Tutor: Johnny Fernando Hidalgo R.

Problem Statement (1/2)

The paradigm shift toward decentralized power grids exposes distribution networks to unprecedented operational vulnerabilities due to the uncontrolled adoption of Distributed Energy Resources (DER). Developing countries face severe informational constraints that prevent the direct application of standard international forecasting architectures.

The Grid Decoupling Challenge

  • Stochastic Peak Demands: Mass integration of Electric Vehicles (EV) shifts traditional residential load profiles, triggering critical peak-demand hours.
  • Bidirectional Power Flows: Rooftop Photovoltaic (PV) systems inject highly variable power surpluses back into sub-transmission infrastructure, causing localized overvoltages.
  • Operational Uncertainty: Grid operators lack baseline tools to predict where and when high-stress integration thresholds will be breached at sub-national scales.

Socioeconomic Scaling Drivers

  • DER adoption is not merely a technical or meteorological phenomenon; it is strictly bound to macro-demographic capabilities.
  • Localized economic output (VAB) and urbanization rates (Population) dictate the financial feasibility of shifting toward private green infrastructure.

The Data Asymmetry Constraint

  1. Smart Metering Deficit: Unlike developed smart grids, emerging networks like Ecuador’s lack ubiquitous real-time, high-frequency residential tracking.
  2. Institutional Time Lags: Official energy accounting registers disaggregated local demand with multiple years of delay, disabling proactive planning.
  3. Over-Parameterized Failures: Advanced Machine Learning setups exhibit low empirical parsimony and extreme overfitting when dealing with highly sparse cross-sectional matrix data.

Problem Statement (2/2)

The Core Research Question

“How can sub-national energy planning balances be accurately modeled to anticipate DER deployment when recent high-frequency disaggregated data is entirely non-existent?”

This paper answers this question by designing a robust, parsimonious structural framework leveraging mathematical scaling laws alongside macro-demographic proxies.

Research Gaps

Current Literature Limitations

  1. Granularity Scarcity: Absence of open-source, high-frequency residential electricity consumption data disaggregated at provincial layers for the current fiscal years.
  2. Over-parameterized Frameworks: Prevalence of highly complex machine learning structures that fail to capture steady-state macroeconomic determinants.
  3. Elasticity Omission: Lack of explicit, empirical estimation regarding localized Gross Value Added (VAB) and population scaling factors in the Andean residential energy landscape.

Objectives

Main Objective

To analyze the structural and economic determinants of provincial electricity consumption in Ecuador by estimating a parsimonious cross-sectional econometric model for 2024, quantifying the true impact of macro-demographic scaling factors over contemporary climate variables.

Specific Objectives

1. Historical Proportional Disaggregation

Design and apply a historical-share allocation method (ARCONEL 2015–2021) to reconstruct 2024 electricity consumption across 23 mainland provinces, resolving official open data scarcity (Gap 1).

2. Parsimonious Econometric Modeling

Formulate a log-linear OLS framework with heteroskedasticity-corrected standard errors (HC3), prioritizing robustness and parsimony over complex, over-parameterized ML setups (Gap 2).

3. Empirical Elasticity Estimation

Empirically estimate and statistically test electricity demand elasticities with respect to localized Gross Value Added (VAB) and population to fill the metric void in Andean energy planning (Gap 3).

4. Climate vs. Socioeconomic Assessment

Evaluate the explanatory power of annual climate variables (temperature, radiation, precipitation) against macroeconomic factors using benchmark models to inform sub-national DER planning.

Study Area

Socio-Spatial Scope

  • Horizon: 23 mainland provinces of Ecuador (excluding Galápagos due to its isolated grid nature).
  • Baseline: Fiscal year 2024 structured via ARCONEL/SISDAT records.

Macroeconomic Drivers

  • VAB: Localized Gross Value Added captures structural differences between industrial zones and rural networks.
  • Scale: Population densities define baseline residential load profiles.

Data Problem

Part 1: Proportional Allocation

To circumvent the lack of recent open-source localized residential electricity tracking, a structural mathematical breakdown was developed to project provincial baselines.

1. Historical Weight Derivation (\(\pi_i\))

The historical participation factor for each province \(i\) is calculated using the historical horizon (2015–2021) from ARCONEL records, neutralizing annual volatility:

\[\pi_i = \frac{1}{T} \sum_{t=2015}^{2021} \frac{C_{i,t}^{\text{ARCONEL}}}{C_{t}^{\text{nat}}}\]

Where \(T\) represents the total number of historical periods analyzed.

2. Spatial Distribution Formula

The aggregate national residential consumption reported in the latest National Energy Balance (\(C_{2024}^{\text{nat}} = 35,640\text{ GWh}\)) is spatially distributed based on these historical weighted shares:

\[\sum_{i=1}^{23} \pi_i = 1 \implies C_{i,2024}^{\text{base}} = \pi_i \cdot C_{2024}^{\text{nat}}\]

Data Problem

Part 2: Econometric Validation

To ensure that the historical allocation (\(C_{i,2024}^{\text{base}}\)) reflects recent structural shifts, the baseline undergoes an econometric validation against localized macroeconomic drivers.

Structural Driver Elasticity Model

The interaction between the estimated consumption, the Localized Gross Value Added (\(\text{VAB}_i\)), and the Population Density (\(\text{Pob}_i\)) is validated through a log-log multi-variable regression model:

\[\ln(C_{i,2024}^{\text{base}}) = \beta_0 + \beta_1 \ln(\text{VAB}_i) + \beta_2 \ln(\text{Pob}_i) + \varepsilon_i\]

Where:

  • \(\beta_1, \beta_2\): Represent the sub-national elasticities of demand relative to economic production and demographic scale.
  • \(\varepsilon_i\): Stochastic error term capturing localized efficiency anomalies or unconventional grid behaviors.

Methodological Note: This dual-stage framework guarantees that any spatial projection remains bound to national control totals while anchoring local behavior to validated macroeconomic realities.

Model Variables

The cross-sectional matrix integrates structural macroeconomic proxies, demographics, and environmental control parameters.

Variable Specification Matrix

  • Dependent Variable (\(C_i\)): Estimated annual residential electricity consumption per province (GWh).
  • Population (\(Pop_i\)): Local provincial census counts projected through official INEC baselines.
  • Economic Activity (\(VAB_i\)): Provincial Gross Value Added at constant prices, extracted from the Central Bank of Ecuador (BCE).
  • EV Penetration Proxy: Monitored via regional electric vehicle registrations and official charging spot deployment.

Econometric Robustness Protocol (For Statistical Review)

  • Logarithmic Linearization: Variables are transformed into natural logarithms (\(\ln\)) to stabilize variance, achieve homoscedastic residuals, and allow direct interpretation of coefficients as constant elasticities.
  • Scale Bias Mitigation: The inclusion of \(Pop_i\) and \(VAB_i\) simultaneously controls for multi-collinearity via Variance Inflation Factors (VIF), ensuring that massive provincial outliers do not distort the stochastic error term \(\varepsilon_i\).

Econometric Model

A log-linear specifications model was estimated via Ordinary Least Squares (OLS) to interpret estimated beta parameters as clean, constant percentage elasticities.

Core Structural Equation

\[\ln(C_i) = \alpha + \beta X_i + \gamma_1 \ln(Pop_i) + \gamma_2 \ln(VAB_i) + u_i\]

HC3 Heteroscedasticity-Consistent Covariance Derivation

Due to the bounded cross-sectional sample size (\(N = 23\)), a Davidson-MacKinnon HC3 degrees-of-freedom correction is mathematically formulated to safeguard inference:

\[\widehat{Var}(\hat{\theta}) = (X'X)^{-1} (X'\hat{\Omega}_{HC3}X) (X'X)^{-1}\]

Where the skedasticity matrix is explicitly defined as: \[\hat{\Omega}_{HC3} = \text{diag}\left( \frac{\hat{u}_1^2}{(1 - h_{11})^2}, \, \frac{\hat{u}_2^2}{(1 - h_{22})^2}, \, \dots, \, \frac{\hat{u}_N^2}{(1 - h_{NN})^2} \right)\]

  • \(\hat{u}_i\): Represents the OLS residual for the \(i\)-th province.
  • \(h_{ii}\): Leverage values extracted from the diagonal of the projection Matrix \(H = X(X'X)^{-1}X'\). The quadratic discount \((1 - h_{ii})^2\) aggressively heavily penalizes high-leverage provincial observations to eliminate downward bias in small samples.

Climate Dynamics

Environmental parameters were extracted via georeferenced provincial centroids linking to the NASA POWER database to evaluate the significance of cooling/heating loads.

Geo-Referenced Bio-Climatic Parameters (\(X_i\))

  • Solar Radiation: All-sky surface shortwave downward irradiance (\(KT\)).
  • Thermal Drift: Mean surface air temperature at 2 meters altitude (°C).
  • Rainfall / Utility: Isolating if meteorological variables cause major load shifts or if demand is driven entirely by socioeconomics.

Results

Part 1: Elasticity Inferences

The core structural model yields an exceptional cross-sectional goodness of fit (\(R^2 = 0.9461\)), confirming the high explanatory power of the structural parameters.

Model Elasticity Metrics

  • \(\ln(VAB)\) Elasticity: \(0.7399\) (\(p < 0.001\)). A \(1\%\) increase in provincial economic output expands residential energy demand by \(0.74\%\).
  • \(\ln(Population)\) Elasticity: \(0.5125\) (\(p = 0.0103\)). Robust scale factor reflecting demographics as a baseline stabilizer.

Results

Part 2: Residual Diagnostics

To validate that the Davidson-MacKinnon correction successfully mitigated heteroscedastic layouts, the standardized error structure was mapped across all 23 territorial assets.

Heteroscedasticity Clearance

  • Stochastic Stability: Residuals exhibit an isotropic distribution across the fitted values scale, verifying the suppression of provincial scale variance.
  • Outlier Shielding: Highly leveraged nodes do not display persistent bias patterns under the HC3 structure.

Model Diagnosis

Diagnostic specification tests were performed to verify compliance with the classical Gauss-Markov assumptions.

Assumption Validation & Robustness

  • Multicollinearity: Controlled via variance inflation factors (\(VIF\)) well within acceptable thresholds for scale variables, discarding informational redundancy.
  • Heteroscedasticity: Successfully mitigated by estimating robust standard errors consistent with the HC3 analytical framework.
  • Climate Effects: When controlling for VAB and population, temperature and radiation coefficients lose annual statistical significance, confirming the dominance of long-term economic drivers.

Conclusions

Part 1: Methodological Contributions

The dual-stage structural and econometric framework successfully bridges the localized data gap while ensuring full mathematical alignment with national energy baselines.

Framework Achievements

  • Resolution of Localized Data Gaps: The proportional allocation protocol effectively circumvents the lack of open-source regional tracking, delivering verifiable provincial energy baselines.
  • Mathematical Consistency: By ensuring \(\sum \pi_i = 1\), all sub-national projections remain strictly bound to national energy totals, neutralizing year-over-year volatility.
  • Econometric Validation: The log-log specification confirms that \(94.61\%\) of provincial consumption variance is driven by underlying structural economics rather than transitory noise.

Conclusions

Part 2: Policy Implications & Future Outlook

The empirical elasticities derived under robust inference provide a foundational toolkit for regional grid expansion and strategic energy planning.

Strategic Takeaways

  • Economic Dominance: The high elasticity of \(\ln(VAB)\) (\(0.74\)) demonstrates that regional electrical demand is heavily tethered to sub-national economic production and industrial scale.
  • Demographic Baseline: Population density acts as a rigid scalar stabilizer (\(0.51\)), allowing utilities to accurately project load growth based on official demographic trajectories.
  • Climate Decoupling: Long-term weather variations show negligible statistical significance when economic factors are controlled, shifting focus toward economic expansion.

Future Horizons

  • Granular Expansion: The model lays the structural foundation to integrate micro-level parameters, such as localized Electric Vehicle (EV) charging node deployments.
  • Predictive Simulation: These robust parameters can be directly loaded into power system modules to simulate grid stress under alternative macroeconomic scenarios.

Thank You!

Ing. Braulio Balseca

Tlf: 0995789874

Correo: braulio.balseca@upec.edu.ec