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288 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
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Homework Problem 11.2

A tidal turbine is connected to a generator operating in variable rotational speed. The blade radius is
given as 6 m, and the density of the flowing water ρ = 1 kg/m .
3
a. Suppose an engineer devises a turbine controlled to limit the rotational speed. Compute the
minimum power rating of the generator/power converter (assume a Type 4 turbine) to limit
the maximum speed to 13 rpm by stalling the turbine. (Hint: Use Figure 11.19. The answer is
approximately 225 kW.)
b. Compute and plot the corresponding output power as a function of the rotational speed.
c. Compute and plot the corresponding performance coefficient, C p , as a function of the rota-
tional speed.

Homework Problem 11.3

A tidal turbine is connected to an induction generator operating in constant rotational speed. The sta-
tor winding of the induction generator can be connected in two different configurations such that the
generator can be operated at 1800 rpm for high speeds of water flow and at 1200 rpm for low speeds of
water flow. A gearbox is used to maximize the power coefficient, C p , at the water flow of 2.5 m/s. The
blade radius is given as 6 m, and the density of the flowing water is ρ = 1 kg/m .
3
a. Choose the gear ratio of the gearbox so that the turbine will operate at maximum C p at the
generator speed of 1800 rpm.
b. Compute the performance coefficient, C p , when the generator is operating at 1200 rpm at the
same water flow (2 m/s).
c. Compute the water flow that will maximize the turbine when the generator is operating at
1200 rpm.

11.7 SUMMARY

The MHK renewable energy has great potential to provide a significant contribution to the electricity
supply. However, MHK technologies are still emerging, and the cost of energy from MHK devices is
not yet competitive with other forms of renewable energy. The cost of the PTOS represents approxi-
mately 10%–20% of the overall cost of energy and has a great influence on the power generation
performance. MHK covers a broad spectrum of prime movers (i.e., PTOS) for electrical generators.
This chapter presented many aspects of MHK generation to explore the potential of utilizing differ-
ent types of electrical generators (linear or rotary), power converters, and energy storage systems
and thus enable optimum energy capture, extend the life span of MHK generators, and enhance
power system grid integration. The experience gained during the past few decades in the develop-
ment of other forms of renewable energy generation (e.g., wind and solar) from technical, policy,
market-driven, and power system integration points of view and the significant cost reduction of
power electronics and energy storage will certainly help future developments in MHK generators.
In the near future, it is likely that MHK research and development will focus on the development
of hardware for harsh ocean environments. Several concepts will compete to lower the capital and
O&M costs. Eventually, the winning concepts will emerge with mature technologies that are eco-
nomically viable for massive commercial deployment.

ACKNOWLEDGMENT

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-
08-GO28308 with the National Renewable Energy Laboratory.