Q. Line impedances for the power system shown in Figure. In this system, the impedance distance relay is located in place of the power switch 1. Relay is set to protect line GH and serve as the back-up protection for line HR and HS. Reach for the zone1 impedance relays is set for 2/4 and zone2 is set for 4/5 For a bolted three-phase fault at line HR, The pre-fault voltages of both generators are 1<0 a. What is the actual impedance seen by the relay for this error? will the relay stop commanding for this error to occur? The relay operates? b. with this setting, what percentage (%) of the HR line and what percentage (%) of the HS line is protected by this relay?

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Gradient of a Scalar Field

Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will show the direction at that point by moving away from (x, y, z). How far will the rise in temperature in that direction be determined by the gradient magnitude? Consider a surface that has a height above sea level at point (x, y) which is given by H(x, y). At that point, pointing in the direction of the steepest slope or grade is the gradient of H. The magnitude of the gradient of the vector gives the steepness of the slope at that point. How a scalar field changes in another direction can be measured by the gradient by taking a dot product rather than just the direction of the greatest change?