14-06-2013, 12:23 PM
An exercise in “Vector Processing” – HVDC transmission.
An exercise.pdf (Size: 221.53 KB / Downloads: 75)
Background:
High voltage DC transmission lines are the natural choice for sending electrical power over very large distances (distances in the order of several hundreds of kilometres). AC transmission is not suitable for these applications because the capacitance of the cable itself becomes significant and then not all of the current going in the “sending” end of the line actually comes out of the “receiving end”.
In this work, we consider how to design a HVDC transmission line with minimum cost. For simplicity, we pay no attention to the cost of the power conversion hardware required at each end of the line. With HVDC, there are 2 main options:
Option A: Current passes out through one cable and back through another.
Option B: Current passes out through one cable and returns through the ground/seawater.
In the case of option B, the total voltage between the conductor and the ground (or seawater) at the outside of the line is about twice as great as the total voltage between the conductor and ground for Option A. For most of the tasks of this coursework, we will assume that we are working with Option B (a single cable). In the final task, we consider Option A as an alternative possibility. For simplicity, we assume that the conductor must be copper and that the insulator must be polythene.
The figure above shows the cross section of a single line of cable. The cross-section is described by three radii: R0, R1 and R2. The area inside radius R0 is hollow. The area between R0 and R1 is solid copper. The area between R1 and R2 is polythene insulation material. The cost of the cable itself is calculated based on the total volumes of copper and polythene required. We also consider the cost of power loss in the cable.
The calculations required are set out in detail in the following section but we outline them in broad strokes here. The formulae for the cross-sectional areas of copper and polythene are obvious. Larger cross-sections of copper account for proportionately higher material costs but also proportionately higher losses for a given current. The power dispatched from the “sending” end is the product of current and voltage difference between the conductor and the outside at that end. We can choose to operate the transmission line at any voltage. Operating at very high voltages means that very thick insulation will be required but the current carried will be small for the same power so this requires smaller cross-sections of copper. Conversely, operating at low voltages means that the insulation can be thin but the currents required will be larger so that more copper is required. It is not immediately intuitive why the cable should be hollow. The reason for this has to do with the fact that the electrical potential gradient within the insulation is not constant. For very low-voltage power transmission, (R2 – R1) is small compared with R1, the potential gradient is approximately constant and the optimum R0 is indeed 0. For high voltage power transmission, using a solid conductor means that the potential gradient at R1 is much higher than that at R2. R2 must then be very large to ensure that the insulation does not fail at R1.
Calculations:
The set of symbols used in these calculations is given below – together with the relevant SI units. Some of these
values are set individually for each student and these are indicated by set. Each student must use the set values
allocated to him/her in the EXCEL spreadsheet SDATA.xls uploaded to the same location in WebCT as this
assignment. Some other values are constants common to all students and these are given below. For each
student, there are two independent parameters: V and R1.