Removing Cross-Border Capacity Bottlenecks in the European Natural Gas Market—A Proposed Merchant-Regulatory Mechanism

Abstract

We propose a merchant-regulatory framework to promote investment in the European natural gas network infrastructure based on a price cap over two-part tariffs. As suggested by Vogelsang (J Regul Econ 20:141–165, 2001) and Hogan et al. (J Regul Econ 38:113–143, 2010), a profit maximizing network operator facing this regulatory constraint will intertemporally rebalance the variable and fixed part of its two-part tariff so as to expand the congested pipelines, and converge to the Ramsey-Boiteaux equilibrium. We confirm this with actual data from the European natural gas market by comparing the bi-level price-cap model with different reference cases. We analyze the performance of the regulatory approach under different market scenarios, and identify relevant aspects that need to be addressed if the approach were to be implemented.

Appendix

For the MPEC formulation the optimization problem defined in Section 3.1.1 is reformulated as Mixed Complementarity Problem (MCP) by deriving the KKT conditions. In addition to the variables presented in Section 3 the shadow prices on the different capacity constraints are indicated by λ and the shadow price on the storage balance by μ. The demand function P(D) is represented by a linear function in the form of P = a – bD, with a and b as intercept and slope of the function, respectively. Only the shadow variable on the storage balance, μ, and the nodal price, P, are free variables; all other variables are positive with a lower bound of zero. The MCP formulation of the lower level problem is as follows:

$$ \begin{array}{ccc}\hfill {P}_{n,y,s}-\left({\mathrm{a}}_{n,y,s}-{\mathrm{b}}_{n,y,s}{\mathrm{D}}_{n,y,s}\right)\ge 0\perp \hfill & \hfill {\mathrm{D}}_{n,y,s}\ge 0\hfill & \hfill \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{cccc}\hfill {c}_{n,y}+{\lambda}_{n,y,s}^{prod}-{P}_{n,y,s}\ge 0\hfill & \hfill \perp \hfill & \hfill {\mathrm{G}}_{n,y,s}\ge 0\hfill & \hfill \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(16)

$$ t{c}_{n,m,y}^{pipe}+{\lambda}_{n,m,y,s}^{pipe}-{P}_{m,y,s}+{P}_{n,y,s}\ge 0\perp {T}_{n,m,y,s}^{pipe}\ge 0\forall n,\kern0.5em m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se $$

(17)

$$ t{c}_{n,m,y}^{LNG}+{\lambda}_{n,m,y,s}^{LNG}+\frac{1}{\eta^{{}_{liq}}}{\lambda}_{n,m,y,s}^{liq}+{\eta}^{reg}{\lambda}_{n,m,y,s}^{reg}-{P}_{m,y,s}+{P}_{n,y,s}\ge 0\perp {T}_{n,m,y,s}^{LNG}\ge 0\forall n,\kern0.5em m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se $$

(18)

$$ \begin{array}{llll}{\mu}_{n,y,s}^{store}-{\mu}_{n,y,s+1}^{store}+{\lambda}_{n,y,s}^{store}-{\lambda}_{n,y,s}^{store\_ out}\ge 0\hfill & \perp \hfill & {\mathrm{S}}_{n,y,s}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(19)

$$ \begin{array}{llll}{P}_{n,y,s}-{\eta}^{store}{\mu}_{n,y,s}^{store}\ge 0\hfill & \perp \hfill & {S}_{n,y,s}^{in}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{llll}-{P}_{n,y,s}+{\lambda}_{n,y,s}^{store\_ out}+{\mu}_{n,y,s}^{store}\ge 0\hfill & \perp \hfill & {S}_{n,y,s}^{out}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(21)

$$ \begin{array}{llll}ca{p}_{n,y}^{prod}-{G}_{n,y,s}\ge 0\hfill & \perp \hfill & {\lambda}_{n,y,s}^{prod}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(22)

$$ \begin{array}{llll}ca{p}_{n,m,y}^{pipe}-{T}_{n,m,y,s}^{pipe}\ge 0\hfill & \perp \hfill & {\lambda}_{n,m,y,s}^{pipe}\ge 0\hfill & \forall n,\kern0.5em m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{llll}ca{p}_{n,m,y}^{LNG}-{T}_{n,m,y,s}^{LNG}\ge 0\hfill & \perp \hfill & {\lambda}_{n,m,y,s}^{LNG}\ge 0\hfill & \forall n,\kern0.5em m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{llll}ca{p}_{n,m,y}^{liq}-{\displaystyle \sum_m\frac{1}{\eta^{{}_{liq}}}{T}_{n,m,y,s}^{LNG}}\ge 0\hfill & \perp \hfill & {\lambda}_{n,m,y,s}^{liq}\ge 0\hfill & \forall n,\kern0.5em m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{llll}ca{p}_{n,m,y}^{reg}-{\displaystyle \sum_m{\eta}^{reg}{T}_{m,n,y,s}^{LNG}}\ge 0\hfill & \perp \hfill & {\lambda}_{n,m,y,s}^{reg}\ge 0\hfill & \forall n,\;m\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

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$$ \begin{array}{llll}ca{p}_{n,y}^{store}-{S}_{n,y,s}\ge 0\hfill & \perp \hfill & {\lambda}_{n,y,s}^{store}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(27)

$$ \begin{array}{llll}{S}_{n,y,s}-{S}_{n,y,s}^{out}\ge 0\hfill & \perp \hfill & {\lambda}_{n,y,s}^{store\_ out}\ge 0\hfill & \forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se\hfill \end{array} $$

(28)

$$ {S}_{n,y,s}-{S}_{n,y,s-1}-{\eta}^{store}{S}_{n,y,s}^{in}+{S}_{n,y,s}^{out}=0,{\mu}_{n,y,s}^{store}\kern0.5em free\forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se $$

(29)

$$ {G}_{n,y,s}+{S}_{n,y,s}^{out}+\sum_m{T}_{m,n,y,s}^{pipe}+\sum_m{T}_{m,n,y,s}^{LNG}-{D}_{n,y,s}-{S}_{n,y,s}^{in}-\sum_m{T}_{n,m,y,s}^{pipe}-\sum_m{T}_{n,m,y,s}^{LNG}=0,{P}_{n,y,s}\kern0.5em free\forall n\in No,\kern0.5em y\in Ye,\kern0.5em s\in Se $$

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The regulatory model (Regulated) consists of the objective function (Eq. 10), the regulatory constraint (Eq. 11), the new investment definition (Eq. 13) and the above described MCP formulation of the market clearing with new capacity (invested by the Transco) added as indicated by Eq. 12. For reference simulations with a purely profit maximizing Transco (Profit Based) the regulatory constraints (Eq. 11) is omitted and the fixed fee F is set to zero, otherwise the model is identical to the regulatory model. For the Welfare Benchmark model the upper level is changed by replacing the profit objective with the welfare objective function (Eq. 14) and omitting the regulatory constraint. The remainder of the model is again similar to the regulatory model. The No Extension base case counterfactual consists only of the above described MCP model.

In the welfare-optimal benchmark problem of 3.1.3 (the basic market model, No Extension), the objective function is concave (thus, with convex level curves), and the constraints define convex sets. Therefore, the theorem of separating hyper planes applies. For the bi-level programming model in the regulatory model (Subsection 3.1.2, Regulated), under convexity of the choice set in the lower-level problem, the KKT conditions are necessary and sufficient so that inserting them into the upper-level provides a solution (see Gabriel et al. 2013).

The MPEC models are incorporated into GAMS and solved using the NLPEC solver while the MCP base case model is solved using PATH. The solve options for NLEPC are set to utilize inner-product reformulation of the MPEC formulation which transfers the lower level MCP into a system of equalities and inequalities while retaining the upper level equations in their stated form (NLPEC solver manual, section 3.1). Other solver options (e.g., penalty approaches) led to a reduced performance and lower objective values.

The obtained solutions are necessarily only local optima. All models are solved using the same starting point (the solution of the base case MCP model, which provides all market outcomes when no extensions take place). We performed tests with multiple other starting points (e.g., no preliminary market results, arbitrary extension patterns). However, they all provide a slightly lower objective value while the basic result pattern remained unchanged. The Welfare Benchmark model can also be solved without reformulation as MPEC by keeping the welfare objective (Eq. 14) and the basic market representation (Eqs. 2–9) adjusted for the new capacity extension (Eqs. 12 and 13). This version of the Welfare Benchmark model is a quadratically constrained programming (QCP) problem due to the quadratic part in the objective function (the gross consumer surplus) while all other aspects remain linear. The QCP version can be solved using the CPLEX solver providing the global optima to the problem.

Comparing the results of the derived local optima obtained from the MPEC solution with the global optima of the QCP solution shows a difference in the resulting welfare value of ca. 0.01 %. The main differences between the two solutions are the exact timing and quantity of the added capacity, although the general extension pattern with respect to corridors, overall quantity and time schedule is similar. The development of consumer and producer surplus, demand, production, and prices are identical in both model formulations. Thus, the MPEC version of the Welfare Benchmark provides a respectable fit to the global solution. As the Regulated model in turn converges towards the Welfare Benchmark we consider the obtained locational end results as sufficient for our analysis.

If the spatial and temporal resolution is to be extended and more complex market structures (e.g. strategic company behavior on the wholesale market) or investment behavior (e.g. lumpiness and decommissioning) are to be considered the NLPEC reformulation may not be sufficient requiring direct model reformulations/decompositions of the underlying MPEC model (e.g., see Gabriel and Leuthold 2010; Siddiqui and Gabriel 2013).