Transient Stability Lecture JETS 2020_v2 (1)

Southern California Edison Power System Stability Fundamentals

Presenter: David Piper, PE Operating Engineer, SCEEvent: JETS 2020

Learning Objectives

  • Overview of power system stability

  • Leading indicators of transient instability

  • Components of a transient stability study

  • Limitations of RTCA (Real-Time Contingency Analysis)

  • Comparison of power flow vs transient stability limits and criteria

  • Impacts of renewable resources on transient stability

Introduction to Power System Stability

Definition:

The ability to remain in operating equilibrium.

Types of Stability:

  1. Rotor Angle Stability:

    • Definition: The capacity of the power system to maintain synchronism among synchronous machines under small disturbances.

    • Factors Influencing Stability: Generator output, transmission system characteristics, and load dynamics contribute to rotor angle stability, especially during system disturbances.

    • Swing Equation: The swing equation is a fundamental representation in rotor angle stability, expressed as T = P_e - P_m, where T is the acceleration (or deceleration) of the rotor, P_e is the electrical power output, and P_m is the mechanical power input. This equation illustrates the balance between the driving mechanical power and counteracting electrical power, which must be maintained to prevent rotor oscillations.

    • Power-Angle Relationship: Describes how the power output (P) of a generator relates to the difference in rotor angle (δ) between synchronous machines. This relationship can be approximated by the equation P ≈ 1/2 sin(δ), showcasing that power output increases with the sine of the angle; as the angle increases, the generator can deliver more power, but too large an angle can lead to instability and loss of synchronism.

  2. Frequency Stability:

    • Definition: The system's ability to maintain steady-state frequency in the face of disturbances such as sudden load changes or generator outages.

    • Key Considerations: Essential to balance supply and demand; dependent on system inertia and the responsiveness of generation sources.

  3. Voltage Stability:

    • Definition: The ability of the power system to retain acceptable voltage levels during and after disturbances.

    • Influences: The ability to control reactive power and the characteristics of transmission networks affect voltage stability.

Classification of Power System Stability:

  • Transient Stability: Refers to the power system's ability to maintain synchronism after being subjected to a significant disturbance. The focus is on short-term dynamics occurring right after a disturbance, typically within the transient time frame of a few seconds. During this time, the behavior of the rotor angles and system frequencies is studied to ensure stability is maintained.

  • Small Signal Stability: Deals with the system's ability to maintain stability under small disturbances. This involves analyzing oscillations and damping of the system's response, emphasizing the importance of control systems in stabilizing operations over the long run. Small signal stability studies often employ state-space models to analyze the damping ratios and the eigenvalues of the system's linearized equations.

  • Long-Term Stability: Concerned with the system's ability to achieve and maintain stability over longer time spans, through mechanisms such as feedback control and changes in system configuration. This often involves frequency and voltage stability assessments and can include the review of operational policies and modifications in system interconnections to mitigate potential long-term risks.

Time Scales for Stability

  • Transient Timeframe: 10 ms – 10 seconds

  • Mid/Long-term Timeframe: 100 ms – minutes/hours

Stability in the Transient Time Period

  • Focus on rotor angle stability and short-term dynamics

  • Key studies: Rotor angle, short-term frequency, transient voltage stability

Tools for Studying Stability

Categories of Stability Analysis:

  • Rotor Angle Stability Assessment

  • Frequency Stability Analysis

  • Voltage Stability Assessment

Assessment Methods:

  • Transient Stability Assessment

  • Governor Analysis

  • Powerflow Analysis

  • Small-Signal Stability Analysis

Essential Concepts for Rotor Angle Stability

  • Swing Equation: T = P_e - P_m

  • Power-Angle Relationship: P ≈ 1/2 sin(δ)

Short-Term Frequency Stability

  • System’s ability to maintain equilibrium across frequency variations

  • Dependencies: System inertia and risks from generator loss

Transient Voltage Stability

  • System’s ability to support voltage during disturbances

  • Importance of models for accurate system behavior

Small Signal Stability

  • Instabilities caused by small disturbances leading to oscillations

Long-Term Dynamics in Stability Assessments

  • Focused on frequency and voltage stability

References

  • Comprehensive list of resources for further study.

Effect of Shunt Capacitor on Power Transfer Capability

Definition: A shunt capacitor is a device connected in parallel with a power system, primarily to improve voltage stability and enhance the overall performance of the electrical network.

Key Effects:

  1. Reactive Power Support: Shunt capacitors provide reactive power to the system, which is essential for maintaining voltage levels and reducing voltage drops across transmission lines.

  2. Increased Power Transfer Capacity: By improving voltage levels, shunt capacitors allow for higher real power transfer capabilities. This is because they compensate for the inductive loads that consume reactive power, thereby reducing the total reactive power demand from the generators.

  3. Reduction in Line Losses: With better voltage support, the active power flowing through the transmission lines can be increased, which often leads to a decrease in losses due to resistive heating in the lines.

  4. Enhanced System Stability: By maintaining higher voltage levels, shunt capacitors contribute to overall system stability and can help avert voltage collapse during peak demand periods.

Conclusion: Shunt capacitors play a crucial role in improving the power transfer capability of a power system by providing reactive power support, reducing losses, and enhancing voltage stability.

Equal Area Criterion in Power System Stability

Definition: The Equal Area Criterion is a graphical method used to analyze the transient stability of power systems following a disturbance such as a fault or a sudden change in load.

Purpose: It determines whether a power system will return to steady-state stability after experiencing a disturbance.

Key Concepts:

  1. Areas Under the Curve: The criterion involves assessing the areas on a power-angle curve (or P-δ curve) that represent kinetic energy and potential energy changes during the transient period.

    • Positive Area: Represents the increase in kinetic energy as the rotor swings away from its equilibrium position.

    • Negative Area: Reflects the reduction in potential energy as the system attempts to return to the stable equilibrium.

  2. Stability Condition: For the system to be considered stable after the disturbance, the area representing the positive energy must be equal to or smaller than the area representing the negative energy. If the positive area exceeds the negative area, the system will experience instability, leading to loss of synchronism.

Application: This criterion is essential for power engineers in the design and analysis of systems to ensure stability under transient conditions, helping in decision-making regarding system configurations and protective measures.

Role of Power System Stabilizer (PSS)

Definition: A Power System Stabilizer (PSS) is a device installed in generators to enhance the overall stability of power systems by dampening oscillations in rotor angles and frequencies.

Key Functions:

  1. Damping Oscillations: PSS helps to mitigate low-frequency oscillations that can occur in power systems, particularly during disturbances or changes in load.

  2. Improving Transient Stability: By providing supplemental control signals to the excitation system of the generator, PSS improves the transient stability of the system after disturbances, ensuring that generators remain synchronized.

  3. Enhancing System Responsiveness: PSS adjusts the output of the excitation system based on measurements of speed deviation and rotor angle, allowing for more responsive control as system conditions change.

  4. Coordination with Other Controls: It works in conjunction with other automatic voltage regulators (AVRs) and system control mechanisms to optimize performance across the power grid.

Conclusion: Overall, PSS is critical in maintaining the stability and reliability of electrical power systems by ensuring that generators can respond effectively to disturbances.

Higher System Inertia and Rate of Change of Frequency

Definition: System inertia refers to the capacity of a power system to resist changes in frequency due to disturbances.

Impact on Frequency Changes:

  1. Increased Inertia: A power system with higher inertia can absorb changes in generation or load more effectively. This is because inertia is related to the physical mass and rotational energy of generators connected to the grid.

  2. Rate of Change of Frequency (RoCoF): Higher inertia results in a lower rate of change of frequency during disturbances, as the energy stored in the rotating masses helps to counteract sudden changes in power balance.

  3. Stability: As a result, systems with higher inertia experience smaller and slower fluctuations in frequency, contributing to greater overall system stability during events such as generator outages or rapid load changes.

Conclusion: Higher system inertia decreases the rate of change of frequency, leading to a more stable power system during disturbances.

Momentary Sensation in Inverter-Based Resources

Definition: Momentary sensation refers to the temporary response of inverter-based resources (IBRs) to disturbances in the power system, notably during transitory events such as faults or sudden load changes.

Key Aspects:

  1. Transient Response: IBRs can experience momentary sensation as they quickly adjust to fluctuations in system conditions, often aiming to maintain stability and support the grid during brief disturbances.

  2. Control Mechanisms: These resources utilize advanced control strategies to manage the momentary sensation, ensuring that their performance aligns with grid requirements after disturbances.

  3. Energy Storage: Many IBRs incorporate energy storage systems to enhance their ability to respond to momentary sensations, thereby sustaining power supply and improving reliability.

Importance: Understanding momentary sensation is crucial for optimizing the performance of inverter-based resources and ensuring their effective integration into modern power systems.

Impact of Lagging Power Factor Load on Power Transfer Capability

Definition: A lagging power factor load typically refers to electrical loads that consume reactive power as part of their operation, such as inductive loads like motors and transformers.

Key Impacts:

  1. Reduction in Power Transfer Capability: Lagging power factor loads can reduce the overall capacity of transmission lines to transfer real power. This is due to the increased demand for reactive power, which limits the amount of real power that can be transmitted without exceeding voltage limits.

  2. Voltage Drops: These loads can cause significant voltage drops along transmission lines, particularly if the system is heavily loaded. This can lead to operational issues and may require voltage regulation measures.

  3. Increased Losses: Lagging power factor results in higher current flows for the same amount of real power delivered, which increases resistive losses in the transmission lines (I²R losses).

  4. Need for Reactive Power Support: To maintain voltage levels and reduce losses, reactive power support (e.g., from capacitors or synchronous condensers) may be necessary, which adds to the complexity and cost of the power system operation.

Conclusion: Lagging power factor loads adversely affect power transfer capability by increasing the demand for reactive power, causing voltage drops, and leading to higher losses, which can complicate power system management and stability.

Effect of High Impedance Lines on Power Transfer Capability

Definition: High impedance lines are transmission lines characterized by a greater opposition to alternating current (AC) compared to low impedance lines.

Key Effects:

  1. Reduced Power Transfer: High impedance results in lower maximum power transfer capabilities, as more voltage is needed to push current through the line, limiting the amount of real power that can be transmitted.

  2. Increased Voltage Drop: Due to higher resistance, there will be greater voltage drops along high impedance lines, which can lead to inefficiencies in power delivery and potential voltage regulation issues.

  3. Higher Losses: The line losses increase due to the resistive heating effect (I²R losses), making high impedance lines less efficient compared to lower impedance alternatives.

  4. Impact on Stability: High impedance can affect the stability of the power system by reducing the ability to maintain synchronous operation among connected generators, especially under fault conditions.

  5. Dependence on Load Factors: Power transfer capability can also be significantly affected by load conditions; high impedance lines are more sensitive to sudden changes in load, which can lead to stability issues.

Conclusion: High impedance lines reduce power transfer capability and can contribute to increased losses and stability challenges within the power system.