Solver Comparison & Selection Guide

Choosing the right optimization model is critical for balancing accuracy, computational speed, and analysis goals. This guide helps you select among ED, UC, DC-OPF, and AC-OPF.

Quick Decision Tree

flowchart TD
    A[Start] --> B{Need 
commitment 
decisions?}
    
    B -->|Yes| C{Network 
constraints 
matter?}
    B -->|No| D{Network 
constraints 
matter?}
    
    C -->|Yes| E[UC + OPF 
Chained]
    C -->|No| F[Unit 
Commitment]
    
    D -->|Yes| G{Voltage/reactive 
critical?}
    D -->|No| H[Economic 
Dispatch]
    
    G -->|Yes| I[AC Optimal 
Power Flow]
    G -->|No| J[DC Optimal 
Power Flow]
    

Comprehensive Comparison

Feature Matrix

Feature	ED	UC	DC-OPF	AC-OPF
Problem Type	LP/QP	MIP	LP/QP	NLP
Network Model	None	None	DC (linearized)	AC (full)
Time Periods	Single	Multiple (24+)	Single	Single
Commitment Decisions	✗	✓ Binary	✗	✗
Transmission Limits	✗	✗	✓	✓
Voltage Constraints	✗	✗	✗	✓
Reactive Power	✗	✗	✗	✓
Transmission Losses	✗	✗	✗	✓
Startup Costs	✗	✓	✗	✗
Ramping Limits	✗	✓	✗	✗
Min Up/Down Time	✗	✓	✗	✗
Reserve Requirements	✗	✓	✗	✗
Solving Speed	Fastest	Slow	Fast	Medium

Detailed Model Comparison

Economic Dispatch (ED)

graph TB
    A[Input: Demand, Costs] --> B["ED Solver (LP/QP)"]
    B --> C[Output: Dispatch]
    
    D[Ignores: 
Network, 
Time, 
Commitment]
    

• Strengths:

  • Fastest solving speed
  • Convex formulation
  • Easy to understand
  • Good for teaching
  • Merit order analysis

• Weaknesses:

  • No network constraints
  • May be infeasible in reality
  • Cost is lower bound only
  • No temporal dynamics

• Best for:

  • Screening studies
  • Fuel cost sensitivity
  • Technology comparisons
  • Educational purposes

→ ED Details

---

Unit Commitment (UC)

graph TB
    A["Input: 24h Profile"] --> B[UC Solver 
MIP]
    B --> C["Output: Schedule"]
    
    D[Includes: 
- Commitment uit 
- Startup costs 
- Ramping 
- Reserves]
    
    E[Ignores: 
- Network 
- Voltage 
- Reactive]
    

• Strengths:

  • Realistic scheduling
  • Startup/shutdown costs
  • Temporal constraints
  • Reserve provision
  • Day-ahead markets

• Weaknesses:

  • No network constraints
  • Slow (MIP)
  • May not be AC feasible
  • High memory usage

• Best for:

  • Day-ahead planning
  • Generator scheduling
  • Cycling cost analysis
  • Reserve studies

→ UC Details

---

DC Optimal Power Flow (DC-OPF)

graph TB
    A[Input: Network, Demand] --> B[DC-OPF Solver
LP]
    B --> C[Output: Dispatch + Flows]
    
    D[Includes:
- Transmission limits
- Power flow
- LMPs
- Congestion]
    
    E[Ignores:
- Voltage
- Reactive Q
- Losses]
    

• Strengths:

  • Network-aware
  • Fast (LP)
  • Locational prices (LMPs)
  • Congestion analysis
  • Always converges

• Weaknesses:

  • Voltage fixed
  • No reactive power
  • Ignores losses
  • DC approximation errors

• Best for:

  • Market clearing
  • LMP calculation
  • Congestion studies
  • Large-scale analysis

→ DC-OPF Details

---

AC Optimal Power Flow (AC-OPF)

graph TB
    A[Input: Full Network] --> B[AC-OPF Solver
NLP]
    B --> C[Output: Complete Solution]
    
    D[Includes:
- Full AC flow
- Voltages Vb
- Reactive Qi
- Losses]
    
    E[Challenges:
- Nonlinear
- Local optima
- May not converge]
    

• Strengths:

  • Complete physics
  • Voltage and reactive
  • Accurate losses
  • True feasibility
  • Highest accuracy

• Weaknesses:

  • Slower (NLP)
  • May not converge
  • Local optima possible
  • Sensitive to initialization

• Best for:

  • Feasibility validation
  • Voltage studies
  • Reactive planning
  • Detailed operations

→ AC-OPF Details

Selection by Application

Research Applications

• Decarbonization Studies

  • Primary: UC (capture cycling costs)
  • Secondary: DC-OPF (transmission needs)
  • Validation: AC-OPF (feasibility check)

• Renewable Integration

  • Primary: UC (ramping, reserves)
  • Secondary: DC-OPF (congestion from variable generation)
  • Detailed: AC-OPF (voltage impact)

• Transmission Planning

  • Primary: DC-OPF (congestion, LMPs)
  • Validation: AC-OPF (true flow limits)
  • Optional: UC (temporal patterns)

• Market Design

  • Primary: DC-OPF (locational pricing)
  • UC: Day-ahead commitment
  • Validation: AC-OPF (deliverability)

Operational Applications

• Day-Ahead Markets

  • Stage 1: UC (commitment schedule)
  • Stage 2: DC-OPF (dispatch + LMPs)
  • Post-analysis: AC-OPF (feasibility)

• Congestion Management

  • Primary: DC-OPF (identify constraints)
  • Validation: AC-OPF (verify relief)

Cost and Accuracy Trade-offs

Accuracy Ladder

graph LR
    A[ED 
Lower Bound] -->|+Network| B[DC-OPF 
Better]
    B -->|+Losses/Voltage| C[AC-OPF 
Accurate]
    
    D[UC 
+Temporal] -->|+Network| E[UC+DC-OPF 
Realistic]
    E -->|+AC| F[UC+AC-OPF 
Most Accurate]
    

Solver Capabilities

What Each Model Can Answer

1. Economic Dispatch (ED)

• Questions ED can answer:

  • What is the minimum possible generation cost?
  • Which generators should run based on merit order?
  • What is the system marginal price?
  • How do fuel prices affect dispatch?

• Questions ED cannot answer:

  • Is the dispatch AC feasible?
  • Are transmission lines overloaded?
  • What are the locational prices?
  • How should units be scheduled over time?

2. Unit Commitment (UC)

• Questions UC can answer:

  • Which units should be online each hour?
  • When should units start up and shut down?
  • What are the total cycling costs?
  • Are reserve requirements met?
  • How much ramping capability is needed?

• Questions UC cannot answer:

  • Are there transmission constraints?
  • What are locational prices?
  • Is reactive power adequate?
  • Are voltages within limits?

3. DC Optimal Power Flow (DC-OPF)

• Questions DC-OPF can answer:

  • Which transmission lines are congested?
  • What are locational marginal prices?
  • Where should new transmission be built?
  • How much does congestion cost?
  • What is the optimal dispatch with network?

• Questions DC-OPF cannot answer:

  • Are voltages acceptable?
  • Is reactive power sufficient?
  • What are the transmission losses?
  • How should units be scheduled over time?

4. AC Optimal Power Flow (AC-OPF)

• Questions AC-OPF can answer:

  • Is the dispatch truly feasible?
  • What are the actual voltages?
  • How much reactive power is needed?
  • What are the transmission losses?
  • Are generator capability curves violated?

• Questions AC-OPF cannot answer:

  • How should units be scheduled? (single period)
  • What are startup costs? (no commitment)

Speed vs. Accuracy

Pareto Frontier

graph TD
    A["Trade-off Space"]
    
    B["ED (Fastest, Least Accurate)"]
    C["DC-OPF (Fast, Medium Accuracy)"]
    D["UC (Slow, Good Temporal)"]
    E["AC-OPF (Medium, High Accuracy)"]
    F["UC+AC-OPF (Slowest, Best Overall)"]
    
    B --> C
    C --> E
    D --> F
    

Best Practices

Model Selection Checklist

1. Time horizon?

   • Single period → OPF
   • Multiple periods → UC

2. Network important?

   • No → ED/UC
   • Yes → DC-OPF/AC-OPF

3. Voltage critical?

   • No → DC-OPF
   • Yes → AC-OPF

4. Speed requirement?

   • Fast → ED/DC-OPF
   • Moderate → AC-OPF
   • Can wait → UC

5. Accuracy need?

   • Approximate → ED/DC-OPF
   • High → AC-OPF
   • Complete → UC + AC-OPF

Validation Strategy

flowchart LR
    A[Simplest Model] --> B[Run & Analyze]
    B --> C{Need more
accuracy?}
    C -->|Yes| D[Next Complex Model]
    C -->|No| E[Done]
    D --> B
    
    F[ED] --> G[DC-OPF]
    G --> H[AC-OPF]
    
    I[UC] --> J[UC + DC-OPF]
    J --> K[UC + AC-OPF]
    

• Progressive refinement:
  1. Start simple (ED or DC-OPF)
  2. Check if results reasonable
  3. Add complexity if needed
  4. Validate with more accurate model
  5. Iterate until confidence achieved

Next Steps

• Learn each model:
  • Economic Dispatch →
  • Unit Commitment →
  • DC Optimal Power Flow →
  • AC Optimal Power Flow →
• Start using KPG Run: Getting Started →