• Optimization
• Optimization Overview
  • About Optimization
    • System-wide Approach
    • Preemptive Linear Goal Programming
    • Optimization Variables
    • Physical Constraints
    • Prioritized Policy
  • Advantages of Optimization
  • Optimization License
• Mathematics of Preemptive Linear Goal Programming
  • About Preemptive Linear Goal Programming
    • Linear Programming
    • Goal Programming
    • Preemptive Goal Programming
  • Soft Constraints and Derived Objectives
    • Prevent Infeasibilities
      • Two-dimensional Example
      • Goal Programming With Many Dimensions
      • Water Resource Management Example
    • Satisfaction Variables in Soft Constraints
    • Derived Objectives
      • Summation
      • Single Maximin
      • Repeated Maximin
      • Summation with Reward Table
  • Freezing Constraints and Variables
    • Freezing Constraints
    • Freezing Variables
  • Shrinking Constraints
• Combining Optimization With Simulation
  • Standard Controller Sequence
    • Simulation
    • Optimization
    • Post-optimization Rulebased Simulation
  • Post-optimization Ruleset
    • Automatically Generated Ruleset
    • Custom Post-optimization Ruleset
  • Initialization Rules
    • Usage
    • Enable or Disable Initialization Rules based on Controller
    • Timing
  • Limitations of Optimization
    • Optimization License Required
    • Linear Relationships
    • Linear Constraint Expressions
    • Approximation Error
    • Solution Time
    • Perfect Foresight
    • Limited Objects and Method Selections
    • Debugging
• Variables, Constraints, and Objectives
  • RPL Optimization Goal Set
    • Prioritized Policy
    • Goal Types
      • Hard Constraints
      • Soft Constraints
      • Objectives
    • Statements in Goal Sets
      • Objective
      • Soft Constraint Set
      • Constraint
      • Freeze
      • With Reward Table
      • For
      • With
      • If
      • If Else
      • Else If Branch
      • Else Branch
      • Print
      • Notice
      • Warning
      • Alert
      • Stop Run
    • Timestep References in Optimization
  • Optimization Variables
    • Slots and Variables
      • Slots as CPLEX Variables
      • Linearized Slots
      • Variables Unrelated to Slots
      • Slots Unused by Optimization
    • Constraints Define Variables
    • Physical Constraints
    • Variable Bounds
    • User-defined Variables
  • Linearization, Approximation, and Replacement
    • Link Substitution
    • Constraint Substitution
    • Expression Substitution
    • Variable Substitution
      • Direct Substitution
      • Tangent Approximation
      • Two-point Line Approximation
      • Piecewise Approximation
      • Lambda Method
• Optimization Objects and Methods
  • How Objects Are Described
  • Canal
    • General Slots
    • User Methods
    • Canal Flow Numerical Approximation
    • Modeling a Canal
  • Confluence
  • Data Objects
  • Inline Power Plant
  • Level Power Reservoir
    • General Slots
    • User Methods
    • Avoidance Zones
      • None
      • Unit Head Based Avoidance Zones
    • Bank Storage
      • None
      • CRSS Bank Storage
    • Cavitation
      • None
      • Unit Head and Tailwater Based Regions
    • Diversion from Reservoir
      • None
      • Available Flow Based Diversion
    • Energy in Storage
      • None
      • EIS Table Lookup
    • Frequency Regulation
      • None
      • Unit Frequency Regulation
    • Future Value
      • None
      • Cumulative Storage Value Table
    • Head Loss
      • None
      • Shared Penstock Head Loss method
    • Hydrologic Inflow
    • Optimization Evaporation
      • None
      • Opt Input Evaporation
    • Optimization Future Value
      • None
      • Opt Cumulative Storage Value Table
    • Optimization Power
      • None
      • Independent Linearizations
      • Power Coefficient
      • Power Surface Approximation
    • Optimization Reserves
      • None
      • Constraint Based Single Timestep
    • Optimization Spill
      • None
      • Opt Monthly Spill
      • Opt Unregulated
      • Opt Regulated
      • Opt Regulated and Unregulated
      • Opt Regulated and Bypass
      • Opt Regulated, Bypass and Unregulated
      • Opt Bypass, Regulated and Unregulated
    • Optimization Tailwater
      • Opt Linked or Input
      • Opt Base Value Only
      • Opt Base Value Plus Lookup Table
      • Opt Stage Flow Lookup Table
      • Opt Coefficients Table
    • Power
      • Plant Power Coefficient
      • Plant Efficiency Curve
      • Peak Power
      • Peak and Base
      • Unit Power Table
      • Turbine Capacity
    • Startup
      • None
      • Unit Lumped Cost
    • Modeling a Level Power Reservoir
  • Pumped Storage Reservoir
    • General Slots
    • User Methods
    • Avoidance Zones
      • None
      • Unit Head Based Avoidance Zones
    • Bank Storage
      • None
      • CRSS Bank Storage
    • Cavitation
      • None
      • Unit Head and Tailwater Based Regions
    • Diversion from Reservoir
      • None
      • Available Flow Based Diversion
    • Energy in Storage
      • None
      • EIS Table Lookup
    • Frequency Regulation
      • None
      • Unit Frequency Regulation
    • Future Value
      • None
      • Cumulative Storage Value Table
    • Head Loss
      • None
      • Shared Penstock Head Loss
    • Hydrologic Inflow
    • Optimization Evaporation
      • None
      • Opt Input Evaporation
    • Optimization Future Value
      • None
      • Opt Cumulative Storage Value Table
    • Optimization Head Computation
    • Optimization Power
      • None
      • Independent Linearizations
      • Power Coefficient
      • Power Surface Approximation
    • Optimization Reserves
      • None
      • Constraint Based Single Timestep
    • Optimization Spill
      • None
      • Opt Monthly Spill
      • Opt Unregulated
      • Opt Regulated
      • Opt Regulated and Unregulated
      • Opt Regulated and Bypass
      • Opt Regulated, Bypass and Unregulated
      • Opt Bypass, Regulated and Unregulated
    • Optimization Tailwater
      • Opt Linked or Input
      • Opt Base Value Only
      • Opt Base Value Plus Lookup Table
      • Opt Stage Flow Lookup Table
      • Opt Coefficients Table
      • Pump Power Numerical Approximation
    • Pool Elevation Linearization Automation
    • Power
      • Plant Power Coefficient
      • Plant Efficiency Curve
      • Peak Power
      • Peak and Base
      • Unit Power Table
      • Turbine Capacity
    • Startup
      • None
      • Unit Lumped Cost
    • Modeling a Pumped Storage Reservoir
  • Reach
    • General Slots
    • User Methods
    • Diversion from Reach
      • None
      • Available Flow Based Diversion
    • Gain Loss
      • None
      • Constant Gain Loss
    • Local Inflow and Solution Direction
      • Min Diversion Bypass
    • Routing
      • No Routing
      • Time Lag
      • Impulse Response
    • Numerical Approximation
    • Modeling a Reach
  • Slope Power Reservoir
    • General Slots
    • User Methods
    • Avoidance Zones
      • None
      • Unit Head Based Avoidance Zones
    • Bank Storage
      • None
      • CRSS Bank Storage
    • Cavitation
      • None
      • Unit Head and Tailwater Based Regions
    • Diversion from Reservoir
      • None
      • Available Flow Based Diversion
    • Energy in Storage
      • None
      • EIS Table Lookup
    • Frequency Regulation
      • None
      • Unit Frequency Regulation
    • Future Value
      • None
      • Cumulative Storage Value Table
    • Head Loss
      • None
      • Shared Penstock Head Loss method
    • Hydrologic Inflow
    • Optimization Backwater
      • Lambda
      • Independent Linearizations
    • Optimization Evaporation
      • None
      • Opt Input Evaporation
    • Optimization Future Value
      • None
      • Opt Cumulative Storage Value Table
    • Optimization Power
      • None
      • Independent Linearizations
      • Power Coefficient
      • Power Surface Approximation
    • Optimization Reserves
      • None
      • Constraint Based Single Timestep
    • Optimization Spill
      • None
      • Opt Monthly Spill
      • Opt Unregulated
      • Opt Regulated
      • Opt Regulated and Unregulated
      • Opt Regulated and Bypass
      • Opt Regulated, Bypass and Unregulated
      • Opt Bypass, Regulated and Unregulated
    • Optimization Tailwater
      • Opt Linked or Input
      • Opt Base Value Only
      • Opt Base Value Plus Lookup Table
      • Opt Stage Flow Lookup Table
      • Opt Coefficients Table
    • Power
      • Plant Power Coefficient
      • Plant Efficiency Curve
      • Peak Power
      • Peak and Base
      • Unit Power Table
      • Turbine Capacity
    • Slope Storage
    • Slope Storage Coefficients
    • Startup
      • None
      • Unit Lumped Cost
    • Modeling a Slope Power Reservoir
  • Storage Reservoir
    • General Slots
    • User Methods
    • Bank Storage
      • None
      • CRSS Bank Storage
    • Diversion From Reservoir
      • None
      • Available Flow Based Diversion
    • Energy in Storage
      • None
      • EIS Table Lookup
    • Evaporation and Precipitation
    • Future Value
      • None
      • Cumulative Storage Value Table
    • Hydrologic Inflow
    • Optimization Evaporation
      • None
      • Opt Input Evaporation
    • Optimization Future Value
      • None
      • Opt Cumulative Storage Value Table
    • Optimization Spill
      • None
      • Opt Monthly Spill
      • Opt Unregulated
      • Opt Regulated
      • Opt Regulated and Unregulated
      • Opt Regulated and Bypass
      • Opt Regulated, Bypass and Unregulated
      • Opt Bypass, Regulated and Unregulated
      • Release Capacity Numerical Approximation
    • Modeling a Storage Reservoir
  • Thermal
    • User Methods
    • Load
    • Modified Load
      • None
      • Calculate Modified Load
    • Preferred Customer
    • Regulation
    • Economic Valuation User Methods
    • Block Economic Value
      • None
      • Calculate Block Economic Value
    • Linear Economic Value
      • None
      • Calculate Linear Economic Value
    • Thermal Unit Replacement Value
      • None
      • Calculate Thermal Unit Replacement Value
    • Modeling a Thermal Object
• Setting Up and Running an Optimization Model
  • Select Timestep and Run Range
  • Set Up and Test a Simulation Model
  • Select Optimization Methods
  • Add a Thermal Object
  • Enter Lower and Upper Bounds
    • Bounds on Variables
    • Setting Bounds
    • Optimization Limits for Data Verification
  • Provide Approximation Points
    • Data Table Slots
    • LP Param Table Slots
    • Additional Guidelines
      • Turbine Capacity Approximation
      • Power Approximation
      • Initialization Rules to Set Approximation Points
  • Create an Optimization Goal Set
  • Create a Post-optimization Ruleset
  • Run the Model
• Debugging and Solution Analysis
  • Optimization Debugging Tools
  • Priority-oriented Optimization Solution Analysis Tool
    • Accessing the Analysis Tool
    • Save/Load Problem
    • Solution Information Panel
      • Solutions Without a Freeze Statement
    • Frozen Constraints Tabs
    • Frozen Variables Tabs
    • Export as CSV
  • Tooltips on Variables
• Technical Appendix
  • Optimization Units and Scaling
  • Mixed-integer Programming
    • Variables That Bring Integer Programming Into the Problem
    • How Integer Programs Are Solved
    • Timestep Approach
    • Defining Constraints
    • Additional Parameters for Controlling This Solution
      • Setting Parameters
      • Lower Cutoff Parameter
      • Limiting the Number of Solutions
      • Time Limit
      • Optimality Tolerance
    • Unit Power
    • Mathematical Formulation of MIP for Unit Power
      • Triangulation
        • Pseudocode for Triangulation
      • Lambda Variables for Convex Combinations of Discrete Operating Points (Triangles)
      • Defining Constraints
        • Notes on Variables and Notation
        • Binary Variables
        • Continuous Variables
        • Symbols
        • Unit-level Constraints
        • Defining Constraints for Lambda Variables
        • Unit/Plant Relationship Constraints
        • Redefining Existing Plant-level Linearizations
        • Thermal Object

Technical Documentation Version 8.2

Mixed-integer Programming