Migration complete. cusp.umn.edu will be discontinued and all the content will continue to be available here.

Power Generation, Operation & Control

Graduate-level treatment of the economic, optimization, network-analysis, scheduling, and control methods used to operate modern electric-power systems. The course develops generation-unit cost models, economic dispatch, unit commitment, limited-energy scheduling, power flow, security analysis, optimal power flow, state estimation, automatic generation control, interchange, auctions, power markets, and financial transmission rights through 23 lecture modules and 27 worked problem sessions.

Instructor
Objectives
  • Model generation-unit input-output, heat-rate, incremental-cost, and operating-limit characteristics.
  • Formulate and solve economic-dispatch problems using Lagrange multipliers, Karush-Kuhn-Tucker conditions, and participation factors.
  • Account for transmission losses using incremental losses, penalty factors, and locational marginal prices.
  • Apply linear programming and dynamic programming to power-system operating problems.
  • Formulate unit commitment and solve representative schedules using dynamic programming and Lagrangian relaxation.
  • Schedule fuel-limited thermal generation, take-or-pay gas contracts, hydroelectric generation, and pumped storage.
  • Build bus-and-branch network models and solve AC, decoupled, and DC power-flow problems.
  • Perform security and contingency analysis using PTDF and LODF sensitivity factors.
  • Formulate DC and AC optimal-power-flow problems and interpret their engineering and economic results.
  • Apply weighted least-squares state estimation, bad-data detection, and observability concepts to power-system measurements.
  • Explain turbine-governor response, frequency regulation, tie-line control, and automatic generation control.
  • Analyze interchange transactions, power pools, brokers, auctions, organized markets, and financial transmission rights.
  • Relate optimization results to marginal costs, congestion, losses, ancillary services, and transmission pricing.
  • Use MATLAB-based laboratory programs and power-system data sets to reproduce and extend course calculations.
Textbooks

Power Generation, Operation, and Control, 3rd Edition

Allen J. Wood, Bruce F. Wollenberg, Gerald B. Sheblé · Wiley

View textbook →
Modules
1 Module 1: Introduction to Economics of Power Generation
Download slide

Description: Introduces the economic-dispatch and unit-commitment problems, limited fuel and hydro resources, transmission constraints, system security, optimal power flow, state estimation, automatic generation control, and market transactions that organize the course.

2 Module 2: Characteristics of Power Generation Units
Download slide

Description: Develops input-output, heat-rate, and incremental-cost characteristics for steam, combined-cycle, and hydroelectric generating units, including valve-point effects and common-header plants.

3 Module 3: Industrial Organization, Managerial Economics and Finance
Download slide

Description: Compares regulated and competitive electric-industry structures and introduces utility organization, generation competition, spot markets, transmission access, financial statements, and investment decisions.

4 Module 4: Optimization Within Constraints
Download slide

Description: Builds constrained-optimization fundamentals using gradients, equality and inequality constraints, Lagrange functions, multipliers, and Karush-Kuhn-Tucker optimality conditions.

5 Module 5: Linear Programming
Download slide

Description: Formulates linear programs in canonical form and explains feasible regions, slack variables, basic feasible solutions, the simplex method, dual variables, and sensitivity interpretations.

6 Module 6: Dynamic Programming
Download slide

Description: Introduces multistage decision problems, the principle of optimality, recursive cost calculations, state transitions, and backtracking through a shortest-path example.

7 Module 7-1: Economic Dispatch of Thermal Units, Part 1
Download slide

Description: Formulates thermal economic dispatch, derives equal-incremental-cost and KKT conditions, enforces generator limits and load balance, and develops lambda-iteration solution logic.

8 Module 7-2: Economic Dispatch of Thermal Units, Part 2
Download slide

Description: Extends economic dispatch to piecewise-linear costs, linear-programming formulations, base-point and participation-factor methods, transmission losses, penalty factors, LMP, and auction mechanisms.

9 Module 8-1: Unit Commitment, Part 1
Download slide

Description: Introduces unit-combination scheduling over changing load, start-up and shut-down costs, minimum up/down times, spinning reserve, priority-list methods, and dynamic-programming commitment.

10 Module 8-2: Unit Commitment, Part 2
Download slide

Description: Develops Lagrangian-relaxation unit commitment, separates unit subproblems from the system loading constraint, updates multipliers, and discusses ramp-rate and operating constraints.

11 Module 9-1: Generation with Limited Energy Supply, Part 1
Download slide

Description: Formulates limited-fuel scheduling for take-or-pay gas contracts, storage and delivery constraints, multiple time intervals, and linear-programming allocation of fuel-constrained generation.

12 Module 9-2: Generation with Limited Energy Supply, Part 2
Download slide

Description: Develops hydrothermal coordination with reservoir-volume, discharge, generation, and load-balance constraints and examines linear- and dynamic-programming approaches to hydro scheduling.

13 Module 10-1: Transmission System Effects, Part 1
Download slide

Description: Moves from substation topology to bus-and-branch network models and develops equipment modeling, dispatcher power-flow applications, the bus-admittance matrix, and Newton-Raphson power flow.

14 Module 10-2: Transmission System Effects, Part 2
Download slide

Description: Compares decoupled, Gauss-Seidel, and DC power-flow methods and develops transmission-loss calculations, incremental losses, reference-bus penalty factors, and their use in dispatch.

15 Module 11-1: Power System Security, Part 1
Download slide

Description: Introduces scheduled and forced outages, the N-1 criterion, system monitoring, contingency analysis, security-constrained corrective action, and ranking or selection of important contingencies.

16 Module 11-2: Power System Security, Part 2
Download slide

Description: Develops fast linear sensitivity analysis using power-transfer and line-outage distribution factors, then applies PTDF and LODF calculations to generation and transmission contingencies.

17 Module 12-1: Optimal Power Flow, Part 1
Download slide

Description: Combines economic dispatch with network equations to formulate AC and DC optimal power flow, generator and line limits, nodal balances, Lagrangians, and constrained network examples.

18 Module 12-2: Optimal Power Flow, Part 2
Download slide

Description: Examines AC-OPF solution with iterative linear programming and interior-point methods, incorporates voltage and transmission limits, and relates OPF multipliers to LMP, losses, and congestion.

19 Module 13-1: Power System State Estimation, Part 1
Download slide

Description: Introduces system state variables, redundant and noisy measurements, weighted least-squares estimation, measurement covariance, linear and AC models, and iterative estimation of bus voltages and angles.

20 Module 13-2: Power System State Estimation, Part 2
Download slide

Description: Covers modeling and measurement errors, chi-squared bad-data detection, normalized residuals, bad-measurement identification, observability, pseudo-measurements, and phasor measurement units.

21 Module 14: Control of Generation
Download slide

Description: Models turbine-generator, load, prime mover, governor, and tie-line dynamics and develops frequency regulation, area control error, economic participation, and automatic generation control.

22 Module 15-1: Interchange, Pooling, Brokers and Auctions, Part 1
Download slide

Description: Explains why utilities interconnect, classifies energy and reliability transactions, evaluates interchange economics, and introduces contracts, wheeling, transfer capability, and power pools.

23 Module 15-2: Interchange, Pooling, Brokers and Auctions, Part 2
Download slide

Description: Develops energy-broker and auction mechanisms, bid matching and market clearing, transmission-aware auctions, market power, congestion charges, and financial transmission rights.

24 Problem Session 1: Generator Input-Output and Economic Dispatch
Download slide

Description: Works from generator input-output and incremental-cost curves to equal-incremental-cost dispatch, operating limits, total production cost, and system lambda.

25 Problem Session 2: Economic Dispatch Using Linear Programming
Download slide

Description: Recasts economic dispatch with piecewise-linear generation costs as a linear program and interprets its variables, constraints, and optimal dispatch result.

26 Problem Session 3: Transmission Losses and Locational Marginal Pricing
Download slide

Description: Extends dispatch to a network with transmission losses and demonstrates how incremental losses and network location affect marginal generation cost and LMP.

27 Problem Session 4: Unit Commitment Using Dynamic Programming
Download slide

Description: Constructs a multistage dynamic-programming solution for unit commitment, including feasible unit combinations, transition decisions, operating cost, and backtracking.

28 Problem Session 5: Unit Commitment Using Lagrangian Relaxation
Download slide

Description: Works a Lagrangian-relaxation commitment problem by relaxing the loading constraint, solving unit subproblems, updating multipliers, and checking schedule feasibility.

29 Problem Session 6: Fuel Scheduling
Download slide

Description: Formulates fuel-limited generation across multiple periods with take-or-pay, storage, delivery, and generator constraints and solves the schedule using linear programming.

30 Problem Session 7: Hydro Scheduling
Download slide

Description: Develops hydroelectric power and water-discharge relationships and applies reservoir volume, inflow, discharge, generation, and load-balance constraints to hydrothermal scheduling.

31 Problem Session 8: Hydro Scheduling Using Dynamic Programming
Download slide

Description: Solves a staged hydro-scheduling problem with reservoir state, allowable discharge decisions, thermal replacement cost, recursive optimization, and terminal-volume constraints.

32 Problem Session 9: Power System Security
Download slide

Description: Frames the operating-security problem through outage risk, the N-1 criterion, limit monitoring, contingency selection, and preventive or corrective operating actions.

33 Problem Session 10: Incremental Losses and Penalty Factors
Download slide

Description: Uses a six-bus power-flow case to calculate incremental transmission losses and reference-bus penalty factors and then incorporates those factors into economic dispatch.

34 Problem Session 11: Security Analysis
Download slide

Description: Performs AC and DC contingency analysis on a six-bus system, comparing base and stressed cases, line or generator outages, overload detection, and corrective actions.

35 Problem Session 12: PTDF and LODF Factors
Download slide

Description: Calculates power-transfer and line-outage distribution factors and applies them to estimate post-transfer and post-outage line flows without resolving a full power flow.

36 Problem Session 13: Optimal Power Flow
Download slide

Description: Builds a network-constrained optimal-power-flow calculation from generator costs, nodal balances, line limits, and sensitivity factors and interprets the optimal generation schedule.

37 Problem Session 14: LMP and Optimal Power Flow
Download slide

Description: Uses three- and six-bus OPF cases to calculate locational marginal prices and examine how generator deratings and transmission constraints create congestion-price differences.

38 Problem Session 15: DC and AC Optimal Power Flow
Download slide

Description: Compares DC- and AC-OPF formulations, line and voltage constraints, iterative linear programming, security-constrained OPF, and the relationship among LMP, losses, and congestion.

39 Problem Session 16: Interior Point Method and LMP Calculation
Download slide

Description: Works through interior-point optimal-power-flow mechanics and uses optimality multipliers and network sensitivities to calculate and interpret locational marginal prices.

40 Problem Session 17: Introduction to State Estimation
Download slide

Description: Introduces measurement redundancy, regression, weighted least squares, state variables, residuals, and the use of line-flow sensitivity calculations in state-estimation examples.

41 Problem Session 18: State Estimation Calculations
Download slide

Description: Carries out weighted least-squares state-estimation calculations, assembling measurement and Jacobian matrices, weighting measurements, iterating the state, and evaluating residual error.

42 Problem Session 19: AC State Estimation Applications
Download slide

Description: Applies AC state estimation to multiple six-bus measurement cases, including missing angle measurements, zero injections, observability, bad data, and practical estimator operation.

43 Problem Session 20: Automatic Generation Control
Download slide

Description: Analyzes turbine-governor and load-frequency response after a generator or load disturbance and develops tie-line bias control, area control error, and AGC participation.

44 Problem Session 21: Power Interchange and Power Pools
Download slide

Description: Evaluates multiarea interchange schedules, economy transactions, tie-line flows, reliability support, power-pool coordination, and the allocation of benefits among interconnected utilities.

45 Problem Session 22: Power Auctions
Download slide

Description: Constructs supply and demand bids, clears a power auction, calculates buyer and seller outcomes, and compares bilateral, brokered, and centralized market arrangements.

46 Problem Session 23: Power Markets
Download slide

Description: Compares regulated and deregulated electricity systems and examines competitive generation, transmission access, market operators, auction theory, market clearing, and market power.

47 Problem Session 24: Power Auctions Using Optimal Power Flow
Download slide

Description: Clears a transmission-constrained power auction with OPF, showing how bids, transactions, line limits, ancillary services, and network feasibility affect dispatch and prices.

48 Problem Session 25: Power Market Example
Download slide

Description: Works a complete network power-market example, linking bids, dispatch, transactions, congestion, market settlement, and the operating constraints enforced by the market calculation.

49 Problem Session 26: Loss Allocation and Ancillary Services
Download slide

Description: Examines transmission-loss allocation, transmission-company revenue, usage and congestion charges, generation-to-load responsibilities, and pricing of ancillary services.

50 Problem Session 27: Financial Transmission Rights Auctions
Download slide

Description: Calculates and auctions financial transmission rights, applies simultaneous-feasibility constraints, and relates FTR payouts to congestion revenue and transmission-price risk hedging.

Assignments

Problem Session 1 - Generator Input-Output and Economic Dispatch

Download assignment

Problem Session 2 - Economic Dispatch Using Linear Programming

Download assignment

Problem Session 3 - Transmission Losses and Locational Marginal Pricing

Download assignment

Problem Session 4 - Unit Commitment Using Dynamic Programming

Download assignment

Problem Session 5 - Unit Commitment Using Lagrangian Relaxation

Download assignment

Problem Session 6 - Fuel Scheduling

Download assignment

Problem Session 7 - Hydro Scheduling

Download assignment

Problem Session 8 - Hydro Scheduling Using Dynamic Programming

Download assignment

Problem Session 9 - Power System Security

Download assignment

Problem Session 10 - Incremental Losses and Penalty Factors

Download assignment

Problem Session 11 - Security Analysis

Download assignment

Problem Session 12 - PTDF and LODF Factors

Download assignment

Problem Session 13 - Optimal Power Flow

Download assignment

Problem Session 14 - LMP and Optimal Power Flow

Download assignment

Problem Session 15 - DC and AC Optimal Power Flow

Download assignment

Problem Session 16 - Interior Point Method and LMP Calculation

Download assignment

Problem Session 17 - Introduction to State Estimation

Download assignment

Problem Session 18 - State Estimation Calculations

Download assignment

Problem Session 19 - AC State Estimation Applications

Download assignment

Problem Session 20 - Automatic Generation Control

Download assignment

Problem Session 21 - Power Interchange and Power Pools

Download assignment

Problem Session 22 - Power Auctions

Download assignment

Problem Session 23 - Power Markets

Download assignment

Problem Session 24 - Power Auctions Using Optimal Power Flow

Download assignment

Problem Session 25 - Power Market Example

Download assignment

Problem Session 26 - Loss Allocation and Ancillary Services

Download assignment

Problem Session 27 - Financial Transmission Rights Auctions

Download assignment

Problem Session 28 - Ejebe Graduate Seminar on Markets

Download assignment