Power System Control and Generation Models

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Questions and Answers

What is the primary function of the Load Frequency Control (LFC) in a power system?

  • To regulate the reactive power and voltage magnitude.
  • To control the real power and frequency. (correct)
  • To manage the mechanical power of the turbine.
  • To adjust the steam valve position in response to load changes.

If a generator's electrical load suddenly increases, what is the immediate source of the additional power?

  • Increased electrical power from AVR.
  • Increased mechanical power from the turbine.
  • Increased input from the governor model.
  • Kinetic energy stored in the rotating system. (correct)

What does the parameter 'D' in the load model represent?

  • The change in mechanical power output.
  • The change in steam valve position.
  • The change in motor speed.
  • The percent change in load divided by percent change in frequency. (correct)

In the context of a power system, what does the term 'Δw' represent?

<p>The frequency-sensitive load change. (C)</p> Signup and view all the answers

Which of the following best describes the immediate effect of an increased electrical load on the turbine speed and generator frequency?

<p>Both turbine speed and generator frequency decrease. (C)</p> Signup and view all the answers

What is the characteristic polynomial equation derived from the given open-loop transfer function?

<p>$s^3 + 7.08s^2 + 10.56s + 0.8 = 0$ (A)</p> Signup and view all the answers

According to the Routh-Hurwitz criterion, what condition must be met for control system stability, given a positive value of K?

<p>R &gt; 0.0135 (C)</p> Signup and view all the answers

At what point does the root locus cross the vertical axis in the s-plane?

<p>s = j3.25 (B)</p> Signup and view all the answers

What is the approximate value of K calculated using the magnitude condition at the point where the root locus crosses the vertical axis?

<p>K = 73.983 (B)</p> Signup and view all the answers

What is the approximate governor speed regulation (R) value calculated using the value of K?

<p>R ≈ 0.0135 (B)</p> Signup and view all the answers

What is the steady-state frequency deviation (in hertz) due to a sudden application of a 50MW load?

<p>-0.481 Hz (B)</p> Signup and view all the answers

Which of the following would be the correct representation of the closed loop transfer function of the system?

<p>$T(s) = \frac{K}{s^3 + 7.08s^2 + 10.56s + 0.8 + K}$ (B)</p> Signup and view all the answers

What is the final value of the system's step response, according to its plot?

<p>-0.00962 (C)</p> Signup and view all the answers

What is the role of the turbine governor in a power system?

<p>To sense speed changes and adjust the turbine input valve to control mechanical power output (D)</p> Signup and view all the answers

In the load frequency control block diagram, what does ( \Delta P_g ) represent?

<p>The difference between the reference power change and the change in speed divided by the speed regulation (D)</p> Signup and view all the answers

What is the significance of the closed-loop transfer function relating the load change ( \Delta P_L ) to the frequency deviation ( \Delta \omega )?

<p>It relates the change in system load directly to how frequency changes in the system. (C)</p> Signup and view all the answers

If the frequency sensitive load (D) is zero, what primarily determines the steady-state deviation in frequency?

<p>The governor speed regulation (D)</p> Signup and view all the answers

What is the main function of the Routh-Hurwitz array in the given example?

<p>To find the range of R for control system stability (C)</p> Signup and view all the answers

In the example, the load varies by 0.8 percent for a 1 percent change in frequency. What does the value D=0.8 represent?

<p>The frequency sensitive load characteristic of the system (D)</p> Signup and view all the answers

In the example, if a sudden load change of 50 MW occurs, and the turbine is rated at 250 MW, what is the per-unit change in load expressed as ( \Delta P_L )?

<p>0.2 per unit (A)</p> Signup and view all the answers

If several generators with speed regulations ( R_1, R_2, ..., R_n ) are connected to the system, how is the steady-state deviation in frequency determined?

<p>By considering the equivalent parallel of the regulation values as one composite value (A)</p> Signup and view all the answers

Flashcards

What is LFC?

Load Frequency Control (LFC) is a system that automatically adjusts the output of power generators to maintain frequency and real power balance in an electrical grid.

What is AVR?

Automatic Voltage Regulator (AVR) is a system that controls the voltage output of a power generator by adjusting the excitation current.

What is the Generation Model?

It represents the relationship between the mechanical power input to a generator (Pm) and the electrical power output (Pe), with angular velocity (w) as the key factor.

How do motor loads respond to frequency changes?

Changes in frequency alter the amount of power consumed by motor loads. This effect is quantified by the parameter D, which represents load sensitivity to frequency changes.

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What is the prime mover model?

This model describes how the mechanical power output of a turbine (Pm) changes in response to adjustments in steam valve position (Pv).

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Load Frequency Control (LFC)

The ability of a power system to maintain frequency stability despite changes in load. It involves automatically adjusting the turbine's power output to compensate for fluctuations.

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Turbine Time Constant (tT)

The time it takes for a turbine to respond to a change in valve position, measured in seconds.

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Governor Speed Regulation (R)

A parameter that reflects how much the system’s frequency changes for a given change in active power, usually expressed as a percentage of frequency change per unit change in power.

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Governor Time Constant (tg)

The time it takes for a governor to respond to a change in speed, measured in seconds.

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Generator Inertia Constant (H)

A measure of the ability of a power system to store energy, expressed in seconds.

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Frequency Sensitive Load (D)

Describes how much the load changes in response to a change in frequency, usually expressed as percentage change in load per percentage change in frequency.

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Steady-State Frequency Deviation (Δw)

The steady-state frequency deviation resulting from a load change, measured in Hertz (Hz).

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Routh-Hurwitz Array

A mathematical tool used to determine the stability of a system by analyzing the roots of its characteristic equation.

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Routh-Hurwitz Stability Criterion

The Routh-Hurwitz stability criterion is a mathematical test to determine the stability of a linear, time-invariant (LTI) system. It's based on the coefficients of the characteristic polynomial of the system.

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Open-Loop Transfer Function

In control systems, the open-loop transfer function describes the system's behavior without any feedback. It represents the relationship between the input signal and the output signal before the feedback is applied.

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Closed-Loop Transfer Function

The closed-loop transfer function represents the overall behavior of the system, including the feedback loop. It shows the relationship between the input signal and the output signal considering the feedback loop.

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Characteristic Equation

The characteristic equation is a mathematical equation that represents the system's stability. Its roots, also known as eigenvalues, determine if the system is stable or unstable.

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Root Locus

The Root Locus is a graphical tool used to visualize the locations of the closed-loop poles as a system parameter, like gain (K), varies. It helps in analyzing the system's stability and transient response.

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Magnitude Condition

The Magnitude Condition is a crucial part of analyzing the root locus. It helps determine the Gain (K) for which the magnitude of the open-loop transfer function is 1. This point in the root locus often indicates the system's stability boundary.

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Study Notes

Power System Control

  • Power systems require control to maintain stable real power and frequency, as well as voltage magnitude.
  • Basic Generator Control Loops:
    • Load Frequency Control (LFC): Controls real power and frequency.
    • Automatic Voltage Regulator (AVR): Regulates reactive power and voltage magnitude.

Generation Model

  • A simplified model shows the relationship between changes in mechanical power (ΔPm) and changes in frequency (Δω).
  • The transfer function is shown as: Δω(s) = (ΔPm(s) - ΔPe(s))/2Hs.

Load Model

  • Motor loads react to frequency changes.
  • The change in load (ΔP) is determined by the sum of a frequency-insensitive load (APL) and a change in frequency-sensitive load (DΔω).

Prime Mover Model

  • The turbine model describes mechanical power output (ΔPm) changes in relation to steam valve position (ΔPv).
  • The transfer function is Gr(s) = (ΔPm(s))/(ΔPv(s)) = 1 / (1 + Trs).
  • The time constant (Tr) is typically between 0.2 and 2.0 seconds.

Governor Model

  • When electrical load increases exceeding mechanical power, the rotating system's kinetic energy compensates for the difference
  • The governor adjusts turbine input valves to restore speed and frequency to a new steady state—in response to changes in speed detected.

Speed Governing System

  • A block diagram represents the speed governing system for a steam turbine.,
  • Key relationship: ΔP = ΔPref – 1/R Δω

Load Frequency Control

  • The complete block diagram shows the interrelation of governor, turbine, rotating mass, and load.
  • Transfer function in terms of frequency change & overall load: ΔΩ(s)/-ΔPL(s) = (1 + Tgs)(1 + Trs) /((2Hs + D)(1+Tgs)(1 + Trs) + 1/R)

Stability Analysis

  • Routh–Hurwitz criterion used for evaluating stability of control systems.,
  • Matlab used to find stability with root locus plots.,
  • System's characteristic polynomial determined and then analyzed.
  • Parameter values like turbine time constant (τT), governor time constant (τg), generator inertia (H), and speed regulation (R) significantly impact the stability and performance of LFC.

Steady-State Frequency Deviation

  • Steady-state frequency deviation in response to load changes calculated using the system's transfer function.
  • Deviation affects parallel generators with speed-governed systems.
  • Single and multi-machine systems modeled and evaluated.

Step Response

  • Time domain plots and performance specifications obtained using Matlab.
  • Step response and time domain performance specifications assist in evaluating the system's efficiency and stability.
  • Specific examples involving parameter values, load variations, calculated frequency deviations and step responses presented.

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