Summary of EE722-L23

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

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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 Cost_i = λ × Penalty Factor_i
  • 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 C_i(P_Gi)
  • Subject to:
    ∑_i P_Gi = 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:
    ∂C_i/∂P_Gi = λ × Penalty Factor_i
  • Penalty Factor:
    Penalty Factor_i = 1 / (1 - ∂P_loss/∂P_Gi)
  • 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

Notable Quotes

— 15:29 — « The price at this node now is going to be 1 + 2k d into the marginal cost and it's no longer the same; the prices at both nodes have changed not because there is a transmission limit at play, rather you are considering losses. »

— 25:30 — « If you had a generator who when catering to demand leads to a whole lot more losses on the network versus you had an option to dispatch a generator who when catering to the demand leads to lesser amount of losses, which one would you dispatch? The less lossy one, correct? »

— 44:30 — « The system operator computes penalty factors using spatial temporal averaging of network conditions. It's very difficult to exactly attribute charges to the topology at the time of executing your trade because network topology keeps changing very often. »

— 48:51 — « Power engineers think of the slack bus as this one magic bus which is compensating for all the losses in the network. »

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Educational

Video