Electrical Power Systems

Cheatsheet Content

1. Power Generation Fundamentals 1.1 Basic Principles Faraday's Law of Induction: $EMF = -N \frac{d\Phi_B}{dt}$, where $EMF$ is electromotive force, $N$ is number of turns, and $\Phi_B$ is magnetic flux. Synchronous Generator: Most common for large-scale generation. Converts mechanical energy to electrical energy. Prime Movers: Turbines (steam, gas, hydro, wind) or diesel engines drive generators. 1.2 Major Generation Methods A. Thermal Power Plants (Steam Cycle) Fuel: Coal, natural gas, nuclear, biomass. Process: Fuel heats water to steam $\rightarrow$ steam drives turbine $\rightarrow$ turbine drives generator. Components: Boiler, Steam Turbine, Generator, Condenser, Cooling Tower. Efficiency: Typically 35-45% for fossil fuels, higher for combined cycle gas turbines (CCGT). B. Hydroelectric Power Plants Principle: Potential energy of water $\rightarrow$ kinetic energy $\rightarrow$ mechanical energy $\rightarrow$ electrical energy. Types: Impoundment: Dam creates reservoir. Run-of-River: Diverts portion of river flow. Pumped-Storage: Pumps water to higher reservoir during off-peak, generates during peak. Advantages: Renewable, flexible (dispatchable), low operating costs. Disadvantages: Environmental impact (dams), dependent on water availability. C. Nuclear Power Plants Fuel: Uranium-235 (fission). Process: Nuclear fission generates heat $\rightarrow$ boils water $\rightarrow$ steam drives turbine. Reactor Types: Pressurized Water Reactor (PWR), Boiling Water Reactor (BWR). Advantages: High power output, low greenhouse gas emissions during operation. Disadvantages: Radioactive waste, safety concerns, high capital cost. D. Wind Power Principle: Wind kinetic energy $\rightarrow$ rotor (blades) mechanical energy $\rightarrow$ gearbox $\rightarrow$ generator. Types: Onshore, Offshore. Generator Types: Induction generators, synchronous generators. Advantages: Renewable, no fuel cost, no emissions. Disadvantages: Intermittent, visual/noise impact, grid integration challenges. E. Solar Photovoltaic (PV) Power Principle: Photons from sunlight strike semiconductor material (e.g., silicon) $\rightarrow$ electrons are dislodged $\rightarrow$ current flow (photovoltaic effect). Components: PV modules (panels), inverters (DC to AC), mounting systems. Advantages: Renewable, no emissions, modular. Disadvantages: Intermittent, dependent on sunlight, efficiency varies with temperature. F. Geothermal Power Principle: Uses heat from Earth's interior to generate steam $\rightarrow$ drives turbine. Types: Dry steam, flash steam, binary cycle. Advantages: Renewable, continuous (baseload), small land footprint. Disadvantages: Geographically limited, potential for emissions (e.g., $\text{H}_2\text{S}$). 1.3 Generator Characteristics Synchronous Speed: $N_s = \frac{120f}{P}$ (RPM), where $f$ is frequency (Hz) and $P$ is number of poles. Voltage Regulation: Percentage change in terminal voltage from no-load to full-load. Reactive Power (VARs): Generators can absorb or supply reactive power to control system voltage. 2. Power Transmission 2.1 Necessity of Transmission Transmit bulk power from generation sites to load centers. Minimize power losses ($P_{loss} = I^2 R$). Voltage step-up: $P = V I \cos\phi$. For constant power $P$, increasing $V$ decreases $I$, thus reducing $I^2 R$ losses. 2.2 Components of a Transmission System Step-up Transformer: Increases voltage at the generation end (e.g., 25 kV to 230 kV, 400 kV, 765 kV). Transmission Lines: Overhead lines (ACSR conductors), underground cables (less common for bulk transmission due to cost and reactive power issues). Transmission Towers: Support conductors. Insulators: Electrically isolate conductors from towers. Substations: Connect different voltage levels, provide switching and protection. Circuit Breakers: Interrupt fault currents. Relays: Detect faults and trip circuit breakers. Reactors/Capacitors: For reactive power compensation, voltage control. 2.3 Transmission Line Parameters Resistance (R): Causes $I^2 R$ losses. Dependent on conductor material, length, cross-section. Inductance (L): Due to magnetic field around conductors. Causes voltage drop and limits power transfer. $X_L = \omega L$. Capacitance (C): Due to electric field between conductors. Generates reactive power, especially at higher voltages and longer lines. $X_C = \frac{1}{\omega C}$. Characteristic Impedance: $Z_c = \sqrt{\frac{L}{C}}$. 2.4 Transmission Line Models Short Line Model ($\text{length} Resistance and inductance only. Shunt capacitance neglected. $V_S = V_R + I_R Z$ $Z = R + jX_L$ Medium Line Model ($80 \text{ km} Resistance, inductance, and capacitance. Nominal $\pi$-model: Shunt capacitance divided into two halves at each end. Nominal T-model: Shunt capacitance concentrated at the middle. Long Line Model ($\text{length} > 250 \text{ km}$): Distributed parameters. Uses hyperbolic functions. $V_S = V_R \cosh(\gamma l) + I_R Z_c \sinh(\gamma l)$ $I_S = I_R \cosh(\gamma l) + \frac{V_R}{Z_c} \sinh(\gamma l)$ $\gamma = \sqrt{ZY}$ (propagation constant), $Z = R+j\omega L$, $Y = G+j\omega C$ 2.5 Voltage Control and Reactive Power Management Reactive Power: Required by inductive loads (motors, transformers). Does not perform useful work but flows through the system. Voltage Control: Managed by controlling reactive power balance. Generators: Can supply or absorb VARs. Shunt Capacitors: Supply VARs, raise voltage. Shunt Reactors: Absorb VARs, lower voltage. Synchronous Condensers: Over-excited (supply VARs), under-excited (absorb VARs). SVC (Static VAR Compensator): Fast-acting reactive power source. STATCOM (Static Synchronous Compensator): Voltage source converter based, more dynamic. Tap-changing Transformers: Adjust voltage ratios. 2.6 Power Transfer Capability Thermal Limit: Maximum current a conductor can carry without overheating. Voltage Stability Limit: Maximum power that can be transferred while maintaining stable voltage. Steady-State Stability Limit: Maximum power that can be transferred without loss of synchronism between generators. $P = \frac{|V_S||V_R|}{X} \sin\delta$, where $\delta$ is the power angle. 2.7 High Voltage Direct Current (HVDC) Transmission Advantages: Lower losses over very long distances. Asynchronous interconnections (e.g., connecting different AC grids). No reactive power flow. Enhanced stability. Lower right-of-way for overhead lines. Disadvantages: High cost of converter stations. Harmonic issues. Difficulty in breaking DC current. Components: Converter stations (rectifier and inverter), DC transmission line. 3. Power Distribution 3.1 Role of Distribution System Delivers electric power from transmission system to individual consumers. Typically operates at lower voltages (e.g., 33 kV, 11 kV, 400 V, 230 V). 3.2 Components of a Distribution System Distribution Substation: Steps down transmission voltage to sub-transmission or primary distribution voltage (e.g., 132 kV to 33 kV or 11 kV). Feeders (Primary Distribution): Higher voltage lines from substation to load areas. Radial: Simplest, least reliable. Ring Main: More reliable, can supply load from two directions. Interconnected/Network: Most reliable, complex. Distribution Transformers: Step down primary distribution voltage to secondary distribution voltage (e.g., 11 kV to 400/230 V). Located near consumers. Secondary Distribution Lines: Low voltage lines from distribution transformers to consumer service drops. Service Drops: Connect secondary lines to consumer premises. Protection Devices: Fuses, reclosers, sectionalizers, circuit breakers. Voltage Regulators: Maintain voltage within acceptable limits. Capacitor Banks: For power factor correction and voltage support. 3.3 Types of Distribution Systems AC Distribution: Most common. Single Phase: For residential, small commercial loads. Three Phase: For industrial, large commercial loads. DC Distribution: Emerging for specific applications (e.g., data centers, electric vehicles, renewable energy integration). 3.4 Voltage Levels and Standards Primary Distribution: 11 kV, 22 kV, 33 kV. Secondary Distribution: Three-phase: 400 V (line-to-line), 230 V (line-to-neutral) in many parts of the world. Single-phase: 230 V, 120 V. Voltage Tolerance: Typically $\pm 5-10\%$ of nominal voltage. 3.5 Power Losses in Distribution Higher losses compared to transmission due to lower voltages and higher currents for a given power. Minimization through: Optimal conductor sizing. Power factor improvement (capacitor banks). Voltage regulation. Optimal feeder routing. 3.6 Power Factor Correction Power Factor ($\cos\phi$): Ratio of active power to apparent power. $PF = \frac{P}{S}$. Low Power Factor: Caused by inductive loads. Leads to higher current, increased losses, reduced voltage. Correction: Install shunt capacitors near inductive loads to supply reactive power. Benefits: Reduced current, lower $I^2 R$ losses, improved voltage profile, increased system capacity. 3.7 Protection in Distribution Systems Fuses: Overcurrent protection for low fault currents. Reclosers: Detect and interrupt fault currents, then reclose automatically. Used on feeders. Sectionalizers: Coordinate with reclosers to isolate faulted sections. Circuit Breakers: Manual or automatic interruption of fault currents. Protective Relays: Detect abnormal conditions (overcurrent, undervoltage, etc.) and trip circuit breakers. Coordination: Ensures that the protective device closest to the fault operates first. 4. Grid Operations and Management 4.1 Smart Grid Concepts Integration of advanced sensing, communication, control, and information technologies into the power grid. Objectives: Improve reliability, efficiency, security, sustainability, and enable consumer participation. Key Features: Two-way communication: Between utility and consumers. Self-healing: Detects and responds to disturbances automatically. Optimized asset utilization: Better management of grid infrastructure. Integration of distributed generation: Solar, wind at local level. Demand response: Managing consumer electricity demand in response to supply conditions. 4.2 SCADA (Supervisory Control and Data Acquisition) Computerized system for controlling and monitoring power system elements. Functions: Data acquisition, remote control, alarm processing, event logging. Components: Master station, RTUs (Remote Terminal Units), communication network. 4.3 Energy Management System (EMS) Software application used by transmission system operators to monitor, control, and optimize grid performance. Functions: State estimation, optimal power flow, contingency analysis, security assessment, load forecasting. 4.4 Distributed Energy Resources (DERs) Small-scale power generation or storage units located close to load. Examples: Rooftop solar PV, small wind turbines, battery storage, combined heat and power (CHP). Challenges: Intermittency, grid integration, bidirectional power flow, protection coordination. 4.5 Microgrids Localized group of electricity sources and loads that typically operates connected to a conventional grid (macrogrid) but can disconnect and operate autonomously (island mode). Benefits: Increased local reliability, resilience, reduced losses, integration of local DERs. 4.6 Grid Stability Rotor Angle Stability: Ability of synchronous machines to remain in synchronism. Small-signal stability: Response to small disturbances. Transient stability: Response to large disturbances (e.g., short circuits). Voltage Stability: Ability to maintain acceptable voltages at all buses. Voltage collapse: Progressive drop in voltage leading to blackout. Frequency Stability: Ability to maintain system frequency within acceptable limits. 4.7 Economic Dispatch Optimization problem to determine the output of each generating unit to meet the load demand at minimum cost, subject to operational constraints. Objective: Minimize $\sum C_i(P_i)$, where $C_i$ is cost function of generator $i$. Constraint: $\sum P_i = P_{load} + P_{losses}$. Lambda Iteration Method: Often used to solve, based on incremental cost $\lambda$. 5. Environmental and Regulatory Aspects 5.1 Environmental Impact Fossil Fuels: Greenhouse gas emissions ($\text{CO}_2$, $\text{CH}_4$), air pollutants ($\text{SO}_2$, $\text{NO}_x$, particulate matter), water usage, ash disposal. Nuclear: Radioactive waste disposal, risk of accidents. Hydro: Ecosystem disruption, methane emissions from reservoirs, seismic activity. Wind/Solar: Land use, visual impact, noise (wind), material sourcing/disposal. Transmission Lines: Right-of-way, visual impact, electromagnetic fields (EMF). 5.2 Renewable Energy Integration Challenges: Intermittency, variability, forecasting uncertainty, grid stability, need for energy storage. Solutions: Advanced forecasting, energy storage (batteries, pumped hydro), demand-side management, flexible generation, grid modernization. 5.3 Deregulation and Market Structures Shift from vertically integrated utilities to unbundled structures. Generation: Competitive market. Transmission: Regulated monopoly (Independent System Operator/Transmission System Operator - ISO/TSO). Distribution: Regulated monopoly. Retail: Competitive market or regulated. Wholesale Markets: Energy, capacity, ancillary services. 5.4 Reliability Standards NERC (North American Electric Reliability Corporation): Sets mandatory reliability standards. Key Metrics: SAIDI (System Average Interruption Duration Index), SAIFI (System Average Interruption Frequency Index), CAIDI (Customer Average Interruption Duration Index).