Battery Component in PSCAD/EMTDC

Secondary electrochemical batteries (rechargeable batteries) are of great importance in

power systems because they give the electric engineer a means for storing small

quantities of energy in a way that is immediately available. Some of the main battery uses

are:

Batteries within Uninterruptable Power Supplies (UPS)

Battery Energy Storage System (BESS) to be installed in power grids with the

purpose of compensating active and reactive power (in this sense they are an

extension of the SVCs, and therefore are sometimes called also SWVCs).

Batteries of the main energy source of electric vehicles.

There are many types of batteries and many factors that affect battery performance. To

predict the performance of batteries, different mathematical models exist. None of them

are completely accurate nor do any include all necessary performance effecting factors.

This report introduces a battery component in PSCAD/EMTDC which is based on

electrochemical battery model and tabulated battery data models. It includes the

following sections:

A brief introduction of the electrical characteristic of batteries

The general battery component in PSCAD/EMTDC

tests for the component

There are four main cell chemistries in use for rechargeable batteries: lead-acid, nickel-

cadmium (Ni-Cd), nickel metal hydride (Ni-MH), and lithium-ion (Li-ion).

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1. Electrical characteristics of batteries

The main characteristics of battery are the charge and discharge characteristics. The

discharge characteristic is shown as follow:

Fig.1. Discharge characteristic of batteries

The charge characteristic has a very similar shape to that of discharge. For low C-rate

charge and discharge currents, if superimposed, the two curves are almost the same

(Fig.2). Hence for the purposes of most system studies, the charge and discharge

characteristic can be described by the same equation if the battery hysteresis effect is

neglected.

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Fig.2. Charge and discharge characteristic of batteries

The important terminology of batteries:

1. Rated capacity: the ampere-hours a fully charged battery can deliver at a

specified rate (C/5 or C/20 rates are typically used here)

2. Nominal voltage: The voltage of the battery under normal operating

conditions.

3. State of charge (SOC): An expression of the present battery capacity as a

percentage of maximum capacity.

4. Charging rate (C rate): the amount of current that a battery can deliver for 1

hour from fully charged to the end of life. For a 100 Ah battery, 1C means

the discharging current is 100A, 0.2C means 20A, 5C means 500A

5. Internal resistance: the Thevenin resistance within the battery

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2. Battery model in PSCAD/EMTDC

A battery component created for PSACD simulation is introduced in this section. The

model of the component is based on Shepherd equation which is used to represent the

battery electrochemical performance [1].

The interface of the component in the PSCAD is then illustrated. The tabulated battery

data is used in the component as an option to represent the Voltage-SOC characteristic

directly.

2.1 The electrochemical battery model

2.1.1 Modified Shepherd model

The battery is modeled by a controlled voltage source in series with a constant

resistance, as shown in Fig.3 [2].

Fig.3. Equivalent circuit of batteries

The equivalent circuit is represented by the following equations which are based on

Shepherd equation:

(1)

(2)

Where:

Ebat: internal voltage (V)

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E0: battery voltage constant (V)

K: polarisation voltage (V)

SOC: state of charge (%)

Q: battery capacity (Ah)

A: exponential zone amplitude (V)

B: exponential zone time constant inverse

Vbat: terminal voltage (V)

Ibat: battery current (A)

Rbat: internal resistance (Ω)

The model is based on a few simplifying assumptions:

1. The internal resistance is assumed constant during the charge and discharge

cycles and doesn’t vary with the amplitude of the current

2. The model’s parameters are deduced from the discharge characteristics and

assumed to be the same for charging

3. The capacity of the battery doesn’t change with the amplitude of the current

(i.e. No Peukert effect).

4. The temperature doesn’t affect the model’s behavior

5. The self-discharge of the battery is not represented

6. The battery has no memory effect

7. Charge and discharge history does not affect battery characteristics (ie. No

hysteresis)

2.1.2 Determining the parameters of the model

Fig.4 shows the typical discharge characteristic of a 1.2V 6.5Ah nickel-metal-hydride

(Ni-MH) cell. It is used here as an example of how to set up the parameters of the battery

model.

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Fig.4. Typical discharge characteristic

As shown in Fig.4, the shape of the curve is decided by three points: fully charged

voltage, end of exponential zone voltage, and the end of the nominal zone voltage. The

zone occurring after the nominal zone is not generally useful and so is not covered here.

(1)

The internal voltage characteristic (Equation (1)) is described by the sum of three

mathematical functions:

1. The exponential curve , which represents the section from fully

charged to the end of the exponential zone

2. The nominal zone line , which represents the middle section from the

end of the exponential zone to the end of the nominal zone

3. The DC transition level of E0, which is the value at the transition between the end of

the exponential zone and the beginning of the fully charged zone.

The equations can be fit to the example data as follows:

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A: voltage drop during the exponential zone (V)

3/B: Charge at the end of exponential zone (Ah)

K: the polarization voltage

E0: voltage constant (V)

2.2 The battery component in PSCAD

The component in PSCAD is shown as bellow:

Fig 5 the component “battery” in PSCAD

Where:

Ibat: the current of the battery, input signal.

Reset: the control signal used to control charge or discharge the battery, input signal.

SOC: output signal

The dialog box and input is shown as below:

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Fig 6 the dialog box of “battery”

Where:

Battery type: there are five options:

User defined model: the characteristics of voltage vs.SOC and the internal

resistance vs. SOC are defined as the tabulated inputs directly. It allows

variable internal resistance

The other four are electrochemical models based on the modified Shepherd

model. There are lead-acid, nickel-cadmium (Ni-Cd), nickel metal hydride (Ni-

MH), and lithium-ion (Li-ion). The internal resistances are constant

Nominal Voltage (V): The nominal voltage represents the end of the linear zone of the

discharge characteristics

Rated Capacity (Ah): The rated capacity is the rated capacity of the battery

Initial Capacity (Ah): used as an initial condition for the simulation and does not affect

the discharge curve

Nominal capacity (Ah): extracted from the battery until the voltage drops under the

nominal voltage

Voltage at exponential point (V): The voltage corresponds to the end of the exponential

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zone.

Maximum Voltage (V): The fully charged voltage

Internal Resistance (ohm): it is constant for all electrochemical models

3. Example

A case is developed in PSCAD for two purposes:

1. To test the charge and discharge characteristics of the battery model

2. To illustrate the usage and functionality of this model and to illustrate the intended

usage of the control signals.

Fig.7 Charging and discharging circuit

Fig.7 shows a charging and discharging circuit using this battery model. A 4.2V

voltage source and a 3.6V, 1Ah Li-ion battery are connected in parallel with different

loads (1.8, 3.6, 7.2 and 18 Ω) respectively. The Li-on battery discharge curves with

different C rate are plotted in Fig 8.

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the discharge curves of Li-on

Time (sec)

0.0 2.0k 4.0k 6.0k 8.0k 10.0k 12.0k 14.0k 16.0k 18.0k2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

Ba

tte

ry t

erm

ina

l vo

lta

ge

(V

)

2.0C 1.0C 0.5C 0.2C

Fig 8 the discharge curves of Li-on

Another test is conducted on this case. When the battery capacity is lower than 30%

(SOC<0.3) of the rated capacity, the voltage source begins to charge the battery and

supplies the load. The voltage source stops charging the battery after the capacity reaches

to 80% (SOC=0.8), and the battery takes over the load until its SOC<0.3. Then charge-

discharge repeats again. The simulation results are shown below (Fig.9):

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Main : Graphs

x 0.0 2.0k 4.0k 6.0k 8.0k 10.0k 12.0k 14.0k 16.0k 18.0k 20.0k ... ... ...

3.40

3.60

3.80

4.00

4.20

4.40

y

battery terminal voltage (V)

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

y

SOC

-1.00

-0.50

0.00

0.50

1.00

y

Batttery current (A)

0.30

0.40

0.50

0.60

0.70

y

load current (A)

Fig.9. Charging and discharging process

At first the battery supplies the load with 0.5C (0.5A when load resistance = 7.2 Ω).

At 5000-8600 sec, it is charged with 0.5C by the voltage source, and then discharge at

8600-12200 sec.

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References:

1. Shepherd, C. M., Design of Primary and Secondary Cells - Part 2. An equation

describing battery discharge, Journal of Electrochemical Society, Volume 112,

July 1965, pp 657-664.

2. Olivier Tremblay1, Louis-A. “Dessaint Experimental Validation of a Battery

Dynamic Model for EV Applications”, World Electric Vehicle Journal Vol. 3 -

ISSN 2032-6653, 2009 AVERE

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