This document summarizes the design of a 3 kW bidirectional AC-DC converter for a battery energy storage system. It analyzes a dual active bridge topology with a 100 kHz transformer to interface a 300 V battery bank to a 110 V, 60 Hz grid. The dual active bridge design is presented, showing how the phase shift between bridges can control both the power flow direction and magnitude. Simulation results validate the design and control approach. The grid interface stage is also briefly discussed.

1. 1
Design of a Single Phase Isolated Bidirectional AC to
DC Converter for Battery Energy Storage Systems
Queen’s University ELEC 497 Research Project
Tom Gibson 10163463 14tagg@queensu.ca
Completed with the assistance of Prof. Praveen K. Jain and Mr. Behnam Koushki.
Abstract— This paper analyses the design of a 3 kW isolated
bidirectional ac to dc converter for Battery Energy Storage
Systems (BESS). This is an increasingly popular solution to
overcome the differences seen in electricity supply and demand
introduced by renewable energy sources. In order to connect these
systems to the grid an ac to dc converter is required. In this paper
a converter is considered to interface a 300 V battery bank to the
grid at 110 V, 60 Hz ac. A dual active bridge is implemented with
a 100 kHz transformer. Control systems for the converter are also
considered allowing autonomous regulation of the power flow to
and from the storage.
Index Terms—Battery energy storage, dual active bridge,
bidirectional isolated ac-dc converter.
I. INTRODUCTION
Over recent years a huge increase has been seen in the use of
renewable power generation in our energy supply networks as
many governments aim to promote clean sources over fossil
fuels as a response to global climate change. While renewable
technologies are much cleaner than traditional methods of grid
scale generation they lack the controllability of traditional
generation. For example a wind farm will typically be more
productive at night when winds are stronger, but at this time
demand is low. The output of a coal or gas power plant can be
adjusted accordingly within reason, but this is more
complicated with renewable power sources so imbalances
between supply and demand often occur.
Figure 1. presents the typical electricity supply and demand
for a day in Ontario [1]. During the daytime demand is greater
than total supply, and at night demand is much lower than
supply. Where these imbalances occur power is normally
imported from or exported to other regions.
One approach to overcome these imbalances is to implement
an energy storage system. These can range in size from large
systems such as megawatt scale hydro storage to smaller
projects such as kilowatt scale flywheels. As battery technology
is improved and the demand for distributed generation is
increased, battery energy storage systems (BESS) are growing
in popularity. The high charge and discharge efficiency and
energy density of lithium-ion based battery systems makes
them a highly favorable solution [2].
Fig. 1. Ontario Power Supply and Demand over 8 April 2015 [1].
In order to connect the dc BESS to the ac grid some form of
voltage converter is required. A popular approach is to use the
bridge circuit in Fig. 2. [3]. This circuit uses four metal-oxide-
semiconductor field-effect-transistors (MOSFETs), each
paralleled with a lossless diode to alter the voltage signal.
The circuit operates as a boost rectifier when power needs to
be transferred from the ac grid to the dc batteries. The current
flows for this operation are shown in Fig. 2.(a). When the
MOSFET switches are off (or open) the current flows through
the diodes to reach Vdc. i.e. for the positive cycle of vac there is
current flow through the diodes D1 and D3 following the solid
blue lines. Similarly, during the negative cycle of vac there is
current flow through the diodes D2 and D4, in the direction of
the dashed orange lines. When the MOSFETs are turned on (or
are closed) current is allowed to flow through them, thus
bypassing the capacitor and charging the inductor (i.e. for the
positive ac cycle the current flow is through D1 and S2, along
the dotted green line). This stored charge is injected back into
the capacitor once the switches are opened again at a high
voltage. This allows Vdc to be much larger than vac. The
magnitude of the dc voltage can be controlled by altering the
duty cycle of the MOSFETs.
When operating in inverter mode (Fig. 2.(c)) the diodes
become redundant and the MOSFETS are used to control the ac
voltage frequency and RMS magnitude. The graph in Fig. 2.(d).
indicates when each of the switches is turned on and the ac
waveform which is subsequently produced. The ac voltage has
fundamental and odd harmonics and is given by Eq. 1.
Ontario demand
Projected
Actual
Market demand
Projected
Actual

2. 2
Fig. 2. (a) Circuit schematic for bidirectional ac/dc converter in rectifier mode; (b) Rectifier input and output waveforms (vac and Vdc respectively);
(c) Circuit schematic for bidirectional ac/dc converter in inverter mode; (d) Inverter input and output waveforms (Vdc and vac respectively).
𝑣 𝑎𝑐 𝑝𝑒𝑎𝑘 =
4𝑉 𝑑𝑐
𝜋
∑
1
𝑛
sin (
𝑛𝜋
2
) sin (
𝑛𝛿
2
)sin(𝑛𝜔𝑡)∞
𝑛=1,3
(1) [4]
The RMS magnitude of vac can be controlled by adjusting the
pulse angle δ as shown in Fig. 3. Therefore adjusting the switch
period alters the voltage. The ac voltage frequency is half of the
switching frequency and can be controlled by adjusting the
switching frequency.
Fig. 3. Fundamental and harmonics of inverter ac output voltage against pulse
width angle δ.
While this makes an effective voltage converter it also
requires a high dc bus voltage, higher than the ac source
voltage. A reduction in the dc voltage would have the advantage
of reducing the battery pack voltage or the required number of
series battery cells. The system stability would also be
increased. One method of reducing the voltage would be to add
a transformer at the grid side, however at the low grid frequency
transformers need to be large and tend to be expensive. An
alternative solution is to add an isolated dc to dc converter to
the dc side, composed of two more bridges tied together by a
high frequency transformer, as in Fig. 4. [5]. This is known as
a dual active bridge (DAB) [6], [7]. The high frequency
transformer can be made much smaller and less expensive than
the low frequency equivalent and will have improved
efficiency.
The converter shown in Fig. 4. can be considered as a two
stage device. Stage 1 uses a single converter bridge to convert
the ac grid voltage to dc. In Stage 2, Bridge B converts the dc
voltage, Vo, back to ac but at a much higher frequency than the
source voltage. The ac voltage is reduced by the transformer
then converted back to dc by Bridge C for connection to the
batteries.
In this paper the analysis and design of this system is
considered for a BESS with the parameters outlined in Table I.
The DAB design is considered first before being applied to the
rest of the system.
0 20 40 60 80 100 120 140 160 180
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
delta (degrees)
|Vacrms|(pu)
n = 1
n = 3
n = 5
n = 7
Positive half cycle Negative half cycle
Positive cycle inductor charging
Vac
Vdc
(a)
(c)
-1.5
-1
-0.5
0
0.5
1
1.5
0 60 120 180 240 300 360
PerUnitVoltage
ωt (degrees)
vac Vdc
S1S3 S1S4 S2S4 S2S3
δ
(b)
(d)
δ
-2
0
2
4
6
0 60 120 180 240 300 360
PerUnitVoltage
ωt (degrees)
vac vdc Vdc

3. 3
Fig. 4. Circuit schematic of a single phase isolated bidirectional ac/dc converter.
TABLE I. CONVERTER DESIGN PARAMETERS
Voltage Supply (vs) 110 VRMS, 60 Hz AC
Voltage Output (Vo) DC Batteries, 300 V nominal
(Range 250 – 400 V)
Power Output (Po) 3 kW
Stage 1 switching
frequency (fs1)
20 kHz
Stage 2 switching
frequency (fs2)
100 kHz
Switch type MOSFET
II. ANALYSIS AND DESIGN
A. Dual Active Bridge
Analysis of the system is carried out looking from the output
side, under idealized conditions the output power is given by
Eq. 2. [6]
𝑃𝑜 =
𝑉 𝑖
𝑋 𝐿
𝑑𝜑 (1 −
|𝜑|
𝜋
) (2)
where
𝑋 𝐿 = 𝜔𝐿 = 2𝜋𝑓𝑠2 𝐿, 𝑑 =
𝑉𝑜
𝑁𝑉 𝑖
In addition to the parameters in Table I., Vi is the dc bus voltage
(voltage over C1 in Fig. 1.), φ is the phase shift between Bridge
B and Bridge C, L is the primary referred leakage inductance of
the transformer and N is the transformer turns ratio.
Po, Vo and fs1 are known from the design parameters. For a
full range of zero voltage switching it is preferred that d = 1,
therefore N = Vo/Vi. Vi needs to be chosen as a value greater
than the maximum source voltage, so for the purpose of this
design Vi = 400 V dc was chosen, giving N = 3/4. With all other
variables (including L) being constant the output power varies
with the phase difference, φ. This relationship is shown in Fig.
5. It is seen that φ can be used to control the output power, and
the maximum occurs when φ = 90°. For the design under
consideration a nominal phase shift of 60° is considered
appropriate so that the output power can be increased slightly if
required or if the system is overloaded. Also, L varies to φ in
the same manner as Po so a smaller φ means smaller L.
Taking these values into consideration the leakage reactance,
XL, can be calculated from Eq. 2 and is found to be 37.23 Ω.
Therefore from this value and at fs2 = 100 kHz, L = 59.26 μH.
Fig. 5. Converter output power (magnitude and direction of flow) against the
phase shift between Bridge B and Bridge C.
Also seen in the above figure is that the direction of power
flow can be controlled by φ as well as its magnitude. Therefore
a closed loop control system can be designed to adjust the phase
shift based on the battery state of charge (SOC) and grid power
requirements. Since the output side is constant voltage the
current flow varies directly with power, so this control system
will also regulate the current flow.
Following the analysis of the DAB converter system it was
assembled in PSIM for proof of concept. The design was
configured as in Fig. 6. with a simple control system. The
capacitors C1 and C2 are introduced to suppress the dc current
ripple caused by switching and for the simulation these were
each set to 1 nF. L represents the transformer primary referred
leakage inductance and was set at 60 μH based on the previous
calculation. The dc voltage sources VDC and Vbattery represent
the desired dc bus and battery voltages respectively. A small
inductor and resistor are connected in series with Vbattery to
represent non-ideal battery characteristics.
Fig. 6. PSIM circuit diagram for dual active bridge.
-1
-0.5
0
0.5
1
-120 -90 -60 -30 0 30 60 90 120
OutputPower,Po(pu) Phase Shift φ°Backwards Power Flow Forwards Power Flow
dc bus
Bridge A Bridge B Bridge C
Stage 1: Bidirectional
AC/DC Converter
Stage 2: Dual Active Bridge DC/DC Converter
High Frequency
Transformer

4. 4
Control of the system was achieved using step voltage inputs
to control each MOSFET bridge. These sources, labelled
VBridgeB and VBridgeC were set to 100 kHz to match the
switching frequency of this stage. The phase delay between
bridges B and C was also controlled using these sources and thus
allowed control over the output current and direction of power
flow. For example under idealised conditions when the phase
delay, φ, is equal to zero degrees the overall power flow should
also be zero, according to Eq. 2. This is observed in Fig. 7.(a).
where the average values of primary transformer current, Ires,
and battery current, Ibattery, are also near zero. When the phase
delay of VBridgeB is set to 60°, i.e. φ =-60°, the result in Fig.
7.(b). is observed. In this case the average current flowing into
the battery is negative, this is the discharging mode. When the
phase delay is applied to VBridgeC, i.e. φ = 60°, the power flow
is reversed and the battery current is positive as in Fig. 7.(c).
This is the charging mode.
(a)
(b)
(c)
(d)
Fig. 7. PSIM simulation results for DAB, (a) when φ = 0°; (b) φ = -60°;
(c) φ = 60°; (d) dc link and battery voltages (similar for each case).
Note that the battery current is not strictly dc due to the
switching effects and phase delay. The resonant circuit current
remains above or below zero in each case due to the leakage
reactance, and has a frequency of 100 kHz, the same as fs2.
In the above analysis it is considered that the winding
resistances are negligible compared to the transformer leakage
reactance. It is also assumed that the magnetizing inductance of
the transformer is infinitely large however this may not be the
case in a real system. The effect of this on the range of soft
switching for the system is considered in the literature [6].
It is given that the magnetizing inductance can be
approximated as Lm = K*L given that L is the leakage
inductance calculated above and K ≥ 1. Therefore for this
system to remain stable Lm ≥ 60 μH.
Simulating the circuit again for stage 2 with the given and
calculated parameters produced the waveforms in Fig. 8. for
K >> 1 and K = 1. It is indicated that the magnetizing
inductance has an effect on the circuit currents. When K >> 1,
i.e. Lm >> L, the currents through the systems follow fairly
smooth and ideal characteristics. As K is reduced the current
edges become sharper with a more triangular waveform
developing. Therefore as K is decreased the region for soft
switching is increased but comes with a trade-off of low
transformer utilization.
(a)
(b)
(c)
Fig. 8. Simulated dual active bridge converter: (a) Primary and secondary
transformer voltages; (b) Input and output current for K >> 1; (c) Input and
output current for K = 1.

5. 5
B. AC Grid Interface
After designing the DAB part of the system the grid and
battery connections may be considered. On the grid side another
converter bridge is connected as mentioned before, indicated as
Stage 1 in Fig. 4. This controls the voltage of the dc bus as well
as acting as a rectifier/inverter between the ac grid and dc bus
[8].
As previously noted when operating as an inverter the ac
voltage magnitude can be adjusted by altering the pulse width,
δ. In this mode the inverter will produce harmonics, the
magnitudes of which are also shown in Fig. 3. However, it is
desirable to have only the fundamental voltage component, so
an LC filter could be implemented at the grid side. In this case
the required pulse width angle to achieve the desired ac voltage
can be found from Eq. 1 where n = 1:
vac1 RMS =
4Vdc
π
𝑠𝑖𝑛 (
δ
2
) ∗
1
√2
𝛿 = 2𝑠𝑖𝑛−1
(
𝑣 𝑎𝑐1∗𝜋
2√2𝑉 𝑑𝑐
)
Therefore for this system where Vdc = 400 V and vac RMS = 110
V it is required that δ = 35.57°. This would switch at the source
frequency, i.e. 60 Hz. A control system can be implemented to
adjust this angle when required based on the grid and battery
conditions, for instance if the dc bus voltage was to change as
the batteries discharge.
In rectifier mode the dc voltage can be given by Eq. 3:
𝑉𝑑𝑐 =
2vac
π
cosα −
2𝐼 𝑑𝑐 𝜔𝐿 𝑠
𝜋
(3)
In this equation α is the control angle and is the phase
difference between vac and the MOSFET firing pulses and Ls is
the source inductance. Therefore the dc voltage varies with Idc
and α, assuming all other parameters are constant. The control
angle is required to be adjusted by a closed loop controller
depending on the required current.
C. Energy Storage Considerations
A number of energy storage solutions are considered by
Vazquez in [3], with their main characteristics outlined in Table
II. For similar applications Li-ion batteries are the preferred
technology thanks to their relatively high energy and power
densities, meaning that more energy can be stored per kilogram
of mass in Li-ion batteries compared to their lead acid or nickel
based counterparts. However due to the relatively low
availability of lithium and the increasing popularity of lithium
based batteries in applications such as electric vehicles the raw
material cost of lithium is likely to increase [9]. In this case
cheaper battery technologies may be used for lower power
applications.
In [8] Li-ion batteries are used for experimental testing of the
isolated bidirectional ac to dc converter. Battery modules are
used, each containing seven cells. With each cell rated at 3.8 V,
each module can supply 26.6 V. Therefore for the system
considered here fifteen series connected batteries are required
TABLE II. Comparison of Energy Storage Systems [3].
to provide the maximum battery voltage of 400 V. Each battery
module is rated at 40 Ah and can be connected to additional
modules in parallel to boost the capacity.
D. Control System
It is preferable for the system to be autonomous and self-
regulate its operation, especially where used in smaller scale or
smart-grid applications. Each stage of the converter requires a
control systemto maintain the desired voltage and current levels.
For stage 1 the system must regulate the dc bus voltage as well
as the grid current to maintain the correct voltage phase and
maintain unity power factor. Meanwhile the control system for
stage 2 maintains the battery current and voltage by means of
controlling φ to regulate the charging and discharging of the
batteries. A potential control strategy is outlined in [5] as
depicted in Fig. 9.
In this example each control system implements a double
closed loop, each with an inner current loop and outer voltage
loop. For Stage 1 (Bridge A) the voltages V1 and vs are
monitored as well as the grid current is. Through altering the
gate signal of each MOSFET (i.e. adjusting δ) control over the
phase and amplitude of vso can be achieved, thus enabling
control over the phase and amplitude of is. This allows for
control over the power flow between the grid and the dc bus,
and regulation of the dc bus voltage, V1. As mentioned
previously the switching frequency is the frequency of vac when
operating in inverter mode, therefore in this mode the switching
frequency should be 60 Hz.
The controller for stage 2 controls the switching signals for
bridges B and C. It does this through monitoring the battery
current and voltage and adjusting d accordingly to regulate the
magnitude and phase of iL. Using these values the state of
charge (SOC) of the batteries can be estimated. However,
determining the exact SOC can be challenging [2] so
monitoring current and voltage can improve the system
accuracy.
Additional control parameters may be applied to the
batteries to provide protection against undervoltage or
overvoltage, overheating and overcurrent. This is necessary
with Li-ion batteries to prevent the internal resistance of the
cells from heating up and failing [3]. Measures to balance the
cell voltages and SOCs are also favorable to maintain the cell
lifetime [2], [3].

6. 6
Fig. 9. Control Strategy for Grid Connected Isolated
Bidirectional AC to DC Converter [5].
E. Converter Efficiency
As with most electronic circuits the considered converter
design is susceptible to energy losses. These losses will mainly
occur in the MOSFETs and the transformer coils. Each switch
will exhibit switching losses due to its rise and fall times,
particularly at high frequencies. However, since this system uses
zero voltage switching these losses should be minimised. There
are also conduction losses through each switch due to the finite
switch resistance. This can be a disadvantage for the converter
using the DAB compared to the single bridge converter since
three times the number of switches are required, tripling the
switching power loss. However since the efficiency of the high
frequency transformer is expected to be much higher than the
equivalent low frequency design the power loss savings here
may outweigh the switching losses, meaning that the isolated
system operates at a higher efficiency overall.
As outlined in [5], with traditional power and magnetic
components it can be difficult to achieve high efficiency and
power density. For this reason it is suggested that newer
switching and transformer technologies are introduced. These
include using silicon carbide (SiC) devices as opposed to the
traditional silicon (Si) devices, as well as replacing ferrite with
nanocrystalline soft magnetic material in transformers and
inductors. However the use ofthese materials will incur a greater
expense when building the system so may not be advised for
lower power applications. From similar reports an efficiency of
around 95% can be expected [5], [8].
III. CONCLUSION
This paper has discussed the role of battery energy storage
systems in our electricity grids for peak shaving and grid
stabilization. The requirement of a bidirectional ac to dc
converter was reviewed in the role of connecting the BESS to
the electricity grid. Furthermore the isolated bidirectional ac to
dc converter was taken into consideration for analysis and
design, the benefits of this system being stated as reducing the
battery bank voltage and the required number of series cells, as
well as increasing system safety by isolating the battery bank
from the grid. This was a two stage converter, with stage one
being a basic full bridge bidirectional ac to dc converter, and
stage two being a dual active bridge dc to dc converter.
During the design process the ideal leakage inductance of the
high frequency transformer was calculated to be L = 59.26 μH.
This would allow for nominal operating conditions when the
phase shift across the DAB was 60°. Simulation of this stage
confirmed that these values were appropriate. Following this a
control method was considered which could adjust the phase
shift on order to regulating the power flow across the DAB,
thereby controlling the charging or discharging of the batteries.
For the battery bank, lithium ion cells were chosen for their high
efficiency and high power density.
Finally the estimated power losses of the system were
discussed and it was noted that the efficiency could be increased
using more advanced switching and transformer materials.
Future work to be carried out could include a more detailed
analysis and design of the control system to devise a solution of
fully automated control. A full system simulation could be
completed and analyzed under various loading conditions,
comparing this converter to alternative designs, before a real
converter is built.
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7. 7
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