Page 340 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

Batteries and Ultracapacitors for Electric Power Systems with Renewable Energy Sources 327

The SOC and the terminal voltage, V , are calculated as
t
t
1
()
SOCt () = SOC − ∫ it d() t (13.2)
⋅
0
c cap 0
V t = V OC ( SOC) −( V Rs + V C + V C + V C ) (13.3)
2
1
3
where
V , V , and V are the voltages across capacitors
C1
C2
C3
V is the voltage drop across the internal resistor (R )
Rs
s
An open-circuit voltage, V , versus SOC characteristic is exemplified in Figure 13.5.
oc
13.3 ULTRACAPACITOR ENERGY STORAGE: TYPES,
CHARACTERISTICS, AND MODELING
13.3.1 Ultracapacitor Types and Characteristics
Ultracapacitors, which are also referred to as super capacitors, provide energy storage, and they are
able to fast charge/discharge and delivering high power for a very short period of time, in the order of
fraction of seconds. The significant improvements in capacity and energy density over conventional
capacitors, while maintaining the same high power density values, are possible through the use of a
much larger surface area for the electrodes and thinner dielectrics. In comparison with other energy
storage devices, ultracapacitors have a very high power density while their energy density is substan-
tially lower than that of electric batteries. Ultracapacitors are especially suitable for applications that
require high-rate and short deep cycles, such as backup power supplies, HEVs, automotive start–stop
applications, DC link voltage support in converter, and power quality correction in utility applications.
Based on their electrode design, ultracapacitors may be classified into three main groups: electri-
cal double-layer capacitors, pseudocapacitors, and hybrid capacitors (see Figure 13.6). The double-
layer capacitors rely on the electrostatic field between two plates, while pseudocapacitors employ
electrochemical reactions in order to store the electric charge. The hybrid capacitors combine the
two phenomena and include the popular Li-ion ultracapacitors [27, 28].
Ultracapacitors are superior to batteries both in terms of life cycling, with more than 10 cycles
5
being possible, as well as in energy efficiency. Deep cycling does not have a significant influence
on ultracapacitors’ life span, while this is definitely not the case for the lead-acid or Li-ion batteries.
Examples of Li-ion ultracapacitors of 2200 F, 2300 F, and 3300 F Li-ion ultracapacitors are shown in
Figure 13.7. In order to reach higher voltages, currents, or capacities, ultracapacitors are connected
in series or parallel in banks as the one shown in Figure 13.8, which have been used in the UWM lab
for demonstrating grid integration methods for intermittent renewable energy generation [29, 30].

Electric double-layer
capacitors (EDLC)

Ultracapacitors
(supercapacitors) Pseudocapacitors

Hybrid capacitors

FIGURE 13.6 Classification of ultracapacitors based on the electrode design.