Fundamental Energy Needs Quantification for QoL Improvement

Abstract

Previous chapters conducted energy analysis in terms of the proposed QoL indicator at international level. Moreover, the analysis of Chap. 3 revealed that QoL will increase three times if final energy consumption per capita reaches to 548 kgoe. Additionally, poverty rate decreases around three times through supplying same final energy for each person in pre-developing countries. Energy consumption at family level is the scope of current chapter, to measure fundamental energy needs (FENs). Then, it will investigate to what extent FENs reduces final energy consumption. In other word, the share of FENs in energy poverty reduction is considered. The proposed method is based on time use analysis which is independent from place and families. Thus, the proposed method can be conducted in different countries and different families to extend the results. Measuring FENs across households provides an insight into the poor households’ energy needs and energy poverty reduction. Household’s fundamental energy needs consists of energy for heating, cooling, cooking, and lighting services, which vary from one country to another. This chapter proposes the time use analysis to figure out energy consumption among households, while the “power” side of energy is assumed as an exogenous variable (Energy = Time × Power). A set of household activities related to a family with two persons is selected and their corresponding cycle times and frequencies are modeled by different statistical distributions due to the intrinsic uncertainty of cycle times. Then, a simulation model is created to extract robust results related to the household energy consumption based on the whole set of activities, weather data and selected statistical distributions. For the aforementioned family, the results of simulation showed that on average, the daily FENs is 63.3 MJ; while its highest share belongs to the cooking activities (39.2%), followed by heating (23.6%), cooling (18.3%), and lighting (5.2%). The results of chapter emphasize the importance of heating, cooking, and cooling services for poverty reduction at the household level than lighting service.

Appendices

Appendix 1: The Statistical Distributions Used in This Article (Shape (α), Scale (β), Mean (μ), Standard Deviation (σ), and Threshold (or Location) (γ) Parameters)

Name of distribution	Distribution function (f(x))	Expected value (E(X))	Variance (Var(X))	Reference
3-Parameter lognormal	$\frac{{e^{{ - 0.5\left( {\frac{{\ln \left( {x - \gamma } \right) - \mu }}{\sigma }} \right)^{2} }} }}{{\left( {x - \gamma } \right)\sigma \sqrt {2\pi } }}$	$\upgamma + {\text{e}}^{{\left( {\mu + \frac{{\sigma^{2} }}{2}} \right)}}$	$({\text{e}}^{{\sigma^{2} }} - 1){\text{e}}^{{\left( {2\mu + \sigma^{2} } \right)}}$	[44]
3-Parameter log-logistica	$\frac{\alpha }{\beta }\left( {\frac{x - \gamma }{\beta }} \right)^{\alpha - 1} \left( {1 + \left( {\frac{x - \gamma }{\beta }} \right)^{\alpha } } \right)^{ - 2}$	$\upbeta \uptheta { \csc }\left(\uptheta \right) +\upgamma;$ $\uptheta = \frac{\pi }{\alpha }\;where\; \alpha > 1$	$\upbeta^{2}\uptheta \left[ {2{ \csc }\left( {2\uptheta} \right) - \theta { \csc }^{2} \left( \theta \right)} \right],$ $where\,\alpha > 2$	[45]
3-Parameter Gammab	$\frac{{\left( {x - \gamma } \right)^{\alpha - 1} }}{{\beta^{\alpha } \Gamma \left( \alpha \right)}}{\text{e}}^{{ - \frac{{\left( {x - \gamma } \right)}}{\beta }}}$	$\upgamma +\upalpha \upbeta$	$\upalpha \upbeta ^{2}$	[46]
Triangular	$\left\{ {\begin{array}{*{20}c} 0 & {x \le a} \\ {\frac{{\left( {x - a} \right)^{2} }}{{\left( {b - a} \right)\left( {c - a} \right)}}} & {a < x \le c} \\ {1 - \frac{{\left( {b - x} \right)^{2} }}{{\left( {b - a} \right)\left( {b - c} \right)}}} & {c < x < b} \\ 1 & {b \le x} \\ \end{array} } \right.$	$\frac{{{\text{a}} + {\text{b}} + {\text{c}}}}{3}$	$\frac{{{\text{a}}^{2} + {\text{b}}^{2} + {\text{c}}^{2} - ab - - ac - bc}}{18}$	[47]
Beta	$\begin{aligned} & \frac{1}{{B\left( {\alpha _{1} ,\alpha _{2} } \right)}}\frac{{\left( {x - p} \right)^{{\alpha _{1} - 1}} \left( {q - x} \right)^{{\alpha _{2} - 1}} }}{{\left( {q - p} \right)^{{\alpha _{1} + \alpha _{2} - 1}} }}, \\ & \quad p \le x \le q \\ \end{aligned}$	${\text{p}} + \left( {{\text{q}} - {\text{p}}} \right)\frac{{\alpha_{1} }}{{\alpha_{1} + \alpha_{2} }}$	$\left( {{\text{q}} - {\text{p}}} \right)^{2} \left[ {\frac{{\alpha_{1} \alpha_{2} }}{{\left( {\alpha_{1} + \alpha_{2} } \right)^{2} \left( {\alpha_{1} + \alpha_{2} + 1} \right)}}} \right]$	[48]
Weibull	$\frac{\alpha }{\beta }\left( {\frac{x - \gamma }{\beta }} \right)^{\alpha - 1} {\text{e}}^{{ - \left( {\frac{x - \gamma }{\beta }} \right)^{\alpha } }}$	$\upgamma +\upbeta\,\Gamma \left( {1 + \frac{1}{\alpha }} \right)$	$\upbeta^{2} \left[ {\Gamma \left( {1 + \frac{2}{\alpha }} \right) - \left( {\Gamma \left( {1 + \frac{1}{\alpha }} \right)} \right)^{2} } \right]$	[49]
Uniform	$\frac{1}{{x_{max} - x_{min} }}$	$\frac{{x_{min} + x_{max} }}{2}$	$\frac{{\left( {x_{max} - x_{min} } \right)^{2} }}{12}$	[45]
Empirical function	$f_{t} = \frac{{\mathop \sum \nolimits_{i = 1}^{k} I\left( {x_{i} \le t} \right)}}{n};$ $I\left( x \right) = \left\{ {\begin{array}{*{20}c} 1 & {x \le t} \\ 0 & {x > t} \\ \end{array} } \right.$	$\frac{{\mathop \sum \nolimits_{i = 1}^{n} x_{i} }}{n}$	$\left( {\frac{n}{n - 1}} \right)\left( {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {x_{i} - E\left( x \right)} \right)^{2} }}{n}} \right)$	[50]
Generalized Extreme Value	$\left\{ {\begin{array}{*{20}c} {\frac{1}{\beta }\left[ {1 + \alpha \left( {\frac{x - \gamma }{\beta }} \right)} \right]^{ - 1 - 1/\alpha } {\text{e}}^{{\left( { - \left( {1 + \alpha \left( {\frac{x - \gamma }{\beta }} \right)} \right)^{ - 1/\alpha } } \right)}} } & {\alpha \ne 0} \\ {\frac{1}{\beta }{\text{e}}^{{\left( { - \left( {\frac{x - \gamma }{\beta }} \right) - {\text{e}}^{{ - \left( {\frac{x - \gamma }{\beta }} \right)}} } \right)}} } & {\alpha = 0} \\ \end{array} } \right.$			[51]
	$E\left( x \right) = \left\{ {\begin{array}{*{20}c} {\gamma + \beta \frac{{\left( {\Gamma \left( {1 - \alpha } \right) - 1} \right)}}{\alpha }} & {\alpha \ne 0,\, \alpha < 1} \\ {\gamma + 0.577 \times \beta } & {\alpha = 0} \\ \infty & {\alpha \ge 1} \\ \end{array} } \right.$
	$Var\left( x \right) = \left\{ {\begin{array}{*{20}c} {\beta^{2} \frac{{\left[ {\Gamma \left( {1 - 2\alpha } \right) -\Gamma ^{2} \left( {1 - \alpha } \right)} \right]}}{{\alpha^{2} }}} & {\alpha \ne 0, \,\alpha < 0.5} \\ {\beta^{2} + \frac{{\pi^{2} }}{6}} & {\alpha = 0} \\ \infty & {\alpha \ge 0.5} \\ \end{array} } \right.$

1. ^a“csc” stands for Cosecant function
2. ^bErlang distribution is a special case of the Gamma distribution where the shape parameter is a positive integer

Appendix 2: Parameter Values of the Statistical Distributions

Activity Name	Distribution (Time use)	Parameters	Distribution (Frequency of activity)	Parameters
Meal	3-Parameter lognormal	σ = 0.55581, μ = 3.8218, γ = 8.5225	Normal	μ = –1.715, σ = 52.18
Food warm-up/start-up	Generalized extreme value	α = 0.24398, β = 1.7941, γ = 16.923
Boiling water	Uniform	Xmin = 3, Xmax = 6	Uniform	Xmin = 1, Xmax = 60
TV	Beta	α1 = 1.5993, α2 = 3.285, p = 7.2, q = 404.0	Uniform	Xmin = 120, Xmax = 180
Bath	3-Parameter lognormal	σ = 0.4345, μ = 2.466, γ = 6.738	3-Parameter log-logistic (Waking hours)	α = 2.174, β = 91.914, γ = 891.04
Shower	3-Parameter log-logistic	α = 5.7257, β = 7.5957, γ = 0
Hand washing clothes	Triangular	a = 42.855, b = 74.0, c = 76.957
Mobile charging	Gamma	α = 1.2509, β = 55.079, γ = 41.568
Hand dishwashing	Gamma	α = 5.1821, β = 1.3207, γ = 0	–
Dwelling bulb	3-Parameter log-logistic	α = 7.5928, β = 274.08, γ = 63.784	–
Kitchen bulb	Erlang	α = 1, β = 15.581, γ = 10.0	–