Ris) Co) Problem 3. Plot the root loci for the system shown 100 +1 in the Figure. Show that the system may become unstable for large values of K. use Pade approximation for the exponential term which represent transportation delay.
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- Derive the full solution to the driven LRC circuit shown below using complex exponentials. Start withKirchhoff’s rule for the loop and assume a complex V (t) = V0eiωt (where by convention V0 is real) andassume that I(t) = I0eiωt where I0 is a general complex number (which can be written quite generallyas I0 = |I0|e−iδ), and where one gets physical answers at the end by taking the real part of thecomplex answers. Find an algebraic complex expression that expresses the sum of the voltages. Solve this expression directly using algebra, no pictures of “phasors” really required. Factor out the solution to obtain|I0|, δ, Z (the complex impedance), and the voltages across each element as a function of time.If the values of real power and reactive power is specified for a bus, then it is called as PQ bus. Select one: True FalseSuppose a power system consists of two isolated regions: a western region and an eastern region. Five units have been committed to supply 3090 MW as shown below. The two systems are separated by a transmission line that can handle a maximum transfer of 550 MW in either direction. Calculate the spinning reserve for the overall system and for eachregion.
- Assume that the system recorded by the block diagram is reliable. a) Determine the position constant, kp, of velocity, kv, and of acceleration, ka, of the system. b) Determine the steady-state errors for a magnitude 5 input in step, ramp, and parabola, respectively.a) Calculate the unit ramp input steady state error (e_ss) for the following control system. b) Δ(s)=2s^3+2s^2+s+K calculate the range of K values over which the system is stable, given the characteristic polynomial.a) You have been employed as an electrical engineer by a power transmission company to design a short transmission line to supply power to a light-industrial load consumer with power system specification as follows, a 3-ph, 60Hz overhead short transmission line with a line-to-line voltage of 23KV at the load end, line impedance of 2.48 ±j6.57Ω/phase, the industry has a cumulative consumption of 9MW with a power factor of 0.85 of lagging as a result of several induction motor on its production lines.As part of the regulations for connections to the grid, you are to provide justifications and values to the Energy Commission of Ghana.(i) What would be value of the voltage between the live conductor and the neutral, between live and live voltages at the industrial premises of the factory?(ii) What load angle would expect the factory to be operating at?
- Use DFT method to compute the circular convolution of x(n)={4,4} and h(n)={2, 6}.S.2) The serial impedance of the 300 km power transmission line is 23 + j75 ohm / phase and the shunt acceptance is j500 microS / phase. A power of 50 MW with a power factor of 0.88 under 220 kV interphase voltage from the end of the power transmission line being shot. Using these data of the energy transmission line, a) Characteristic impedance of the energy transmission line, b) Natural apparent power of the energy transmission line according to the 220 kV interphase operating voltage, c) The values of the line parameters A, B, C and D of the transmission line using hyperbolic functions, d) Calculate the maximum power that the power transmission line can transmit.The sample large power system network data's are given below, The total number of buses is 5 Three-phase short circuit fault subjected at the bus 5 The initial voltage of the faulted bus is 1.0 p.u The Zbus matrix element Z55 is 0.704 p.u Fault impedance Zf= 0.33 p.u Fault current (If )in p.u ..........
- Consider a radial distribution system given in figure below supplied by a 100% reliable source and consisting of two feeders connected in series. Each feeder has Tf = 5000 h and Tr = 5 h. Calculate the Reliability Indices and total system availability (A). Mathematically prove that parallel interconnection is going to increase reliability for the above scenario.How do distributed energy resources (DERs) such as solar panels and wind turbines impact the operation and planning of power systems? Analyze their integration challenges.Discuss the future trends and technologies in power systems, such as microgrids and energy storage systems.