Modelling the Hourly Consumption of Electricity during Period of Power Crisis Samuel Asante Gyamerahab Henry Ofoe Agbi-Kaisera Keziah Ewura Adjoa

2025-05-06 0 0 1.82MB 30 页 10玖币
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Modelling the Hourly Consumption of Electricity during
Period of Power Crisis
Samuel Asante Gyamerah
a,b
, Henry Ofoe Agbi-Kaiser
a
, Keziah Ewura Adjoa
Amankwaha, Patience Anipaa, Bright Arafat Belloa
aDepartment of Statistics and Actuarial Science, Kwame Nkrumah University of Science
and Technology, Kumasi-Ghana
bLaboratory for Interdisciplinary Statistical Analysis – Kwame Nkrumah University of
Science and Technology (KNUST-LISA), Kumasi-Ghana
Abstract
In this paper, we capture the dynamic behaviour of hourly consumption of
electricity during the period of power crisis (“dumsor” period) in Ghana using
two-state Markov switching autoregressive (MS-AR) and autoregressive (AR)
models. Hourly data between the periods of January 1, 2014, and December
31, 2014 was obtained from the Ghana Grid company and used for the study.
Using different information criteria, the MS(2)-AR(4) is selected as the optimal
model to describe the dynamic behaviour of electricity consumption during
periods of power crisis in Ghana. The parameters of the MS(2)-AR(4) model
are then estimated using the expectation-maximization algorithm. From the
results, the likelihood of staying under a low electricity consumption regime is
estimated to be 87%. The expected duration for a low electricity consumption
regime is 7.8 hours daily, and the high electricity consumption regime is
expected to last 2.3 hours daily. The proposed model is robust as compared
to the autoregressive model because it effectively captures the dynamics of
Icorrespondence: saasgyam@gmail.com
Preprint October 27, 2022
arXiv:2210.14555v1 [stat.AP] 26 Oct 2022
electricity demand over time through the peaks and significant fluctuations
in consumption patterns. Similarly, the model can identify distinct regime
changes linked to electricity consumption during periods of power crises.
Keywords: Energy Consumption; Regime changes; Power crisis; Energy
Sustainability
1. Introduction
While energy supply in Ghana has been relatively stable in recent years, the
country has been beset by energy supply issues in the past, which have had
a substantial impact on the country’s economic status [
1
]. This is due to
either low levels of water in the dams or technical malfunctions of equipment
caused by high amounts of water. However, the issue of electricity generation
and delivery does not appear to be limited to Ghana; it appears to be a
concern in many developing countries, including all members of the Economic
Community of West African States (ECOWAS). In Ghana, electricity con-
sumption is constantly plagued with power outages and fluctuations popularly
known as “DumSor”. According to [
2
], the Economic Community of West
African States (ECOWAS) aims to achieve 100% electrification in all member
countries by 2030, and that in order to do so, energy generation capacities
must be greatly increased. Ghana’s electricity sector is in a period of transi-
tion and its electricity consumption growth rate for the past five years has
been increasing by 10.3% annually, with supply falling short of expectations,
[
3
]. Projections were made in line with ECOWAS’ aim to make electricity
accessible to all Ghanaians by 2020 [
4
]. But as at the end of 2019, the access
rate was 83.5% and with a growth rate of 3.13%, the country missed the target
2
by 14%. The actual challenge is ensuring that this aim is met and, more
importantly, that supply is both consistent and enough. Ghana, as at 2021,
still experiences nationwide blackouts like on Sunday, March 7th, 2021 and
load shedding exercises like the Volta and Oti Region load shedding operation
from Thursday, March 18th, to Monday, March 21st, 2021. In addition, the
annual increase in electricity demand has caught up with available generation,
leaving very little spare capacity to deal with a system outage.
Different techniques for modelling hourly electricity consumption have been
studied in the literature. For instance, [
5
] used the self-exciting threshold
autoregressive (SETAR) model and the smooth transition regression (STR)
model to model, analyze, and forecast the residential electricity consumption
in Ethiopia. The study showed that the SETAR model was more effective
than the STR model. [
6
] used a back propagation neural network to model
electricity consumption. In a study conducted by [
7
], a regression model was
used to generate hourly electricity consumption over the course of a year
for the commercial and industrial sectors of three US cities. The model was
built using hourly datasets from the previous four years. [
8
] considered a
new extension of the stochastic Gamma diffusion process by introducing time
functions to model electric power consumption during a period of economic
crisis. [
9
] employed bottom-up stochastic models to simulate high-resolution
heating and cooling electricity consumption profiles. In a recent study, [
10
]
used the Markov process technique, feature selection, and clustering to model
electricity consumption forecasting for Bushehr-Iran Power Distribution Com-
pany. [
11
] used principal component analysis to model the monthly electricity
consumption of public sanitary buildings using climatological variables.
3
Globally, household electricity consumption is affected by factors like seasons,
the number of occupants living in the house, the income of the household,
and time of day. People also consume electricity in different ways and with
different degrees of urgency. The variation in Ghana’s household electricity
consumption is greatly affected by the time of day, where low consumption is
recorded during the early hours of the day and high consumption is usually
in the evening and nighttime since most people are employed during the day.
Understanding how variation in residential electricity demand affects con-
sumers and businesses alike is crucial for sustainability programs. Typically,
time series models are commonly used to evaluate the transient behaviour of
variables like power demand, exchange rates, and temperature, among others.
The mixed autoregressive moving averages (ARMA), moving average (MA),
and autoregressive (AR) models are the most popular and often used models.
Although these models are highly effective in a variety of applications, they
are incapable of representing certain nonlinear dynamic patterns, such as
asymmetry, amplitude dependency, and volatility clustering. For example,
electricity consumption normally fluctuates during the time of the day, with
high and low consumption depending on the time of the day (see Figure 2).
With this kind of data, it would be inefficient to think that a single linear
model could explain all of these different behaviors. Markov switching models
(MSM) are a type of nonlinear time series model that has become popular for
explaining how different time series regimes behave.
According to [
12
], the Markov switching model consists of a set of models
that may characterize time series behavioural patterns under various regimes.
The switching technique is regulated by a latent state variable that assumes
4
the process of a “first-order Markov chain,” which is a distinctive aspect
of the Markov switching model. For instance, [
13
] modeled electricity spot
prices using regime-switching models. [
14
] used full-period, pre-reform, and
post-reform sample times to model the demand for electricity in Ghana based
on the effects of policy regime switching. The study found that technology
changes were energy-saving during the pre-reform period, while technology
changes were energy-consuming during the post-reform period. Using the
entire sample period, electricity demand in the long run is highly influenced
by GDP and industry efficiency. [
15
] developed a time-dependent two-state
Markov Regime Switching (MRS) model to capture the hourly spot price of
electricity. The constructed model was efficient as it was able to capture the
main characteristics exhibited in the hourly electricity spot price. To model
the dynamics of temperature for weather derivatives, [
15
] used a time-changing
mean-reversion Levy regime-switching model to capture both normal and
extreme temperature fluctuations. [
16
] described “El Nino Southern Oscilla-
tion (ENSO)” patterns using a two-state Markov regime-switching framework.
They discovered that the behavioral patterns of both research phases (El Nino
and La Nina events) are diametrically opposed and distinct. The findings
of the study also show that, while the Box-Jenkins approach produces a
decent representation of the time series under review, it is unable to capture
some nonlinearities that arise as a result of the presence of changing regimes.
Furthermore, it was shown that the presence of weather cycles necessitates
the origin of non-linear factors in many climatic time series for describing
climatic variables. The model was able to reflect the index’s properties across
time. This study therefore employs a Markov regime switching model to
5
摘要：

ModellingtheHourlyConsumptionofElectricityduringPeriodofPowerCrisisSamuelAsanteGyameraha,b,HenryOfoeAgbi-Kaisera,KeziahEwuraAdjoaAmankwaha,PatienceAnipaa,BrightArafatBelloaaDepartmentofStatisticsandActuarialScience,KwameNkrumahUniversityofScienceandTechnology,Kumasi-GhanabLaboratoryforInterdisciplin...

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