*3.2. Kinetic Energy in a Wind Turbine: Calculation*

Suppose a wind turbine with a diameter of 60 metres and a radius of 30 metres and the wind speed (*v*) of 9 metres per second.


The principles of kinetic energy suggest that the longer the wind blade and the faster the wind speed, the more energy will be transformed from kinetic energy to electric energy (i.e., electricity). The modern type of wind turbine has a capacity of 1.8 MW [23].

#### *3.3. Economic Considerations of Wind Energy*

The cost of wind energy can be calculated as follows. This calculation is based on the information given in Boyle [23]:

The cost per unit (*g*) is expressed in Equation (1):

$$\mathbf{g} = \frac{(\mathbb{C} \times \mathbb{R})}{E} + \mathcal{M} \tag{1}$$

where:

*g* = the cost per unit of electricity generated;

*C* = the capital cost of the wind farm;

*R* = the capital recovery factor or the annual capital charge rate (expressed as a fraction);

*E* = the wind farm annual energy output;

*M* = the cost of operating and maintaining the wind farm annual output.

The required annual rate of return net of inflation (*R*) is expressed as:

$$R = \left[ \mathbf{x} / (1 - (1 + \mathbf{x}))^{-\mathbf{n}} \right] \tag{2}$$

where:

x = the required annual rate of return net of inflation;

n = the number of years over which the investment in the wind farm is to be recovered.

The annual energy output of the wind farm (*E*) is expressed as:

$$E = (\hbar P\_r F)T \tag{3}$$

where:

*h* = the number of hours in a year (8760);

*Pr* = the rated power of each wind turbine in kilowatts;

*F* = the net annual capacity factor of the turbines at the site;

*T* = the number of turbines.

The cost of operating and maintaining the wind farm annual output (*M*) is expressed as:

$$\mathcal{M} = \mathbb{K} \mathbb{C} / \mathbb{E} \tag{4}$$

where:

*M* = the operation and maintenance costs;

*K* = the factor representing the annual operating costs of a wind farm as a fraction of the total capital cost.

Generally, a wind turbine operates at only around 25 percent of turbine capacity due to inconsistent, imperfect wind. On better land-based wind sites, a capacity factor of 35 percent to 40 percent or more is achievable [23]. A wind turbine is quick to install, so it will be generating power before significant interest on capital. It is competitive with conventional power generation at sufficiently windy sites.

#### *3.4. Unit or Levelised Costs of Wind Energy*

A typical wind turbine has three parts: fiberglass blades, a standard gearbox, and a generator. Boyle [23] described the cost of a 600-kilowatt (kW) wind turbine in Denmark. Installation costs are \$1800 to \$2200 per kW, the turbine lasts about 20 years, the load factor is 25 percent, and the turbine generates 1,314,000 kilowatt-hours (kWh) per year. If a real discount or interest rate is assumed at 10 percent, the installation cost is \$2000 per kW, or about \$1,200,000. The unit or LCOE are \$0.106 per kWh.

Table 3 presents the cost of generating electric power by various sources. The data are taken from estimated generation costs in the United States in 2017 for a comparison purpose.


**Table 3.** Estimated Cost of Generating Electric Power, 2017.

\* Includes carbon capture and sequestration. Source: [24].

Wind energy appears to be competitive with gas and coal. Moreover, the cost of electricity generated from wind is even lower than that of geothermal, although hydro is lower than wind. The cost competitiveness of wind in terms of power generation is also confirmed by the latest cost data provided by IRENA (Table 4).



LCOE = levelized cost of energy. Notes: 1. The LCOE is the weighted average LCOE from utility-scale renewable power generation technologies from 2010 to 2019. 2. The fossil fuel LCOE range: = is \$0.05–\$0.18 per kilowatt-hour. Source: [25].

> The LCOEs of geothermal and hydropower slightly increased in 2019 compared to 2010. The LCOEs of solar photovoltaic and concentrated solar power decreased immensely, while the LCOEs of offshore and onshore wind energy fell a small amount. Among various renewable power technologies, however, the LCOE of onshore wind energy is the second lowest after hydro. The LCOE of fossil fuels ranges from about \$0.05 per kWh to about \$0.18 per kWh [25]. Except for concentrated solar power and offshore wind energy, all

other renewable power-generation technologies have become competitive with fossil fuel power-generation technologies. The cost-competitiveness of wind energy is confirmed further if the cost of carbon disposal and the price of carbon are added to the LCOE.

Boyle [23] presented a comparison of the costs of various sources of electricity generation at a 10 percent discount rate. The cost included capital payments, operation and maintenance, fuel, carbon disposal, and carbon price. Fifteen power-generation technologies were considered: combined-cycle gas turbine, conventional coal, combined-cycle gas turbine with carbon capture and storage, coal with carbon capture and storage, nuclearpressurised water reactor, roof-mounted solar photovoltaic thin-film panels, large biomass non-combined heat and power, run of river, reservoir hydro, onshore wind, offshore wind, tidal barrage, tidal stream, floating, and geothermal. The five lowest-cost technologies were run of river, reservoir hydro, combined-cycle gas turbine, onshore wind energy, and nuclear-pressurised water reactor. The LCOE of onshore wind is still higher than combined-cycle gas turbine. If a carbon price is added or the costs of carbon disposal for the combined-cycle gas turbine are included, then onshore wind energy is competitive with these technologies.
