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Marine and Hydrokinetic Power Generation and Power Plants 285

0.5

Performance coefficient (Cp) 0.3
0.4

0.2

0.1

0
0 2 4 6 8
(a) Tip-speed ratio (TSR)

TSR Cp
2.45 0.03
2.55 0.05
3.3035 0.25
3.675 0.32
4 0.37
4.5 0.434
5 0.45
5.75 0.36
6.75 0.12
7.25 0
(b)

FIGURE 11.18 The performance coefficient of a water turbine. (Image from Bahaj.)

The tentative performance coefficient of the turbine is shown in Figure 11.18. The performance
coefficient of a hydroturbine is sharper than the performance coefficient of a wind turbine, and the
tip-speed ratio (TSR) of the C pmax occurs at a lower value (around 2–5 instead of 8 as in a wind
turbine generator).
This type of C characteristics has a major advantage because the turbine can be stalled to control
p
the rotational speed and thus prevent a runaway condition from occurring without the need for pitch
control as in a wind turbine. The corresponding power versus speed characteristic for different flow
speeds is given in Figure 11.19.
The performance coefficient can be approximated by a polynomial equation as follows:

a
C p λ () = a 6 λ 6 + a 5 λ 5 + a 4 λ 4 + a λ 3 + a 2 λ 2 + λ + a o (11.8)
1
3
The TSR is defined as the ratio of the linear speed of the tip of the blade to the water speed:
ωR
TSR = (11.9)
V

where the rotational speed, ω, is the rotational speed of the blade. As shown in Figure 11.19, there
is a specific TSR that has a maximum operating C . This TSR corresponds to TSR cp_max = 5, cor-
p
responding to the C pmax = 0.45.