Variables nominales y reales y la medici´on de la inflaci´on

Grid integration of variable wind power is confronted with several challenges. Energy storage such can play an important role to enhance the voltage stability and LVRT capability of the wind firm. There are several energy storage technologies available for wind turbine applications such as battery, supercapacitor (SC), flywheel, and their hybrid combinations [116]-[119]. A STATCOM with supercapacitor energy storage is the most promising solution to solve the problems associated with grid integration of wind firm. 96 110 117 123 127

Grid voltage per voltage level at the grid connection point in (kV)

0.41 0.33 0.228 0.0 0.228 0.33 0.41 0.48 Q/P_nin pu (Grid) 0.925 0.95 0.975 1.0 0.975 0.95 0.925 0.90 cos Φ (Grid)

Under excited Over excited 193 220 233 245 253 350 380 400 420 440 49.5≤ f ≤ 50.5 Hz; P =Pn; U/f ≤ 1.05 1 1 0 k V 2 2 0 k V 3 8 0 k V 50 40 23 0 -30 - 48 -80 -100 -120 -40 -60 -20

Under excited Q/│Pinstall│(%) Over excited

Pnom /│ Pins tal l │ (%)

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6.4.1 Construction and Features of Supercapacitor

Supercapacitor formerly known as electric double layer capacitor or ultracapacitor is an electrochemical capacitor [120]. Supercapacitors do not have a conventional solid dielectric like dielectric capacitors. Each supercapacitor cell has multiple electric double layers which consist of a porous electric insulator and electrodes on either side [121]. The cells are tightly packed together and immersed in an electrolyte as shown in Fig.6.6 [120]. The capacitance value of an electrochemical capacitor is determined by two storage principles, which both contribute indivisibly to the total capacitance [120];

 Double-layer capacitance – Electrostatic storage achieved by separation of charge in a Helmholtz double layer at the interface between the surface of a conductive electrode and an electrolyte [120]. The separation of charge is of the order of a few angstroms (0.3–0.8 nm), much smaller than in a conventional capacitor [120]

 Pseudocapacitance – Faradaic electrochemical storage with electron charge- transfer, achieved by redox reactions, intercalation or electrosorption [120]. Supercapacitor consists of two electrodes separated by an ion permeable membrane (separator), and an electrolyte connecting electrically the both electrodes. As shown in Fig.6.6(b), an electric double layer at both electrodes is formed by applying a voltage to the capacitor, which has a positive or negative layer of ions deposited in a mirror image on the opposite electrode [120].

The capacitance of the supercapacitor is given by [120];

d A

C  (6-1)

where, - permittivity, A-Surface area, d- distance between plates.

The capacitance is highest in capacitors made from materials with a high permittivity, large electrode plate surface areas and reciprocal to the distance between plates [120]. The two electrodes form a series circuit of two individual capacitors C1 and C2. The

161 2 1 2 1 C C C C C_T    (6-2)

(a) Structure of an ideal supercapacitor.

(b) Function of an ideal supercapacitor.

Figure 6.6. Construction and function of a supercapacitor [120].

The value of a supercapacitor can be in the order of thousands of times greater than an electrolytic capacitor. Larger super-capacitors have capacities up to 5000 farads [116]. The highest energy density in production is 30 Wh/kg, below rapid-charging Lithium- titanate batteries [117]. Due to the high permeability and close proximity of the electrodes, SCs have a low-voltage-withstand capability (typically 2–3 V) [118],[119]. Supercapacitors store energy by physically separating unlike charges. This has profound implications on cycle life, efficiency, energy, and power density. SCs have a long cycle life due to the fact that there are no chemical changes on the electrodes ideally in normal

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operation [43]. SCs have superior efficiency. It is only a function of the ohmic resistance of the conducting path. SCs also provide exceptional power density, since the charges are physically stored on the electrodes [43]. Conversely, energy density is low since the electrons are not bound by chemical reactions. This lack of chemical bonding also implies that the SCs can be completely discharged, leading to larger voltage swings as a function of the state of charge [43], [118],[119].

Supercapacitors store energy by accumulating opposite charges on the electrodes [120] without involving chemical reaction. Therefore, they are faster and durable then the electrochemical energy storage such as batteries [122]. Supercapacitors have highest energy density among capacitors. They support up to 10,000 F/1.2 volt and up to 10,000 times that of electrolytic capacitors [120].

The supercapacitor contains a higher power density than the battery, which allows the supercapacitor to provide more power over a short period of time which is vital in wind energy applications [43]. For a corresponding high-efficiency discharge, batteries would have a much lower power capability. Conversely, the battery has a higher energy density to store more energy and release that over a longer period of time [43]. The supercapacitor has lower energy density than the battery and able to store far less amount of energy than a battery [118], [119].

Table 6.1 summarizes the characteristic parameters of different energy storage technologies [43], [119].

Table 6.1: Comparison of Energy Storage Systems Energy density (Wh/Kg) Power (W/Kg) Charge- Discharge efficiency Self dis- Charge, (%/month) Durability Cycle Time Durability (Yrs) Battery 30-200 150-3000 65-100% 3-30% 500-1K 2-10 Flywheel 100-130 1000 90% - >20K >20 PHS 0.3 - 75% Negligible - >75

SMES 30 Very High 95% Negligible - -

CAES 10-30 - 50% Negligible - >40

Super capacitor

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6.4.2 Supercapacitor Model

There are various models for supercapacitors. Depending on the type of application, more or less detail may be required. Fig.6.7 shows a supercapacitor model which contains inductance Lsc, equivalent series resistance, Rsc and capacitance Csc. This first-

order supercapacitor model is a series RLC circuit, which is frequency, temperature, and voltage dependent in very accurate model as shown in Fig. 6.7 [123], [124]. This modelling is valid over the entire frequency spectrum, where the frequency-dependent part of the model is given by [124]:

𝑍_𝑝(𝑗𝜔, 𝑉𝑠𝑐) = 𝜏(𝑉𝑠𝑐_𝐶(𝑉) coth(√𝑗𝜔𝜏(𝑉𝑠𝑐))

𝑠𝑐)√𝑗𝜔𝜏(𝑉𝑠𝑐) (6-3)

where, Vsc is the voltage across the capacitor which has a DC capacitance of Csc and τ is

the time constant.

Supercapacitors operate in a frequency range well below its self-resonant frequency in wind turbine applications. Therefore, the inductance is normally ignored. A constant capacitance and equivalent series resistance (ESR) model gives enough accuracy [124].

Figure 6.7. Supercapacitor model.

C_sc Lsc

Rsc

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