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ENGI4487-WE01

MEng: Smart Energy Networks 4

2021

For a balanced three-phase fault at bus 3 with a fault impedance of zf , the fault current  magnitude is 3 pu. Determine the fault current for the following faults with the same fault impedance in all cases.

(i)  A single line-to-ground fault at bus 3.

(ii) A line-to-line fault at bus 3.

(iii) A double line-to-ground fault at bus 3. Also calculate the phase currents in this case.  [30%]

(c) A  50-Hz synchronous generator has a transient reactance of 0.2 per unit and an inertia constant of 4 MJ/MVA. The generator is connected to an infinite bus through a transformer and two parallel transmission lines, as shown in Figure Q1(c). Resistances are neglected and impedances are expressed on a common MVA base and are marked on the diagram. The generator is delivering a real power of 0.83 per unit to the infinite bus (Bus 1), when the terminal voltage of the machine (vt ) is 1.0 per unit. The infinite bus voltage is vbus  = 1.0∠0° pu.

If a fault happens at the top transmission line at a distance of 30% of the line length from bus 2, determine the swing equation for this system.

[40%]

Question 2

(a) Discuss the technical and economic choices facing electricity companies looking to provide low-carbon electricity to communities, and improve reliability, security and efficiency (economic and energy) of the electric system. [40%]

(b) Consider the circuit shown in Figure Q2, in which a 33kV line (i.e. phase to phase) voltage three-phase power line connects a grid supply point to a load. The load is always at unity   power factor, and consists of base load (unvarying) and flexible load (varying). The 33/11  kV transformer has an on-load tap changer that maintains the load voltage at 11 kV. You   may assume that the phase RMS current I in a three-phase circuit with line voltage V and  real power flow P at unity power factor is

(i)  If the base load Lb  is 1 MW throughout the day, calculate the daily energy loss on the 33 kV line due to the base load. [20%]

(ii) The flexible load Lf    (unit MW) is a function of electricity price p (unit £/MWh) as given by the following expression:

where the electricity price p(t) shall be positive, and t denotes the time for any hour in a day. Determine the levels of flexible load when p(t) = 50  fort  = 0, 1, 2, … ,23, and calculate the daily energy loss on the 33 kV line due to both base load and flexible load. [20%]

(iii) If the electricity pricing scheme can be modified to p(t) = 40  fort  = 0, 1, … ,11, and p(t) = 60  fort = 12, 13, … ,23, discuss the advantages of this electricity pricing scheme against the flat electricity pricing scheme of p(t) = 50  fort  = 0, 1, 2, … ,23. [20%]