⚡Smart Grid Optimization Unit 14 – Economic Dispatch in Electricity Markets

Fundamentals of Economic Dispatch

• Economic dispatch involves allocating generation among available generating units to minimize total operating cost while meeting system constraints
• Aims to balance electricity supply and demand in the most cost-effective manner
• Takes into account the incremental cost of each generating unit, which is the cost of producing one additional unit of electricity
• Considers transmission losses and constraints to ensure feasible and reliable power delivery
• Utilizes optimization algorithms to determine the optimal generation schedule
  • Common techniques include linear programming, quadratic programming, and dynamic programming
• Plays a crucial role in power system operation and electricity market clearing
• Helps maintain system stability, reliability, and efficiency by dispatching generators based on their cost and operational characteristics

Power System Basics and Market Structure

• Power systems consist of generating units, transmission lines, transformers, and loads
• Generators produce electricity, which is transmitted over high-voltage lines to load centers
• Electricity markets facilitate the trading of electricity between generators and consumers
  • Market participants include generators, utilities, and independent power producers
• Market structures vary, but common types include bilateral markets, pool markets, and hybrid markets
• In bilateral markets, buyers and sellers directly negotiate contracts for electricity supply
• Pool markets involve a centralized entity (e.g., independent system operator) that clears the market based on bids from generators and demand from consumers
• Hybrid markets combine elements of bilateral and pool markets, allowing for both long-term contracts and short-term market transactions
• Market clearing determines the market price and the dispatch schedule for each generator

Cost Functions and Generator Characteristics

• Cost functions represent the relationship between a generator's output and its operating cost
• Typically modeled as quadratic functions, with coefficients reflecting fuel costs, efficiency, and maintenance expenses
• Incremental cost curves derive from the derivative of the cost function and indicate the cost of producing an additional unit of electricity
• Generator characteristics include minimum and maximum output limits, ramp rates, and startup costs
  • Minimum output limit is the lowest stable operating point of a generator
  • Maximum output limit is the highest output a generator can safely produce
  • Ramp rates specify how quickly a generator can change its output level
• Generating units have different operational constraints and cost structures
  • Thermal units (coal, gas) have higher fuel costs but lower capital costs
  • Hydro units have low operating costs but limited energy availability
  • Renewable units (wind, solar) have near-zero marginal costs but intermittent output
• Accurate modeling of cost functions and generator characteristics is essential for efficient economic dispatch

Optimization Techniques for Economic Dispatch

• Economic dispatch is formulated as an optimization problem, aiming to minimize total operating cost subject to system constraints
• Linear programming is used when cost functions are approximated as piecewise linear and constraints are linear
  • Simplex method is a common solution algorithm for linear programming problems
• Quadratic programming is employed when cost functions are quadratic and constraints are linear
  • Interior point methods and active set methods are popular solution techniques for quadratic programming
• Dynamic programming is applied when the dispatch problem has a temporal component, such as in multi-period dispatch or unit commitment
• Heuristic methods, such as genetic algorithms and particle swarm optimization, are used for large-scale, non-convex dispatch problems
• Optimization software packages (e.g., CPLEX, Gurobi) are often utilized to solve economic dispatch problems efficiently
• Advances in optimization algorithms and computational power have enabled the solution of increasingly complex dispatch problems

Constraints and System Limitations

• Economic dispatch must respect various constraints to ensure system reliability and feasibility
• Power balance constraint ensures that total generation equals total demand plus losses
• Generator output limits constrain each unit's production within its minimum and maximum capacity
• Transmission line thermal limits restrict the amount of power that can flow through each line
  • Exceeding thermal limits can cause line overheating and potential failure
• Voltage limits maintain voltages within acceptable ranges at each bus in the system
• Spinning reserve requirements ensure sufficient backup capacity to handle unexpected generator outages or demand spikes
• Ramp rate constraints limit the rate at which generators can change their output levels
• Emission constraints may be imposed to limit the environmental impact of electricity generation
• Incorporating constraints into the dispatch problem results in a constrained optimization formulation
  • Lagrange multipliers and duality theory are used to handle constraints in optimization algorithms

Real-Time vs. Day-Ahead Dispatch

• Economic dispatch is performed in both real-time and day-ahead timeframes
• Real-time dispatch (RTD) optimizes generation based on actual system conditions and short-term forecasts
  • Typically runs every 5-15 minutes to adjust generator setpoints in response to changing demand and system state
  • Handles unexpected events, such as generator outages or transmission congestion
• Day-ahead dispatch (DAD) optimizes generation based on forecasted demand and system conditions for the next day
  • Clears the day-ahead market and determines the generation schedule and prices for each hour of the upcoming day
  • Allows generators to plan their operations and fuel procurement in advance
• DAD provides a baseline generation schedule, while RTD fine-tunes the dispatch based on actual conditions
• Coordination between DAD and RTD is crucial for efficient and reliable system operation
  • Deviations between DAD and RTD can result in imbalances and affect market settlements
• Intra-day markets and adjustments help bridge the gap between DAD and RTD, allowing for updates based on revised forecasts and system conditions

Impact of Renewable Energy on Economic Dispatch

• Increasing penetration of renewable energy sources, such as wind and solar, poses challenges for economic dispatch
• Renewable generation is intermittent and less predictable compared to conventional generation
  • Output depends on weather conditions, such as wind speed and solar irradiance
  • Forecasting techniques are used to predict renewable generation, but uncertainty remains
• Renewable units have near-zero marginal costs, displacing conventional generation in the dispatch order
  • Merit order effect: renewable generation reduces the market clearing price and displaces higher-cost units
• Variability and uncertainty of renewable generation require increased flexibility from the power system
  • Ramping capabilities, energy storage, and demand response help balance supply and demand
• Economic dispatch must account for the stochastic nature of renewable generation
  • Stochastic optimization techniques, such as scenario-based and robust optimization, are used to handle uncertainty
• Renewable energy integration may require changes in market design and dispatch rules
  • Negative prices, curtailment rules, and ancillary service markets are adapted to accommodate renewable generation
• Coordination between renewable generation and conventional units is essential for maintaining system stability and reliability

Case Studies and Real-World Applications

• Economic dispatch is a fundamental tool in power system operation and electricity markets worldwide
• PJM Interconnection (U.S.): one of the largest competitive wholesale electricity markets
  • Employs a two-settlement system with day-ahead and real-time markets
  • Uses a security-constrained economic dispatch (SCED) algorithm to optimize generation while respecting transmission constraints
• European Power Exchange (EPEX SPOT): operates day-ahead and intraday markets across several European countries
  • Clears the market using a price coupling algorithm, considering cross-border transmission capacities
  • Integrates large shares of renewable energy, particularly wind and solar
• California Independent System Operator (CAISO): manages the power grid and wholesale electricity market in California
  • Implements a multi-interval dispatch model, optimizing generation over multiple time horizons
  • Deals with high levels of renewable penetration and the "duck curve" phenomenon
• China's power system: undergoing reforms to introduce market mechanisms and competition
  • Transitioning from a centrally-planned system to a more market-based approach
  • Implementing regional electricity markets and exploring spot market designs
• These case studies demonstrate the practical application of economic dispatch principles and the adaptation to specific market structures and system characteristics