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Testing regulatory regimes for power transmission expansion with fluctuating demand and wind generation

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Abstract

Adequate extension of electricity transmission networks is required for integrating fluctuating renewable energy sources, such as wind power, into electricity systems. We study the performance of different regulatory approaches for network expansion in the context of realistic demand patterns and fluctuating wind power. In particular, we are interested in the relative performance of a combined merchant-regulatory price-cap mechanism compared to a cost-based and a non-regulated approach. We include both an hourly time resolution and fluctuating wind power. This substantially increases the real-world applicability of results compared to previous analyses. We show that a combined merchant-regulatory regulation, which draws upon a cap over the two-part tariff of the transmission company, leads to welfare outcomes superior to the other modeled alternatives. This result proves to be robust over a range of different cases, including such with large amounts of fluctuating wind power. We also evaluate the outcomes of our detailed model using the extension plans resulting from a simplified model based on average levels of load and wind power. We show that this distorts the relative performance of the different regulatory approaches.

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Notes

  1. Schill (2014) studies the effects of fluctuating wind and solar power generation on German residual load patterns.

  2. While we focus on regulated transmission expansion in the Western European transmission system, Egerer and Schill (2014) analyze RES-related network expansion requirements within the German system, taking also into account investments into power plants and storage.

  3. For an Italian case study, Boffa et al. (2010) find that transmission expansion leads to cost savings for consumers. In our paper, we show that while removing congestion in the Western European interconnection harms consumers in Germany and France because of increasing spot prices, consumers in Belgium and the Netherlands benefit from network expansion.

  4. During the 1990s, an ‘uplift management rule’ was applied in England and Wales (Léautier 2000). Such a rule made the Transco responsible for the full cost of an ‘out-turn’ plus any transmission losses. The out-turn defined the cost of congestion as the difference between the price actually paid to generators and the price that would have been paid absent congestion. In Norway, a revenue-cap approach—which precludes having to exactly define the output produced by a Transco—has also been used in practice (Jordanger and Grønli 2000).

  5. See Rosellón and Kristiansen (2013) for a detailed analysis on theory and practice of FTR auctions. There is shown the practical international implementation of such auctions as well as a discussion on its potential application in Europe.

  6. See Rosellón et al. (2012). Under a conventional linear definition of the transmission output—similar to the output definition for other economic commodities—well-behaved cost and demand functions may not hold in an electricity network with loop flows (see Wu et al. 1996). Decreasing marginal cost segments and discontinuities in costs can arise during a transmission expansion project.

  7. The HRV model aims to be applicable for any expansion project and in any type of transmission topology. Its piecewise differentiability and continuity is analyzed in Rosellón et al. (2012) and tested in Rosellón and Weigt (2011), Rosellón et al. (2011), and Ruíz and Rosellón (2012).

  8. More precisely, congestion rents are redistributed to FTR holders. The Transco’s FTR auction revenues thus include these payments. As we do not explicitly model FTR auctions, we make the simplifying assumption that congestion rent is transferred to the Transco.

  9. Gabriel et al. (2013) give an introduction to complementarity modeling in energy markets. Further mathematical background is provided by Facchinei and Pang (2003).

  10. Hobbs et al. (2000) were among the first to apply an MPEC approach to power market modelling.

  11. We assume that the power plant fleet does not change over the whole modeled period. In the real world, we would expect interactions between generation capacity investments and transmission investments, as shown both theoretically and numerically by Sauma and Oren (2006). In a companion paper, we study the impact of a changing generation mix on both welfare-optimal and regulated transmission investment (Egerer et al. 2015).

  12. We do not consider capital costs of the initial network or operational expenses of the Transco.

  13. Note that this requires the regulator to have sufficient knowledge about which lines should be increased.

  14. The distribution of the total capacity among the different nodes on Belgium and the Netherlands is in line with original COMPETES data used in Neuhoff et al. (2005).

    Table 2 Variable generation costs and available capacity
  15. Because of a lack of data, we use the German wind feed-in pattern for the other countries, as well.

  16. Sensitivity tests have shown that other random assignments of hourly wind feed-in values lead to very similar results.

  17. Additional model runs with returns on costs higher than 8 % show that results hardly differ. There are two reasons for this finding: (i) we do not allow the Transco to increase line capacities beyond the levels of the welfare-maximizing benchmark; (ii) additional profits related to cost-regulation are small compared to related losses in congestion rents.

  18. For actual extension cost assumptions approved by the German regulator, see Hertz et al. (2012), Appendix 9.3.

  19. We use appropriate weights for winter, summer and shoulder days, distinguishing weekdays and weekends.

    Fig. 5
    figure 5

    Line extension results (final period)

  20. We accordingly calculate network expansion benefits of around €77,000 per MW between Germany and France, €72,000 per MW between Germany and the Netherlands, and €17,000 per MW between the Netherlands and Belgium. Note that these are indicative values that do not reflect loop flows in the system. Moreover, the marginal benefit of line extension substantially decreases with increasing investments because nodal price differences are levelled.

  21. Note that we allow for continuous line extension. In the real world, line investments are lumpy. Accounting for indivisibilities may lead to different HRV results. Finding optimal solutions of discretely constrained MPECs, however, would be extremely challenging. Notwithstanding, Rosellón et al. (2012) suggest that lumpiness should not stand in the way of applying price-cap incentive mechanisms to real-world transmission expansion.

    Fig. 6
    figure 6

    Time path of overall network extension

  22. For Belgium and the Netherlands, average values are provided.

    Fig. 7
    figure 7

    Hourly nodal prices before network extension

  23. Strictly speaking, Transco profits are not defined in NoExtension and WFMax, as welfare is maximized in these cases. However, we interpret congestion rents as Transco profits in these cases.

    Table 4 Welfare results (baseline): differences to case without extension in bn €
  24. In WFMax, unweighted average prices increase by around 2 % in Germany and 16 % in France, whereas prices in Belgium and the Netherlands decrease by 16 and 14 %, respectively.

  25. This approach is comparable to Birge’s determination of the value of a stochastic solution (Birge 1982).

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Acknowledgments

The authors thank two anonymous referees, Jean-Michel Glachant, Bill Hogan, Thomas-Olivier Léautier, Christian von Hirschhausen, as well as the participants of the IDEI-Toulouse Conference 2011 and the IAEE International Conference 2011 for helpful comments. We also thank Özge Özdemir of ECN for providing us with network data. Juan Rosellón acknowledges support from a Marie Curie International Incoming Fellowship within the \(7\mathrm{th}\) European Community Framework Programme, as well as from Conacyt (p. 131175).

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Appendix

Appendix

1.1 ISO’s constrained welfare maximization problem

$$\begin{aligned}&\mathop {\mathop {\mathop {\max }\limits _{q,g,\Delta ,}}\limits _{\lambda _1 ,\lambda _2 ,p,}} \limits _{\lambda _4 ,\lambda _5 ,} \sum \limits _{t\in T} {\left( {\sum \limits _{\tau \in \mathrm{T}} {\sum \limits _{n\in N} {\left( {\int \limits _0^{q_{_{n,t,\tau } }^{*} } {p_{n,t,\tau } (q_{n,t,\tau } )d} q_{n,t,\tau } -\sum \limits _{s\in S} {c_s g_{n,s,t,\tau } } } \right) } } \frac{1}{\left( {1+\delta _s } \right) ^{t-1}}} \right) } \nonumber \\&\begin{array}{lll} s.t. \quad \sum \limits _n {\frac{I_{l,n} }{X_{l,t} }} \Delta _{n,t,\tau } -P_{l,t} \le 0 &{} (\lambda _{1,l,t,\tau } ) &{} \forall l,t,\tau \\ \qquad \quad -\sum \limits _n {\frac{I_{l,n} }{X_{l,t} }} \Delta _{n,t,\tau } -P_{l,t} \le 0 &{} (\lambda _{2,l,t,\tau } ) &{} \forall l,t,\tau \\ \qquad \quad \sum \limits _s {g_{n,s,t,\tau } } -\sum \limits _{nn} {B_{n,nn} } \Delta _{nn,t,\tau } -q_{n,t,\tau } =0 &{} (p_{n,t,\tau } ) &{} \forall n,t,\tau \\ \qquad \quad g_{n,s,t,\tau } -\bar{{g}}_{n,s} \le 0 &{} (\lambda _{4,n,s,t,\tau } ) &{} \forall n,s,t,\tau \\ \qquad \quad slack_n \Delta _{n,t,\tau } =0 &{} (\lambda _{5,n,t,\tau } ) &{} \forall n,t,\tau \\ \end{array} \end{aligned}$$
(17)

1.2 Solution routine

Due to the non-convex nature of our MPEC problem, the NLPEC solver only generates local optima instead of unique global optima. We aim to get as closely as possible to global optima by using numerous different starting points. This could in principle be implemented by using randomized starting points. This, however, is not an option as the solver fails to find feasible solutions—let alone optimal ones—from most random starting points we have tried. Instead, we develop a routine of (i) finding feasible starting points, and (ii) searching for optima starting from these feasible points. First, we solve all regulatory cases—as well as the welfare-maximizing benchmark—with the extension variable fixed to zero. This leads to feasible solutions in all cases; afterwards, we release the extension variable and solve again. Second, we solve all regulatory cases using the welfare-optimal solution as a starting point. Third, we iteratively solve all regulatory cases one after another several times, each starting from the solution of the previous one. In all cases, we solve the same problem three times in a row, as we have found the CONOPT solver to find slightly better solutions if the solve is repeated in some instances. The solution point file is updated every time a better solution is found. After several iterations, we find convergence to some characteristic local optima, which are then considered to be global optima.

For the HRV case, the first option (starting with fixed extension and relaxing the extension variable afterwards) always leads to the best results. In contrast, the NoReg and CostReg cases often improve substantially during the second and third steps of our search routine. Due to the size of the numerical problem and the extensive search process, finding good solutions for all regulatory cases requires more than 600 h of computation time even on a high-performance computer. Some sensitivities take even longer.

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Schill, WP., Egerer, J. & Rosellón, J. Testing regulatory regimes for power transmission expansion with fluctuating demand and wind generation. J Regul Econ 47, 1–28 (2015). https://doi.org/10.1007/s11149-014-9260-0

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