6.2 Turbine modeling for different prime movers

Steam turbines, hydro turbines, and gas turbines are the heart of power generation. Each type has unique components and behaviors that affect how they respond to changes in power demand. Understanding these differences is crucial for designing effective governor control systems.

Accurate turbine models are essential for simulating power system dynamics. They capture how turbines react to disturbances, influencing frequency response and stability. Choosing the right model complexity is key to balancing accuracy and computational efficiency in power system studies.

Mathematical Models for Steam Turbines

Components and Configurations

Top images from around the web for Components and Configurations

• 

  Steam turbine - Wikimedia Commons View original

  Is this image relevant?

• 

  Westinghouse Combustion Turbine Systems Division - Wikipedia View original

  Is this image relevant?

• 

  File:Modern Steam Turbine Generator.jpg - Wikipedia View original

  Is this image relevant?

• 

  Steam turbine - Wikimedia Commons View original

  Is this image relevant?

• 

  Westinghouse Combustion Turbine Systems Division - Wikipedia View original

  Is this image relevant?

1 of 3

Top images from around the web for Components and Configurations

• 

  Steam turbine - Wikimedia Commons View original

  Is this image relevant?

• 

  Westinghouse Combustion Turbine Systems Division - Wikipedia View original

  Is this image relevant?

• 

  File:Modern Steam Turbine Generator.jpg - Wikipedia View original

  Is this image relevant?

• 

  Steam turbine - Wikimedia Commons View original

  Is this image relevant?

• 

  Westinghouse Combustion Turbine Systems Division - Wikipedia View original

  Is this image relevant?

1 of 3

• Steam turbines convert the thermal energy of pressurized steam into mechanical energy through the expansion of steam across multiple stages of rotating blades
• The basic components of a steam turbine include:
  • Steam chest
  • Governor valve
  • Control valve
  • High-pressure turbine
  • Intermediate-pressure turbine
  • Low-pressure turbine
  • Generator
• Non-reheat steam turbines have a single expansion process
• Reheat steam turbines have multiple expansion processes with reheating of steam between stages (high-pressure and intermediate-pressure stages)

Mathematical Modeling and Dynamic Response

• The mathematical model of a steam turbine consists of transfer functions representing:
  • Steam chest
  • Piping system
  • Turbine stages
  • Governing system
  • Control valves
• The steam turbine model captures the dynamic response of the turbine to changes in:
  • Steam flow
  • Pressure
  • Temperature
  • Effect of the governing system on the turbine output
• The reheat steam turbine model includes additional transfer functions to represent:
  • Reheater
  • Intermediate-pressure turbine stages
  • Accounts for the time delay and pressure losses in the reheating process
• Example: A typical steam turbine model may include a first-order transfer function for the steam chest, a second-order transfer function for the piping system, and multiple first-order transfer functions for the turbine stages
• Example: The governing system model may include a proportional-integral-derivative (PID) controller to regulate the steam flow based on the turbine speed and load demand

Dynamic Behavior of Hydro Turbines

Types and Characteristics

• Hydro turbines convert the potential energy of water into mechanical energy through the rotation of turbine blades driven by the flow of water
• The main types of hydro turbines are:
  • Impulse turbines (Pelton wheel)
  • Reaction turbines (Francis and Kaplan turbines)
  • Each type is suitable for different head and flow conditions
• The dynamic behavior of hydro turbines is influenced by:
  • Water column inertia
  • Penstock elasticity
  • Governor-turbine interaction

Mathematical Modeling and Response

• The mathematical model of a hydro turbine includes transfer functions representing:
  • Penstock
  • Turbine
  • Governing system
  • Hydraulic servomotor
  • Gate opening mechanism
• The hydro turbine model captures the transient response of the turbine to changes in:
  • Water flow
  • Head
  • Gate position
  • Effect of the governing system on the turbine output
• The response characteristics of hydro turbines are typically slower compared to steam and gas turbines due to:
  • Inertia of the water column
  • Mechanical limitations of the gate opening mechanism
• Example: A Pelton wheel hydro turbine may have a faster response compared to a Francis turbine due to the absence of a draft tube and the direct impact of water jets on the buckets
• Example: The penstock model may include a second-order transfer function to represent the elastic water column effect and the penstock-turbine interaction

Modeling Gas Turbines and Combined Cycles

Gas Turbine Components and Operation

• Gas turbines convert the chemical energy of a fuel (usually natural gas) into mechanical energy through the compression, combustion, and expansion of air and exhaust gases
• The basic components of a gas turbine include:
  • Compressor
  • Combustion chamber
  • Turbine
  • Generator
• Combined cycle plants integrate gas turbines with steam turbines to improve overall efficiency by utilizing the waste heat from the gas turbine exhaust to generate steam for the steam turbine

Mathematical Modeling and Control

• The mathematical model of a gas turbine consists of transfer functions representing:
  • Compressor
  • Combustion chamber
  • Turbine
  • Governing system
  • Fuel system
  • Exhaust temperature control
• The gas turbine model captures the dynamic response of the turbine to changes in:
  • Fuel flow
  • Air flow
  • Exhaust temperature
  • Effect of the governing system on the turbine output
• The combined cycle plant model integrates the gas turbine model with the steam turbine model, accounting for:
  • Thermal coupling between the two systems through the heat recovery steam generator (HRSG)
  • Coordinated control of the gas and steam turbines
• Example: A simple cycle gas turbine model may include a first-order transfer function for the compressor, a time delay for the combustion process, and a first-order transfer function for the turbine
• Example: A combined cycle plant model may include a gas turbine model, an HRSG model with multiple pressure levels, and a reheat steam turbine model, along with a coordinated control system for the gas and steam turbines

Turbine Models in Power System Simulations

Importance and Influence

• Turbine models are critical components in power system dynamic simulations, as they represent the primary source of mechanical power input to the generators
• The accuracy and fidelity of turbine models directly influence the simulated dynamic behavior of the power system, including:
  • Frequency response
  • Oscillatory modes
  • Transient stability

Model Selection and Validation

• Simplified turbine models, such as first-order or second-order transfer functions, may be sufficient for high-level stability studies
• Detailed models are required for accurate representation of the turbine dynamics and control systems
• The choice of turbine model depends on:
  • Specific requirements of the stability study
  • Available data
  • Computational resources
• Proper validation and calibration of turbine models against actual plant data are essential to ensure the reliability and credibility of the simulation results

Sensitivity Analysis and Comparative Studies

• The impact of turbine models on power system dynamic simulations should be carefully assessed through:
  • Sensitivity analysis
  • Comparative studies
  • Considering different modeling assumptions and parameter variations
• Example: A sensitivity analysis may involve varying the turbine governor parameters (droop, time constants) to assess their impact on the system frequency response following a disturbance
• Example: A comparative study may involve simulating a power system with different levels of turbine model detail (simplified vs. detailed) to evaluate the trade-offs between accuracy and computational efficiency