IEEE Computational Intelligence Magazine - November 2023 - 19

ofgrid electricity system, CHP, and boilers, respectively.
Gtotal ¼ Ggrid þGgas
(4)
where Ggrid is the amount ofCO2 emissions from grid electricity,
approximated at 500 g=kWh. The term Ggas
refers
to the amount ofCO2 emissions from operating the CHP
and boilers, set at 185 g=kWh.
4) Resilience in seconds. The term resilience refers to the duration
the company would be able to operate in case no grid
power is available, i.e., energy is only provided by local production
(PV system and CHP) and battery energy storage.
This is, for example, relevant in cases of severe mal-functions
due to extreme weather conditions, malicious physical
or cyber-attacks. The resilience is in our case computed as
R ¼ min
bSOC CB
Pload
(5)
where bSOC is the battery's state ofcharge vector (for all simulation
time steps), CB refers to the battery capacity and Pload
is the grid load vector. Resilience thus refers to the minimum
(of time) over all 15 min time periods in the simulation of
energy in the battery ðbSOCðtÞ CBÞ divided by the respective
power consumption PLoadðtÞ. This can be interpreted as
the time period, for which the company would still be able
to operate all electric components, at the worst point in time,
i.e., the lowest ratio of battery state of charge and current
electric load. Since all objectives need to be minimized,
Equation (5) is formulated negatively as
R0 ¼R
(6)
5) Mean battery state of chargebSOC, between 0 and 1:bSOC
is the average state of charge of the stationary battery over
the entire simulation. On one hand, a high mean state of
charge enables the battery to discharge large amounts of
energy to mitigate high peak costs when the overall power
consumption is high. However, on the other hand, a high
battery SOC over large periods of time is undesirable, as it
leads to faster battery degradation.
6) Yearly energy discharged from battery Ebatt;discharge
in
kWh. A second indicator for battery degradation is the
amountofenergythatisdischargedfromit. Themore
energy discharged (and charged) from it, the faster the
degradation.
7) Maximum power peak Ppeak;supply in kW. The maximum
power demand peak is treated as an individual objective.
Aside from contributing to higher annual costs due to peak
demand charges for the customer, a high maximum power
peak may lead to instability ofthe grid.
8) Time share tm between 0 and 1 of the time in which the
battery SOC is between 30% and 70%. As a trade-off
between battery degradation and the ability to react to
high demand charges, this objective creates an additional
incentive to charge the battery with a medium amount of
9) Yearly energy Efeed fed into the grid in kWh. Minimizing
the amount of energy that is fed into the grid has multiple
advantages. It maximizes PV power self-consumption and
creates a higher level of independence from the energy
supplier. It also reduces CO2 emissions and leads to lower
annual costs, since the feed-in tariff is lower than the grid
supply rate. Yearly energy Efeed is already included in objective
annual operation costs, but might be of special interest
for some decision makers.
10)Maximum feed-in power peak Ppeak;feed in kW. Similar to
the previous objective, a lower maximum feed-in power
peak relates to higher PV power self-consumption and
generally an efficient usage of self-produced energy. Furthermore,
penalizing the maximum feed-in peak might be
a realistic option for the supplier to reduce grid instability
and frequency issues in the future. This would create additional
costs for the consumer. In the present cost structure,
there is no monetary impact of Ppeak;feed, but due to its
impact on the grid stability, it is, however, also considered
as a separate objective.
In BEM, all decision values have an impact on the internal
electricity consumption (vector over time) ofthe building that
is simulated and all objectives (except for Cinvest) are affected by
this consumption, either directly (like Cannual) or indirectly via
the amount ofenergy that is stored in the stationary battery, or
when this energy is discharged. Sensitivity analysis between
the decision variables and all objectives is carried out, which
confirms that nine ofthe ten objectives are affected by all decision
variables, except that Cinvest is determined by PPV, CB, and
bSOC;max only. The details ofthe sensitivity analysis are not provided
here due to space limit. In summary, the simulation
setup offers multiple directions to consider when optimizing
the configuration. A large PV system enables the building to
produce a significant share of the overall used energy, keeping
the annual costs, peak power, and emissions low, while at the
same time requiring a high initial investment. Orientation and
inclination of the PV system can be tuned to define at which
points in time (daily and seasonal) the system produces the
most power. A large battery is also costly, though advantageous
with regard to resilience and supply power peak. Many
of the objectives are very sensitive to the four parameters that
define the operation of the battery (bSOC;max, bSOC;min, Pcharge,
Pdischarge) and therefore, create a challenging optimization task.
IV. Methods
A.AdoptedAlgorithms
Five multi-objective SAEAs, i.e., GP-iGNG, RVMM,
K-RVEA, KTA2, and REMO, and one MOEA, i.e., RVEAiGNG,
are adopted to optimize the BEM problem. RVEANOVEMBER
2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 19
energy. Since the objectives are minimized to an intermediate
charge (SOC) level, it is formulated as
t0
m ¼ 1 tm
(7)
IEEE Computational Intelligence Magazine - November 2023

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2023
