6.3 Speed-droop characteristics and load sharing

Speed-droop is a key feature of generator governor control systems. It allows generators to adjust power output based on frequency changes, enabling stable load sharing among multiple units. This characteristic is crucial for maintaining the balance between power generation and consumption in the grid.

Understanding speed-droop is essential for optimizing power system performance. It affects how generators respond to load changes and share power. By carefully setting and coordinating speed-droop values, engineers can ensure efficient and reliable operation of interconnected power systems.

Speed-droop in Governor Control

Role of Speed-droop in Governor Control Systems

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• Speed-droop is a characteristic of a generator's governor control system that allows the generator's speed to decrease slightly as the load on the generator increases
• The speed-droop characteristic is achieved by designing the governor control system to have a proportional relationship between the change in speed and the change in power output
• The primary role of speed-droop is to enable stable and efficient load sharing among multiple generating units connected to the same power system
• The speed-droop characteristic allows the generator to automatically adjust its power output in response to changes in system frequency, helping to maintain the balance between generation and load (load-frequency control)
• The speed-droop setting is typically expressed as a percentage, representing the percent change in speed required to cause a 100% change in power output (5% droop means a 5% change in speed causes a 100% change in power output)

Mathematical Representation of Speed-droop

• The speed-droop characteristic can be represented mathematically as: $\frac{\Delta f}{f_0} = -\frac{1}{R} \frac{\Delta P}{P_0}$ where:
  • $\Delta f$ is the change in frequency
  • $f_0$ is the nominal frequency
  • $R$ is the speed-droop setting (in per-unit)
  • $\Delta P$ is the change in power output
  • $P_0$ is the nominal power output
• The negative sign in the equation indicates that an increase in power output results in a decrease in frequency, and vice versa
• The speed-droop setting $R$ determines the slope of the speed-droop characteristic, with a smaller $R$ resulting in a steeper slope and a more sensitive response to load changes

Speed-droop and Load Sharing

Load Sharing among Generating Units

• Load sharing refers to the distribution of the total system load among multiple generating units connected to the same power system
• The speed-droop characteristics of the governors in each generating unit play a crucial role in determining how the load is shared among the units
• Generating units with identical speed-droop settings will share the load proportionally to their rated capacities, assuming they have the same nominal speed and are operating in parallel
• If the speed-droop settings of the generating units are different, the load sharing will be unequal, with units having lower speed-droop settings taking on a larger share of the load compared to units with higher speed-droop settings (a unit with a 4% droop will take on more load than a unit with a 5% droop)

Mathematical Representation of Load Sharing

• The relationship between speed-droop and load sharing can be expressed mathematically as: $\frac{P_1}{P_2} = \frac{R_2}{R_1}$ where:
  • $P_1$ and $P_2$ are the power outputs of generating units 1 and 2, respectively
  • $R_1$ and $R_2$ are the speed-droop settings of generating units 1 and 2, respectively
• This equation shows that the load taken by each generator is inversely proportional to its speed-droop setting
• For example, if generator 1 has a speed-droop setting of 4% and generator 2 has a speed-droop setting of 5%, then generator 1 will take on 25% more load than generator 2 ($\frac{P_1}{P_2} = \frac{5\%}{4\%} = 1.25$)

Optimal Speed-droop Settings

Factors Affecting Optimal Speed-droop Settings

• The optimal speed-droop settings for a power system depend on various factors, including:
  1. Characteristics of the generating units (rated capacity, response time, etc.)
  2. System's stability requirements (frequency limits, oscillation damping, etc.)
  3. Desired load sharing arrangement (equal sharing, priority-based sharing, etc.)
• In general, lower speed-droop settings result in a more sensitive response to load changes and a larger share of the load being taken by the corresponding generating unit
• Higher speed-droop settings result in a less sensitive response to load changes and a smaller share of the load being taken by the corresponding generating unit

Coordinating Speed-droop Settings

• The speed-droop settings of all generating units in a system should be coordinated to ensure stable operation and prevent undesirable oscillations or hunting behavior
• Optimal speed-droop settings can be determined through power system studies, considering factors such as the system's inertia, the response times of the generating units, and the expected range of load variations
• In some cases, adaptive or variable speed-droop settings may be employed to optimize load sharing under different operating conditions (e.g., adjusting droop settings based on the available spinning reserve)

Speed-droop vs Governor Non-linearities

Impact of Governor Dead-band

• Governor dead-band refers to a small range of speed variation around the nominal speed within which the governor does not respond to changes in speed
• The presence of governor dead-band can lead to a non-linear speed-droop characteristic, where the generator's response to load changes is not proportional to the change in speed
• The impact of governor dead-band on speed-droop characteristics can include:
  1. Reduced sensitivity to small load changes
  2. Unequal load sharing among generating units
  3. Potential instability in the power system

Impact of Governor Non-linearities

• Non-linearities in the governor control system, such as backlash in mechanical linkages or hysteresis in electronic components, can also contribute to non-linear speed-droop characteristics
• The effects of governor non-linearities on speed-droop characteristics can include:
  1. Reduced accuracy in load sharing
  2. Potential oscillations or hunting behavior in the power system
  3. Difficulty in tuning the governor control system for optimal performance

Mitigating the Effects of Dead-band and Non-linearities

• The effects of governor dead-band and non-linearities can be mitigated through proper design and maintenance of the governor control system, as well as through the use of advanced control techniques such as:
  1. Deadband compensation (adding a compensating signal to offset the effect of the dead-band)
  2. Adaptive control (adjusting the control parameters based on the operating conditions)
• Power system studies and simulations can be used to analyze the impact of governor dead-band and non-linearities on speed-droop characteristics and to develop strategies for ensuring stable and efficient operation of the power system