Modeling and prediction of primary energy supply and electricity generation structures based on Markov chain: an insight with focus on the role of natural gas in Pakistan

ABSTRACT

This study aims to develop an alternative trended matrices approach of structural prediction as a counterpart to the classical Chapman-Kolmogorov approach. Methodological addition lies within the way of preservation of stochasticity of the transition matrices originated from the alternative approach for the case of initial non-stochasticity due to all negative row elements. Ten datasets (various case studies) of historic energy structures have been modeled, simulated, and extended as Markov chains followed by their respective error assessments. Linear regression-based alternative approach is found to be the nearest counterpart to the classical approach for the majority of datasets. This approach is subsequently applied for the prediction of primary energy supply and electricity generation structures in Pakistan in business as usual scenario for 2018–2030 period. Fossil fuels will share about 90% in the primary energy supply and electricity generation. Moreover, gas will prevail as the major fossil fuel for both primary energy supply and thermal-dominant electricity generation mixes. Gas share will be about 70% within the thermal electricity generation mix. Some results depict the hurdles in the development of a low carbon future. The alternative prediction approach may be used for comparable fields of resource allocation, planning, and management.

KEYWORDS:

• Markov chain
• modeling and prediction
• natural gas
• primary energy

Acknowledgments

The authors would like to pay thanks to the anonymous editors and reviewers whose valuable feedback helped improve the quality of the article.

Disclosure statement

The authors declare that this study did not involve any conflict of interests with anybody or any organization. The authors also declare that this study did not involve any violation of human or animal rights.

Nomenclature

CKA	=	Chapman-Kolmogorov approach (a classical structural prediction approach along time series Markov chain)
Euv	=	A random element in uth row and vth column of the transition matrix, Euv ϵ R
E’uv	=	A random stochasticated element according to first case of initial non-stochasticity (from an already published research article), E’uv ϵ R and E’uv ≥ 0
E’’uv	=	A random stochasticated element according to second case of initial non-stochasticity (as methodological addition to the previously published research article), E’’uv ϵ R and E’’uv ≥ 0
GJ	=	Giga Joule: A unit of energy
k	=	Serial number of a random prediction year along time series, k ϵ N
MAPD	=	Mean absolute percentage difference, in the units of %, between corresponding elements within predicted SSVs from classical and alternate approaches (from an already published research article)
N	=	Set of natural numbers {1, 2, 3…}
n	=	Serial number of terminal year in historic time series, n ϵ N
PJ	=	Peta Joule, A unit of energy, 1 PJ = 106 GJ
r	=	Order of polynomial regression, and, 1 ≤ r ≤ 6, r ϵ N
SSV	=	Structural state vector (SSVs for plural)
T	=	Random transition matrix
TMA	=	Trended matrices approach of structural prediction (an alternative structural prediction approach along time series Markov chai; TMA1 for linear regression, TMA2 for second order regression…TMA6 for sixth order regression)
u	=	Serial number of a random row in the transition matrix, u ϵ N
v	=	Serial number of a random column in the transition matrix, v ϵ N

Additional information

Funding

This research work is at the cost of the authors’ own income without obtaining any grant from funding agencies, in the public, private and/or not-for-profit organizations, etc.