IEEE Power Electronics Magazine - March 2021 - 52

bill. Note that the second term in (7) represents the maximum
demand price, which forces the optimization to schedule the
battery output in a way that the maximum exchanged power
between the customer and distribution system remains in a
minimum possible value.

Power (kW)

4
2
0
-2
-4
-6
-8

Days
Exchanged Power (PG)
Battery Power
FIG 5 Exchanged power and the battery (dis)charge power for
ideal battery pack under TOU electricity tariff.

Power (kW)

6
4
2
0
-2
-4
0

3
4
Days

FIG 6 Exchanged power and the battery (dis)charge power for
the nonideal battery pack under TOU electricity tariff.

Table 1. Impact of the nonlinear inverter
efficiency under TOU tariff.
Customer's
Bill ($)

Throughput
of the Battery
(kWh)

Maximum
Exchanged
Power (kw)

Ideal battery
pack

56.5

2041

6.7

Nonideal
battery pack

69.5

1008

6.9

IEEE POWER ELECTRONICS MAGAZINE

z March 2021

In the TOU policy, employing the battery facilitates the
demand-side management to take advantage of different
electricity rates during the peak and off-peak time. During
the off-peak time, the battery charges at a lower price and
sells the electricity back to the grid during the peak time.
The exchanged power between the distribution system and
the customer at POD (blue line) and the battery (dis)charging power (red line) are shown in Fig. 5 for an ideal battery.
Figure 5 shows that the battery (dis)charge with maximum
capacity to maximize the customer's benefit. The
exchanged power and battery (dis)charge power for the
battery with nonlinear inverter efficiency are represented in
Figure 6, showing the impacts of the nonideal inverter efficiency on battery performance compared to the ideal
inverter. The battery with a nonideal inverter has a limited
(less than fifty percent) contribution in demand-side management to avoid battery power loss due to the inverter's
lower efficiency in lower powers. The customer's electricity
bill, total battery throughput, and the maximum exchanged
power for TOU tariff are summarized in Table.1. For a (dis)
charge power less than ten percent of its nominal power, in
which the inverter has a considerably lower efficiency, the
number of battery (dis)charges shows a significant drop
compared to the battery with an ideal inverter. The lower
contribution of the battery results in a slightly higher electricity bill and a higher load peak at POD.

B. Scenario 2: MD Tariff

Exchanged Power (PG)
Battery Power

In this section, we run two simulation scenarios on our
case study model (see Figure 1) under TOU and MD tariffs,
as formulated in (6) and (7). Both scenarios consider two
battery choices: (i) an ideal battery pack; and (ii) a realistic battery pack with nonlinear inverter efficiency, as
shown in Figure 4.

A. Scenario 1: TOU Tariff

-6

Simulation Results and Discussion

In the MD tariff, the battery (dis)charges such that the maximum exchanged power, PG max, stays at a minimum level to
reduce the customer's electricity bill. The simulation results
for optimization formulated in (6) for an ideal inverter are
shown in Figure 7. A comparison between results in Figure 7 with Figure 5 indicates that the battery under MD tariff (dis)charges in lower powers to maintain a minimum
exchanged power. Battery operation in lower powers
implies higher impact expectation for a nonideal battery
application. Figure 8 shows the exchanged power for the
battery with a non-ideal inverter. Due to the nonlinear
inverter efficiency, battery operation in lower powers is no
longer beneficial, yet, to minimize the customer bill, battery
operation is adjusted to reach the optimal solution. The
impacts of the inverter nonlinear efficiency on the customer's bill and load profile are summarized in Table. 2. The
total contribution of the battery has been decreased to
maximize the battery efficiency (performance); thus, the
maximum exchanged power has been increased.

IEEE Power Electronics Magazine - March 2021

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