IEEE Power Electronics Magazine - March 2021 - 50

the studies in demand-side energy management, the battery
pack (battery and its inverter) is either modeled as an ideal
battery with a hundred percent efficiency or formulated
with a constant efficiency. However, the inverter efficiency
is a nonlinear function depending on operating conditions
such as (dis)charge power [10], [11]. Considering a constant
battery pack's efficiency is trivial, as a battery with constant efficiency is an ideal battery with a lower capacity and
the same behavior in the system.

Solar Power

Ppv
POD

Power Grid
Pb

Small-Scale Battery Sizing for
Demand-Side Load Management

Load (kW)

FIG 1 Schematic of residential load connected to the grid in
the presence of the solar panels and battery.

4
3.5
3
2.5
2
1.5
1
0.5
0

12
(h)

Maximum Expected Load
Maximum Load
Minimum Expected Load
Minimum Load
FIG 2 Maximum and minimum load consumption profile.

Solar Output (kW)

3.5
3
2.5
2
1.5
1
0.5
0

12
(h)

Min Solar
Max Solar

IEEE POWER ELECTRONICS MAGAZINE

Max Expected
Min Expected

FIG 3 Maximum and minimum solar generation.

Moreover, for an effective demand-side management,
electricity tariffs should be considered in the optimization.
Utilities use tariffs as a powerful tool to manage their customers' load consumption behavior and to flatten the electricity demand curve [12]. Thus, considering the battery's
optimum size, to study the battery's optimal contribution
in demand-side management, tariff policy is required. This
study focuses on the effect of the inverter's nonlinear efficiency in demand-side energy management while considering electricity tariffs. To study the impact of the inverter
efficiency on the customers load profile, a residential customer with small-scale renewables is considered as a case
study model. A battery sizing approach suitable for load
management study is introduced; then, the inverter's efficiency and its impacts on the battery's (dis)charging power
and the exchanged power between the customer and distribution system are studied under two different tariffs.

z March 2021

Considering the maximum load consumption of a customer
to size the battery is not economically beneficial and will
result in over-sizing. Moreover, customers with a larger battery will be able to sell more power to the grid, which is not
necessarily beneficial for utilities, especially with the higher
penetration level of the renewables [13]. In this study, we
consider a residential customer equipped with renewables
as our case study. The case study's schematic is depicted in
Figure 1, where arrows represent direction of power flow in
the system. A double arrow denotes the battery's power
flow, emphasizing that it can be a consumer/supplier of electrical energy to the home/power grid, depending on its state
of charge (SOC).
The exchanged power, P Gt, between the customer and
the distribution system at the point of delivery is formulated as:

P Gt = Plt - P tpv + P bt (1)

Where Plt is the customer's original load consumption, P tpv
is the solar output, and P bt denotes stationary battery's (dis)
charging power at time interval t. P Gt is considered as customer's new load profile from the power system's point of
view at point of delivery (POD).
We collect historical data for the customer's load profile and solar output power generation from EPRI [14] and
NREL [15] websites. For the obtained data, the maximum
and minimum of the load demand and the solar power is
established for every hour of the day, as shown with dashed
lines in Figure 2 and Figure 3, respectively. Next, based on
the collected data, probability density functions (PDFs) are
fitted for customer's load consumption and solar power.
Using the PDF functions, we form the statistical distribution for the power consumption (load) and solar panels'
output to calculate an expected upper and lower boundary
for the load and solar output power. The expected values

IEEE Power Electronics Magazine - March 2021

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