather Conditions
Severe weather conditions are low-probability, high-impact events that affect grid operations. The majority of power outages are caused by severe weather conditions. Grid resiliency to weather events can be enhanced by decreasing the reliance on its affected sections. One way to do this is to reduce the power flow through lines vulnerable to severe weather. If a line is disconnected, its initial power flow is distributed through the neighbor lines, which may cause congestion in the grid. FACTS devices can be used to control the power flow of lines that have a higher chance of power outages. Most previous works do not consider weather events in power flow control. In this work, a linearized optimal power flow (OPF)–based algorithm is developed to minimize the real power flow of vulnerable lines considering the thermal limits of lines to prevent infeasible solutions; the simulation is fast, making it suitable for large-scale systems. The proposed optimization problem is presented as a mixed-integer linear program (MILP), making it capable of using short-term load forecasting due to its high solution speed. The proposed optimization problem considers multiple lines with different outage probabilities and the uncertainties of the weather forecast. Moreover, it estimates the power reduction in vulnerable lines due to changes in the series FACTS devices. The performance of the proposed optimization problem is tested on IEEE 14-, 30-, and 118-bus systems for several scenarios. The results are validated with the AC power flow results from MATPOWER.