Power System Control Lecture PDF

POWER SYSTEM CONTROL BASIC GENERATOR CONTROL LOOPS Load frequency control (LFC) Controls the real power and frequency Automatic voltage regulator (AVR) Regulates the reactive power and voltage magnitude Generation Model  Where Pm is mechanical po...

POWER SYSTEM CONTROL BASIC GENERATOR CONTROL LOOPS Load frequency control (LFC) Controls the real power and frequency Automatic voltage regulator (AVR) Regulates the reactive power and voltage magnitude Generation Model  Where Pm is mechanical power Pe is electrical power w is angular velocity Taking Laplace transformation  Load Model Motor loads are sensitive to changes in frequency where ΔPL is the nonfrequency sensitive load change. D is express as percent change in load divided by percent change in frequency Δw is the frequency sensitive load change  Prime Mover Model The model for the turbine relates changes in mechanical power output ΔPm to changes in steam valve position ΔPv The resulting transfer function is  Governor Model When the generator electrical load is suddenly increased, the electrical power exceeds the mechanical power input. This power deficiency is supplied by the kinetic energy stored in the rotating system. The reduction in kinetic energy causes the turbine speed and, consequently, the generator frequency to fall. The change. in speed is sensed by the turbine governor which acts to adjust the turbine input valve to change the mechanical power output to bring the speed to a new steady-state Where R is speed regulation ΔPg is the difference between ΔPref and Δw/R (power) ΔPv the steam valve position command The complete block diagram of the load frequency control Redrawing the block diagram with the load change as the input and the frequency deviation as the output results in the block diagram shown below The closed-loop transfer function relating the load change ΔPL to the frequency deviation ΔW Where: tT is Turbine time constant tg is governor time constant H is generator inertia constant R is governor speed regulation D is the frequency sensitive load  The load change is step unit, then ΔPL (s) = ΔPL /s Utilizing the final value theorem, the steady-state value of Δw is It is clear that for the case with no frequency-sensitive load (i.e., with D = 0), the steady-state deviation in frequency is determined by the governor speed regulation When several generators with governor speed regulations R1, R2, … , Rn are connected to system the steady-state deviation in frequency is given by  Example (1): An isolated power station has the following parameters: Turbine time constant tT =0.5 sec Governor time constant tg = 0.2 sec Generator inertia constant H = 5 sec Governor speed regulation = R per unit The load varies by 0.8 percent for a 1 percent change in frequency, i.e., D = 0.8 (a) Use the Routh-Hurwitz array to find the range of R for control system stability. (b) Use MATLAB rlocus function to obtain the root locus plot and then find the value of R for control system stability. (c) The governor speed regulation is set to R = 0.05 per unit. The turbine rated output is 250 MW at nominal frequency of 60 Hz. A sudden load change of 50 MW (ΔPL = 0.2 per unit) occurs. (I) Find the steady-state frequency deviation in Hz. (II) Use MATLAB to obtain the time-domain performance specifications and the frequency deviation step response. Solution: By substituted the parameters values, the block diagram obtained as: The open loop transfer function is The characteristic equation is which results in the characteristic polynomial equation The characteristic equation is which results in the characteristic polynomial equation The Routh-Hurwitz array for this polynomial then With positive values of K, for control system stability for control system stability, the governor speed regulation must be R > 0.0135  Root Locus 4 3 System: sys Gain: 73.6 2 Pole: -0.00234 + 3.24i Damping: 0.00072 1 Overshoot (%): 99.8 Frequency (rad/s): 3.24 0 -1 -2 -3 -4 -6 -5 -4 -3 -2 -1 0 1 Real Axis (seconds -1) From the figure the cross point of the root locus with vertical axis is s = j3.25 by using the Magnitude Condition: | KG(s)H(s) | = 1 K  | s 3  7.08s 2  10.56s  0.8 | s  j 3.25  73.983 then governor speed regulation must be 1 R   0.0135 K  The closed loop transfer function of the system shown on the block diagram is: The steady-state frequency deviation due to a step input is: Thus, the steady-state frequency deviation in hertz due to the sudden application of a 50MW load is: To obtain the step response and the time-domain performance specifications. we use the following commands  Step Response 0 -0.005 Amplitude System: untitled1 Final value: -0.00962 -0.01 -0.015 0 1 2 3 4 5 6 7 8 9 Time (seconds)