Critical Peak Pricing Research Articles

Economic management of microgrid using flexible non-linear load models based on price-based demand response strategies

Demand response programmes are used in microgrid research without considering the different price elasticity of distinct load types. To evaluate the impacts of demand response efforts, it is necessary to utilise a mix of nonlinear and linear models for creating load-responsive models in a manner that is realistic. With an aim to address this gap in research, an exhaustive technoeconomic investigation is being conducted to determine the effect that price-dependent demand response programmes have on the optimal scheduling of microgrids when linear and nonlinear load models are present. The flexible elasticity model is used to accurately describe how customers respond to changes in electricity price. Four load models, including exponential, hyperbolic, linear, and logarithmic, were constructed for each demand response programme. Rime is a newly created physics-based algorithm that has been deployed to handle the anticipated energy management problem that the microgrid may be experiencing. To evaluate the efficacy of the proposed strategy, four case studies based on grid price and participation scenarios have been carried out. The findings from our research are notably impactful, revealing an 8 % reduction in energy consumption when applying the critical peak price (CPP) load demand model. This efficiency gain translates into a notable enhancement in the load factor, increasing from 0.83 to 0.86, and a significant drop in overall generation costs from $25,463 to $21,823 under optimal conditions. These results vividly illustrate the practical value of our proposed research work, showcasing their ability to generate substantial energy savings and cost efficiencies in microgrid operations. The improvements in operational efficiency and cost-effectiveness underscore the potential of these models to refine microgrid management, delivering both economic and performance gains that are crucial for advancing sustainable energy solutions.

Optimal Sizing and Economic Analysis of Community Battery Systems Considering Sensitivity and Uncertainty Factors

Efficient sizing and economic analysis of community battery systems is crucial for enhancing energy efficiency and sustainability in rooftop PV panel-rich communities. This paper proposes a comprehensive model that integrates key technical and economic factors to optimize the size and operation of the prosumer-owned battery, maximizing the financial returns over the life span of the battery. Sensitivity and uncertainty analyses were also conducted on a number of factors that are constantly changing over the years such as per-unit cost of the battery and interest rate. Monte Carlo simulations were utilized to replicate the unpredictable PV generations and the volatility of house load demands. The developed model is evaluated under three scenarios: a shared community battery for all houses, individual batteries for each house, and a combined system with an additional large load. Particle Swarm Optimization (PSO) is utilized to maximize the formulated objective function subject to the considered constraints. The findings indicate that integrating community batteries offered a substantial economic advantage compared to individual home batteries. The additional revenue stream of incorporating larger consumers looking to reduce their carbon footprint (e.g., commercial) returned a further augmented net present value (NPV). The influence of different tariff structures was also assessed and it was found that critical peak pricing (CPP) was the most prolific. The outcomes offer valuable insights for policymakers and stakeholders in the energy sector to facilitate a more sustainable future.

Economic Scheduling Strategy for Multi-Energy-Integrated Highway Service Centers Considering Carbon Trading and Critical Peak Pricing Mechanism

This study proposes an optimized economic scheduling strategy for multi-energy-integrated highway service centers (MEIHSCs) within a 24 h operational timeframe. With the imperative of carbon peaking and carbon neutrality, highway areas are increasingly incorporating renewable energy systems, such as photovoltaic arrays, to capitalize on abundant resources along highways. Considering the diverse load demands of new energy vehicles and the mismatch between energy supply and demand on the highway, MEIHSCs must adapt to these trends by establishing integrated networks for electricity, natural gas, and hydrogen refueling. However, there is a lack of coordination between equipment switching and the phases of low electricity prices and peak renewable energy periods. To address this challenge and improve economic efficiency, this study proposes an economic dispatch strategy that combines economic incentives based on carbon trading and critical peak pricing mechanisms. This strategy aims to maximize economic benefits while fully meeting the load demands of new energy vehicles. Case studies indicate that operating costs are reduced by 28.04% compared to strategies without new energy installations, and by 47.85% compared to strategies without optimization. The results demonstrate that this integrated and optimized strategy significantly reduces energy costs and enhances economic benefits in highway service centers.

On grid-serving grid tariff design in Local Energy Markets

Local Energy Markets (LEMs) are virtual market places that allow for energy sharing of prosumers in proximity to each other. In LEMs, participants’ offers and bids are coordinated by a pricing mechanism, which sets price signals for generation and loads. This impacts distribution grid utilization. Dynamic grid fees could be used by the distribution system operator to add price signals for market participants that are beneficial to the distribution grid operation. To develop such a grid-serving LEM design, we propose a framework for the design of alternative grid tariffs as a trade-off between cost-reflective and cost-recovering grid tariffs. We analyse three alternative grid tariff components in the context of LEMs: time-varying energy fees, critical peak pricing (CPP) and capacity fees for power not traded on the LEM. A case study on a synthetically generated grid region shows that while the alternative tariff components can reduce the aggregated peak load of the region by up to 31% with the CPP, the fees can also lead to increased line utilization. Also, while total local added value can be increased with all alternative grid tariffs, especially capacity-based grid tariffs are connected to a strong redistribution of grid costs from flexible to inflexible prosumers.

The greenhouse gas reduction effect of critical peak pricing for industrial electricity: Evidence from 285 Chinese cities, 2003–2019

This paper assesses the impact of the Pilot of Critical Peak Pricing for Industrial Electricity (PCPPIE) on industrial Greenhouse Gas (GHG) emissions by employing the Difference-in-Differences (DID) methodology. It is found that the cities participating in PCPPIE underwent a significant 11.3% reduction in the GHGs emitted per industrial enterprise. These findings remain robust across various methodologies, including staggered DID estimators, propensity score matching, instrumental variable methods, and spatial econometric regression. The generalized DID analysis shows that a higher critical peak price corresponds to a more substantial decrease in GHG emissions. PCPPIE achieves weaker GHG reduction in higher-administrative level cities but stronger in those with higher industrial share, and the effectiveness of PCPPIE is compromised by cross-regional electricity imports. PCPPIE reduces GHG emission intensity of the power industry and contributes to additional reductions in GHG emissions from other sources by fostering green technological innovation and facilitating energy substitution. The practical significance of this paper is to reveal a richer dynamic mechanism for China's green and sustainable development, indicating that critical peak pricing is a power pricing strategy worthy of strengthening and optimization in the process of China's carbon peak and carbon neutrality.

Electricity Retail Rate Design in a Decarbonizing Economy: An Analysis of Time-of-use and Critical Peak Pricing

Currently, the main component of most U.S. consumers’ electricity bills is based on a constant price per kWh consumed. As intermittent renewable resources and flexible loads that can be shifted within days (such as electric vehicle charging) gain prominence in the electricity system, the efficiency gains to be realized from basing bills instead on wholesale spot prices increase. There is little political support for this change, however. We focus on second-best alternatives: time-of-use (TOU) rates and critical peak pricing (CPP). We introduce alternative assessment criteria that focus on intra-day load shifting. Using historical data, we find that TOU rates can reasonably replicate the intra-day load-shifting incentives provided under spot pricing. Thus, TOU rates, especially when complemented with CPP involving load control during infrequent scarcity price events, can be considerably more socially valuable than previously estimated.

Balancing urban energy considering economic growth and environmental sustainability through integration of renewable energy

This paper delves into the critical intersection of urban energy management, economic growth, and environmental sustainability through the integration of renewable energy sources in smart urban homes. The escalating demand for power has created an energy scarcity, necessitating innovative solutions to balance supply and consumption. In this context, the transition from traditional electric grids to smart grids (SG) is gaining prominence. To harness the potential of smart urban homes, particularly in the context of renewable energy, solar panels on rooftops have become indispensable. Smart grid technologies enable users to engage in demand response strategies, offering incentives and financial benefits for flexible device usage. This study introduces a novel optimization algorithm, the Polar Bear Optimization Algorithm (PBOA), designed to schedule domestic device usage patterns efficiently. To evaluate the effectiveness of PBOA, this paper conducts comparative analyses with other optimization algorithms such as Differential Evolution (DE) and Particle Swarm Optimization Algorithm (PSOA). Energy cost metrics, including Critical Peak Price (CPP) and Real-Time Price (RTP), are employed to assess cost reduction strategies. The primary focus of this study is to minimize energy costs and reduce the Peak to Average Ratio (PAR), thereby promoting economic growth and environmental sustainability in smart urban homes. It should be noted that neural network (NN) machine learning technique has been used for forecasting the weather and renewable energies output power.

Field Experimental Evidence on the Effect of Pricing on Residential Electricity Conservation

This study examines how electric utilities and regulators can encourage residential consumers to conserve electricity during the hottest summer days and shift electricity load from the day to off-peak, nighttime hours. We analyze a two-year field experiment involving 280 Texas households that explores approaches to conservation and load-shifting to enable emission reductions and reduce generation costs. Our critical peak pricing intervention reduces electricity consumption by 14% on the peak hours of the hottest days, leading to greenhouse gas emission reductions of about 16%. A key contribution of this study is the use of high-frequency appliance-level data. We show that 74% of the critical peak response is from reducing air conditioning. In a complementary nighttime pilot program, consumers respond strongly to lower prices by programming the timing of electric vehicle charging. Our work highlights how automation can influence the consumer tradeoffs relating to effort costs, discomfort, monetary incentives, and warm glow. This paper was accepted by Rajesh Chandy, Special Section of Management Science on Business and Climate Change. Supplemental Material: The data and online appendices are available at https://doi.org/10.1287/mnsc.2020.02074 .

Optimization-based optimal energy management system for smart home in smart grid

The introduction of advanced technologies has led to an unprecedented rise in automated appliances in the housing sector. Building new administrative structures to satisfy electrical needs has grown more crucial to ensure the safety of residential devices. One of the approaches to achieve this is Demand Side Management (DSM), a key component of both micro-grid and Smart Grid technology. DSM can be accomplished by carefully controlling requirements while upholding the trust of clients. Most of the DS Management which has been covered in the research is aimed at helping households manage their power plan. The innovative HBA+DMO technique inherits Honey Badger Optimization (HBA) and Dwarf Mongoose Optimization (DMO) for executing the DSM program. The groundwork for the proposed framework implemented in this investigation is provided by the Critical-Peak-Price (CPP) and Real-Time-Price (RTP) payment processes. Two operational instances (60 min and 12 min) are being taken into consideration to evaluate client requirements and behavior over the suggested strategy. In accordance with the results from simulations, the suggested strategy arranges the devices in the best possible way, leading to fewer energy expenses while maintaining user comfort (UC). Customers sometimes pay a premium as a result of gadget waiting periods in order to gain the most comfort. As equipment is turned on in response to user comfort, the amount of time spent waiting during an unscheduled situation is close to zero. Tools for lowering energy expenditures and consumption for buildings, communities, or enterprises are frequently provided through energy management software. The three main uses of the energy data that EMS collects are reporting, monitoring, and engagement. The computational time of the proposed approach is (∼213.42). Future testing involving different conditions and control methods for study into HRES microgrid infrastructure may be done on the medium of the experiment bench.

SELECTION OF ELECTRICITY TARIFF DESIGNS FOR DISTRIBUTION NETWORKS USING ANALYTIC NETWORK PROCESS

In electricity distribution networks, tariff designs set the interface between the users and network operators or service providers. Tariff designs provide the reference base for tariff schedules covering multiple categories of network users. It is widely accepted that electric utility rate designs have subjective and objective multi-criteria dependencies. Based on utility rate making literature, subcriteria for selection of tariff designs can be listed under the economic, technological, and social criteria. In this study, two widely used electricity tariff designs, volumetric or energy charges and capacity or demand charges are considered. In addition, real-time pricing and a hybrid tariff design that combines energy and capacity charges with critical peak pricing are also included in the comparison. Performance evaluation of these tariff designs on quantifiable parameters relating to economic aspects is carried out using the Tariff Design and Analysis Tool. Literature on electricity tariff designs and pricing provides the metadata on performance relating to qualitative criteria covering mainly the technological and social aspects. A synthesis of the quantitative and qualitative criteria evaluations was done by developing a Benefits-Opportunities-Costs-Risks (BOCR) model in the Analytic Network Process (ANP), a Multi-Criteria Decision Making methodology. A quantitative assessment of inconsistencies in evaluation and synthesis of the model using a consistency index shows that the developed ANP framework for tariff design selection is a valid approach. The developed BOCR model in ANP shows that the hybrid tariff design of Energy and Capacity charges with Coincident Peak Pricing is the best alternative. A sensitivity analysis shows that the ranking is variable when the BOCR priorities change.

Integrated Multi-Criteria Planning for Resilient Renewable Energy-Based Microgrid Considering Advanced Demand Response and Uncertainty

Weather-driven uncertainties and other extreme events, particularly with the increasing reliance on variable renewable energy (VRE), have made achieving a reliable microgrid operation increasingly challenging. This research proposes a comprehensive and integrated planning strategy for capacity sizing and operational planning, incorporating forecasting and demand response program (DRP) strategies to address microgrid operation under various conditions, accounting for uncertainties. The microgrid includes photovoltaic systems, wind turbines, and battery energy storage. Uncertainties in VREs and load fluctuations are modeled using Monte Carlo simulations (MCSs), while forecasting is based on the long short-term memory (LSTM) model. To determine the best techno-economic planning approach, six cases are formulated and solved using a multi-objective particle swarm optimization with multi-criteria ranking for these three objectives: total lifecycle costs (TLCC), reliability criteria, and surplus VRE curtailment. Shortage/surplus adaptive pricing combined with variable peak critical peak pricing (SSAP VP-CPP) DRP is devised and compared with a time-of-use VP-CPP DRP in mitigating the impacts of both critical and non-critical events in the system. The simulation results show that the integrated planning, which combines LSTM forecasting with DRP strategies, achieved about 7% and 5% TLCC reductions for deterministic and stochastic approaches, respectively. The approach allowed optimal sizing and operation planning, improving the utilization of VREs and effectively managing uncertainty, resulting in the most cost-effective and robust VRE-based microgrid with enhanced resilience and reliability.

Analysis of critical peak electricity price optimization model considering coal consumption rate of power generation side.

As a flexible electricity pricing mechanism, critical peak pricing (CPP) is one of the important means of demand response under the electricity market. The existing CPP research does not take into account the carbon emission problem of units and weakens the difference between the use of terminal loads on critical peak days and non-critical peak days in the establishment of electricity price model, so this paper studies the feedback mechanism of CPP on coal consumption of power generation side units and proposes a dynamic CPP mechanism that takes into account terminal consumption satisfaction and coal consumption of power generation side units. Firstly, the influence mechanism of CPP on the power generation side is studied. Secondly, the consumer psychology theory is used to construct a user demand response model under critical peak days and non-critical peak days. Then, based on the difference in load usage of end users on critical peak days and non-critical peak days, a multi-objective CPP optimization model that considers the benefits of coal consumption and end user electricity expenditure on the power generation side is constructed. Finally, three scenarios were established to analyze the sensitivity of the user demand response model parameters, terminal satisfaction constraints, prices, and rate restrictions on CPP pricing, load improvement, and unit coal consumption reduction and verify the model's effectiveness. The results show that the proposed CPP optimization model has a significant effect on load improvement and carbon emission reduction; the user response gradient, terminal satisfaction, prices, and rate restrictions have a greater influence on the model optimization results, while the threshold and saturation values have little influence on the model optimization results.

Research on fair residential critical peak price: Based on a price penalty mechanism for high-electricity consumers

We construct a fair residential critical-peak price (CPP) optimization model based on a penalty mechanism to address the peaking pressure on the grid and the cost of new energy abandonment caused by the yearly increase in residential electricity load and the significant increase in new energy capacity. According to the electricity consumption habits of different residential consumers, we use the K-means clustering method to identify and classify high-electricity consumers (HECs), low-electricity consumers (LECs), and normal-electricity consumers (NECs) during the critical peak and valley load hours respectively, and design a penalty mechanism of electricity price for HECs (PMEP-H) that penalizes HECs during the critical peak load hours, and compensates the total penalty amount to LECs during the critical peak load hours and HECs during the valley load hours, then calculate the residential electricity load after implementation of PMEP-H based on consumer psychology. The CPP optimization model is constructed by considering the constraints of consumer satisfaction with electricity, tariff penalty, compensation balance, penalty and compensation price, power balance and new energy-generating units output power, and the objective function of high comprehensive system efficiency represented by the difference between peak cost of thermal generation, the benefit of new energy consumption and benefit of the grid side. The model is then solved using an improved particle swarm optimization algorithm for a real residential area in a populated area in northern China. The results show that the developed model can connect the generation, grid and user sides through the electricity consumption tariff, which generates considerable benefits in both peak cutting and new energy consumption targets and can enhance the comprehensive benefits of the generation, grid and user sides system to achieve the supply-grid-load linkage, providing a reference for the improvement of the CPP mechanism in China.

Efficient power management optimization based on whale optimization algorithm and enhanced differential evolution

Daily increases in electricity prices accompany daily increases in energy consumption and use. An effective load-balancing scheduling system is necessary for the lowest cost of use and the lowest cost. Despite these devices having a significant capacity for power consumption, they must find a means to balance the load at a low price. Even if lowering the voltage is challenging, it is possible to do it at the lowest cost. Hybrid Whale Differential Evolution (HWDE) is a new optimization method that combines the well-known approaches of the Whale Optimization Algorithm (WOA) and Enhanced Differential Evolution (EDE). By balancing the required Real-Time Price (RTP) and Critical Peak Price (CPP) loads, WOA and EDE capabilities can save costs and ensure the device receives sufficient voltage. The three most recent performance indicators are kWh per charge, energy usage, and the maximum-average ratio. Existing models are evaluated according to their expenses (in rupees), energy consumption, cost per kilowatt-hour, and total cost. All simulation results indicate that HWDE is the optimal solution in every circumstance. In MATLAB simulations, HWDE consistently outperforms its rivals.

Efficient Techniques for Residential Appliances Scheduling in Smart Homes for Energy Management Using Multiple Knapsack Problem

The evolution of the smart grid has enabled residential users to manage the ever-growing energy demand in an efficient manner. The smart grid plays an important role in managing this huge energy demand of residential households. A home energy management system enhances the efficiency of the energy infrastructure of smart homes and provides an opportunity for residential users to optimize their energy consumption. Smart homes contribute significantly to reducing electricity consumption costs by scheduling domestic appliances effectively. This residential appliance scheduling problem is the motivation to find an optimal appliance schedule for users that could balance the load profile of the home and helps in minimizing electricity cost (EC) and peak-to-average ratio (PAR). In this paper, we have focused on appliance scheduling on the consumer side. Two novel home energy management models are proposed using multiple scheduling options. The residential appliance scheduling problem is formulated using the multiple knapsack technique. Serial and parallel scheduling algorithms of home appliances namely MKSI (Multiple knapsacks with serial implementation) and MKPI (Multiple knapsacks with parallel implementation) are proposed to reduce electricity cost and PAR. Price-based demand response techniques are incorporated to shift appliances from peak hours to off-peak hours to optimize energy consumption. The proposed algorithms are tested on real-time datasets and evaluated based on time of use pricing tariff and critical peak pricing. The performance of both the algorithms is compared with the unscheduled scenario and existing algorithm. Simulations show that both proposed algorithms are efficient methods for home energy management to minimize PAR and electricity bills of consumers. The proposed MKSI algorithm achieves cost reduction of 20.26% and 42.53% for TOU and CPP, respectively as compared to the unscheduled scenario while PAR is reduced by 45.07% and 39.51% for TOU and CPP, respectively. The proposed MKPI algorithm achieves 22.33% and 46.36% cost reduction compared to the unscheduled case for TOU and CPP while the PAR ratio is reduced by 46.47% and 41.16% for TOU and CPP respectively.

Targeted demand response for flexible energy communities using clustering techniques

The present study proposes clustering techniques for designing demand response (DR) programs targeting commercial and residential prosumers. The goal is to alter the consumption behavior of the prosumers within a distributed energy community in Italy. This aggregation aims to: (a) minimize the reverse power flow at the primary substation, occurring when generation from solar panels in the local grid exceeds consumption, and (b) shift the system wide peak demand, that typically occurs during late afternoon. Regarding the clustering stage, we consider daily prosumer load profiles and divide them across the extracted clusters. Three popular machine learning algorithms are employed, namely k-means, k-medoids and agglomerative clustering. We evaluate the methods using multiple metrics including a novel metric proposed within this study, namely peak performance score (PPS). The k-means algorithm with dynamic time warping distance considering 14 clusters exhibits the highest performance with a PPS of 0.689. Subsequently, we analyze each extracted cluster with respect to load shape, entropy, and load types. These characteristics are used to distinguish the clusters that have the potential to serve the optimization objectives by matching them to proper DR schemes including time of use, critical peak pricing, and real-time pricing. Our results confirm the effectiveness of the proposed clustering algorithm in generating meaningful flexibility clusters, while the derived DR pricing policy encourages consumption during off-peak hours. The developed methodology is robust to the low availability and quality of training datasets and can be used by aggregator companies for segmenting energy communities and developing personalized DR policies.

Smart energy management system for minimizing electricity cost and peak to average ratio in residential areas with hybrid genetic flower pollination algorithm

Demand Side Management (DSM) plays a significant role in the smart grid to minimize Electricity Cost (EC). Home Energy Management Systems (HEMSs) have recently been studied and proposed explicitly for HEM. In this paper, we propose a novel nature-inspired hybrid Genetic Flower Pollination Algorithm (GFPA) to minimize cost with an affordable delay in appliance scheduling. Our proposed GFPA algorithm combines elements of the Genetic Algorithm (GA) and Flower Pollination Algorithm (FPA) to create a hybrid approach. To assess the effectiveness of the proposed algorithm, we consider a scalable town consisting of 1, 10, 30, and 50 homes, respectively. The proposed solution finds an optimal scheduling pattern that simultaneously minimizes EC and Peak to Average Ratio (PAR) while maximizing User Comfort (UC). We assume that all homes are homogeneous in terms of appliances and power consumption patterns. Simulation results show that our proposed scheme GFPA performs better when applying Critical Peak Pricing (CPP) signal using different Operational Time Intervals (OTIs) and compared with unscheduled, GA, and FPA-based solutions in terms of reducing cost since they achieve on average 98%, 36%, 23%, and 22%, respectively. Similarly, PAR averages 98%, 36%, 59%, and 55%, respectively. While, UC comparing to GA and FPA, are around 88%, 48%, and 63%, respectively. Our proposed scheme achieves better results by applying Real Time Pricing (RTP) signals and different OTIs. As these schemes, i.e., unscheduled, GA, FPA, and GFPA, achieve cost on average 92%, 50%, 29%, and 28%, respectively. While PAR on average 94%, 39%, 62%, and 56%, and UC for GA, FPA, and GFPA on average 98%, 52%, and 49%, respectively. Overall, our proposed GFPA algorithm offers a more effective solution for minimizing EC with an affordable delay in appliance scheduling while considering PAR and UC.

Research on Critical Peak Price Decision Optimization Considering Industrial Consumer’s Risk Appetite under the Carbon Neutrality Goal

The existing research on critical peak price (CPP) decision-making ignores the difference in risk appetite between industries within the consumer population, resulting in a serious lag in the enthusiasm of some users to respond to CPP, and unsatisfactory improvement of power systems and carbon emission reduction on the supply and demand side. Firstly, the problem of consumer risk appetite was comprehensively analyzed, and the industrial consumer population was secondarily stratified according to the influencing factors and the enthusiasm of responding to CPP, namely: stubborn, active and conformist, and quantitatively verified by cluster analysis. Secondly, by combing the relevant paths of CPP decision-making, the critical-peak window determination model and CPP multi-objective optimization model were constructed, and the calculation of relevant indicators was introduced. Finally, taking 10 industrial enterprises in a city in Sichuan Province as an example, the clustering method was used to verify the stratification results, and the index analysis method was used to measure the load and carbon emission improvement of two typical enterprises after CPP optimization. The results showed that the stubborn users insist on using electricity, the improvement effect of load and carbon emission reduction was poor, and additional production costs will be caused. The conformist and active users had high sensitivity to electricity price fluctuations, good load and carbon emission reduction improvement effects, and significantly reduced electricity costs.

Optimally Scheduling Public Safety Power Shutoffs

In an effort to reduce power system-caused wildfires, utilities carry out public safety power shutoffs (PSPSs), in which portions of the grid are deenergized to mitigate the risk of ignition. The decision to call a PSPS must balance reducing ignition risks and the negative impact of service interruptions. In this work, we consider three PSPS scheduling scenarios, which we model as dynamic programs. In the first two scenarios, we assume that N PSPSs are budgeted as part of the investment strategy. In the first scenario, a penalty is incurred for each PSPS declared past the Nth event. In the second, we assume that some costs can be recovered if the number of PSPSs is below N while still being subject to a penalty if above N. In the third, the system operator wants to minimize the number of PSPSs such that the total expected cost is below a threshold. We provide optimal or asymptotically optimal policies for each case, the first two of which have closed-form expressions. Lastly, we establish the applicability of the first PSPS model’s policy to critical peak pricing and obtain an optimal scheduling policy to reduce the peak demand based on weather observations. Funding: This work was funded in part by the Natural Sciences and Engineering Research Council of Canada, the Institute for Data Valorization, the National Science Foundation [Award 1351900], the Advanced Research Projects Agency-Energy [Award DE-AR0001061], and the University of California Office of the President Laboratory Fees Program [Grant LFR-20-652467].

Optimally Scheduling Public Safety Power Shutoffs

In an effort to reduce power system-caused wildfires, utilities carry out public safety power shutoffs (PSPSs), in which portions of the grid are deenergized to mitigate the risk of ignition. The decision to call a PSPS must balance reducing ignition risks and the negative impact of service interruptions. In this work, we consider three PSPS scheduling scenarios, which we model as dynamic programs. In the first two scenarios, we assume that N PSPSs are budgeted as part of the investment strategy. In the first scenario, a penalty is incurred for each PSPS declared past the Nth event. In the second, we assume that some costs can be recovered if the number of PSPSs is below N while still being subject to a penalty if above N. In the third, the system operator wants to minimize the number of PSPSs such that the total expected cost is below a threshold. We provide optimal or asymptotically optimal policies for each case, the first two of which have closed-form expressions. Lastly, we establish the applicability of the first PSPS model’s policy to critical peak pricing and obtain an optimal scheduling policy to reduce the peak demand based on weather observations. Funding: This work was funded in part by the Natural Sciences and Engineering Research Council of Canada, the Institute for Data Valorization, the National Science Foundation [Award 1351900], the Advanced Research Projects Agency-Energy [Award DE-AR0001061], and the University of California Office of the President Laboratory Fees Program [Grant LFR-20-652467].