AI-Based Temperature Sensitivity Modeling for Electricity Demand

Executive Summary

Electricity load forecasting has evolved from a point-prediction problem into a broader demand-intelligence problem. Utilities, Load Serving Entities (LSEs), electricity retailers, and their trading, forecasting, planning, and system-operations teams increasingly need forecasts that are accurate across operating regimes, probabilistic rather than purely deterministic, interpretable in terms of weather sensitivity, and capable of answering counterfactual questions such as how a colder or hotter weather path would alter demand.

This paper presents a general methodology for AI-based electricity load forecasting and weather-sensitive demand analysis steaming from research and developments around QR ALPS, QR AI Load Prediction System. The framework separates three analytically distinct but coupled functions:

• forecasting the baseline load distribution
• decomposing weather-sensitive demand into interpretable structural components
• transforming the baseline forecast under explicit weather scenarios.

The methodology combines adaptive heating and cooling base temperatures, constrained statistical estimation, machine-learning response modeling, balanced central finite differences for local sensitivity estimation, derivative-balance calibration, optional thermal-memory operators, regime-dependent nonlinear response functions, and probabilistic scenario transformation. The design is meant for a universal solution intended to remain portable across regions rather than relying on fixed regional rules.

A central principle is numerical stability. Temperature sensitivity estimates can become noisy when weather observations are sparse, regimes change, or local coefficients are estimated independently. QR ALPS therefore treats stability, shrinkage, continuity, and out-of-sample validation as first-class requirements rather than as post-processing.

The paper distinguishes the core methodology from advanced extensions and research directions. This distinction is deliberate: a technically credible forecasting platform should make clear which methods are production components, which are optional extensions, and which require further empirical validation.

The result is an interpretable AI forecasting architecture in which machine learning provides nonlinear predictive power while structural decomposition provides a controlled representation of temperature response and scenario sensitivity.

1. Introduction: From Load Prediction to Load Intelligence

1.1 The operational requirement

Short-term load forecasting is commonly evaluated through MAE, RMSE, MAPE, bias, or related forecast-error measures. These metrics remain essential, but forecast accuracy alone does not answer several operational questions:

1. How much of expected demand is structural rather than weather-driven?
2. How does marginal load sensitivity change between mild and severe heating or cooling conditions?
3. How does a specified temperature shock propagate into hourly demand?
4. How should a baseline probabilistic forecast be transformed under an alternative weather path?
5. Are estimated weather-response parameters stable enough to support production scenario analysis?

QR ALPS addresses these questions by coupling a nonlinear AI forecasting engine with an interpretable decomposition and scenario layer. The architecture is intentionally modular: forecasting, explanation, and scenario transformation are related but are not treated as the same statistical task.

1.2 Core analytical architecture

The same framework can support short-term, day-ahead, intraday, and longer-horizon applications provided that the input data, forecast horizon, and model validation protocol are appropriate to the use case.

2. Weather-Sensitive Demand Decomposition

2.1 Adaptive heating and cooling degree-hour operators

Fixed degree-day conventions such as a universal 65°F base temperature are useful descriptive conventions but are not necessarily optimal statistical representations of a particular load footprint. Building stock, appliance saturation, climate, customer behavior, electrification, and time-of-day effects can shift the temperature range over which load responds materially.

HDH_t = max (0, T_H,base – T_t ) (2.1a)

CDH_t = max (0, T_t – T_C,base ) (2.1b)

where

T_t is the ambient temperature.
T_H,base is the thermal turning point below which space heating systems activate (typically near 68°F or 20°C).
T_C,base is the thermal turning point above which air conditioning systems activate (typically near 72°F or 22°C).

QR ALPS. Scatter Plot of MISO LRZ2–7 Demand versus Temperature, Illustrating the Load Response Around the Estimated Heating and Cooling Base Temperatures.

The important methodological point is that T_H,base and T_C,base are treated as a model parameter to be estimated using the actual demand data, rather than as a universal physical constant. The region between the two thresholds can be interpreted as a modeled thermal deadband. The parameters may vary by season, day type, sub-region, or interval when the available data supports such granularity.

2.2 Structural load model

L_t = a_r,t + b_r,t · CDH_t + c_r,t · HDH_t − d_r,t · GHI_t + ε_t(2.2 a)

The terms have the following interpretation:

• a_r,t : structural or non-weather demand for the relevant regime;
• b_r,t : marginal cooling sensitivity, expressed in MW per CDH;
• c_r,t: marginal heating sensitivity, expressed in MW per HDH;
• d_r,t · GHI_t : effective net-load reduction associated with behind-the-meter photovoltaic generation.
• ε_t : remaining unexplained variation.

The GHI coefficient should be interpreted as an effective net-load response parameter, not as a physical photovoltaic conversion efficiency. BTM-PV capacity, orientation, cloud cover, inverter behavior, and customer self-consumption can all affect the observed relationship.

2.3 More advanced concepts

2.3.1 Thermal memory

Current ambient temperature is not always a sufficient statistic for building thermal state. Prolonged heating or cooling conditions can create thermal accumulation in building envelopes and equipment. An optional thermal-memory representation can therefore augment instantaneous HDH:

HDH_t* = θ · HDH_t + (1- θ)· Σ_k=1..K w(k) · HDH_t-k

w(k) ∝ e^−λk

The parameters θ, λ, and K should be estimated or validated for the application rather than assumed universally. This component is best regarded as an advanced extension when historical load and weather data demonstrate meaningful persistence beyond contemporaneous temperature.

2.3.2 Nonlinear heating and cooling response

A constant heating coefficient c_t assumes that every additional unit of HDH has the same marginal impact. That assumption can become restrictive in highly electrified heating systems. Heat-pump performance, auxiliary resistance heating, customer behavior, and building thermal state can produce a change in marginal response during severe weather.

Electricity demand may not respond to cold weather at the same rate across the entire heating range. For example, conceptually:

• Moderate cold → heating demand increases at one rate, β₁.
• Extreme cold → heating demand could increase at a different rate, β₂.
• H_threshold is the point where the response changes.

This is essentially a piecewise-linear approximation of a nonlinear temperature response:

f_heat(HDH*) = β₁· HDH*, if HDH* ≤ H_threshold

β₁· H_threshold + β₂· (HDH* – H_threshold), if HDH* > H_threshold

The piecewise formulation is an example of a regime-dependent response model. It does not assert that β₂ must exceed β₁ in every system; that relationship should be estimated and validated. Similar nonlinear functions can be constructed for cooling response when the data indicate saturation or regime changes.

This extension is especially useful for stress testing because a severe-weather scenario can move the system into a response regime that is weakly represented in ordinary operating conditions.

3. Adaptive Parameter Estimation and Numerical Stability

3.1 Why stability matters

Weather-response estimation is notoriously statistically unstable. A local region may have limited observations in a particular temperature regime; temperature and calendar variables may be highly correlated; extreme events may be rare; and independent estimation of many hourly coefficients can create artificial jumps. A model that produces a plausible coefficient in one training window but changes substantially after a modest change in the sample is unsuitable for robust scenario analysis.

QR ALPS therefore treats parameter stability as part of model quality. Accuracy and interpretability are necessary but not sufficient; the estimated response must also be numerically and operationally stable.

3.2 Adaptive T_base estimation

The relationship between electricity demand and temperature is not necessarily characterized by fixed heating and cooling base temperatures. Customer type composition, building characteristics, operating practices, climate, seasonality, and other load characteristics can cause the effective temperature response to vary across locations and operating regimes. QR ALPS therefore treats the heating and cooling base temperatures as model parameters that can be evaluated from historical data rather than assuming universal fixed values.

The resulting HDH_t and CDH_t variables (2.1a & b) provide the temperature representation used by the load model. Different candidate base-temperature pairs therefore produce different representations of the same historical temperature series and can result in different estimated load-response relationships.

Candidate Evaluation

QR ALPS evaluates candidate base-temperature definitions using time-ordered validation rather than randomly shuffling observations. This preserves the temporal structure of the electricity-load and weather series and provides a more meaningful assessment of how a temperature definition performs on observations outside the corresponding estimation period.

For each candidate pair (T_H,base,T_C,base) the corresponding HDH_t and CDH_t variables are generated and supplied to the mathematical load model (2.2 a). The model parameters are then estimated for that candidate representation, and the resulting load predictions are evaluated against observed load.

A representative validation objective is:

Q_validation(T_H,base,T_C,base) = ∑_t∈V w_t [L_t – ^̂ L_t]² (3.2 a)

where:

• L_t = observed electricity load at time t;
• ^̂ L_t = load predicted by the model for the candidate base-temperature definition;
• w_t = optional observation weight;
• V = set of observations used for validation.

The candidate base-temperature configuration is selected according to its validation performance, subject to the stability and model-quality checks described below:

(T_H,base^*,T_C,base^*) = argmin_{TH,base,TC,base} Q_validation

The notation * denotes the selected base-temperature configuration rather than a universally optimal physical temperature.

The search can be implemented using bounded grid search, coordinate search, profile optimization, segmented regression, or bounded nonlinear optimization. Grid search is a transparent initialization and candidate-selection mechanism; it should not automatically be interpreted as proof that the selected temperature is physically optimal.

Stability and Robustness Assessment

Numerical stability is a key challenge in implementation. Validation error alone is not sufficient to establish that a particular base-temperature configuration is appropriate. Candidate configurations are therefore assessed for stability across different historical samples and operating conditions.

Relevant checks include:

• stability of the selected base-temperature configuration across rolling or sequential training windows;
• sensitivity to reasonable changes in the historical weather sample;
• consistency of the resulting heating and cooling response;
• continuity across neighboring time periods or operating regimes where continuity is expected; and
• out-of-sample forecast performance.

This process reduces the risk that the selected T_base values reflect a temporary characteristic of a particular historical sample rather than a persistent feature of the load-temperature relationship.

3.3 Regularized weighted estimation

Demand has diurnal and seasonal patterns. Numerical instabilities frequently occur when load response parameters are estimated separately across time intervals or operating regimes. Regularization is one approach that can be used to discourage unnecessary changes between adjacent parameter estimates. However actual implementation method and algorithms remain proprietary: λ_{c smooth}

A representative smoothness penalty is:

Ω_smooth = λ_b Σ [b_t-b_(t-1)]² +λ_c Σ [c_t-c_(t-1)]²

where:

• Ω_smooth = smoothness penalty
• λ_b = regularization strength applied to cooling sensitivity
• λ_c = regularization strength applied to heating sensitivity

The smoothness penalty can be added to the minimization objective function (3.2 a).

The regularized estimation balances accurate fitting of observed load with stability of the estimated load-response parameters. Where appropriate, additional constraints may be applied to maintain physically or statistically reasonable parameter behavior, such as nonnegative heating and cooling sensitivities and reasonable parameter bounds.

Importantly, the regularization parameters λ_b and λ_c control the parameter-estimation process; they are not additional load-model variables and do not directly define the heating or cooling base temperatures. The selection of T_H,base and T_C,base remains the validation-based process described in Section 3.2.

This separation provides a clear estimation sequence:

Candidate T_base values → HDH/CDH calculation → load-model estimation → validation → base-temperature selection → final regularized parameter estimation.

4. Machine Learning as the Nonlinear Forecasting Engine

4.1 Failure of Regression and least-square Methods

Conventional regression and least-squares estimation can be used to estimate heating and cooling sensitivities from historical load and temperature observations.

A representative formulation is:

minΣ_t[L_t – a_t – b_t CDH_t – c_t HDH_t]².

In estimating the cooling and heating sensitivity parameters b_t and c_t, time t spans diurnal as well as seasonal patterns. Over relatively short rolling periods, however, the resulting coefficients can be highly sensitive to the particular weather and load conditions contained in the estimation window. In practice, this can produce substantial variation in the estimated heating and cooling sensitivities from day to day, making it difficult to derive a stable diurnal and seasonal response profile.

The behavior can also vary substantially across seasons and demand types. A relationship that provides a reasonable fit during a summer period, for example, may not provide a stable response representation during spring or under a different load composition.

This limitation motivates the use of a controlled machine-learning temperature-response approach in QR ALPS.

4.2 ML-Based Temperature-Response Estimation

Reconsider the load model

^̂ L_t = a_t + b_t · CDH_t + c_t · HDH_t − d_t · GHI_t + ε_t(2.2 a)

This relationship can also be viewed more generally as an ML response function:

^̂ L_t = F(CDH_t , HDH_t , Z_t ) (4.1 b)

Where Z_t represents the other features used by the ML model.

b_t = ∂ ^̂ L_t / ∂CDH_t≈ Δ ^̂ L_t / ΔCDH_t(4.1 c)

c_t = ∂ ^̂ L_t/ ∂HH_t≈ Δ ^̂ L_t / ΔHDH_t(4.1 d)

More generally let X_t be CDH_t , HDH_t

∂ ^̂ L_t / ∂X_t= Δ ^̂ L_t / ΔX_t = ( ^̂ L_t (X_t +ΔX) – ^̂ L_t (X_t) ) / ΔX (4.1 e)

The computation of these derivatives can be assisted by an ML model

^̂ L_t (CDH_t , HDH_t, Features)

The ML model is trained on historical observations using relevant Features. These may include:

• CDH(t) and HDH(t);
• hour of day;
• day of week;
• month and season;
• calendar indicators;
• temperature;
• lagged and rolling load variables;
• lagged and rolling CDH and HDH variables;
• solar variables; and
• other validated variables relevant to the load-forecasting application.

Because tree-based machine learning models are piecewise constant, they are not differentiable in the classical sense with respect to CDH_t and HDH_t. However, they can be quite good at predicting perturbations. When a temperature-derived input is perturbed, dependent must be treated consistently. This ensures that the resulting prediction represents a controlled temperature perturbation rather than an internally inconsistent feature combination.

The ML model can therefore be evaluated over a grid of controlled perturbations, for example ^̂ L_t(X_t +ΔX). The resulting predictions are then used with finite-difference formulas to estimate the local heating and cooling sensitivities (4.1.c) and (4.1.d).

The perturbation size ΔX (ΔCDH and ΔHDH), the perturbation grid, and the finite-difference formulation should be evaluated over a reasonable range. Material variation in the estimated sensitivity across perturbation specifications provides a useful stability diagnostic.

QR ALPS incorporates proprietary procedures for controlling the numerical and modeling instabilities associated with this process and for producing stable heating and cooling response profiles.

4.3 Seasonal and Diurnal Temperature-Response Profiles

Temperature sensitivities estimated from the ML perturbation and finite-difference process can exhibit substantial variability across observations. Differences in weather conditions, load composition, operating conditions, and other factors can affect the estimated heating and cooling response.

QR ALPS therefore estimates temperature sensitivities by season and hour of day, rather than relying on a single sensitivity coefficient for an entire seasonal period.

For each seasonal period, the resulting estimates are organized by hour to form 24-hour heating and cooling sensitivity profiles:

b_s= {b_s,1, …, b_s,24}

c_s= {c_s,1, …, c_s,24}

where:

• s : represents the seasonal operating period, e.g., winter, spring, summer, fall. These can be configured to match the climate of the demand region.
• t : represents the hour of day;
• b_s,t : represents the cooling sensitivity for hour t;
• c_s,t : represents the heating sensitivity for hour t.

Because individual sensitivity estimates can exhibit substantial variability, QR ALPS applies robust statistical filtering and smoothing techniques to reduce the influence of extreme estimates. The retained estimates are then aggregated separately for each hour and season to produce representative diurnal temperature-response profiles.

This process preserves the underlying diurnal structure of the heating and cooling response while reducing the influence of unusually high or low individual sensitivity estimates.

The resulting profiles provide an interpretable representation of how electricity demand responds to heating and cooling conditions across different hours of the day and seasonal operating periods.

The objective is not to create an unnecessarily large number of independent coefficients. Rather, QR ALPS seeks to capture meaningful seasonal and diurnal response structure while limiting the influence of estimation variability and noise.

The specific filtering, aggregation, and stabilization procedures used to construct the production profiles are implementation details of the QR ALPS forecasting framework.

The MISO LRZ2-7 example is provided solely to illustrate the methodology. QR ALPS is designed for application across load-serving regions and market environments and is not specific to MISO or any particular market operator.

5. Numerical Example

5.1 Load Model Parameters

For illustration, consider QR ALPS applied to MISO LRZ2-7 for the winter of Year Y. The temperature-response parameters used in this example are seasonal parameters estimated for the winter operating period.

These seasonal diurnal parameters can be applied to observed demand during the corresponding winter period and can also be used as the temperature-response parameters for applicable forecasts for the subsequent winter, subject to the QR ALPS forecasting framework.

5.2 Historic Heating Degree Load Component

Assume that the MISO LRZ2-7 peak load interval occurs at 18:00 on January 21 of Year Y, with a net load of 23,228.19 MW and an ambient temperature of 0.77°F.

The corresponding model inputs are:

Calculation of HDH 

HDH₁₈ = max (0, T_H,base – T_t ) = 52 – 0.77 = 51.23

Calculation of the Heating-Sensitive MW Component 

The Heating MW components of load, for hour 18, is

L_(HDH,t)= c_t* HDH_t= c₁₈* HDH₁₈ = 74.50 * 51.23 = 3816.635 MW

Calculation of Base Load at hr 18: a₁₈  

a₁₈ = L_(HDH,t) – c_t* HDH_t= 23,228.19 – 3816.635 = 19,411.56 MW

This provides an illustrative decomposition of the historical load into a heating-sensitive component and a residual base-load component.

5.3 Application to Forecast Load Decomposition

The preceding calculation illustrates how the seasonal diurnal heating-sensitivity coefficient can be used to decompose load into a temperature-sensitive component and a residual component.

Once the seasonal diurnal coefficients have been estimated from historical data, QR ALPS can apply the corresponding coefficients to future AI demand forecasts to estimate the heating and cooling-sensitive portions of forecast load.

For example, assume a 7-day-ahead load forecast is generated on February 2 of Year Y+1 for MISO LRZ2-7. For the 18:00 interval on February 3 of Year Y+1, assume:

For February 3, Y+1:

• Calculation of HDH forecast for Fe 

HDH₁₈ = max (0, T_H,base – T_t ) = 52 – 5 = 47

• Calculation of the Forecasted Heating-Sensitive MW Component 

L_(HDH,t)= c_t* HDH_t= c₁₈* HDH₁₈ = 74.50 * 47 = 3501.5 MW

• Calculation of Base Load at hr 18: a₁₈  

a₁₈ = L_(HDH,t) – c_t* HDH_t= 23,500 – 3816.635 = 19,998.5 MW

Thus, under this illustrative decomposition, the 23,500 MW forecast load consists of approximately:

• 3,501.50 MW attributable to the heating-sensitive component; and
• 19,998.50 MW representing the residual/base component.

6. Temperature Scenario Analysis

For utilities, LSEs, and electricity retailers, the probabilistic forecast supports energy-position and demand-risk assessment. For forecasting, planning, and system-operations teams, the same forecast provides an interval-level view of expected load and forecast uncertainty.

6.1 AI Probabilistic Net-Load Forecasting

QR ALPS generates probabilistic net-load forecasts at user-defined percentiles from P1 to P99, at resolutions ranging from 5 minutes to hourly. The platform uses automated machine-learning methods to model nonlinear relationships and interactions among load drivers.

QR ALPS No-Coding On-Screen Load Forecast Platform

The probabilistic forecast distribution can be explored through web dashboards or exported through API. For example, P5 represents a lower-tail forecast, P50 the median forecast, and P95 an upper-tail forecast. These percentiles characterize the uncertainty distribution of the forecasted demand and answer the question:

What level of load corresponds to a given forecast percentile?

The CDH/HDH decomposition answers a different and complementary question:

What portion of the forecasted load is attributable to modeled weather-sensitive thermal demand?

The two approaches therefore serve different purposes. Probabilistic forecasting quantifies uncertainty in the load outcome, while load decomposition explains the modeled drivers of that outcome. Combining the two enables temperature-stress scenarios to be applied consistently across the forecast distribution.

For commercial and trading organizations, these scenarios quantify weather-driven demand exposure for procurement, scheduling, and portfolio risk analysis. For forecasting and system-operations organizations, they provide a controlled way to evaluate peak demand, ramps, and operational stress under alternative weather paths.

6.2 Deterministic weather scenarios

Given a baseline temperature path and an alternative scenario temperature path, QR ALPS calculates the resulting load response from the model-estimated heating and cooling sensitivity coefficients rather than by applying an arbitrary fixed MW adjustment. By equation (4.1.d)

• Cooling MW impact

Δ ^̂ L_Coolt = b_t ΔCDH_scenario,t= b_t (CDH_scenario,t – CDH_baseline,t) (6.2.a)

• Heating MW impact

Δ ^̂ L_Heatt = c_t ΔHDH_scenario,t= c_t (HDH_scenario,t – HDH_baseline,t) (6.2.b)

The resulting scenario load can therefore be expressed as:

• Cold-snap scenario incremental load

L_scenario,t = L_baseline,t+ Δ ^̂ L_Coolt (6.2.c)

• Heatwave scenario incremental load

L_scenario,t = L_baseline,t+ Δ ^̂ L_Heatt(6.2.d)

The baseline load, L_Baseline,t, can represent either historical demand or an AI-generated load forecast. The same scenario framework can therefore be applied to both observed and forecast load.

When applied to forecast demand, L_Baseline represents the load forecast generated under the normal or baseline temperature forecast. QR ALPS can then apply a deterministic temperature scenario to the baseline forecast to quantify the incremental demand associated with the specified weather change. The probabilistic nature of the baseline forecast is preserved. A temperature scenario, such as a −10°F temperature shock, is not itself a forecast percentile. Rather, it represents an additional deterministic weather scenario that can be applied to P5, P50, P95, or any other percentile in the probabilistic forecast distribution.

This allows users to distinguish between two separate sources of uncertainty:

• Forecast uncertainty: represented by the probabilistic load forecast distribution; and
• Weather scenario impact: represented by the incremental load response to the specified temperature scenario.

The next step is to distribute the specified temperature shock across the forecast hours using the diurnal weather-scenario profile, after which the corresponding scenario temperatures and HDH/CDH values are calculated.

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6.3 Diurnal temperature-shock profiles

A temperature shock specified as a single value, such as -10^∘F, does not necessarily imply that the same temperature departure should be applied uniformly to every hour of the day. The magnitude and timing of weather impacts can vary throughout the day.

QR ALPS therefore represents a temperature scenario using a diurnal temperature-shock profile:

T_scenario,t = T_baseline,t + ΔT_nominal,t ϕ(t) (6.3.a)

where:

• T_baseline(t) is the baseline temperature at hour t;
• ΔT_shock is the specified scenario temperature shock;
• ϕ(t) is a dimensionless diurnal profile describing how the nominal shock is distributed across the hours of the day; and
• T_scenario(t) is the resulting scenario temperature.

The profile ϕ(t) can be derived from historical weather events and calibrated to preserve the characteristic intraday shape of the temperature response. Depending on the application, the profile may incorporate historical hourly temperature departures, robust aggregation across comparable events, seasonal conditioning, day-type conditioning, and appropriate smoothing.

The normalization convention is an important part of the scenario definition. For example, the profile may be normalized so that the specified scenario represents a particular peak temperature departure, average departure, or another operationally meaningful measure. The normalization determines how the nominal temperature shock is distributed across the 24 hours and therefore directly affects the resulting load scenario. Once the scenario temperature path has been generated, QR ALPS recalculates the corresponding degree-hour variables:

Then T_scenario is used in computing  HDH_scenario  and CDH_scenario:

CDH_scenario,t = max (0, T_scenario,t– T_C,base) (6.3.b)

HDH_scenario,t = max (0, T_H,base – T_scenario,t ) (6.3.c)

These scenario CDH and HDH are then replaced in (6.2.a) to (6.2.d) to compute the incremental heating or cooling load and the corresponding demand under each scenario.

This approach ensures that the scenario calculation respects the hourly structure of the weather shock and the heating and cooling breakpoints, rather than treating a temperature scenario as a uniform MW adjustment. The specific construction, calibration, normalization, and stabilization procedures used by QR ALPS to generate production temperature-shock profiles are implementation details of its framework.

Audience and case-study note: The MISO LRZ2–7 data used below are solely an illustrative test case for demonstrating the QR ALPS methodology. The methodology is not specific to MISO or to any particular market operator. QR ALPS is intended for utilities, LSEs, electricity retailers, and their trading, forecasting, planning, and system-operations teams.

6.4 Numerical Example

Extreme winter weather events can produce substantial and nonlinear increases in electricity demand. A cold-snap scenario allows utilities, LSEs, electricity retailers, and their trading, forecasting, planning, and system-operations teams to quantify the incremental demand and associated hourly load impacts under a specified temperature shock.

6.4.1 Modeling Temperature Shock Profile

Consider a −10°F temperature scenario. QR ALPS first distributes the temperature shock across the 24-hour period using the method diurnal temperature-shock profile (6.3.1). The scenario temperature and corresponding HDH and CDH values are then calculated using Equations (6.3.a – c):

 T_{Scenario-10F,t} = T_Baseline – 10 ϕ(t)

HDH_{Scenario-10F,t} = max (0, T_H,base – T_{Scenario-10F,t} )

For the MISO LRZ2–7 example, a day-ahead net-load forecast is generated at 07:00 on February 23, 2026, for February 24, 2026. We analyze the application of a ΔT = −10°F temperature shock scenario to the forecast.

For the February 24, 07:00 interval:

where the scenario inputs Temp_Profile₀₇  and historic HT_base are estimated by the load model.

Therefore, the forecast weather scenario under the -10 F shock becomes

T_{Scenario-10F,07} = T_Baseline,07 + (-10) * 1.49 = 21.99 – 10.49 = 7.09 F

Substituting the stressed weather, we derive the corresponding scenario HDH_{Scenario-10F,07}:

HDH_{Scenario-10F,07} = max (0, HT_base– T_{Scenario-10F,07} )

= max (0, 52 – 7.09) = 44.91 

The baseline HDH is

HDH_Baseline,07 = max (0, HT_base– T_Baseline,07) = max (0, 52 – 21.99) = 30.01 

Therefore,

ΔHDH_{Scenario-10F,07} = 44.91 – 30.01 = 14.90

6.4.2 The Demand Under Temperature Shock Profile

For 7:00 am, QR AMPS model estimates the heating sensitivity coefficient to be

c_(07:00)= 52.09 MW/HDH.

The incremental demand attributable to the temperature shock is, using (6.2.b):

Δ ^̂ L_Cool07= c₀₇ ΔHDH_scenario,07 = 52.09 * ( 14.92 ) = 776.14 MW

Thus, the −10°F weather scenario produces an incremental modeled demand of approximately 776 MW for this interval.

Finally, the net load scenario corresponding to the -10F shock to the baseline load forecast  (such as the median P50 or high P95 profile) is given by the equation (6.2.c):

L_scenario,07 = L_baseline,07+ Δ ^̂ L_Cool07 = 20,396 + 777.18 = 21,172.14

Thus, the −10°F weather scenario produces a modeled demand shift of approximately 21,172 MW.

The same calculation can be applied independently to P5, P50, P95, or any other percentile of the probabilistic forecast distribution.

Because both the heating sensitivity coefficient and the temperature-shock profile are calibrated as diurnal patterns, the model can represent different load responses across the hours of the day. This provides utilities, LSEs, electricity retailers, and their trading, forecasting, planning, and system-operations teams with hour-by-hour visibility into the incremental demand, ramping requirements, and potential system stress associated with an extreme temperature scenario.

QR ALPS provides the baseline and scenario temperatures, HDH/CDH values, sensitivity coefficients, component MW values, and resulting net-load forecasts through multiple analytical reports.

7. Validation and Model Governance

A production forecasting methodology should be evaluated using time-ordered out-of-sample testing. Validation should assess not only forecast accuracy, but also the stability and consistency of the estimated temperature-response parameters.

Key validation dimensions include:

• Forecast accuracy: MAE, RMSE, bias, and peak-period forecast error.
• Probabilistic forecast quality: calibration, coverage, and appropriate probabilistic forecast metrics.
• Temperature-response stability: stability of the estimated heating and cooling sensitivities across rolling estimation periods.
• Seasonal and diurnal consistency: stability of the resulting hourly response profiles across comparable periods.
• Scenario-response validation: comparison of modeled temperature responses with observed load behavior during historical weather events.
• Extreme-weather performance: evaluation during periods of unusually high or low temperatures and high system demand.
• Regional validation: evaluation of both forecast performance and parameter stability when the methodology is applied to different market regions or load zones.

The validation process should use time-ordered training and testing periods to avoid information leakage between model estimation and evaluation.

Particular attention should be given to the stability of the estimated b_t, c_t, and temperature-base parameters. A model that produces accurate aggregate forecasts but highly unstable temperature-response parameters may not provide a reliable decomposition or scenario-analysis framework.

Production acceptance should therefore consider both forecast performance and stability of the derived temperature-response profiles.

8. Regional Portability

The methodology is designed to be applicable across different utilities, LSEs, electricity retailers, operating organizations, markets, and regions with footprints that can differ materially in climate, customer composition, electrification, distributed energy resources, load shape, and weather regimes.

Consequently, the numerical values of the heating and cooling sensitivity coefficients should not be assumed to be universally transferable between regions. The methodology instead uses common modeling principles while estimating the numerical parameters locally for the applicable load region and season. This allows the same framework to be applied across different load-serving organizations, operating environments, and regions while preserving region-specific temperature-response characteristics. Where sufficient local observations are available, regional and seasonal profiles can therefore be estimated independently. Where observations are limited, the level of parameter granularity should be reduced to avoid treating estimation noise as genuine regional or hourly behavior.

9. Limitations and Model Governance

The temperature-response decomposition has several important limitations.

• The decomposition is a statistical representation of observed load behavior and should not automatically be interpreted as causal identification.
• Degree-hour variables provide a simplified representation of thermal demand and may not capture the full dynamics of building thermal state and customer response.
• Extreme-weather extrapolation remains subject to uncertainty when historical observations contain few comparable events.
• Structural changes such as electrification, distributed energy resources, tariffs, building efficiency, and changes in customer behavior can alter estimated temperature sensitivities over time.
• Behind-the-meter PV effects may be difficult to separate completely from other weather and load effects when capacity or production information is incomplete.
• Machine-learning-based response estimates are most reliable when scenario inputs remain within a range reasonably supported by the historical training data.
• Increasing the granularity of regional, seasonal, or hourly parameters can reduce aggregation bias but can also increase estimation variance. The selected profile granularity should therefore be supported by the available data.

QR ALPS should therefore periodically reassess model parameters and response profiles as new observations become available and as material changes occur in the underlying load structure.

10. Future Development

Several areas provide opportunities for continued development of the methodology, including:

• dynamic heating and cooling base temperatures;
• improved representation of thermal memory;
• nonlinear temperature-response functions;
• adaptive estimation of temperature-response parameters;
• improved treatment of structural changes in load behavior;
• enhanced extreme-weather scenario analysis; and
• joint treatment of weather uncertainty and load-forecast uncertainty.

These extensions can be evaluated through controlled out-of-sample testing before being incorporated into the production methodology.