A Comprehensive Guide to Power System Voltage Stability by Carson W. Taylor
Power System Voltage Stability: A Comprehensive Guide by Carson W. Taylor
Power system voltage stability is a vital aspect of electric power system operation and planning. It refers to the ability of a power system to maintain acceptable voltages at all buses under normal and contingency conditions. Voltage stability is closely related to the balance between reactive power supply and demand in the system. When this balance is disturbed, voltage instability may occur, leading to voltage collapse and widespread blackouts.
power system voltage stability taylor pdf download
In this article, we will provide a comprehensive guide on power system voltage stability based on the book Power System Voltage Stability by Carson W. Taylor, published by McGraw-Hill in 1994. This book is sponsored by the Electric Power Research Institute (EPRI) and covers both transient and longer-term phenomena, as well as proven solutions to common instability problems. We will cover the following topics:
What is voltage stability and why is it important?
Transmission system reactive power compensation
Power system loads
Voltage stability analysis and assessment
Voltage stability enhancement and control
Voltage stability applications and case studies
Conclusion
FAQs
What is voltage stability and why is it important?
Voltage stability is one of the aspects of power system stability, which is defined as the ability of a power system to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. Voltage stability is concerned with the maintenance of acceptable voltages at all buses in the system.
Definition and types of voltage stability
Voltage stability can be defined as follows:
"Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition."
Voltage instability occurs when a disturbance causes a progressive or uncontrollable drop in voltage, which may lead to voltage collapse or loss of load.
Voltage stability can be classified into two types:
Static voltage stability: This refers to the ability of a power system to maintain steady voltages when subjected to small perturbations, such as gradual changes in load or generation. Static voltage stability is mainly influenced by the steady-state characteristics of the system components, such as generators, transformers, transmission lines, loads, etc.
Dynamic voltage stability: This refers to the ability of a power system to maintain steady voltages when subjected to large disturbances, such as faults, switching, loss of generation, etc. Dynamic voltage stability is mainly influenced by the dynamic behavior of the system components, such as generator excitation systems, load dynamics, voltage regulators, protection systems, etc.
Factors affecting voltage stability
The main factors that affect voltage stability are:
Reactive power balance: Reactive power is the component of electric power that is used to maintain the voltage level in the system. Reactive power is supplied by generators, capacitors, reactors, and synchronous condensers, and is consumed by loads, transmission lines, transformers, and reactors. A mismatch between reactive power supply and demand can cause voltage instability. Generally, a deficit of reactive power leads to voltage drop, while a surplus of reactive power leads to voltage rise.
Load characteristics: Load characteristics refer to the relationship between load active and reactive power demand and the voltage level. Different types of loads have different voltage sensitivity and dynamic response. For example, induction motors consume more reactive power and tend to stall when the voltage drops below a certain level, while lighting loads have a constant power characteristic and tend to increase their demand when the voltage drops. The aggregate load characteristic of a system determines its voltage stability limit.
Transmission system configuration: Transmission system configuration refers to the topology and parameters of the transmission network, such as line impedance, length, loading, etc. The transmission system affects the voltage stability by influencing the power transfer capability and the voltage drop along the lines. Generally, a long and heavily loaded transmission line reduces the voltage stability margin of the system.
Voltage control devices: Voltage control devices refer to the equipment that can regulate or control the voltage level or the reactive power flow in the system, such as generator excitation systems, tap-changing transformers, shunt capacitors or reactors, static var compensators (SVCs), static synchronous compensators (STATCOMs), etc. These devices can enhance or degrade the voltage stability depending on their settings and coordination.
Consequences of voltage instability
Voltage instability can have serious consequences for the power system operation and security. Some of the possible outcomes of voltage instability are:
Voltage collapse: Voltage collapse refers to the phenomenon where a large part of the power system becomes isolated from the rest due to low voltages and tripping of lines or generators. Voltage collapse can result in widespread blackouts and damage to equipment.
Loss of load: Loss of load refers to the phenomenon where some loads are disconnected from the system due to low voltages or protection actions. Loss of load can cause customer dissatisfaction and economic losses.
Overvoltage: Overvoltage refers to the phenomenon where some buses experience abnormally high voltages due to excessive reactive power injection or reduced load demand. Overvoltage can cause insulation failure and equipment damage.
Oscillatory instability: Oscillatory instability refers to the phenomenon where some buses experience sustained or growing oscillations in voltage magnitude or angle due to poorly damped modes of the system. Oscillatory instability can cause resonance and interference problems.
Transmission system reactive power compensation
Transmission system reactive power compensation is one of the methods to improve voltage stability in power systems. It refers to the process of adjusting the reactive power flow in the transmission network by using various devices or schemes.
Reactive power sources and sinks
The main sources and sinks of reactive power in a transmission system are:
Generators: Generators can produce or absorb reactive power by adjusting their excitation systems. The amount of reactive power that a generator can provide depends on its rating, terminal voltage, active power output, and operating limits.
Capacitors: Capacitors are devices that inject reactive power into the system when connected in parallel with the line. The amount of reactive power that a capacitor can provide depends on its rating and the line voltage.
Reactors: Reactors are devices that absorb reactive power from the system when connected in series or parallel with the line. The amount of reactive power that a reactor can absorb depends on its rating and the line current or voltage.
Synchronous condensers: Synchronous condensers are synchronous machines that operate at no-load and can produce or absorb reactive power by adjusting their excitation systems. The amount of reactive power that a synchronous condenser can provide depends on its rating, terminal voltage, speed, and operating limits.
Methods of reactive power compensation
The main methods of reactive power compensation in a transmission system are:
Shunt compensation: This refers to the connection of capacitors or reactors in parallel with the line or at the buses. Shunt compensation can increase or decrease the voltage at the point of connection and reduce the reactive power flow in the line. Shunt compensation can be fixed or switched depending on the load variation.
Series compensation: This refers to the connection of reactors in series with the line. Series compensation can reduce the effective impedance of the line and increase the power transfer capability and the voltage at the receiving end. Series compensation can be fixed or variable depending on the line loading.
Phase-shifting compensation: This refers to the use of phase-shifting transformers or devices that can change the phase angle of the voltage or current in the line. Phase-shifting compensation can control the active and reactive power flow in the line and improve the load sharing among parallel lines.
Flexible AC transmission systems (FACTS): This refers to the use of power electronic devices that can control one or more parameters of the transmission system, such as voltage, impedance, phase angle, etc. FACTS devices can provide fast and flexible reactive power compensation and voltage control. Some examples of FACTS devices are static var compensators (SVCs), static synchronous compensators (STATCOMs), thyristor-controlled series capacitors (TCSCs), unified power flow controllers (UPFCs), etc.
Benefits and challenges of reactive power compensation
The main benefits of reactive power compensation in a transmission system are:
Voltage stability improvement: Reactive power compensation can improve the voltage stability margin and prevent voltage collapse by maintaining adequate voltages at all buses and reducing the reactive power losses in the system.
Power transfer enhancement: Reactive power compensation can enhance the power transfer capability and reduce the congestion in the transmission network by increasing the voltage level and reducing the line impedance.
Loss reduction: Reactive power compensation can reduce the active and reactive power losses in the system by improving the voltage profile and minimizing the reactive power flow.
Voltage regulation: Reactive power compensation can provide fast and accurate voltage regulation and support by adjusting the reactive power injection or absorption according to the load variation and system conditions.
Power quality improvement: Reactive power compensation can improve the power quality and reliability by mitigating voltage fluctuations, flicker, harmonics, etc.
The main challenges of reactive power compensation in a transmission system are:
Cost and complexity: Reactive power compensation devices and schemes require high capital investment and maintenance cost, as well as sophisticated design and coordination.
Protection and coordination: Reactive power compensation devices and schemes may introduce new protection issues and challenges, such as overvoltage, overcurrent, resonance, etc., and require proper coordination with other devices and systems.
Stability and control: Reactive power compensation devices and schemes may affect the stability and control of the system, such as transient stability, small-signal stability, oscillatory stability, etc., and require appropriate modeling and analysis.
Power system loads
Power system loads are one of the key factors that affect voltage stability in power systems. They represent the demand for electric power from various customers, such as residential, commercial, industrial, etc. They have different characteristics and behaviors that influence their impact on voltage stability.
Load characteristics and modeling
the voltage and frequency level. Different types of loads have different voltage and frequency sensitivity and dynamic response. Load characteristics can be classified into three categories:
Constant power: This refers to the loads that have a constant active and reactive power demand regardless of the voltage and frequency level. These loads tend to increase their current when the voltage drops, which may worsen the voltage stability. Examples of constant power loads are lighting, heating, electronic devices, etc.
Constant current: This refers to the loads that have a constant current demand regardless of the voltage and frequency level. These loads tend to increase their active and reactive power when the voltage rises, which may improve the voltage stability. Examples of constant current loads are arc furnaces, welding machines, etc.
Constant impedance: This refers to the loads that have a constant impedance or resistance regardless of the voltage and frequency level. These loads tend to have a proportional relationship between their active and reactive power and the voltage level, which may have a neutral effect on the voltage stability. Examples of constant impedance loads are resistive heating, induction heating, etc.
Load modeling refers to the representation of load characteristics and behaviors using mathematical equations or functions. Load models can be classified into two types:
Static load models: These are load models that describe the steady-state relationship between load active and reactive power demand and the voltage and frequency level. Static load models can be expressed as algebraic equations or curves. Static load models are useful for static voltage stability analysis and power flow studies.
Dynamic load models: These are load models that describe the dynamic behavior of load active and reactive power demand in response to changes in voltage and frequency level. Dynamic load models can be expressed as differential equations or state-space models. Dynamic load models are useful for dynamic voltage stability analysis and transient stability studies.
Load effects on voltage stability
Load effects on voltage stability refer to the impact of load characteristics and behaviors on the voltage stability margin and limit of a power system. Load effects on voltage stability can be analyzed from two perspectives:
Voltage-dependent load: This refers to the load that changes its active and reactive power demand according to the voltage level. Voltage-dependent load can affect the voltage stability by changing the reactive power balance and the loadability curve of the system. Generally, a more voltage-sensitive load reduces the voltage stability margin and limit of the system.
Voltage-controlling load: This refers to the load that has its own voltage control device or scheme, such as an automatic voltage regulator (AVR), a tap-changing transformer, a static var compensator (SVC), etc. Voltage-controlling load can affect the voltage stability by changing the voltage profile and the interaction with other voltage control devices in the system. Generally, a well-coordinated voltage-controlling load enhances the voltage stability margin and limit of the system.
Load control and management for voltage stability
Load control and management for voltage stability refer to the actions or strategies that aim to modify or reduce the load demand or characteristics in order to improve or maintain the voltage stability of a power system. Load control and management for voltage stability can be classified into two types:
Preventive load control and management: These are actions or strategies that are implemented before a contingency or disturbance occurs in order to increase the voltage stability margin and prevent voltage instability. Examples of preventive load control and management are load forecasting, demand-side management, energy efficiency, etc.
the voltage stability and avoid voltage collapse. Examples of corrective load control and management are load shedding, load curtailment, load restoration, etc.
Voltage stability analysis and assessment
Voltage stability analysis and assessment are the processes of evaluating the voltage stability performance and limit of a power system under various operating conditions and contingencies. Voltage stability analysis and assessment can provide useful information and guidance for power system planning and operation.
Static and dynamic voltage stability analysis
Voltage stability analysis can be performed using static or dynamic methods depending on the type and duration of the disturbance and the phenomena of interest.
Static voltage stability analysis: This is a voltage stability analysis method that uses steady-state power flow equations or curves to determine the voltage stability margin and limit of a power system under small or gradual disturbances. Static voltage stability analysis can provide information such as the maximum loading point, the nose point, the PV curve, the QV curve, etc. Static voltage stability analysis is useful for long-term voltage stability studies and planning purposes.
Dynamic voltage stability analysis: This is a voltage stability analysis method that uses time-domain simulation models to determine the voltage stability margin and limit of a power system under large or fast disturbances. Dynamic voltage stability analysis can capture the dynamic behavior and interaction of the system components, such as generator excitation systems, load dynamics, voltage regulators, protection systems, etc. Dynamic voltage stability analysis can provide information such as the transient voltage response, the critical clearing time, the damping ratio, etc. Dynamic voltage stability analysis is useful for short-term voltage stability studies and operation purposes.
Voltage stability indices and margins
Voltage stability indices and margins are numerical indicators or measures that can quantify the degree or proximity of voltage instability in a power system. Voltage stability indices and margins can be calculated using static or dynamic methods depending on the type of analysis.
Voltage stability indices: These are numerical indicators that can reflect the sensitivity or vulnerability of a bus or a system to voltage instability. Voltage stability indices can be based on local or global information, such as bus voltages, reactive power injections, power transfer limits, eigenvalues, etc. Examples of voltage stability indices are L-index, V-Q sensitivity index, modal analysis index, etc.
Voltage stability margins: These are numerical measures that can indicate the distance or reserve of a bus or a system from voltage instability. Voltage stability margins can be expressed in terms of power, voltage, or impedance. Examples of voltage stability margins are loading margin, voltage margin, impedance margin, etc.
Voltage stability assessment tools and techniques
and ranking, voltage stability indices and margins calculation, PV and QV curve generation, eigenvalue and eigenvector analysis,