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

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).

𝑣𝑎𝑐 𝑝𝑒𝑎𝑘 =4𝑉𝑑𝑐

𝜋∑

1

𝑛sin (

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 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

delta (degrees)

|Vac r

ms| (p

u)

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

Per

Un

it V

olt

age

ωt (degrees)

vac Vdc

S1S3 S1S4 S2S4 S2S3

δ

(b)

(d)

δ

-2

0

2

4

6

0 60 120 180 240 300 360

Per

Unit

Volt

age

ωt (degrees)

vac vdc Vdc

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 =𝑉𝑖

𝑋𝐿𝑑𝜑 (1 −

|𝜑|

𝜋) (2)

where

𝑋𝐿 = 𝜔𝐿 = 2𝜋𝑓𝑠2𝐿, 𝑑 =𝑉𝑜

𝑁𝑉𝑖

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

Outp

ut

Pow

er,

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

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

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

π𝑠𝑖𝑛 (

δ

2) ∗

1

√2

𝛿 = 2𝑠𝑖𝑛−1 (𝑣𝑎𝑐1∗𝜋

2√2𝑉𝑑𝑐 )

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

πcosα −

2𝐼𝑑𝑐𝜔𝐿𝑠

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 system to 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

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 of these 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.

REFERENCES

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http://www.ieso.ca/Pages/Power-Data/default.aspx#.

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Grid-Tie Battery Energy Storage System,” IEEE

Transactions on Power Electroinics, vol. 26, no. 3, pp.

886-896, 2011.

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Carrasco, “Energy Storage Systems for Transport and

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Connected Battery Energy Storage System Using

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7

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[9] W. Tahil, “The Trouble With Lithium - Implications of

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