Peak electric load prediction system and method

Abstract

The present disclosure provides a method for predicting coincident peak events in electricity demand. The method includes receiving historical electrical usage data and forecasted demand data for a given timeframe, training a simulation engine based on the historical data, generating a plurality of load scenarios for a target period of time using the trained simulation engine, and computing a probability that the target period of time will include a new record high peak in electricity demand based on the generated scenarios. The method enables accurate prediction of peak demand events without relying on weather or economic data, allowing utilities and consumers to better manage electricity usage and reduce costs associated with peak demand periods.

Description

PEAK ELECTRIC LOAD PREDICTION SYSTEM AND METHOD CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63 / 648,335, titled Peak Electric Load Prediction, filed 05 / 16 / 2024, which is hereby incorporated by reference in its entirety. FIELD OF INVENTION

[0002] The present disclosure relates to electrical load prediction systems, and more particularly to a method and system for predicting coincident peak events in electricity demand using stochastic modeling and publicly available data. BACKGROUND

[0003] The electrical power industry faces significant challenges in managing peak demand periods, which can strain grid infrastructure and lead to increased costs for both utilities and consumers. Coincident peak (CP) events, where multiple customers experience high demand simultaneously, are particularly challenging to predict and manage effectively.

[0004] The cost-causation principle established by regulatory bodies allocates capacity and transmission charges to end-users based on their contribution to peak demand. This approach incentivizes consumers to reduce their electricity usage during peak periods, but effective demand management requires accurate predictions of when these peaks are likely to occur.

[0005] Many commercial and industrial customers face substantial peak demand charges that can represent a considerable portion of their electricity bills. These charges are typically calculated based on the customer's energy usage during the highest demand periods on the grid. As a result, there is a strong economic incentive for customers to reduce their consumption during predicted peak events.

[0006] Existing methods for predicting CP events often rely on proprietary data or complex weather models, which can be costly to implement and maintain. Additionally, these approaches may not be easily adaptable to different regions or utility systems, limiting their broader applicability.SUMMARY

[0007] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0008] According to an aspect of the present disclosure, a method for predicting coincident peak events in electricity demand is provided. The method includes receiving historical electrical usage data and forecasted demand data for a given timeframe. The method includes training a simulation engine based on the historical data. The method includes generating, using the trained simulation engine, a plurality of load scenarios for a target period of time. The method includes computing, based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand.

[0009] According to other aspects of the present disclosure, the method may include one or more of the following features. Training the simulation engine may include fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data, transforming the historical data to have standard Gaussian marginal distributions, estimating a covariance structure using high dimensional nonparametric statistics, and generating Monte Carlo scenarios for the target period of time. The method may further include transforming the Monte Carlo scenarios using the heavy tail marginal distributions. The target period of time may be 24 hours in length. The method may further include computing, for each hour within the 24-hour target period, a probability that the hour includes the highest load of the day. The historical data may be free of weather data and economic data.

[0010] According to another aspect of the present disclosure, a system for predicting coincident peak events in electricity demand is provided. The system includes a data interface configured to receive historical electrical usage data and forecasted demand data. The system includes a processor and a memory storing instructions that, when executed by the processor, cause the system to train a simulation engine based on the historical data, generate a plurality of load scenarios for a target period of time using the trained simulation engine, and compute a probability that the target period of time will include a new record high peak in electricity demand based on the generated scenarios.

[0011] According to other aspects of the present disclosure, the system may include one or more of the following features. Training the simulation engine may include fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data, transforming the historical data to have standard Gaussian marginal distributions, estimating a covariance structure using high dimensional nonparametric statistics, and generating Monte Carlo scenarios for the target period of time. The instructions may further cause the system to transform the Monte Carlo scenarios using the heavy tail marginal distributions. The target period of time may be 24 hours in length. The instructions may further cause the system to compute, for each hour within the 24-hour target period, a probability that the hour includes the highest load of the day. The historical data may be free of weather data and economic data.

[0012] According to another aspect of the present disclosure, a method for inferring peak electricity demand using a trained model is provided. The method includes receiving current electrical usage data and forecasted demand data for a target period of time. The method includes inputting the received data into a model trained using the training method disclosed herein. The method includes obtaining, as output from the model, a probability that the target period of time will include a new record high peak in electricity demand.

[0013] According to other aspects of the present disclosure, the method may include one or more of the following features. The method may further include generating, using the trained model, a plurality of load scenarios for the target period of time based on the received current electrical usage data and forecasted demand data. The method may further include computing, for each hour within the target period of time, a probability that the hour includes the highest load of the day based on the generated load scenarios. The method may further include identifying a threshold computed as a percentile of historical daily maximum loads and adjusting the computed probabilities based on the identified threshold to reduce false positive predictions of coincident peak events.

[0014] According to another aspect of the present disclosure, a non-transitory computer- readable storage medium containing instructions that, when executed by a processor, cause the processor to perform a method for predicting coincident peak events in electricity demand is provided. The method includes receiving historical electrical usage data and forecasted demand data for a given timeframe. The method includes training a simulation engine based on the historical data. The method includes generating, using the trained simulation engine, a plurality ofload scenarios for a target period of time. The method includes computing, based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand.

[0015] According to other aspects of the present disclosure, the method performed by the non- transitory computer-readable storage medium may include one or more of the following features. Training the simulation engine may include fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data, transforming the historical data to have standard Gaussian marginal distributions, estimating a covariance structure using high dimensional nonparametric statistics, and generating Monte Carlo scenarios for the target period of time. The method may further include transforming the Monte Carlo scenarios using the heavy tail marginal distributions. The method may further include identifying a threshold computed as a percentile of historical daily maximum loads and adjusting the computed probability based on the identified threshold to reduce false positive predictions of coincident peak events.

[0016] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive. BRIEF DESCRIPTION OF FIGURES

[0017] Non-limiting and non-exhaustive examples are described with reference to the following figures.

[0018] Figure 1 is a schematic of a system.

[0019] Figure 2 is a flowchart of a method for predicting coincident peak events in electricity demand.

[0020] Figure 3 is a flowchart of a method for training a simulation agent.

[0021] Figure 4 is a flowchart of a method for inferring peak electricity demand using a trained model.

[0022] Figures 5A-5C are plots showing generated scenarios based on Mid Atlantic (MIDATL) forecasts for July 27, 2023 issued at 23 (5A), issued at 5 (5B), and issued at 11 (5C). Current actual load is only plotted for reference, but was not used for the scenario generations (only past data was used for the fitting of the distributions).

[0023] Figures 6A-6C are plots showing the running new CP probability and maximum daily load time-series with different forecasts and a scenario count of 1000 using forecast at 23 (6A), 5 (6B), and 11 (6C).

[0024] Figures 7A-7C are plots showing PSE&G Daily Maximum hourly probability based on forecast 5 for June 6, 2023 (7A), July 5, 2023 (7B), and July 27, 2023 (7C). DETAILED DESCRIPTION

[0025] The following description sets forth exemplary aspects of the present disclosure. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure. Rather, the description also encompasses combinations and modifications to those exemplary aspects described herein.

[0026] For electricity providers and transmitters, a coincident peak (CP) corresponds to the time interval during which the greatest volume of electricity demand is recorded across the grid according to predefined rules. The customer's own peak load may not necessarily coincide with any of the system or utility peaks, but they will be charged according to their own demand during the system wide load peak.

[0027] On average, the capacity and transmission charges can represent between 10% and 40% of a commercial customer's bill. Reducing the demand for electricity during the CP events is the source of significant savings, hence the incentive to predict in advance the days and times of these CPs, even though they can only be known with certainty at the end of the year, or the period covered by a given Independent System Operator (ISO) CP program.

[0028] The process disclosed herein allows for the prediction of the CP events. It is based on a stochastic model which can be tailored to the different existing ISO and Regional Transmission Operator (RTO) programs.

[0029] This model can be fitted and calibrated with a minimum amount of publicly available data on past load and forecasts whenever the latter are available. That is, nothing other than historical data (load and forecasts) is required.

[0030] The present disclosure relates to systems and methods for predicting peak electric load events. In some cases, a peak electric load prediction system may receive historical electrical usage data and forecasted demand data for a given timeframe. The historical data used for predictionmay be free of weather data and economic data, relying solely on past electricity consumption patterns and forecasts.

[0031] In some cases, the system for predicting coincident peak events in electricity demand may include a data interface configured to receive the historical and forecasted data. The system may also comprise a processor and a memory storing instructions for executing the prediction methods.

[0032] The peak electric load prediction method may involve training a model using the historical data. In some cases, this trained model may then be used to infer peak electricity demand for future time periods. The trained model may take current electrical usage data and forecasted demand data as inputs to generate predictions about potential coincident peak events.

[0033] By analyzing patterns in historical usage and comparing them to current conditions, the system may identify periods with a high probability of experiencing new record high peaks in electricity demand. This information may allow utilities and consumers to better prepare for and manage periods of extreme electrical load.

[0034] Systems and methods for predicting coincident peak events in electricity demand may be provided. Referring to FIG. 1, a system (100) may include one or more processors (120) operably coupled to memory (130), non-transitory storage (140), and one or more interfaces (150). These components may be found within one or more compute devices (110). In some embodiments, the components are located in a cloud-based server. In some embodiments, the components are located on a desktop computer. In some embodiments, the components may be located on, e.g., a smartphone or edge device. As used herein, an edge device is a type of computing device that operates at the periphery or "edge" of a network, rather than within a central data center or cloud. These devices are designed to process data locally, enabling faster response times and reducing the amount of data sent to the cloud. Edge devices can include sensors, actuators, gateways, and various other hardware that interact directly with the physical world and perform computations close to the data's origin. Such devices may include, e.g., smart sensors, IoT gateways, Edge routers, Industrial controllers, wearable devices, micro data centers, etc.

[0035] As used herein, the term "processor" may refer to a hardware component capable of executing instructions and performing computations. A processor may include one or more central processing units (CPUs), graphics processing units (GPUs), or other specialized processing units. Processors may be implemented as single-core or multi-core units, and may be based on variousarchitectures such as x86, ARM, or RISC-V. In some cases, a processor may be a general-purpose CPU found in personal computers or servers. In other cases, it may be a specialized chip designed for specific tasks, such as a digital signal processor (DSP) or an application-specific integrated circuit (ASIC). Field-programmable gate arrays (FPGAs) may also function as processors in certain applications. The processor may be integrated into a system-on-chip (SoC) or may be a discrete component on a circuit board. Additionally, the term "processor" may encompass virtual compute components such as virtual machines (VMs), containers, cloud-based compute instances, virtual CPUs (vCPUs), and other software-defined processing resources that emulate physical hardware functionality. These virtual components may be deployed across distributed computing environments, including public, private, or hybrid cloud infrastructures, and may dynamically scale based on computational demands.

[0036] The interface(s) may include interfaces for a user (186) to send and receive information. The interface(s) may include a data interface configured to receive data related to electrical usage. For example, the data interface may be configured to receive historical electrical usage data (e.g., from a database (180)), and forecasted demand data (e.g., from a separate network or server (182)). The data interface may be configured to receive current electrical usage (e.g., from one or more loads (184), such as from a building, company, town, city, etc. communicating via the separate network or server (182)).

[0037] The memory (130) may contain instructions that, when executed by the processor, cause the system to perform steps of one or more methods including, e.g., methods for predicting coincident peak events in electricity demand, inferring peak electricity demand using a trained model, etc. As one example, the steps may include training a simulation engine based on the historical data, generating a plurality of load scenarios for a target period of time using the trained simulation engine, and computing a probability that the target period of time will include a new record high peak in electricity demand based on the generated scenarios.

[0038] In various aspects, a method for predicting coincident peak events in electricity demand may be provided. Referring to FIG. 2, The method (200) may include receiving (202) data. Such data may include historical electrical usage data and forecasted demand data for a given timeframe. Preferably, the received data may only include such data. In a preferred embodiment, the historical data may be free of weather data and economic data.

[0039] The method may include training (204) a simulation engine based on the historical data. Referring to FIG.3, training the simulation engine may include various steps. For example, training (204) may include fitting (302) heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data. Training may include transforming (304) the historical data to have standard Gaussian marginal distributions. Training may include estimating (306) a covariance structure using high dimensional nonparametric statistics. Training may include generating (308) Monte Carlo scenarios for the target period of time. In some aspects, training may include transforming (310) the Monte Carlo scenarios using the heavy tail marginal distributions.

[0040] Referring to FIG.2, once a trained model is provided, the method (200) may include generating (206), using the trained simulation engine, a plurality of load scenarios for a target period of time. The method may then include computing (208), based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand.

[0041] The target period of time may be any appropriate time period. – 1 hour, 4 hours, 6 hours, 8 hours, 12 hours, 24 hours (1 day), 2 days, 3 days, 5 days, 7 days (1 week), 2 weeks, 3 weeks, 4 weeks or 1 month, 2 months, 3 months, 4 months, or 6 months. Preferably, the target period of time is no more than 24 hours, and in some aspects, the preferred target period of time is 24 hours.

[0042] In some aspects, the method may include computing (210), for a subset of time within the target period of time, a probability that the subset of time includes the highest load of the day. Given a 24 hour target period of time, the subset of time could be, e.g., 1 hour blocks (e.g., 10:00:00 am – 10:59:59 am), 2 hours blocks of time (e.g., 10:00:00 am – 11:59:59 am), 3 hour blocks of time, 4 hour blocks of time, 6 hour blocks of time, 8 hour blocks of time, or 12 hour blocks of time. However, any appropriate block of time may be used. In a preferred embodiment, the subset of time is a 1 hour block of time, and the computing (210) step includes computing, for each hour within a 24 hour period, a probability that the 1-hour period of time includes the highest load of the day.

[0043] In various aspects, a method for inferring peak electricity demand using a trained model may be provided. Referring to FIG.4, the method (400) may include receiving (402) current electrical usage data and forecasted demand data for a target period of time. The target period oftime may be any appropriate target period of time as disclosed herein. The method may include inputting (404) the received data into a model trained using the training method disclosed herein.

[0044] In various aspects, the method may include generating (406), using the trained model, a plurality of load scenarios for the target period of time based on the received current electrical usage data and forecasted demand data.

[0045] In various aspects, the method may include computing (408), for each subset of time within the target period of time, a probability that the subset of time includes the highest load of the day based on the generated load scenarios. The subset of time may be any appropriate subset, as disclosed herein.

[0046] The method may include obtaining (410), as output from the model, a probability that the target period of time will include a new record high peak in electricity demand.

[0047] In various aspects, the method may include identifying (412) a threshold computed as a percentile of historical daily maximum loads. The method may include adjusting (414) the computed probabilities (after computing (408) the probabilities), based on the identified threshold to reduce false positive predictions of coincident peak events.

[0048] In some aspects, a non-transitory computer-readable storage medium (such as a storage (140)) may contain instructions that, when executed by a processor, cause the processor to perform a method as disclosed herein. The methods may include, e.g., predicting coincident peak events in electricity demand by: (i) receiving historical electrical usage data and forecasted demand data for a given timeframe; (ii) training a simulation engine based on the historical data, where the simulation engine may be trained as disclosed herein; (iii) generating, using the trained simulation engine, a plurality of load scenarios for a target period of time; and (iv) computing, based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand. The methods may include identifying a threshold computed as a percentile of historical daily maximum loads, and adjusting the computed probability based on the identified threshold to reduce false positive predictions of coincident peak events.

[0049] Capacity and transmission charges can respectively represent on average as much as 10% - 40% of a commercial customer’s bill. Reducing the demand for electricity during the CP events can lead to significant on bill savings. Demand Side Management can be achieved through at least two means: load curtailment and local electricity generation / reserve. For instance, Direct Load Control can involve turning-off non-essential lighting, modifying manufacturing processes,or adjusting the HVAC equipment, while additional generation can involve dialing fossil fuel back pumps with short start and run times, using local Photo-Voltaic (PV) panels or using stored energy during the CP event. Thus, if a company becomes aware of a predicted CP event, they may take appropriate steps (e.g., via a form of demand side management) based on the prediction in order to reduce load from that electricity source for at least some of the predicted CP event.

[0050] Example 1 – Forecasting the Utility Load

[0051] PSE&G is part of the Mid-Atlantic (MIDATL) group of PJM along with utilities described in Table 1, below.

[0052] Table 1. PJM Utility Cost Allocation Methodology Transmission Zone Region CP Methodology Utility Company Acronym Mid-Atlantic # CP Period0 1 0 ? 0 0 1 1 1 100 1 0 1 0 101 100

[0053] The PJM publishes several datasets of interest on (PJM 2011), including: the actual load historical data of the Mid-Atlantic region at an hourly resolution, the actual load historical data of PSE&G at an hourly resolution, and the day-ahead forecast data of the Mid-Atlantic region at an hourly resolution.

[0054] The Pennsylvania-New Jersey-Maryland Interconnection (PJM) publishes several datasets of interest on (PJM 2011), including: the actual load historical data of the RTO at an hourly resolution, and the day-ahead forecast data of the RTO at an hourly resolution

[0055] In particular, four different sets of forecasts are available for each day and are published:at 11:45 pm the day before for hours 0, 1, · · · , 23 of the following day, at 5:45 am the day of, forhours 6, 7, · · · , 23 of the day, at 11:45 am the day of, for hours 12, 13, · · · , 23 of the day, and at 5:45pm the day of, for hours 18, 19, · · · , 23 of the day.

[0056] For simplicity, this example will label these forecasts as respectively 23, 5, 11, 17 for the hour at which they are published. The dataset used in this example covers the period from 01- 01-2018 to 12-31-2023.

[0057] Table 2. Data Availability. Zone Actual Load is available Forecast is available MIDATL✓ ✓

[0058] Scenario Generation.

[0059] The simulation engine PGscen developed by Carmona and Yang 2024 was used to perform Monte Carlo scenario simulations. For the sake of completeness and since the setting is different, described below is the methodology used to generate scenarios from historical data and forecasts. To fix ideas for this example, the forecast set labeled 23 was chosen.

[0060] Given the chosen historical forecast series, for each day d, a vector of Nh= 24 load points were read from the actual load and the load forecasts generated for that same time period to create a time series of load deviations:

[0061] load errord,h = actual loadd,h − load forecastd,h, h∈{0,1,...,Nh−1} (1)

[0062] The day for which one wants to generate scenarios can be denoted by d∗.

[0063] (1) For each time horizon h∈{0,1,...,Nh−1}, one has a time series of load deviations of length N of past data indexed by d such that d < d∗, the day the scenarios are generated for.

[0064] (2) For each time horizon h, a Generalized Pareto Distribution (GPD) is fitted to the load deviations. We denote such a distribution as Gz,h for the sake of later reference. Throughout this example, in order to manipulate GPD distributions, functions from a Python package wrapping the R library Rsafd (Rsafd n.d.) accompanying the book from Carmona 2014 are used.

[0065] (3) For each time horizon h, the load deviation time series is then transformed into a uniform time series ^^^ௗ௭,^^ே^ௗୀ^ by the probability integral transform. Let the cumulative distribution function the GPD be Φீ^,^for every day d<d∗. One can computeΦீ^,^൫^^ௗ௭,^൯. (4) For each lag l, the uniform time series Φீ^൫^^ௗ௭,^൯ is then transformed into a,^standard Gaussian marginal distribution N^0,1^ by probability integral transform.

[0067] ˆ

[0068] For each d < d∗, one can compute ^^^ௗ ି^௭,^ ൌ Φ ^Φீௗ −1^,^൫^^௭,^൯^ where Φ is the quantile function of the standard Gaussian distribution.

[0069] (5) Fit a Gaussian Graphical LASSO model to estimate the temporal covariance matrix.

[0070] (6) Generate samples from a Gaussian distribution with mean zero and the estimated covariance matrix. Applying the inverse of the above distribution transformations, sample from the load deviation distribution. Generate scenarios of the actual load by simply adding back these deviations to the original forecast.

[0071] Scenario generation results. Sample scenarios generated for different days are presented, given the forecast at the four different times. Referring to FIGS.5A-5C, one can see (i) the actual load (solid line) of PSE&G, (ii) a batch of K = 1000 PGscen scenarios (all falling within the dotted lines) for PSE&G; and (iii) the average of the scenarios (dashed line) computed with the conditional scheme based on the MIDATL forecasts labeled 23 (5A), 5 (5B), and 11 (5C) from the top-left pane to the bottom-right one. It is important to note that the current actual load is only plotted for reference, it is not used for the scenario generations. Here, only past data is used for the fitting of the distributions.

[0072] Predicting Probability of Hitting the Running Maximum Load. One can look at the problem of estimating the probability that today is the new running coincident peak (CP) day (inthe sense that today’s maximum load will be the new running maximum for the utility-wide load time-series up until yesterday).

[0073] Denote by d∗the current date, by ^^^ௗ௭,^^ௗ∈ℕ∗,^∈^^,...,ଶଷ^the RTO actual load on day d during the hour h and by ^^^ௗ^ௗ∈ℕ∗the RTO daily maximum actual load of day d. Denote by^^^^ௗ∗ ൌ argmax^ ௗழௗ∗^^ௗ^ the running maximum seen up until the day prior to d∗. Let K be the number of generated scenarios and denote by an upper-script ^^^ௗ,^the load and ^^ௗ^maximum daily load of scenario k∈{1,...,K}for day d and hour h.

[0074] the time-series of probabilities that today’s peak is higher than theprevious the frequency of scenarios whose daily maximum load exceeds the running maximum of days prior to d∗: prob ^

[0075] ^ൌ ^∑^ ୩ୀ^ I^^ౡ^*வେ^^*^

[0076] with the convention that CP0 = 0.

[0077] Referring to FIGS.6A-6C, for each of the forecast sets 23 (6A), 05 (6B), and 11 (6C), average daily RTO system peak load (continuous dotted lines), days when the daily maximum load exceeded the running maximum up until now (open circles), and for each day, a solid vertical bar whose height is the probability that today’s maximum load will exceed the previous ones.

[0078] Each vertical spike corresponds to days for which the probabilities are elevated. The first spike isalways present in order to populate the current CP information. If one uses a signal relying on the CP-day probability being above 0.5, we obtain the results in Table 3. It is essential to note that the disclosed approach does not miss any of the running CP updates and that in the end, the real CP day is caught. The number of warnings sent out using this rule is 10 regardless of the forecast used, but they differ in the height of the spikes for days that have a non-zero probability that is less than 0.5. For instance, using the more recent forecast generated at 5 decreases the estimated probability on some days around July 15, 2023, while the decrease in the probabilities on the same days is even more noticeable with the forecast generated at 11.

[0079] Table 3. Number of warnings based on signal based on probability of CP day for 2023. Forecast # {d : probd> 0.5 } True CP events caught05 10 5 11 10 5ay, one can go further, and can now estimate the probability of each hour being a CP-hour. One can therefore compute the frequency that each hour h is the maximum daily load from the scenario k ∈{1,...,K}on that day and denote it by prob^୦. This leads to a vector of length 24 containing:

[0081] prob୦ ^^ൌ^∑^ ୩ୀ^ I^^ ౡ^*,^ ୀ^ౡ ^*^, h∈^0,…,23^ the time of the CP hour relatively well,an error forecast (05, 11, 18, 23) is used. The forecast 23 leads to estimating the highest probability for the correct hour on, e.g., 2023-06-02 and 2023- 07-27, while it predicts the second highest probability for the correct hour. It is noted that using a more recent forecast does not necessarily improve the prediction, with only the forecast 11 improving the performance on 2023-07-03 but giving a worse probability on 2023-07-05.

[0083] We note that using a more recent forecast does not necessarily improve the prediction, with only the

[0084] forecast 11 improving the performance on 2023-07-03 but giving a worse probability on 2023-07-05.

[0085] In FIGS.7A-7C, for various days, plots are shown of (i) the hourly actual load of the day (continuous dotted line), (ii) the histogram of the hourly probabilities that a given hour is the hour the daily maximum occurs, computed from the generated scenarios, and (iii) the hour when the maximum load actually occurs (open circle).

[0086] Example 2 – 5CP problem.

[0087] For PJM, Zonal coincident summer peak loads are allocated to wholesale and retail customers to compute the customer’s shares of RTO actual peaks. The resulting Peak Load Contributions (PLC) are then used the following year in: (i) the determination of capacity obligations, and (ii) load charges.

[0088] For each summer, hourly metered loads are gathered for the period June 1- September 30. From the RTO hourly loads, the five highest non-holiday weekday peaks (5CP) are identified. PJM publishes information related to the 5CP in mid-October. For load charges,the proportion of the 5CP contributed by a customer is used to compute their charges the following year.

[0089] Thus, PJM’s 5CPs are worth considering, as it is commonly accepted that, just in terms of capacity charges which is one of the profitable programs. Reducing PLC by 1 MW implies a saving of 22K the following year. Thus, the ability to predict CPs could save companies significant amounts of money. Indeed, the earlier one can guess whether a CP will occur that day, the better.

[0090] For this problem, one can start by computing 5 timeseries of different probabilities:

[0091] prob^ ൌ ℙ^^^^^^^^^ ^ CP^^

[0092] probଶ ൌ ℙ^CP^ ^ ^^^^^^^^ ^ CPଶ^

[0093] probଷ ൌ ℙ^CPଶ ^ ^^^^^^^^ ^ CPଷ^

[0094] probସ ൌ ℙ^CPଷ ^ ^^^^^^^^ ^ CPସ^

[0095] probହ ൌ ℙ^CPସ ^ ^^^^^^^^ ^ CPହ^

[0096] where CP^, ^^ ∈ ^1, … ,5^ is the running CP value of rank i (e.g., at time ^^^). In somecases,

[0097] CP^ ൌ maxௗழௗ∗ ^^^ௗ^ , ^^^ ൌ argmax^ ^∗^ ^^^^ௗ,^^, ௗ,^ :ௗழௗ ,^∈ ^,…,ଶଷ

[0098] CP^ ൌ maxௗழௗ∗,ௗ∉^ఛభ,…,ఛೖషభ^ ^^^ௗ^ , ^^ଶ ൌargmax ^^^ௗ,^^ , ^^ ∈భ^,^∈^^,…,ଶଷ^^2, … ,5^.

[0099] This approach is straightforward, but when comparing to actual 5CP events, this simplistic approach often results in false positives. This may be sufficient in some cases, but it could be improved upon.

[0100] To remove some false positives, one option would be to rely on rules of thumb from the industry. A general rule of thumb in the industry would be to set a threshold of 140,000 MW. However, some CPs are below that level (Example: CP5 - 2023-07-05 - RTO Load = 137,807 MW).

[0101] An approach less likely to give false negatives would be to implement a naïve trim of the false positives by using a threshold. Specifically, compute a data-driven percentile threshold (thresh) which corresponds to the k-th percentile of the past daily maximum load for k ∈ {80,90,95}. This selection is motivated by the fact that there are about 80-88 business days in a PJM summer period and in this example, the 5 top values are of interest, which representaround 6% of the days.95 might be too stringent and may miss some values, while 80 might be too large and give too many warnings. The following 5 time-series of different probabilities are computed:

[0102] prob^ ൌ ℙ^daily maximum load ^ max^CP^, thresh^^

[0103] probଶ ൌ ℙ^CP^ ^ daily maximum load ^ max^CPଶ, thresh^^

[0104] probଷ ൌ ℙ^CPଶ ^ daily maximum load ^ max^CPଷ, thresh^^

[0105] probସ ൌ ℙ^CPଷ ^ daily maximum load ^ max^CPସ, thresh^^

[0106] probହ ൌ ℙ^CPସ ^ daily maximum load ^ max^CPହ, thresh^^

[0107] where CP^, ^^ ∈ ^1, … ,5^ is the running CP value of rank i.

[0108] For the data available from PJM from 2022 and 2023, Table 4 provides the cutting values for the chosen percentiles.

[0109] Table 4 Percentile Threshold used for 2022 Threshold used for 2023 95 137,831 137,405

[0110] As expected, the lower the threshold the more warnings are sent. See Table 5, below. The choice of k = 90 gives approximately 15 elevated probabilities of a new CP event. However, it is interesting to see that even with a more stringent threshold k= 95, the method does not miss any of the actual final 5 CP events for 2022 and 2023 (the years considered in this example).

[0111] Warnings or alerts could be issued where a CP is predicted. In some aspects, this could be when a probability of a CP occurring that day was above a particular likelihood (e.g., at least 40%, 45%, 50%, etc.). For 2022 and 2023, the warnings that could have been issued usingthe disclosed approach for predicting CPs, where warnings would be issued if ∑ହ ୧ୀ^ prob୧^0.5 is shown in Table 5.

[0112] Table 5 Percentile 2022 Warnings (5CP) 2023 Warnings (5CP)

[0113] A similar arrangement could be created for, e.g., any given ISO or RTO. For example, the Electric Reliability Council of Texas (ERCOT) has a 4CP program, where, for each summer month, June, July, August and September, for each day of the month and for each 15 mn period, the system load is recorded, and the day and the 15 mn period in which the maximum load occurs is identified as the CP of the month. For each customer, their average demand over these 4CP periods is computed. That average demand is then used to determine their (relative) contribution to the system 4CP load, which serves as a factor to compute their electricity charges throughout the following year. The New York State ISO (NYISO) has a similar program for the one single hour highest peak load in the period of July-August.

[0114] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.

Claims

CLAIMS 1. A method for predicting coincident peak events in electricity demand, comprising: receiving historical electrical usage data and forecasted demand data for a given timeframe; training a simulation engine based on the historical data; generating, using the trained simulation engine, a plurality of load scenarios for a target period of time; and computing, based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand.

2. The method of claim 1, wherein training the simulation engine comprises: fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data; transforming the historical data to have standard Gaussian marginal distributions; estimating a covariance structure using high dimensional nonparametric statistics; and generating Monte Carlo scenarios for the target period of time.

3. The method of claim 2, further comprising transforming the Monte Carlo scenarios using the heavy tail marginal distributions.

4. The method of claim 1, wherein the target period of time is 24 hours in length.

5. The method of claim 4, further comprising computing, for each hour within the 24-hour target period, a probability that the hour includes the highest load of the day.

6. The method of claim 1, wherein the historical data is free of weather data and economic data.

7. A system for predicting coincident peak events in electricity demand, comprising: a data interface configured to receive historical electrical usage data and forecasted demand data; a processor; anda memory containing instructions that, when executed by the processor, cause the system to: train a simulation engine based on the historical data, generate a plurality of load scenarios for a target period of time using the trained simulation engine, and compute a probability that the target period of time will include a new record high peak in electricity demand based on the generated scenarios.

8. The system of claim 7, wherein training the simulation engine comprises: fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data; transforming the historical data to have standard Gaussian marginal distributions; estimating a covariance structure using high dimensional nonparametric statistics; and generating Monte Carlo scenarios for the target period of time.

9. The system of claim 8, wherein the instructions further cause the system to transform the Monte Carlo scenarios using the heavy tail marginal distributions.

10. The system of claim 7, wherein the target period of time is 24 hours in length.

11. The system of claim 10, wherein the instructions further cause the system to compute, for each hour within the 24-hour target period, a probability that the hour includes the highest load of the day.

12. The system of claim 7, wherein the historical data is free of weather data and economic data.

13. A method for inferring peak electricity demand using a trained model, comprising: receiving current electrical usage data and forecasted demand data for a target period of time; inputting the received data into a model trained using the method of claim 1; andobtaining, as output from the model, a probability that the target period of time will include a new record high peak in electricity demand.

14. The method of claim 13, further comprising generating, using the trained model, a plurality of load scenarios for the target period of time based on the received current electrical usage data and forecasted demand data.

15. The method of claim 14, further comprising computing, for each hour within the target period of time, a probability that the hour includes the highest load of the day based on the generated load scenarios.

16. The method of claim 15, further comprising: identifying a threshold computed as a percentile of historical daily maximum loads; and adjusting the computed probabilities based on the identified threshold to reduce false positive predictions of coincident peak events.

17. A non-transitory computer-readable storage medium containing instructions that, when executed by a processor, cause the processor to perform a method for predicting coincident peak events in electricity demand, the method comprising: receiving historical electrical usage data and forecasted demand data for a given timeframe; training a simulation engine based on the historical data; generating, using the trained simulation engine, a plurality of load scenarios for a target period of time; and computing, based on the generated scenarios, a probability that the target period of time will include a new record high peak in electricity demand.

18. The non-transitory computer-readable storage medium of claim 17, wherein training the simulation engine comprises: fitting heavy tail distributions to marginals of deviations between actual loads and forecasts in the historical data; transforming the historical data to have standard Gaussian marginal distributions;estimating a covariance structure using high dimensional nonparametric statistics; and generating Monte Carlo scenarios for the target period of time.

19. The non-transitory computer-readable storage medium of claim 18, wherein the method further comprises transforming the Monte Carlo scenarios using the heavy tail marginal distributions.

20. The non-transitory computer-readable storage medium of claim 19, wherein the method further comprises: identifying a threshold computed as a percentile of historical daily maximum loads; and adjusting the computed probability based on the identified threshold to reduce false positive predictions of coincident peak events.

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