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At least 217 records · Page 12

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy: Preprint

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints

Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. Additionally, we then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗

Managing time-substitutable electricity usage using dynamic controls

A predictive-control approach allows an electricity provider to monitor and proactively manage peak and off-peak residential intra-day electricity usage in an emerging smart energy grid using time-dependent dynamic pricing incentives. The daily load is modeled as time-shifted, but cost-differentiated and substitutable, copies of the continuously-consumed electricity resource, and a consumer-choice prediction model is constructed to forecast the corresponding intra-day shares of total daily load according to this model. This is embedded within an optimization framework for managing the daily electricity usage. A series of transformations are employed, including the reformulation-linearization technique (RLT) to obtain a Mixed-Integer Programming (MIP) model representation of the resulting nonlinear optimization problem. In addition, various regulatory and pricing constraints are incorporated in conjunction with the specified profit and capacity utilization objectives.

Ghosh, Soumyadip↗

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗

Model-Based Framework to Optimize Charger Station Deployment for Battery Electric Vehicles

The development of battery electric vehicles (BEVs) is accelerating due to their environmental advantages over gasoline and diesel-powered vehicles, including a decrease in air pollution and an increase in energy efficiency. The deployment of charging infrastructure will need to increase to keep pace with demand, especially for large commercial vehicles for which few public chargers currently exist. In this paper, a new flexible framework is proposed for optimizing the placement of charging stations for BEVs, within which different physical models and optimization techniques may be used. Furthermore, a set of metrics is suggested to help enforce complex constraints and facilitate direct comparison between different optimization techniques. Unlike many existing charger placement techniques, the proposed method directly considers the historical driving patterns on a vehicle-by-vehicle basis, using transparent models to assess impacts of candidate charger placements, thus improving the explainability of the results. In the developed framework, modeled BEVs are first generated along the road network to mimic historical traffic data and are simulated traveling along a given route according to a simplified vehicle model. During the simulation, the charger placement problem is initially relaxed to allow vehicles to charge at any node along the road network, and vehicle states are tracked to assess areas of high charging demand. Charging stations are then placed based on the results of the relaxed simulation, and suggested placements are evaluated via road network simulation with fixed charger locations. This proposed framework is applied to a sample problem of placing charging stations along five major highway corridors for Class 8 over-the-road electric trucks. A novel mixed integer programming (MIP) formulation is proposed to optimize charger placements based upon the expected charging demand. Constraints were imposed on the final placement results to limit expected wait times at each station and ensure a minimum threshold of trucking routes are viable for BEVs. The results demonstrate the flexibility and potential effectiveness of the developed model-based framework for scalable charger station deployment.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Proactive Operations and Investment Planning via Stochastic Optimization to Enhance Power Systems’ Extreme Weather Resilience

We present scalable stochastic optimization approaches for improving power systems’ resilience to extreme weather events. We consider both proactive redispatch and transmission line hardening as alternatives for mitigating expected load shed due to extreme weather, resulting in large-scale stochastic linear programs (LPs) and mixed-integer linear programs (MILPs). We solve these stochastic optimization problems with progressive hedging (PH), a parallel, scenario-based decomposition algorithm. Our computational experiments indicate that our proposed method for enhancing power system resilience can provide high-quality solutions efficiently. With up to 128 scenarios on a 2,000-bus network, the operations (redispatch) and investment (hardening) resilience problems can be solved in approximately 6 min and 2 h of wall-clock time, respectively. Additionally, we solve the investment problems with up to 512 scenarios, demonstrating that the approach scales very well with the number of scenarios. Moreover, the method produces high quality solutions that result in statistically significant reductions in expected load shed. Our proposed approach can be augmented to incorporate a variety of other operational and investment resilience strategies, or a combination of such strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Less-Complex Method of Classifying MPSK

An alternative to an optimal method of automated classification of signals modulated with M-ary phase-shift-keying (M-ary PSK or MPSK) has been derived. The alternative method is approximate, but it offers nearly optimal performance and entails much less complexity, which translates to much less computation time. Modulation classification is becoming increasingly important in radio-communication systems that utilize multiple data modulation schemes and include software-defined or software-controlled receivers. Such a receiver may "know" little a priori about an incoming signal but may be required to correctly classify its data rate, modulation type, and forward error-correction code before properly configuring itself to acquire and track the symbol timing, carrier frequency, and phase, and ultimately produce decoded bits. Modulation classification has long been an important component of military interception of initially unknown radio signals transmitted by adversaries. Modulation classification may also be useful for enabling cellular telephones to automatically recognize different signal types and configure themselves accordingly. The concept of modulation classification as outlined in the preceding paragraph is quite general. However, at the present early stage of development, and for the purpose of describing the present alternative method, the term "modulation classification" or simply "classification" signifies, more specifically, a distinction between M-ary and M'-ary PSK, where M and M' represent two different integer multiples of 2. Both the prior optimal method and the present alternative method require the acquisition of magnitude and phase values of a number (N) of consecutive baseband samples of the incoming signal + noise. The prior optimal method is based on a maximum- likelihood (ML) classification rule that requires a calculation of likelihood functions for the M and M' hypotheses: Each likelihood function is an integral, over a full cycle of carrier phase, of a complicated sum of functions of the baseband sample values, the carrier phase, the carrier-signal and noise magnitudes, and M or M'. Then the likelihood ratio, defined as the ratio between the likelihood functions, is computed, leading to the choice of whichever hypothesis - M or M'- is more likely. In the alternative method, the integral in each likelihood function is approximated by a sum over values of the integrand sampled at a number, 1, of equally spaced values of carrier phase. Used in this way, 1 is a parameter that can be adjusted to trade computational complexity against the probability of misclassification. In the limit as 1 approaches infinity, one obtains the integral form of the likelihood function and thus recovers the ML classification. The present approximate method has been tested in comparison with the ML method by means of computational simulations. The results of the simulations have shown that the performance (as quantified by probability of misclassification) of the approximate method is nearly indistinguishable from that of the ML method (see figure).

Hamkins, Jon↗

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗

Guaranteeing a Physically Realizable Battery Dispatch Without Charge-Discharge Complementarity Constraints

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. In conclusion, simulation results further illustrate the effectiveness of this approach.

25 ENERGY STORAGE↗

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

Rios, Joseph Lucio↗

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stochastic pre-event preparation for enhancing resilience of distribution systems

Extreme weather events are the common causes for power supply interruptions and power outages in electrical distribution systems. Improving the distribution system and enhancing its resilience is becoming crucial due to the increased frequency of extreme weather events. Preparation and allocation of multiple flexible resources, such as mobile resources, fuel resources, and labor resources before extreme weather events can mitigate the effects of extreme weather events and enhance the resilience of power distribution systems. Here, in this paper, a two-stage stochastic mixed-integer linear programming (SMILP) is proposed to optimize the preparation and resource allocation process for upcoming extreme weather events, which leads to faster and more efficient post-event restoration. The objective of the proposed two-stage SMILP is to maximize the served load and minimize the operating cost of flexible resources. The first stage in the optimization problem selects the amounts and locations of different resources. The second stage considers the operational constraints of the distribution system and repair crew scheduling constraints. The proposed stochastic pre-event preparation model is solved by a scenario decomposition method, Progressive Hedging (PH), to ease the computational complexity introduced by a large number of scenarios. Furthermore, to show the impact of solar photovoltaic (PV) generation on system resilience, three types of PV systems are considered during a power outage and the resilience improvements with different PV penetration levels are compared. Numerical results from simulations on a large-scale (more than 10,000 nodes) distribution feeder have been used to validate the effectiveness and scalability of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Refueling infrastructure planning in intercity networks considering route choice and travel time delay for mixed fleet of electric and conventional vehicles

The range anxiety has been a major factor that affects the market acceptance of electric vehicles. Even with the recent development of battery technologies, a lack of charging stations and range anxiety are still significant concerns, specifically for intercity trips. This calls for more investments in building charging stations and advancing battery technologies to increase the market share of electric vehicles and improve sustainability. This study suggests a configuration for plug-in electric vehicle charging infrastructure to support long-distance intercity trips of electric vehicles at the network level. A model is proposed to minimize the total system cost including infrastructure investment (building charging stations/spots) and travel time delays (charging time, waiting time in the queue, and detour time to access charging stations). This study fills existing gaps in the literature by capturing realistic patterns of travel demand and considering flow-dependent charging delays at charging stations. Furthermore, the proposed model, which is formulated as a mixed-integer program with nonlinear constraints, solves the optimization problem at the network level. At the network level, impacts of charging station locations on the traffic assignment problem with a mixed fleet of electric and conventional vehicles need to be considered. To this end, a traffic assignment module is integrated with a simulated annealing algorithm. The numerical experiments show a satisfactory application of the model for a full-scale case study (intercity network in Michigan). The solution quality and efficiency of the proposed solution algorithm are evaluated against those of an enumeration approach for a small case study. The results suggest that even for the current market share and charging stations’ setting, a significant investment is needed to support intercity trips without range anxiety issues and with acceptable delays. Additionally, through sensitivity analyses, the required infrastructure and battery investments to support intercity trips with acceptable delays are established for hypothetical increased market shares and battery size in the future.

42 ENGINEERING↗

Theory and implementation of a fast algorithm linear equalizer

The theory and implementation of a multiplication-free linear mean-square error criterion equalizer for data transmission are considered. For many real-time signal processing situations, a large number of multiplications is objectionable. The linear estimation problem on a binary computer is considered where the estimation parameters are constrained to be powers of two and thus all multiplications are replaced by shifts. The optimal solution is obtained from an integer-programming-like problem except that the allowable discrete points are non-integers. The branch-and-bound algorithm is used to obtain the coefficients of the equalization TDL. Specific experimental performance results are given for an equalizer implemented with a 12 bit A/D device and a 8080 microprocessor.

Yan, T. Y.↗

Rolling Horizon with K-Position Search Method for Strategic Deconfliction of Package Delivery UAS

In this research, the strategic deconfliction of unmanned aircraft systems for an urban package delivery environment with two depots and multiple drop-off locations is studied. This research aims to formulate a mathematical model to compute both the departure sequence and scheduled time of departure for each unmanned aircraft system at a depot, considering temporal constraints at en-route crossing waypoints and depots for strategic deconfliction. However, the problem formulation results in an NP-hard mixed-integer nonlinear programming problem for the global optimal solution, so instead, a "rolling horizon with𝑘-position search"heuristic method is developed. The simulation studies show that an increase in the value of𝑘(the parameter used to determine the size of the local neighborhood) reduces the average ground delay at the cost of an increase in the computation time for a given problem size. The study also shows an order of magnitude increase in the maximum number of flights scheduled with the integration of rolling horizon (time decomposition) compared to those without the integration of rolling horizon in the heuristic algorithm for a given computation time cut off.

UTM↗