IEEE Computational Intelligence Magazine - November 2023 - 18

TABLE I The range of the decision variables. The hyphen symbol indicates that no unit is associated with the corresponding decision
variable.
PARAMETER
MIN VALUE
MAX VALUE
aPV 045
bPV 0360
PPV
CB
10
5
bSOC;max
bSOC;min
Pcharge
Pdischarge
0.50
0.05
-500
150
UNIT
450
1000
0.95
0.40
149.9
700
kW
kWh
-
-
kW
kW
VCHP 15 m3
DESCRIPTION
PV inclination angle
PV orientation angle
PV peak power
Battery capacity
Maximum battery SOC
Minimum battery SOC
Battery charging threshold
Battery discharging threshold
Heat storage volume
8) Battery Discharging Threshold Pdischarge between 150kW
and 700 kW. The stationary battery is discharged when the
current overall power demand is above the specified value.
9) Heat storage cylinder volume VHeat between 1 m3 and
5m3.
A summary of the decision variables and the affected
system components is given in Table I.For theoptimization
framework, all parameters are normalized to the range
0to1.
B. Objective Function Description
A study comparing different many-objective optimization
algorithms (without surrogate assistance) on this problem
was conducted in [17].However,thisearlier study only
focused on five independent objectives (the fifth objective
battery life is not considered), whereas this work is targeting
to evaluate 10 objectives in total. A summary of the objectives
is given in Table II. As a prerequisite for the optimizer,
all objectives need to be minimized. Note that hardware
installation and other costs are based on data from 2019 and
might have changed. The computation of objectives is based
on the output of the simulation tool (for example, the grid
TABLE II Objective description and range. The hyphen
symbol indicates that no unit is associated with the
corresponding objective, or that there is no upper or lower
bound.
OBJECTIVE MIN VALUE MAX VALUE UNIT DESCRIPTION
Cinvest
Cannual
-
-
-
bSOC
Ebatt;discharge
Ppeak;supply
t0
m
Efeed
Ppeak;feed
1
-
-
1
-
-
Gtotal 0- t
R0
Euro Investment costs
Euro Operation costs
CO2 emissions
s (negative) Resilience
- Mean battery SOC
kWh Discharged energy
kW Supply power peak
- Medium SOC share
kWh Feed-in energy
kW Feed-in power peak
SYSTEM COMPONENT
PV system
PV system
PV system
Battery storage
Battery storage
Battery storage
Battery storage
Battery storage
CHP
electricity demand for every 15 min interval in the
simulation time period). Also note that in contrast to many
linearized simulation models that only employ analytical
functions approximating the systems like the PV system or
battery as in [41], our simulator can model even non-linear
effects in high precision (at the cost of higher and variable
simulation times).
1) Investment costs in Euro. In this paper, mainly three
investment cost components are considered resulting from
purchasing the PV system, the stationary battery, as well as
the combined heat and power plant.
Cinvest ¼ IPV þ IBatt þ IHeatStor;
(2)
where IPV, IBatt, and IHeatStor refer to the investment cost for
the PV system, the stationary battery, and the heat storage
tank, respectively. Linearly scaling cost factors are assumed
for all three components (1000 Euro=kW PV peak power,
250 Euro=kWh battery capacity, 700 Euro=m3 heat
storage).
2) Annual operation costs in Euro per year. Maintaining and
operating the whole system will involve the grid electric
cost, the gas consumption, the peak electricity load cost
and the CHP maintenance cost. Thus, these four costs constitute
the annual cost.
CAnnual ¼ CGrid þCGas þCPeak þCCHP;
(3)
where CPeak is the additional peak cost for the highest energy
demand in a year. CHP maintenance costs of 4:3 Euro
per hour of operation are assumed: a gas price of
0:025 Euro=kWh power demand from gas, a (beneficial)
feed-in tariff of0:07Euro=kWh in case excess energy is fed
into the grid, a (beneficial) subsidy of 0:087 Euro=kWh of
energy produced by the CHP, a fixed base price of
1000Euro, and a price of 0:131 Euro=kWh for electricity
provided from the grid. An additional amount of
100 Euro=kW is charged for the overall maximum power
demand peak.
3) Yearly CO2 emissions in tons. The CO2 emissions are estimated
based on the simulated electricity and gas consumption
18 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2023

IEEE Computational Intelligence Magazine - November 2023

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