Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 101

⎧
⎨
⎩

α is the unit index being analysed
β is the time interval being analysed
nβ is the number of time intervals into which the full period is divided
G Eα , β is the natural gas emissions cost for supplying point α in time β
P Eα , β is the electricity emissions cost for supplying point α in time β
G Pα , β is the spot market natural gas cost for supplying point α in time β
P Pα , β is the spot market electricity cost for supplying point α in time β
ω is the emissions cost vs. spot price cost weighting factor
if ω

where

= 1 minimal emission costs are obtained

if ω = 0 minimal energy costs are obtained

Note : The carbon costs incurred are determined by multiplying the cost of car-
bon (taken from the exchange market) times the amount of energy being supplied.
After obtaining the total emission costs of providing natural gas and electricity, G total
E
and P tota E respectively, these variables are then added, so the total emission costs of
the urban energy system can be calculated, as stated by the following equation:

⎡ ⎤

nG g nP g

nβ

⎣ ⎦

E total
E

G total
E

P total
E

= + = G Eα , β + P Eα , β (5.7)

β = 1 α = 1 α = 1

⎧
⎨

E total
E

is the total cost of energy emissions at spot carbon factors

G total

E is the total cost of natural gas emissions at spot carbon factors
P tota E is the total cost of electricity emissions at spot carbon factors
α is the unit index being analysed
β is the time interval being analysed

where

⎩

Note : For further information, please see Figures 6.4 and 6.5 showing exam-
ples of spot energy prices and carbon factors; also see Table 6.3 displaying carbon
emission coefficients of each generation technology.
Expression (5.6) combines the monetary costs incurred from delivering power
based on spot energy prices and emissions costs from power generation. The bi-
objective function presented here is a weighted linear interaction between operating
strategies, where ω is the emissions costs vs. spot price costs weighting factor and
its value is adjusted on the preference given to a particular objective. Naturally, the
results from weighting different ω values will depict that minimising both emission
costs and spot price costs are conflicting criteria. In other words, decreasing emissions
will yield higher costs and vice versa.

5.3.2 Constraints
Although the objective function formulations might differ, the equality and inequal-
ity constraints share many similarities for all TCOPF formulations. As expected, all
of these constraints are directly responsible in defining the region of feasible solution
for the integrated energy systems being analysed.