Wind Generator

Inverter

A5 DC

Charge Regulator

To Load

Control Unit PV Array Fig. 1. PV-wind hybrid energy system components.

The hybrid power generating system consists of wind turbine generator, PV array, storage batteries, and control unit. A typical autonomous wind-PV HPGS generating system is shown in Fig. 1.

PV Module Performance Model

Fig.2 PV modul I-V curve. Tc = Ta + 0.03 • Ga (1)

The electrical characteristics of a PV module are short circuit current, open-circuit voltage and maximum power point. A typical PV module I-V curve is shown in fig. 2. Current and voltage depend on temperature and irradiance. The temperature coefficient for the open circuit voltage is negative and large, which is approximately equal to -2,3 mV/°C for an individual cell. On the other hand, the current coefficient is positive and small, that is approximately +6 pA/°C for a square centimeter of the module area (Markvart, 1994). The operating temperature of the cell, which differs from the ambient temperature, determines the open-circuit voltage. Operating temperature can be calculated using equation 1 for a given ambient temperature (Lorenzo, 1994).

— exp

(2)

PV module short-circuit current is proportional to the number of parallel connected PV cells and irradiance. PV module open-circuit voltage is a logarithmic function of current and proportional to the number of serial connected PV cells. The PV module’s current IM under arbitrary operating condition can be described as;

The necessary number of PV modules to be connected in series is derived by the number of modules needed to match the bus operating voltage.

V =Vм ■ N

PV OC SM (3)

The current output of a PV array at time t, Iм (t), is related to the number of parallel strings as follows:

Ipv (t) = Iм (t) • Npm ■ fMM (4)

Wind Turbine Performance Model

Manufacturers give the characteristic curves for wind turbines as power output versus wind speed at the hub height. The design parameters of a wind turbine generator (WTG)
determine the amount of energy it can harvest from the wind. A power curve, which is a plot of output power against the average wind speed, can be constructed for a WTG design as shown in Fig. 3.

WTG are designed to start generating at the cut-in wind speed, vci Fig. 3 shows that the power output increases nonlinearly as the wind speed increases from to the rated wind speed (vr) . The rated power is produced when the wind speed varies from to the cut out wind speed (vco), at which the WTG will be shut down for safety reasons. The electrical power generated hourly can be calculated from the wind speed data using the power curve of the wind turbine specified ratio, always dispatching wind energy to allow a maximum of its share. In this way, the useful capacity of the wind turbine can be calculated.

Fig. 3. Manufacturers give the characteristic curves for wind turbine.

Wind turbines are usually only connected in parallel, not in series. Several wind turbines can be connected in parallel to match the system current requirements. This can be done with parallel strings of the same wind turbine type or with strings of a different wind turbine type. It is assumed here that at most two different turbine types are used at the same time in one system. Energy densities for wind are calculated using equation 5.

(5)

PwT-0,5. Cp. pair. V

The power output of the wind turbine array at time t,

pwt (t) — !wt (t) ‘vwt 0)- Npwt (6)

Battery Performance Model

Batteries in a hybrid system are connected in series to obtain the appropriate nominal DC bus voltage. Therefore the number of batteries connected in series for the same type of battery in a battery bank is calculated as follows;

N S Bat=VP V/VBat (7)

The hybrid system can have several battery banks, which typically consist of different battery types. The battery state of charge of a battery bank at time t is calculated based on adding the charge current (positive sign) or discharge current (negative sign) to the battery bank state of charge at the previous time instant. When adding the battery current to the battery state of charge, self discharge losses and battery charging losses need to be taken into account. (Seeling-Hochmuth, 1997)

BatB

SOC(t +1)

(8)

XiSOCi(t) ‘ Qi + ^Bat(t) ‘ ^t ‘ ^i(Ikolbat(t)) J’ NPBat i=0

The inverter characteristics can be described by the inverter input-output relationship. Some of the power going into the inverter will be lost due to transformation losses that are named inverter efficiency losses. Efficiency losses of inverter depend non-linearly on the AC output power, and therefore non-linearly on the AC load current.

PIIP ‘Vi = PIOP, Vim = f (PIOP) (9)

Control Unit performance Model

The control unit provides an interface between all components of hybrid energy system, giving protection and control. The most frequently encountered components of control unit are blocking diodes, charge regulators, energy routing switches, measurement sensors and the controller. In fact charge regulators can be modeled as a switch which connects and disconnects generator to battery or load according to battery state of charge, temperature or load demand (Engin, 2002). The output power, PBCOP of the battery charger equals the input power PBCIP multiplied with the efficiency losses during the energy conversion. Efficiency losses depend non-linearly on the DC output power, and therefore non-linearly on the DC output current of the battery charger.

Pbcip -Vbc ~ Pbcop, Vbc ~ f (PBCOP) (10)

Efficiency losses can be calculated from efficiency losses versus output power curves that are given manufacturers. Energy routing switches position is defined by controller that was defined operation strategy. Efficiency losses of energy routing switches are small and can be neglected.

Costing Model of Hybrid System

The hybrid system life-cycle costs are sum of initial investment costs and discounted operation costs. Using equation 11, LCC can be calculated. The hybrid system operation costs are in general non-linear, and depend on component size and type. It also depends on how system is operated (Engin et al., 2002).

NumberofConpenents

LCC

(11)

Cc + / DiscountedCnp,

m