**1. Introduction**

In residential short-term load forecasting (STLF), future power consumption is projected by applying a preestablished relationship between power load and its influence factors, or by dynamically assessing historical data and adapting the correlation of the influence factor—namely, time and/or weather—with the load [1]. Defining this relationship is a two-part process: (a) identifying the correlation between power consumption and factors that influence that consumption, (b) quantifying the effect on consumption by using a suitable technique to estimate each factor. In order for this analysis to generate results that could be easily multiplied, a good understanding of the consumer to be analyzed is required [2]. A prerequisite for developing an accurate forecasting model under atypical consumption behavior or power load uncertainty is a trigger that announces the decision factors for atypical consumption behavior to occur. This knowledge concerning the behavior of the load curve is determined by correlation between the influence factors, consumer data and statistical analysis of past consumption [3–7].

**Citation:** Hora, C.; Dan, F.C.; Bendea, G.; Secui, C. Residential Short-Term Load Forecasting during Atypical Consumption Behavior. *Energies* **2022**, *15*, 291. https://doi.org/10.3390/ en15010291

Academic Editors: Marcin Kami ´nski and Angel A. Juan

Received: 2 December 2021 Accepted: 28 December 2021 Published: 1 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Papers from a literature review address the issue of the methodology used to model the first COVID-19 lockdown effects on power load. In [3] we can see a comparison of convolutional neural network (CNN)-based model forecasting with multiple linear regression (MLR) and an unknown forecasting method used by the system operator (SOM) using a Romanian database of all consumers. We can see in [3] that CNN was the most accurate method used for the COVID-19 database, with a median mean absolute percentage error (MAPE) of 1.0007% relative to 1.0692% for MLR and 1.1552% for SOM. In addition, we can see in [3] that the CNN method had higher maximum errors than the SOM. A database of New York (NY) consumption for the same atypical COVID-19 lockdown consumption event was analyzed in [4] by deploying three forecasting methods, namely Fully Connected Deep Neural Network (FCDNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU), along with Auto-Regressive Integrated Moving Average (ARIMA) which did not produce meaningful results on their database and therefore was not considered. The MAPE results in [4] were best in GRU with 4.04%, followed by FCDNN with 4.08% and lastly LDTM with 4.26%, all under the 5.35% benchmark for the NY database. The Jordanian National Electric Power Company (NEPCO) power database was used in [5] to evaluate, also during the COVID-19 lockdown period, the forecast efficiency of Autoregressive Integrated Moving Average with Exogenous (ARIMAX) and Artificial Neural Network (ANN). The daily forecast accuracy was also evaluated with MAPE and had better results with ARIMAX (5.5%) than with ANN (5.8%). Covering the largest US deregulated wholesale electricity market—Pennsylvania, New Jersey, Maryland (PJM)—[6] assessed forecasting under uncertainty in the pre-COVID-19 era by using a Gaussian process and obtaining an efficiency between 2.21% and 3.20% MAPE. Even though the atypical consumption was not related to COVID-19, the methodology used was suitable for any power load uncertainty related to an unforeseen event. Paper [7] assessed national European databases from France and Italy, and was the first study applying the lessons learned from the previous COVID-19 affected power load databases. The forecasting methods used in [7], covering data both from a pre-COVID-19 database and collected during lockdown and post-lockdown recovery, included ARIMA, Generalized Additive Models (GAM), Kalman Filtering and a combination of the first two methods (GAM+ARIMA). During the first lockdown the MAPE results were high, ranging from 4.28% for the GAM+ARIMA model through 4.81% for Kalman static filtering and 4.83% for GAM to 5.44% for the ARIMA model. All papers addressing the issue of forecasting under atypical consumption used methods that were altered by the operator to address the changing consumption profile. This limitation offered us a chance to focus on the consumer profile rather than on the historic trend, giving the forecasting methodology a flexibility in tackling unforeseen power consumption events.

The modeled characteristics of the consumer to be analyzed [1] are an essential indicator of the health of the forecast, seen even more during unpredictable power load events, as the previous research states [3–7]. Power consumers absorbing load in similar socio-economic and weather/climate areas usually have similar consumer behavior, and consumption forecast models developed for a type of consumer can easily be adapted for forecasting the consumption of other consumers in the same conditions. The main aim of the work was to identify the best load forecasting methods, of the ones applied, that gave us the smallest forecasting errors in atypical consumption behavior.

Part of an already ongoing COVID-19 pandemic, the first confirmed cases to reach Romania were on 26 February 2020. Following a rather similar European pattern the pandemic evolved and the first load curve-impacting pandemic-related legal measures were deployed on 16 March 2020, when the Romanian president decreed that a state of emergency should be implemented in Romania for a period of 30 days. Growing numbers of new COVID-19 confirmed cases in Romania led to the government announcing Military Ordinance No. 3 on 24 March 2020, instituting a national lockdown. These unprecedented restrictions were enforced by the support of military personnel, police and Gendarmerie [8–12]. People were not allowed to leave their homes or households, although some exceptions (work, buying food or medicine etc.) were allowed. Older people (over 65) were allowed to leave their homes only in the time interval of 11 a.m. to 1 p.m. This rule was applied to 16.4% of the rural population in Bihor County [13], for whom this restriction was assessed as an influence factor. On 14 May 2020 the state of emergency was lifted and replaced with a state of alert, meaning a decrease in the lockdown measures. A second wave of COVID-19 infections led to a partial lockdown on 9 November 2020. A third wave meant a milder lockdown with reduced restriction rules on 9 March 2021, and mainly local quarantines for the affected locations [8–12]. Urban or rural residential consumers included in the database were not affected by local lockdowns.

In order to validate the results of this study, we used a large multiyear database containing hourly consumption [14] separated into residential urban and residential rural consumers in Bihor County, Romania. The advantages of this database are that it contains a huge number of consumers (households) and that the residential consumers are the ones that have the best correlation to the consumption influence factors, e.g., weather. Previous research was conducted [3–7] mainly on national or international databases containing all consumption, including residential, commercial, industrial, transport, etc. This means that the nonresidential consumers, which have the obligation to forecast their own consumption, accounted for more than half of the power consumption forecasted.

By addressing only forecasting for residential consumers, we mitigate the risk of low efficiency STLF in the area in which the power networks are most vulnerable from the financial point of view and from the stability point of view.

The main contributions of this paper can be summarized as follows:


The rest of the paper is structured as follows: Section 2 describes the database used to test and validate the three STLF methods, presenting also the particularities. In Section 3 the Methodology used is presented, mainly the STLF algorithms and succession of steps, as shown in Figure 1. Case analysis and results are presented in Section 4. Section 5 covers a discussion of the findings and state of the research, and finally conclusions and future research best practices are covered in Section 6.

**Figure 1.** Flowchart of STLF in atypical consumption behavior.
