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Transmission Benefits and Cost Allocation under Ambiguity

Han Shu, Jacob Mays

Abstract

Disputes over cost allocation can present a significant barrier to investment in shared infrastructure. While it may be desirable to allocate cost in a way that corresponds to expected benefits, investments in long-lived projects are made under conditions of substantial uncertainty. In the context of electricity transmission, uncertainty combined with the inherent complexity of power systems analysis prevents the calculation of an estimated distribution of benefits that is agreeable to all participants. To analyze aspects of the cost allocation problem, we construct a model for transmission and generation expansion planning under uncertainty, enabling the identification of transmission investments as well as the calculation of benefits for users of the network. Numerical tests confirm the potential for realized benefits at the participant level to differ significantly from ex ante estimates. Based on the model and numerical tests we discuss several issues, including 1) establishing a valid counterfactual against which to measure benefits, 2) allocating cost to new and incumbent generators vs. solely allocating to loads, 3) calculating benefits at the portfolio vs. the individual project level, 4) identifying losers in a surplus-enhancing transmission expansion, and 5) quantifying the divergence between cost allocation decisions made ex ante and benefits realized ex post.

Transmission Benefits and Cost Allocation under Ambiguity

Abstract

Disputes over cost allocation can present a significant barrier to investment in shared infrastructure. While it may be desirable to allocate cost in a way that corresponds to expected benefits, investments in long-lived projects are made under conditions of substantial uncertainty. In the context of electricity transmission, uncertainty combined with the inherent complexity of power systems analysis prevents the calculation of an estimated distribution of benefits that is agreeable to all participants. To analyze aspects of the cost allocation problem, we construct a model for transmission and generation expansion planning under uncertainty, enabling the identification of transmission investments as well as the calculation of benefits for users of the network. Numerical tests confirm the potential for realized benefits at the participant level to differ significantly from ex ante estimates. Based on the model and numerical tests we discuss several issues, including 1) establishing a valid counterfactual against which to measure benefits, 2) allocating cost to new and incumbent generators vs. solely allocating to loads, 3) calculating benefits at the portfolio vs. the individual project level, 4) identifying losers in a surplus-enhancing transmission expansion, and 5) quantifying the divergence between cost allocation decisions made ex ante and benefits realized ex post.
Paper Structure (20 sections, 3 theorems, 17 equations, 7 figures, 7 tables)

This paper contains 20 sections, 3 theorems, 17 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Stochastic Expansion Planning
  3. Notation
  4. Formulation
  5. Establishing Beneficiaries
  6. Establishing a Counterfactual
  7. Generation
  8. Existing generators
  9. New generators
  10. Load
  11. Congestion Rents
  12. Multi-value Planning
  13. Cost Allocation
  14. Numerical Study
  15. Data and Study Assumptions
  16. ...and 5 more sections

Key Result

Theorem 1

Suppose new generation of type $g$ is constructed at bus $b$ in both the expansion scenario, i.e., $\Delta G^*_{0,b,g} > 0$, and the counterfactual scenario, i.e., $\Delta G'_{0,b,g} > 0$. Then existing generation of that type at that bus neither benefits nor suffers losses from the expansion, i.e.,

Figures (7)

  • Figure 1: An illustration of a scenario tree with 7 scenarios and $\mathcal{Y} = \{1,2,3,4\}$.
  • Figure 2: 8-Bus ERCOT network.
  • Figure 3: Benefit– cost ratio for different loads. While the benefit– cost ratio is consistent across all buses when cost allocation is determined on a portfolio basis, the project-by-project allocation can lead to cost being allocated to loads that do not benefit from the overall portfolio.
  • Figure 4: Expected benefits of existing generation of different generation technologies across buses derived from portfolio.
  • Figure 5: Benefits of the portfolio on out-of-sample tests in year 2028 ranked by social benefits.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • proof