Jawaharlal Nehru Technological University Hyderabad B.Tech III WIND AND SOLAR ENERGY SYSTEMS Previous Question Paper (August - 2022 - R18)

India has made significant strides in wind energy, currently ranking fourth globally in installed wind power capacity. As of recent data, the total installed wind power capacity in India exceeds 44 GW. The sector is primarily concentrated in states with high wind potential such as Tamil Nadu, Gujarat, Karnataka, Maharashtra, and Rajasthan, which collectively account for the vast majority of the country's wind energy generation.

Two notable wind turbine generator installations in India include:

1. Muppandal Wind Farm in Tamil Nadu, which is one of the largest onshore wind farms in the world with a capacity of approximately 1,500 MW.
2. Jaisalmer Wind Park in Rajasthan, which is another massive cluster of wind turbines contributing significantly to the national grid with a capacity exceeding 1,000 MW.

The Betz limit represents the maximum theoretical efficiency of a wind turbine, stating that no turbine can capture more than 16/27 (approximately 59.3%) of the kinetic energy present in the wind.

To derive this, consider the power extracted from the wind as the difference in kinetic energy between the upstream and downstream air:

Where m_dot is the mass flow rate (ρ * A * V_avg), V_1 is upstream velocity, and V_2 is downstream velocity. Assuming the average velocity through the rotor disk is V_avg = (V_1 + V_2) / 2, the power becomes:

Defining the induction factor 'a' such that V_2 = V_1 * (1 - 2a) and V_avg = V_1 * (1 - a), the power coefficient C_p is derived as:

To find the maximum, differentiate C_p with respect to 'a' and set to zero:

This yields a = 1/3. Substituting a = 1/3 back into the C_p equation: