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Load duration curve

A load duration curve (LDC) is a graphical representation of the electrical load on a power system, constructed by sorting hourly demand data in descending order from highest to lowest over a specified period, such as a year, to illustrate the duration each load level persists.^[1] This curve transforms chronological load variations into a cumulative distribution that highlights the relationship between power demand magnitude and the time it is equaled or exceeded, providing a tool for analyzing capacity utilization without regard to specific timing.^[2] The LDC is typically derived from historical or projected hourly load data, aggregated across regions and segmented into discrete blocks representing seasons (e.g., summer, winter) and load types (e.g., peak, intermediate, base), often using 8 to 16 vertical slices to approximate the full curve for modeling efficiency.^[2] Adjustments may account for non-dispatchable generation like wind or solar by subtracting their output from the load, creating a "net" LDC that reflects residual demand.^[3] In practice, the curve's shape reveals key metrics, such as the peak-to-average demand ratio, which has risen in regions like New England from 1.52 in 1993 to 1.78 in 2012 due to factors including increased air conditioning use and efficiency gains in off-peak periods.^[1] Load duration curves play a central role in power system planning and operations by enabling the assessment of generating capacity needs, reserve margins, and economic dispatch across load segments to ensure reliability while minimizing costs.^[2] They facilitate the selection of appropriate generation mixes—such as base-load plants for flat portions of the curve and peaking units for high-demand tails—and support evaluations of storage technologies like batteries by quantifying their ability to shift or reduce peak loads.^[3] In modeling frameworks like the U.S. Energy Information Administration's National Energy Modeling System, LDCs inform long-term projections of electricity markets across 25 regions, optimizing investments in transmission, renewables, and fossil fuels under varying demand patterns.^[2]

Fundamentals

Definition

A load duration curve is a graphical representation of electrical load, or power demand, plotted against the duration for which each load magnitude persists, with the loads arranged in descending order from highest to lowest over a specified period, typically one year.^[4]^[5] This arrangement transforms chronological load data into a cumulative distribution that highlights the frequency and persistence of demand levels, enabling engineers to assess overall load variability without regard to specific timing.^[6] In contrast to traditional load curves, which plot demand against time in sequential order, the load duration curve serves as a sorted, non-chronological alternative for summarizing demand patterns.^[7] The curve's primary purpose in power engineering is to provide a concise visualization of load variations, facilitating the analysis of system capacity needs and operational strategies by emphasizing how long high or low demands endure rather than when they occur.^[4] The y-axis typically represents load magnitude, expressed in units such as megawatts (MW) or as a normalized percentage of the peak load (e.g., 0% to 100%), while the x-axis denotes the duration, often in hours (ranging from 0 to 8760 for an annual curve) or as a percentage of the total period.^[5]^[6] For instance, the curve begins at the peak load value (e.g., 100% at 0 hours on the x-axis) and gradually descends to the minimum load as the duration approaches the full period, illustrating the proportion of time spent at or above various demand levels.^[7] This descending profile captures the essential distribution of loads, such as a system where the highest demands might persist for only a few hours, while lower base loads occupy the majority of the time.^[4]

Key Characteristics

The load duration curve (LDC) typically features a monotonically decreasing profile, characterized by a steep initial drop from the peak load—representing short-duration high-demand periods—followed by a gradual flattening that indicates the persistent base load over extended times. This shape reflects the inherent variability in electricity demand, with the sharp descent highlighting infrequent but intense peaks, such as those driven by evening residential usage or industrial surges, and the flatter tail corresponding to minimum loads that occur for the majority of the period. For example, in a daily LDC, loads might drop from 20 MW during peak hours to a steady 5 MW base for over half the day.^[7]^[8]^[9] The curve's smoothness provides an indicator of load diversity within the power system; aggregated demands from diverse sectors, such as residential and industrial consumers, produce smoother profiles due to offsetting patterns—residential peaks in evenings complementing industrial daytime loads—resulting in less pronounced fluctuations. In contrast, systems dominated by uniform load types exhibit steeper curves with more abrupt changes, underscoring lower diversity and higher variability risks. In many US regions, such as New England in the early 2010s, peak-to-average ratios around 1.7 illustrate this, varying by region based on consumer mix and economic activity.^[1]^[10]^[11] LDCs are constructed over different time scales to capture varying demand dynamics: annual curves, covering 8760 hours, incorporate seasonal variations like higher summer air-conditioning loads, while daily or weekly versions highlight intra-period patterns, such as weekday versus weekend differences. For comparability across systems or periods, the y-axis load values are frequently normalized to a percentage of the peak load, transforming absolute megawatts into relative terms (e.g., 100% at peak descending to 30-40% at base).^[12]^[13] Visually, the area under the LDC quantifies total energy demand, equaling the integral of load over time—practically, average load multiplied by total duration in hours—which directly informs energy planning and equates to annual consumption in megawatt-hours for yearly curves. This property emphasizes the curve's role in assessing overall system utilization, with broader areas indicating higher energy needs.^[11]^[7]

Construction

Data Requirements

The construction of a load duration curve requires comprehensive time-series data representing electrical demand in a power system, typically consisting of hourly or sub-hourly measurements of load over the analysis period.^[12] These measurements capture the variability in power consumption, enabling the curve to reflect the distribution of demand levels from peak to base. For instance, hourly data points for an entire year provide 8,760 values, which are essential for sorting and plotting the curve to show the percentage of time demand exceeds specific levels.^[1] The selection of the analysis period is critical to ensure the curve accounts for seasonal, daily, and weather-related variations in load. A full annual period is standard for representative load duration curves, incorporating effects like higher summer peaks due to air conditioning or winter heating demands; shorter intervals, such as monthly or weekly data, may be used for targeted studies like event-specific analyses.^[14] Data resolution has evolved with modern grid technologies, where sub-hourly intervals like 15 minutes better capture intra-hour fluctuations from renewables or electric vehicle charging, improving accuracy over traditional hourly aggregates.^[15] Primary sources for this data include utility records, supervisory control and data acquisition (SCADA) systems, and smart meters that provide real-time or near-real-time measurements. In the United States, independent system operators (ISOs) and regional transmission organizations (RTOs) publish historical load data, such as from PJM or CAISO, which aggregate substation-level readings to system-wide totals.^[1] For future projections, simulated data generated via load forecasting models is often employed, drawing on econometric and end-use projections to estimate evolving demand patterns under scenarios like electrification growth.^[16] Data quality is paramount to avoid distortions in the resulting curve, necessitating rigorous preprocessing to address missing values, outliers, and aggregation challenges. Missing data, which may arise from meter failures or communication issues, can be imputed using interpolation or machine learning techniques based on historical patterns; outliers, such as spikes from blackouts or measurement errors, require detection and removal through methods like wavelet transforms or statistical thresholding to maintain curve integrity.^[17] Aggregation from individual substations to system-wide load involves summing metered values while accounting for transmission losses and ensuring temporal alignment, often using advanced metering infrastructure (AMI) data for precision in distribution-level analysis.^[18]

Methodology

The methodology for constructing a load duration curve (LDC) begins with the collection and cleaning of time-series load data, typically hourly measurements of power demand in megawatts (MW) over a full year, ensuring the dataset covers 8760 hours and is free from outliers or missing values through standard preprocessing techniques such as interpolation or removal of erroneous readings.^[13]^[19] The next step involves sorting the load values in descending order, from the highest demand to the lowest, which rearranges the chronological data to emphasize the frequency and magnitude of load levels.^[12]^[20] Durations are then assigned to each sorted load value as the time the load equals or exceeds that level, with the x-axis representing cumulative exceedance time from the peak (1 hour) accumulating to the full period (e.g., 8760 hours) for the minimum load, often expressed in hours or as a percentage of total time (e.g., the highest load is equaled or exceeded for 1 hour, while lower loads are equaled or exceeded for up to thousands of hours).^[19]^[21] To generate the curve, the sorted load values are plotted on the y-axis against their corresponding durations or percentage of time on the x-axis, creating a descending profile that visualizes load variability; common tools for this include spreadsheets for small datasets, MATLAB for simulation-based analysis, or Python libraries such as pandas for sorting the data array and matplotlib for rendering the plot.^[13]^[20] In cases of ties—where multiple load values are identical—or discrete data with limited resolution, the values can be binned into intervals (e.g., 100 load steps) to smooth the curve and approximate a continuous representation while preserving the total energy under the curve.^[11] For a typical annual dataset of 8760 hourly points, the workflow entails loading the time-series array, sorting it in descending order to produce a load vector, converting the indices to cumulative hours (x-axis from 1 to 8760), and plotting the load vector against these hours to yield the LDC, which maintains the same total area as the original chronological load curve.^[19]^[22]

Analysis and Interpretation

Load Metrics

The load duration curve serves as a foundational tool for deriving several key quantitative metrics that quantify the variability, efficiency, and overall demand patterns in power systems. These metrics provide insights into how effectively the system's capacity is utilized over time, enabling planners to assess operational efficiency without relying on chronological load curves. Load factor is defined as the ratio of the average load to the peak load over a specified period, such as a day, month, or year. It is calculated using the load duration curve as the average load divided by the maximum demand, where the average load is obtained by dividing the area under the curve by the total duration. Mathematically, this is expressed as:

\text{Load Factor} = \frac{\text{Average Load}}{\text{Peak Load}} = \frac{\int_0^T L(\tau) \, d\tau / T}{L_{\max}}

where L(\tau) is the load as a function of duration \tau, T is the total duration (e.g., 8760 hours for a year), and L_{\max} is the peak load. A load factor of 0.6, for instance, indicates that the average load is 60% of the peak, reflecting moderate utilization efficiency and highlighting opportunities for demand management to flatten the curve and reduce costs. Higher load factors signify more consistent demand, which lowers the per-unit cost of generation by better utilizing fixed infrastructure. The average load, a core component of the load factor, represents the mean power demand over the period and is approximated from the load duration curve using numerical integration methods such as the trapezoidal rule for discrete data points. The formula is:

\text{Average Load} = \frac{1}{T} \int_0^T L(t) \, dt

This metric is essential for estimating baseline energy needs and is directly computed as the total area under the curve divided by the time horizon, providing a simple yet precise measure of typical system loading. Total energy consumption is another fundamental metric derived from the load duration curve, calculated as the integral of the load over the entire duration, which corresponds to the area under the curve in units of megawatt-hours (MWh) or gigawatt-hours (GWh). For example, in an annual curve spanning 8760 hours, the total energy E is:

E = \int_0^T L(\tau) \, d\tau

This value quantifies the aggregate electricity demand for the period, serving as a critical input for resource allocation and billing, and underscoring the curve's role in energy accounting. Capacity factor, particularly for generation plants, adapts the load factor concept to evaluate how closely a plant's output matches its maximum rated capacity over time, using the load duration curve to model the loading profile assigned to specific units. It is computed as the ratio of actual energy produced to the maximum possible energy if the plant operated at full capacity throughout the period:

\text{Capacity Factor} = \frac{\text{Actual Energy Output}}{\text{Maximum Possible Output}} = \frac{\int_0^T P_g(\tau) \, d\tau}{P_{\text{rated}} \times T}

where P_g(\tau) is the generated power as a function of duration. The load duration curve facilitates this by segmenting demand into levels that guide plant dispatch, revealing underutilization (e.g., a factor below 0.5 for peaking plants) and informing decisions on reserve margins or technology mixes. Diversity factor measures the non-coincidence of peak demands across consumers or subsystems, calculated as the ratio of the maximum system demand to the sum of individual peak demands. From the load duration curve, it is inferred from the curve's shape: a steeper initial drop indicates lower diversity due to synchronized peaks, while a flatter profile suggests higher diversity from staggered loads. The formula is:

\text{Diversity Factor} = \frac{\text{Maximum System Demand}}{\sum \text{Individual Peak Demands}}

Typically greater than 1, this metric exceeds unity because system peaks rarely align perfectly, and a value closer to 1 implies greater coincidence, necessitating more capacity; higher values (e.g., 1.5–2.0) enhance efficiency by spreading demand.

Peak, Intermediate, and Base Load Identification

The load duration curve (LDC) is segmented into peak, intermediate, and base load regions to classify demand patterns and inform generation resource allocation in power systems. This division reflects the varying durations and intensities of electricity demand, where the top portion represents infrequent high-demand periods, the middle covers moderate and more sustained loads, and the bottom indicates the steady minimum requirements. Such identification aids in matching supply technologies to demand characteristics, ensuring system reliability and efficiency.^[12]^[20] Peak load corresponds to the uppermost section of the LDC, often during short spikes driven by factors like air conditioning in summer or heating in winter. These periods are served by flexible peaker plants such as gas turbines or hydroelectric units capable of rapid startup and shutdown.^[12]^[20]^[23] Intermediate load occupies the middle region of the LDC, accommodating fluctuating but predictable demands from industrial and commercial activities. This segment is typically met by cycling or combined-cycle gas plants that can adjust output efficiently over medium durations. In an example from the Iranian power network in 2001, intermediate load accounted for about 54% of the time at levels between base and peak thresholds, demonstrating regional variations influenced by climate and economic factors.^[23]^[20] Base load forms the lower, flatter portion of the LDC, representing the constant underlying demand from essential services and residential use. It is supplied by baseload units like nuclear, coal, or large hydroelectric plants designed for continuous operation at high capacity factors (90-95%). Segmentation into these categories can employ arbitrary duration cutoffs from the curve's extremes, or statistical methods like identifying knee points where the curve's slope changes significantly. Advanced approaches, such as K-means clustering on hourly load data, determine boundaries by grouping durations into clusters (e.g., base below 15,003 MW, peak above 20,318 MW in the 2001 Iranian case), offering adaptability to diverse system profiles.^[24]^[20]^[23]

Applications

Power System Planning

Load duration curves (LDCs) play a central role in power system planning by providing a visual and analytical framework for assessing long-term demand patterns and ensuring adequate generation and infrastructure capacity. These curves rank hourly load data over a period, typically a year, from highest to lowest, revealing the frequency and magnitude of demand levels. In capacity expansion decisions, planners use LDCs to evaluate how much generating capacity is needed to meet varying loads reliably, focusing on the upper portions of the curve where peaks occur infrequently but require substantial resources. For instance, reserve margins are calculated to cover durations where load exceeds a certain threshold, maintaining system reliability during peaks.^[25]^[26] Seasonal variations in load are analyzed through segmented LDCs, which highlight steeper slopes during summer or winter peaks, guiding the sizing of transmission lines and energy storage systems. By examining curve shapes across seasons, planners identify periods of elevated demand—often driven by air conditioning or heating—and allocate resources accordingly, such as reinforcing transmission for high-summer loads or deploying storage to buffer winter peaks. This approach ensures infrastructure aligns with temporal demand profiles, preventing bottlenecks during critical periods.^[20]^[27]^[28] For reliability assessment, LDCs help pinpoint extended low-load durations, which represent opportunities for scheduling maintenance on generation and transmission assets without compromising service. These flat lower sections of the curve indicate times when system stress is minimal, allowing planners to optimize outage windows and enhance overall dependability. Projections of future LDCs are essential for integrating renewables, as variable generation from wind and solar flattens the curve by reducing net load peaks, informing decisions on additional flexible capacity like batteries or demand response.^[29]^[30] Historically, utilities have employed annual LDCs to justify constructing new plants by demonstrating the expansion of peak load durations amid growing electrification, to match supply with industrial and residential demand growth. In recent years as of 2025, LDCs have been increasingly applied to address emerging load growth from electrification, data centers, and electric vehicles, which introduce sharper peaks and require updated capacity planning to maintain reliability under higher utilization rates.^[31]

Economic and Operational Analysis

Load duration curves (LDCs) are instrumental in computing marginal costs by delineating load segments to which generation resources with varying fuel costs are assigned, ensuring higher-cost units serve peak portions while lower-cost baseload plants cover extended durations. For instance, the long-run marginal cost (LRMC) is derived by perturbing the LDC—such as increasing demand by 1-5%—and recalculating the optimal generation mix, with the LRMC equating the present value of incremental costs divided by the demand change; this approach matches coal plants to base load (e.g., 5,000 MW at high capacity factors) and gas turbines to peaks (e.g., 3,000 MW for short durations) on a typical annual LDC peaking at 12,000 MW.^[32] Similarly, expected marginal cost curves integrate LDC data with unit availability probabilities via convolution, weighting incremental costs to inform time-of-day pricing and dispatch boundaries. In unit commitment, LDCs facilitate cost minimization by segmenting the curve into base, intermediate, and peak loads, committing low-cost units (e.g., nuclear or coal) to prolonged high-availability portions and reserving flexible, higher-cost units for shorter peaks. This process involves economic dispatch along the effective LDC after commitment, calculating energy output as the area under the curve (e.g., 1,401,600 MWh for a base unit) and total production costs via integrals of committed capacities and fuel rates, yielding optimized annual expenses like $99.5 million for a multi-unit system.^[33] Demand-side management (DSM) leverages LDCs to target peak shaving, flattening the curve by shifting or reducing loads during high-duration segments, thereby lowering overall system costs through deferred peaking capacity needs. Techniques model DSM impacts directly on the LDC, adjusting for load reductions (e.g., via time-of-use incentives) to evaluate benefits like decreased loss-of-load probability and unserved energy, while integration with renewables further enhances value by reshaping the curve for better resource utilization.^[34] For revenue estimation in competitive markets, LDCs aid in forecasting energy payments from dispatched generation and capacity payments tied to peak availability, segmenting the curve to estimate inframarginal rents for baseload units and scarcity premiums during rare high-load hours. This distinguishes reliable capacity contributions (e.g., via effective load-carrying capability) from energy-only revenues, ensuring payments cover fixed costs where energy markets alone fall short.^[35] In the PJM Interconnection, LDCs guide bidding strategies by correlating load durations with locational marginal prices (LMPs), enabling demand response providers to bid into real-time and day-ahead markets at strike prices (e.g., $75/MWh), optimizing revenues from subsidies and price reductions—such as $610,000 net present value over five years per MW—while enhancing welfare through peak load mitigation up to 7,500 MW (5% of peak).^[36]

Variations and Extensions

Residual Load Duration Curve

The residual load duration curve (RLDC), also known as the net load duration curve, represents the portion of electricity demand that remains after subtracting generation from variable renewable energy (VRE) sources, such as solar photovoltaic (PV) and wind, from the total system load. This results in a profile that highlights the requirements for dispatchable resources, including conventional generators, storage, and demand response, to balance the grid. Unlike the standard load duration curve, the RLDC accounts for the intermittent nature of VRE, providing insights into how renewables alter the temporal distribution of net demand.^[37]^[38] To construct an RLDC, hourly or sub-hourly time series data for total system load are first adjusted by deducting the corresponding output from VRE sources, yielding residual load values for each period. These values are then sorted in descending order and plotted against the cumulative number of hours, mirroring the methodology of a conventional load duration curve but reflecting the modified net profile. This adjustment reveals the effective demand served by non-VRE capacity, with empirical data often drawn from grid operators' records, such as those from the UK National Grid or European transmission system operators.^[38]^[39] The incorporation of VRE profoundly shapes the RLDC, typically resulting in a steeper curve with pronounced slopes that signify elevated ramping demands for dispatchable plants to accommodate rapid fluctuations in net load. For instance, high solar penetration can produce negative residual loads during midday overgeneration, necessitating curtailment to avoid grid instability, while evening periods may exhibit shifted peaks with ramps exceeding 20 GW per hour in advanced systems. Wind integration tends to flatten the curve more evenly but still amplifies variability, reducing minimum loads without substantially mitigating peaks. These effects underscore the need for enhanced system flexibility as VRE shares grow.^[37]^[39] In grids transitioning to high VRE penetration—anticipated to comprise 30-50% of generation in many regions by 2030 and beyond—the RLDC serves as a critical tool for assessing capacity adequacy, flexibility provisioning, and integration costs. It enables planners to quantify profile-related expenses, such as increased cycling of thermal plants, and to optimize mixes of baseload, mid-merit, and peaking resources under decarbonization scenarios. A prominent example appears in California's Independent System Operator (CAISO) territory, where RLDCs for solar-dominant days depict the "duck curve" dynamic: a deep midday net load trough followed by an inverted, steep evening ramp, illustrating challenges like over 13 GW of ramping within three hours to offset declining solar output.^[37]^[40]

Sector-Specific Adaptations

Load duration curves have been adapted for environmental management, particularly in Total Maximum Daily Load (TMDL) assessments under the U.S. Clean Water Act, to evaluate pollutant loading in water bodies relative to flow regimes. These curves plot pollutant loads (e.g., in kg/day for nutrients or colony-forming units per day for bacteria) against the duration or exceedance percentage of stream flows, derived from hydrological data such as daily average discharges from the U.S. Geological Survey (USGS). By multiplying flow rates (in cubic feet per second) by water quality criteria concentrations and conversion factors (e.g., 8.34 for mass per volume to pounds per day), the curves identify exceedances where observed loads surpass allowable capacities, enabling the allocation of wasteloads to point sources and load allocations to nonpoint sources across flow zones like high (0-10% exceedance), moist (10-40%), mid-range (40-60%), dry (60-90%), and low (90-100%). This approach accounts for seasonal variations, such as wet and dry periods, which influence pollutant dilution and transport, differing from traditional power load duration curves by using mass-based units rather than megawatts and focusing on ecological rather than electrical demand.^[41] A key example from EPA guidelines involves river systems, where load duration curves set wasteload allocations for wastewater treatment plants to meet standards for fecal coliform or total phosphorus. In the Pee Dee River Basin TMDL, the curve established a wasteload allocation of 4.54 × 10^9 colony-forming units per day for the Pageland Northwest wastewater treatment plant across flow conditions, ensuring compliance with geometric mean criteria (e.g., 200 cfu/100 mL) while incorporating a margin of safety (e.g., 5% explicit reduction) to address uncertainties in flow data and pollutant delivery. Similarly, the Quepote Brook TMDL allocated 0.12 tons of organic nitrogen per day to a municipal wastewater plant in high-flow zones, with higher allocations (up to 3.81 tons/day) for stormwater sources in moist conditions, demonstrating how these curves guide implementation plans tailored to hydrological variability.^[41]^[42] In industrial processes, load duration curves are tailored to plant-specific demand patterns for sizing equipment, such as motors, generators, or peak-shaving systems, by rearranging chronological load data in descending order to reveal the frequency and magnitude of power requirements over operational periods. For manufacturing facilities like steel mills, where demand fluctuates due to processes such as electric arc furnace melting (peaking at 50-100 MW intermittently), these curves help select equipment ratings that match the cumulative hours at various load levels, avoiding over-sizing based on rare peaks while ensuring reliability during high-demand shifts (e.g., 8-12 hours daily). Unlike power system curves focused on grid-wide generation, industrial adaptations emphasize shorter horizons (e.g., daily or shift-based) and may incorporate units like kilowatts per process line, prioritizing cost-effective operation under variable production schedules.^[43]^[20] For instance, in steel plant energy management, load duration curves derived from historical meter data guide the optimal sizing of on-site generators for peak shaving, calculating the capacity needed to cover durations where loads exceed utility thresholds (e.g., 80% of peak for 20% of hours), reducing demand charges by 15-30% through targeted investments rather than full-load equivalents. This method integrates with scheduling algorithms to align equipment operation with load profiles, such as minimizing furnace cycling during low-duration high loads.^[44] In transportation electrification, load duration curves aggregate electric vehicle (EV) charging demands into system-level profiles to assess grid impacts, simulating coordinated charging scenarios to flatten peaks and evaluate infrastructure needs. EV loads, typically 3-20 kW per vehicle, are probabilistically modeled (e.g., via Monte Carlo simulations) and added to base grids, revealing shifts in the curve's shape—such as a 10-20% upward peak extension at 80% EV penetration—while vehicle-to-grid (V2G) strategies reverse portions for valley filling. These adaptations differ from conventional power curves by incorporating stochastic elements like arrival times and battery states, often over annual periods but segmented by seasons or peak/off-peak tariffs, using megawatt-hours to quantify energy rather than instantaneous power. Studies show that optimized EV scheduling via quadratic programming can reduce maximum demand by up to 25% on load duration curves, mitigating transformer overloads in high-adoption scenarios (e.g., 30% fleet penetration increasing evening peaks by 15-40 MW in urban feeders), thus informing utility planning for deferring upgrades.^[45]

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[PDF] Capacity Payments and Supply Adequacy in Competitive Electricity ...
CONTRACT DURATION. Locking in the capacity payment for a longer duration has the effect of averaging out price volatility thus, providing the security of a ...
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[PDF] An Economic Welfare Analysis of Demand Response in the PJM ...
For each hour of 2006, we used the actual load duration curve and an econometric model of LMPs for the PJM market to estimate the four regions shown in ...<|control11|><|separator|>
[39]
[PDF] System Costs with High Shares of Nuclear and Renewables
The “Duck curve” – residual load in the CAISO system at ... a steeper and steeper residual load duration curve as the VRE penetration level increases.
[40]
Optimal capacity mix and scarcity pricing - Open Electricity Economics
Residual load duration curve. By sorting hours by residual load, just as it was done for the actual load, we can derive the residual load duration curve (RLDC).
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[PDF] The Residual Load Duration Curve (rLDC) to model an energy system
Wiskich, “Implementing a load duration curve of electricity demand in a general equilibrium model”, in. Energy Economics, 2014, Vol. 45, pp.373–380. [10] W.-G.
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[PDF] What the duck curve tells us about managing a green grid
The duck chart shows the system requirement to supply an additional 13,000 MW, all within approximately three hours, to replace the electricity lost by solar ...Missing: residual | Show results with:residual
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[PDF] An Approach for Using Load Duration Curves in the Development of ...
A flow duration curve relates flow values to the percent of time those values have been met or exceeded. The use of “percent of time” provides a uniform scale ...
[44]
TMDL Support Documents | US EPA
An Approach for Using Load Duration Curves in the Development of TMDLs (pdf), August 2007 (74 pp, 3.4 MB, EPA 841-B-07-006); Establishing TMDL "Daily" Loads ...
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[PDF] Optimal Sizing of Peak-Shaving Generators Using Load Duration ...
This paper presents two models for finding the optimal size and annual operating time for a customer-owned. PSG with constant and declining block rates. The ...
[46]
Electrical load tracking scheduling of a steel plant - ScienceDirect.com
Nov 8, 2010 · This paper presents a scheduling solution for electrical load tracking of a steel plant. In the scheduling problem the electricity ...Missing: duration | Show results with:duration
[47]
Comprehensive impact analysis of electric vehicle charging ...
Aug 5, 2025 · A popular goal for EV coordination is flattening the load duration curve. Several research works [14][15][16][17] [18] [19][20] address the EV ...