12.5 Power systems

Power systems are complex networks that generate, transmit, and distribute electricity. They involve intricate modeling of generators, loads, and transmission lines. Understanding power flow equations and stability is crucial for maintaining reliable operation.

Power system control and protection ensure stable, safe operation. This includes automatic generation control, voltage regulation, and protective relays. Economic dispatch, unit commitment, and optimal power flow help optimize system performance and costs.

Power system modeling

• Power system modeling involves representing the various components of a power system mathematically to analyze and simulate their behavior
• Accurate modeling is essential for understanding the system's response to different operating conditions and contingencies

Generators and loads

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• Generators convert mechanical energy into electrical energy and are modeled as voltage sources with internal impedance
• Synchronous generators are the most common type, characterized by their rotor angle, frequency, and excitation
• Loads represent the power consumed by end-users and are modeled as constant power, current, or impedance
• Examples of loads include residential appliances (lights, TVs) and industrial equipment (motors, furnaces)

Transmission lines

• Transmission lines carry electrical power from generators to loads over long distances
• They are modeled using distributed parameters such as series resistance, inductance, and shunt capacitance
• Short transmission lines (less than 80 km) can be represented by a simple series impedance model
• Medium and long transmission lines require more complex models (π or T equivalent circuits) to account for the distributed nature of the parameters

Power flow equations

• Power flow equations describe the steady-state operating conditions of a power system
• They relate the complex voltages and power injections at each bus in the system
• The equations are based on Kirchhoff's current and voltage laws and can be solved using iterative methods (Newton-Raphson, Gauss-Seidel)
• Power flow analysis is used to determine the voltage magnitudes and angles, real and reactive power flows, and system losses

Power system stability

• Power system stability refers to the ability of a power system to maintain synchronism and equilibrium under normal and disturbed conditions
• Instability can lead to cascading failures, blackouts, and equipment damage

Rotor angle stability

• Rotor angle stability is concerned with the ability of synchronous machines to remain in synchronism after a disturbance
• It depends on the balance between the electromagnetic torque and the mechanical torque of the generator
• Small-signal stability analyzes the system's response to small perturbations around an operating point
• Transient stability deals with the system's response to large disturbances (faults, line trips)

Frequency stability

• Frequency stability refers to the ability of a power system to maintain steady frequency following a severe disturbance
• It depends on the balance between generation and load, as well as the system's inertia and primary frequency response
• Frequency instability can occur due to insufficient generation, load shedding, or generator tripping
• Under-frequency load shedding (UFLS) schemes are used to prevent frequency collapse by disconnecting loads

Voltage stability

• Voltage stability is the ability of a power system to maintain steady voltages at all buses under normal and disturbed conditions
• It is influenced by the reactive power balance, load characteristics, and control systems
• Voltage instability can occur due to insufficient reactive power support, heavily loaded transmission lines, or generator reactive power limits
• Reactive power compensation devices (capacitor banks, SVCs) are used to improve voltage stability

Power system control

• Power system control involves the regulation of various system parameters to ensure stable, reliable, and economical operation
• Control systems are designed to maintain the balance between generation and load, regulate voltage and frequency, and damp oscillations

Automatic generation control (AGC)

• AGC is a control system that regulates the power output of generators to maintain the system frequency at its nominal value (60 Hz in North America)
• It also ensures that the power exchange between areas follows the scheduled values
• AGC consists of primary control (governor response) and secondary control (load frequency control)
• Examples of AGC include tie-line bias control and area control error (ACE) minimization

Voltage and reactive power control

• Voltage and reactive power control maintains the voltage profile within acceptable limits and manages reactive power flows
• It is achieved through the coordination of various control devices (generator excitation systems, tap-changing transformers, capacitor banks)
• Voltage control is typically performed at the transmission level, while reactive power control is done at the distribution level
• Examples include automatic voltage regulators (AVRs) on generators and switched capacitor banks in substations

Power system stabilizers (PSS)

• PSS are control devices that provide supplementary damping to generator electromechanical oscillations
• They use generator speed, frequency, or power as input signals and modulate the generator excitation to produce a damping torque
• PSS are designed to compensate for the phase lag introduced by the generator and excitation system
• Examples of PSS include speed-based, frequency-based, and power-based stabilizers

Power system protection

• Power system protection involves the use of various devices and schemes to detect and isolate faults, minimize damage, and ensure the safety of personnel and equipment
• Protection systems must be reliable, selective, and fast-acting to prevent the propagation of disturbances

Protective relays

• Protective relays are devices that continuously monitor the power system and initiate corrective actions when a fault or abnormal condition is detected
• They compare the measured quantities (current, voltage, frequency) with predetermined settings and send trip signals to circuit breakers
• Examples of protective relays include overcurrent, distance, differential, and undervoltage relays

Circuit breakers

• Circuit breakers are switching devices that can interrupt fault currents and isolate faulted sections of the power system
• They are typically located at the ends of transmission lines, transformers, and generators
• Circuit breakers are rated for their maximum interrupting capacity and are triggered by trip signals from protective relays
• Examples include air-blast, oil, SF6, and vacuum circuit breakers

Fuses and reclosers

• Fuses are protective devices that melt when the current exceeds a predetermined value, interrupting the circuit
• They are commonly used in distribution systems to protect smaller equipment and laterals
• Reclosers are circuit breakers with automatic reclosing capability, used to clear temporary faults and minimize outage times
• Examples of reclosers include hydraulic, electronic, and vacuum reclosers

Power system operation

• Power system operation involves the real-time management of the generation, transmission, and distribution resources to meet the load demand while ensuring reliability and economic efficiency
• Operational decisions are based on forecasts, scheduling, and optimization techniques

Economic dispatch

• Economic dispatch is the process of allocating the required generation among the available generating units to minimize the total operating cost
• It takes into account the fuel costs, efficiency, and operating constraints of each generator
• The optimization problem is solved using mathematical techniques such as Lagrange multipliers or linear programming
• Examples of constraints include generator capacity limits, ramp rates, and transmission line flow limits

Unit commitment

• Unit commitment is the process of determining the optimal schedule of generating units to meet the forecasted load demand over a given time horizon
• It involves deciding which units to start up, shut down, or keep running in each time period
• The objective is to minimize the total cost, including fuel costs, start-up costs, and shutdown costs
• Unit commitment is a mixed-integer nonlinear optimization problem that can be solved using techniques such as dynamic programming or Lagrangian relaxation

Optimal power flow (OPF)

• OPF is an optimization problem that determines the best operating point of a power system while satisfying various constraints
• It aims to minimize an objective function (generation cost, transmission losses) subject to power flow equations, generator limits, and transmission line capacity constraints
• OPF can be formulated as a nonlinear programming problem and solved using techniques such as interior point methods or genetic algorithms
• Examples of OPF applications include economic dispatch, voltage optimization, and congestion management

Power system reliability

• Power system reliability refers to the ability of the system to continuously provide adequate and secure electricity to customers
• It is measured by the frequency, duration, and extent of power outages and is a key performance indicator for utilities

Reliability indices

• Reliability indices are quantitative measures that assess the reliability of a power system
• They are calculated based on historical outage data and reflect the average system performance
• Examples of reliability indices include SAIFI (System Average Interruption Frequency Index), SAIDI (System Average Interruption Duration Index), and CAIDI (Customer Average Interruption Duration Index)
• These indices are used to benchmark the performance of utilities and identify areas for improvement

Contingency analysis

• Contingency analysis is the study of the power system's response to potential outages of transmission lines, transformers, or generators
• It involves simulating the system under various contingency scenarios and evaluating the resulting voltages, power flows, and stability
• The results are used to identify critical contingencies and develop preventive or corrective control actions
• Examples of contingency analysis techniques include full AC power flow, DC power flow, and sensitivity-based methods

Reliability-centered maintenance

• Reliability-centered maintenance (RCM) is a systematic approach to optimizing maintenance strategies based on the reliability characteristics of equipment
• It involves identifying the critical components, failure modes, and consequences of failures
• RCM helps prioritize maintenance activities, reduce costs, and improve system reliability
• Examples of RCM techniques include failure mode and effects analysis (FMEA), root cause analysis (RCA), and condition-based maintenance (CBM)

Power system planning

• Power system planning involves the long-term development of generation, transmission, and distribution resources to meet the growing demand for electricity
• It considers factors such as load growth, technology advancements, environmental regulations, and economic constraints

Load forecasting

• Load forecasting is the process of predicting the future electricity demand based on historical data, weather patterns, economic indicators, and customer behavior
• It is essential for planning the expansion of generation and transmission capacity and ensuring the system's adequacy
• Load forecasts are typically made for short-term (hours to days), medium-term (weeks to months), and long-term (years) horizons
• Examples of load forecasting techniques include regression analysis, time series models, and artificial neural networks

Generation expansion planning

• Generation expansion planning determines the optimal mix and timing of new generating units to meet the forecasted load growth
• It considers factors such as capital costs, operating costs, fuel prices, emissions, and reliability requirements
• The objective is to minimize the total cost while satisfying the demand and reliability constraints
• Examples of generation expansion planning models include capacity expansion models, production cost models, and integrated resource planning (IRP) models

Transmission expansion planning

• Transmission expansion planning identifies the need for new transmission lines and substations to accommodate the growth in generation and load
• It aims to relieve congestion, improve reliability, and facilitate the integration of renewable energy sources
• Transmission planning involves power flow analysis, stability studies, and economic evaluations
• Examples of transmission expansion planning techniques include least-cost planning, multi-criteria decision analysis, and stochastic optimization

Power system dynamics

• Power system dynamics deals with the time-domain behavior of the system under disturbances and control actions
• It involves the modeling and analysis of the dynamic interactions among generators, loads, and control devices

Synchronous machine modeling

• Synchronous machines are the primary sources of electrical energy in power systems and their dynamic behavior is critical for stability analysis
• They are modeled using a set of differential equations that describe the electromechanical and electromagnetic phenomena
• The models capture the dynamics of the rotor, stator, and damper windings, as well as the mechanical and electrical torques
• Examples of synchronous machine models include the classical model, the two-axis model, and the subtransient model

Excitation systems

• Excitation systems provide the field current to the synchronous machine and regulate the generator voltage
• They play a crucial role in maintaining the stability and controllability of the power system
• Excitation systems are modeled using transfer functions that represent the dynamics of the voltage regulator, exciter, and feedback loops
• Examples of excitation system models include the IEEE Type 1, Type 2, and Type 3 models

Governor systems

• Governor systems control the mechanical power input to the synchronous machine and regulate the generator frequency
• They respond to changes in the system frequency and adjust the turbine valves or gate positions accordingly
• Governor systems are modeled using transfer functions that capture the dynamics of the speed governor, turbine, and droop characteristics
• Examples of governor system models include the IEEEG1, IEEEG2, and IEEEG3 models

Power system stability analysis

• Power system stability analysis involves the study of the system's ability to maintain synchronism and equilibrium under various disturbances
• It is essential for ensuring the secure and reliable operation of the power system

Small-signal stability

• Small-signal stability refers to the ability of the power system to maintain synchronism under small disturbances such as minor load or generation changes
• It is analyzed using linearized models of the system around an operating point and eigenvalue techniques
• The eigenvalues of the system matrix provide information about the damping and frequency of the oscillatory modes
• Examples of small-signal stability analysis techniques include modal analysis, participation factors, and sensitivity analysis

Transient stability

• Transient stability refers to the ability of the power system to maintain synchronism under large disturbances such as faults, line trips, or generator outages
• It is analyzed using time-domain simulations of the nonlinear system model and assessing the generator rotor angle trajectories
• The critical clearing time (CCT) is a key metric that indicates the maximum allowable fault duration before the system becomes unstable
• Examples of transient stability analysis techniques include the equal area criterion, time-domain simulation, and direct methods (energy functions)

Dynamic stability

• Dynamic stability encompasses the small-signal and transient stability aspects and considers the long-term behavior of the system
• It includes the effects of slower-acting control systems such as automatic voltage regulators (AVRs), power system stabilizers (PSS), and load tap changers (LTCs)
• Dynamic stability analysis involves the simulation of the system over extended periods (several seconds to minutes) to capture the interactions among various control devices
• Examples of dynamic stability phenomena include interarea oscillations, voltage collapse, and frequency instability

Power system control devices

• Power system control devices are used to enhance the stability, reliability, and controllability of the power system
• They provide fast-acting and flexible control capabilities to mitigate disturbances and optimize the system performance

Flexible AC transmission systems (FACTS)

• FACTS are power electronic-based devices that can control the power flow, voltage, and impedance of transmission lines
• They provide dynamic control of the system parameters and can improve the stability, power transfer capability, and power quality
• Examples of FACTS devices include static var compensators (SVCs), static synchronous compensators (STATCOMs), and thyristor-controlled series capacitors (TCSCs)
• FACTS can be used for voltage support, power flow control, oscillation damping, and congestion management

High-voltage direct current (HVDC)

• HVDC is a technology that enables the transmission of electrical power over long distances using direct current (DC)
• It offers advantages such as lower losses, higher power transfer capability, and asynchronous interconnection of AC systems
• HVDC systems consist of converter stations that rectify AC to DC at the sending end and invert DC to AC at the receiving end
• Examples of HVDC applications include long-distance bulk power transmission, underwater cable transmission, and interconnection of renewable energy sources

Energy storage systems

• Energy storage systems provide a means to store electrical energy during periods of low demand or high generation and release it during periods of high demand or low generation
• They can help balance the variability of renewable energy sources, improve the system flexibility, and provide ancillary services such as frequency regulation and voltage support
• Examples of energy storage technologies include batteries (lithium-ion, flow batteries), flywheels, compressed air, and pumped hydro storage
• Energy storage can be integrated at various levels of the power system, including generation, transmission, distribution, and customer premises