ESRU

Technical-Economic Model

Introduction

To evaluate the chosen site for estimated power outp

ut and resulting cost of power production from an MCT scheme, a basic techno-economic model was developed. The model evaluated three different aspects of the technology and economics. The aspects were:

• Power estimation model
• Cost estimation model
• Financial Analysis Model

The models were developed as a spreadsheet to allow easy modification to values and formulae by the developers and in the end by any users who wish to tailor it to their own specification.

Power Theory and Model

Introduction

This model was developed to estimate the possible energy output from an MCT site. The method of estimation was based on the core assumption that flow within the site was purely tidal. This was to allow a sinusoidal method of calculation to be performed but other types of current flow could be performed by the trapezoid method of calculation. Both methods were utilised within this model so that the values both methods produced could be compared and analysed for accuracy.

Sinusoidal Calculation MethodWhen using the sinusoidal method of calculation it is assumed that the current velocity V follows a cyclic pattern, as shown by following equation:

Typically T for tides is 12h 25mins or 745mins. Also marine current turbines normally generate power when the tide is in flood and ebb (i.e. flow in both directions). Therefore the power characteristic will be the same for each half of the cycle. The magnitude of V Max varies, which is dependant on the stage of the lunar cycle. V Max will vary sinusoidally between a spring tide and a neap tide. There are typically two spring and neap tide a month therefore the period between spring and neap tides is 14 days.

To calculate the power generated by a sites current the following power relationship was used:

where P = power, r = density of fluid, A = cross-sectional area of a channel or the swept area of a MCT’s blades and V = current velocity.

To determine the power generated more specifically by a single rotor MCT turbine the following equation is used:

This equation is similar to the previous though the area term has been replaced by a turbine swept area term and an additional term C p has been included. C p is the power coefficient, which is defined as the ratio of actual power to theoretical power. It also has included into it terms for gearbox/transmission efficiency ( n gear) and generator efficiency ( n gen), which would be dependant on the device type.

To ensure that turbines do not speed out of control they can be rated to a certain current velocity. This therefore means that the power available from a turbine is rated and this is included when calculating energy output.

To determine the energy captured by an MCT during one quarter of a full tidal cycle the following relationship is used:

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Trapezoid Calculation Method

The trapezoid calculation method is another approach of numerical integration when there is no closed form expression for the integral and the data is only available in tabular form. Essentially it determines the area under a curve by dividing the curve into strips and the area of strip is calculated and then summed together.

The calculation then uses the following formulae to approximate the area under the curve:

Both of these methods have been utilised in the estimation of energy output from the MCT site.

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Model Assumptions

In constructing the model some basic assumptions were made, based on a baseline design proposed by MCT Ltd:

• A second generation twin rotor MCT unit was used
• The blade diameter was assumed to be 15.9 m
• Gearbox efficiency was assumed to be 0.94 %
• Generator efficiency was assumed to be 0.95 %
• Cut-in velocity was 0.7 m/s
• Density of water is 1025 kg/m 3
• A constant power coefficient of 0.45 % was taken

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