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Table 3 List of abbreviations

From: A coupled technological-sociological model for national electrical energy supply systems including sustainability

EESS Electrical energy supply system
RF Regression function
IN0 With \( i,{i}_0,{i}^{\prime },{i}_0^{\prime}\in I \) and \( i,{i}_0^{\prime}\le {i}_0,{i}^{\prime}\le {i}_0^{\prime } \)
TR With t, t, ∆t, ∆tR, tA, tE, τT and ∆t = t − t
NR3 With \( {x}_i,{x}_i^{\prime },{x}_j,{x}_{n_0}\in N \), pairwise coprime
ED(t, xi) Energy demand function; short form \( {E}_i^N(t) \)
\( {E}_{\mathrm{max}}^D\left({x}_i\right) \) Maximum energy demand; short form \( {E}_{\max, i}^N(t) \)
\( {f}_i^D(t) \) Time-dependent behavior of user i
ES(t, xi) Energy supply function; short form \( {E}_i^B(t) \)
\( {E}_{j_0}^D\frac{(t)}{E_{j_0}^S}(t) \) Bundled energy demand/supply of j0  microcells
\( {E}_{\mathrm{Nat}.}^D\frac{(t)}{E_{\mathrm{Nat}.}^S}(t) \) Energy demand/supply function of a national macrocell
u Energy density of the electromagnetic field
S Poynting vector
J Current density
E Electric field strength
H Magnetic field strength
ρ Electrical charge density
\( \frac{c_0}{c} \) Speed of light in vacuum/in a medium
\( {E}_i^{ST} \) Stationary supply component of the ith microcell
ciR Stationary state constant of the ith microcell
\( {E}_{j_0}^{ST} \) Stationary supply constant of a macrocell
PS(t, xi) Output power of the ith source; short form \( {P}_i^B(t) \)
\( {P}_i^{D_{\mathrm{max}}} \) Maximum load (power consumption) of the ith microcell
\( {P}_i^{S_{\mathrm{max}}} \) Maximum supply (power generation) of the ith microcell
\( {\dot{P}}^S\left(t,{x}_i\right) \) Power dynamics of the ith microcell; short form \( {\dot{P}}_i^B(t) \)
P(j0) Total power from j0 microcells
P(k0) Total power from k0 current sources
\( {\wp}_{\mathrm{macrocell}}^N \) Maximum load of a macrocell, analogous to power generation
\( {\wp}_{\mathrm{Nat}.}^N \) Maximum load of a national macro cell, analogous to power generation
S1, …, S5 Structure variables, components of S
SR5 Technological structure vector
\( \varDelta {t}_{r_i} \) Time shift in the ith microcell due to the relativity principle
\( \varDelta {t}_{s_i} \) Time shift in the ith microcell considering real sources
\( \varDelta {t}_{j_0} \) Total time delay within a macrocell of j0 microcells
JN0 With j, j0J and j ≤ j0
KN0 With k, k0K and k ≤k0
ΝN0 With n, n0N and n ≤ n0
(N, d) Metric space on the set N with metric d
σ Electrical conductivity
ΩuR4 Technological solution space with uΩu
\( {\varOmega}_{u_0},{\varOmega}_{u_I},{\varOmega}_{u_{II}} \) Subsets of the technological solution space
LE Unit of length
r s Substantial risk factor
r1, r2 Sub-risk factors
μ Failure factor
p i Failure likelihood of the ith microcell
\( {P}_{i_0} \) Failure likelihood of a macrocell with i0  users
SR6 Extension of the structure vector S  with the substantial risk factor
S 6 Structure variable for the substantial risk factor
v tv Availability
v tv, B Sustainability boundary; sustainable availability boundary
\( {v}_{tv}\bullet {E}_{\mathrm{Nat}.}^D(t) \) National sustainability
\( {v}_{tv,n}\bullet {E}_n^D(t) \) Regional sustainability in a macrocell
v State vector with sustainability component
ΩR5 Sustainable technological solution set with
\( {E}_{T_{\mathrm{Ref}.}}^N \) Annual energy demand in a reference year
\( {\lambda}_i^{-} \) ith supply factor
\( {\lambda}_{\mathrm{min}}^{-} \) National supply factor
h(t) Distribution of annual energy demand with \( {\int}_{t_0}^{t_0+365}h(t) dt=1 \)
g(x)  [0; 1] Weights between \( {\lambda}_{min}^{-} \) and rs
\( {E}_{T_{\mathrm{Ref}.}}^D \) Annual reference energy arbitrary initial value \( {\int}_{t_0}^{t_0+365}{E}^D(t) dt \)