Reliable short-term electricity load forecasting is a foundational analytic service in digitally managed cities because demand balancing, fault anticipation, and operational resilience all depend on accurate near-term estimates of urban electricity use. In practice, however, edge-deployed forecasting models experience concept drift when seasonal demand shifts alter the scale, mean, and median of the incoming load series. This challenge is particularly acute in resource-constrained Internet-of-Things environments, where complex retraining and ensemble-maintenance schemes are often impractical. This paper presents a normalization-centered solution based on radian scaling, a bounded angular transformation that converts consecutive load differences into values that remain within a fixed interval and thereby preserve a stable learned representation under seasonal drift. The method is evaluated on the 5-minute New York Independent System Operator Long Island zone dataset, using a deliberately drift-inducing split in which training covers 1 January 2018 to 30 April 2018 and evaluation covers 1 May 2018 to 31 December 2020. Five constrained neural architectures are assessed: recurrent neural network, long short-term memory, gated recurrent unit, temporal convolutional network, and transformer. The empirical results show that radian scaling materially improves out-of-sample robustness while also reducing convergence time. On the evaluation partition, the constrained gated recurrent unit reduces average root mean square error from 158.63 MW under the best prior normalization baseline to 43.375 MW under radian scaling, a 72.657% reduction. Across models, average early-stopping epochs fall from 56.240 to 18.320. A Friedman test confirms statistically significant differences among normalization methods on the evaluation dataset (\(\chi^2=9.2400\), \(p=0.0263\)). Framed for urban energy analytics, the findings show that a lightweight transformation layer can substantially improve smart-city forecasting resilience without changing the forecasting architecture or requiring online retraining.