Summary of "EE722-L23"

Summary of EE722-L23 Video: Accounting for Network Losses in Economic Dispatch and Pricing

Main Ideas and Concepts:

Importance of Network Losses in Power Systems:
- Previous pricing and dispatch models ignored the resistance (R) of transmission lines.
- Resistance causes power losses (I²R losses) which must be accounted for in dispatch decisions and pricing.
- Losses lead to additional generation requirements and affect the Economic Dispatch and electricity prices.
Nature of Network Losses:
- Losses are proportional to the square of the current (I²R).
- Current is related to power demand; thus, losses can be approximated as proportional to the square of demand (Losses ≈ K × D²).
- Losses cause heating and thermal constraints but also result in energy that must be compensated.
Impact of Losses on Pricing:
- Without losses, prices at generation and demand nodes are equal (marginal cost of generation).
- Including losses leads to higher prices at demand nodes due to additional generation needed to compensate losses.
- Price at demand node = marginal cost × (1 + 2K × D), reflecting loss compensation.
- Losses cause price differentiation even without transmission constraints.
Modeling Losses:
- Losses can be represented by quadratic functions involving generation outputs at different nodes.
- Loss expressions often use B-coefficients representing constant, linear, and quadratic terms of generation.
- Actual loss modeling is complex due to network topology, load locations, and demand patterns.
- Simplified models consider average or peak demand scenarios for practical pricing and dispatch.
Economic Dispatch Including Losses:
- Objective: Minimize total generation cost subject to demand plus losses.
- Losses are incorporated as functions of generation outputs.
- Optimality condition for dispatch changes to: Marginal Costi = λ × Penalty Factori
- Penalty Factor > 1 means the generator increases losses (dispatch reduced).
- Penalty Factor < 1 means the generator reduces losses (dispatch increased).
- Dispatch decisions are adjusted to favor generators that contribute less to losses, even if marginal costs are identical.
Penalty Factor and Marginal Losses:
- Penalty Factor is derived from the sensitivity of losses to generator output changes.
- It is related to the change in losses caused by a change in generation relative to the change in demand.
- The Slack Bus (reference node) compensates for all Network Losses.
- The Penalty Factor influences the effective marginal cost used in dispatch.
Point of Connection Charges and Market Implications:
- Loss compensation is handled through Point of Connection Charges at injection and withdrawal nodes.
- These charges are usually pre-computed and published for market participants.
- Dispatch decisions and trades are distinct concepts:
  - Dispatch: Operator decides generation levels to meet demand efficiently.
  - Trade: Contractual agreement between buyers and sellers, which may or may not align with dispatch outcomes.
- Market participants may not know exact real-time penalty factors due to network topology changes but have access to averaged or forecasted charges.

Methodology / Instructions for Incorporating Losses in Dispatch and Pricing:

Step 1: Approximate Losses
- Model losses as Loss = K × D² where D is demand or generation.
- Use power flow studies or analytical approximations to estimate K.
Step 2: Formulate Economic Dispatch Problem
- Minimize total generation cost: min ∑i Ci(PGi)
- Subject to: ∑i PGi = D + Losses
- Losses expressed as a function of generation outputs.
Step 3: Derive Optimality Conditions
- Use Lagrangian and first-order conditions to relate marginal cost and Penalty Factor: ∂Ci/∂PGi = λ × Penalty Factori
- Penalty Factor: Penalty Factori = 1 / (1 - ∂Ploss/∂PGi)
- Calculate penalty factors based on sensitivity of losses to generation changes.
Step 4: Adjust Dispatch According to Penalty Factors
- Generators with Penalty Factor < 1 dispatched more (reduce losses).
- Generators with Penalty Factor > 1 dispatched less (increase losses).
Step 5: Determine Locational Prices
Price