Pricing the connection to an electricity distribution network Claude - PowerPoint PPT Presentation

Pricing the connection to an electricity distribution network Claude CRAMPES 1 Mathias LAFFONT 2 1 Toulouse School of Economics and Institut d’Economie Industrielle 2 Toulouse School of Economics (GREMAQ) 9th Conference on Applied Infrastructure Research - Regulation 1 C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 1 / 19

Figure: The electricity sector C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 2 / 19

Agenda presentation of the sector motivations sketch of the model results at first best linear price under budget constraint two-part tariffs conclusion C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 3 / 19

C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 4 / 19

Presentation of the sector (1/2) distribution networks’ characteristics: ◮ local natural monopoly: independent of the size of the region ◮ essential facility: ensuring a non-discriminatory access to all retailers definition of the institutional framework thanks to: ◮ European regulation ◮ national laws in every Member State, a regulatory entity (benchmarking, incentive regulation) C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 5 / 19

Presentation of the sector (2/2) changes in the business model in electricity distribution: ◮ embedded production sources (climatic challenges); ◮ historical distributors face new competitors (competition for the field) main challenges of the distributors: ◮ increasing the efficiency of the network by reducing the thermal losses ◮ developing smart grids ◮ ensuring the reliability of the network ◮ in some countries, they are in charge of the metering C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 6 / 19

Motivations absence of spatial considerations in the traditional economic literature whereas it is linked to the geographical characteristics of the considered region Key figures concerning the French distributor ERDF 1 : ◮ 1.3 million kilometer of lines ◮ 33 million households ◮ 36 000 employees ◮ 10 million interventions per year ◮ 240 000 new consumers connected to the network in 2009 ⇒ important fixed cost and huge investment for this activity 1 source: www.erdf.fr C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 7 / 19

Sketch of the model (1/2) spatial distribution of consumers: uniform distribution between 0 and ¯ θ mass of homogeneous consumers normalized to 1 the indirect net utility of being connected to the network for customers located at distance θ : v ( p e , K ) − T ( θ ) the alternative is to consume local electricity for which the net-utility is: v ( p a ) the marginal consumer: θ ( K ) = T − 1 � � ˆ v ( p e , K ) − v ( p a ) C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 8 / 19

Sketch of the model (2/2) social surplus from the distribution activity given the tariff T ( . ) : � ˆ � � θ ( K ) v ( p e , K ) − v ( p a ) − θ c � S ( K ) = dF ( θ ) − rK f ( θ ) 0 the distributor has a profit equal to: � � � ˆ θ ( K ) T ( θ ) − θ c dF ( θ ) − rK f ( θ ) 0 C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 9 / 19

Results at first best marginal consumer at first best: � θ ( c , K ∗ ) = ∆ v c ¯ θ interior solution for the maximization of the social surplus ⇒ S ” < 0 ⇒ ∂ 2 v /∂ K 2 << 0 under assumption of strong concavity of v , the level of installed capital is: v ( p e , K ∗ ) − v ( p a ) ∂ v ( p e , K ∗ ) = r (1) c ¯ θ 2 ∂ K Major drawbacks of implementing this solution: negative turnover of the operator: − rK ∗ price payed proportionally to distance ⇒ seen as discriminatory by politicians who favor “postage stamp” principle C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 10 / 19

Linear price and budget constraint (1/2) the program of the distributor under budget constraint is given by: � max S ( p , K ) (2) p , K � ˆ � � θ ( p , K ) c s . t . p − θ dF ( θ ) − rK � 0 (3) f ( θ ) 0 optimal linear price determined by the zero-profit condition and equal to: � 1 − 4 ¯ p SB = 1 − θ Ac (4) 2 A 2 rK ¯ θ where A = (5) [ v ( p e , K ) − v ( p a )] 2 C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 11 / 19

Linear price and budget constraint (2/2) the optimal level of capital follows: p e , K SB � 2 p SB − ¯ θ 2 ˆ ∂ p SB � p SB − ¯ � � � ∂ v ( p e , K SB ) � + v − v ( p a ) θ c θ c = r (6) − ¯ ¯ ∂ K p SB p SB θ p SB ∂ K θ Conclusion of the impact of the budget constraint: higher price than the marginal cost per consumer ⇒ weaker incentives of consumer to be connected the level of installed capital is lower than at first best ⇒ WTP of consumers is reduced ⇒ marginal consumer nearer to the source point and fewer number of connected customers C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 12 / 19

Figure: Linear tariff and budget constraint C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 13 / 19

Two-part tariffs (1/4) additional constraint: reduction of the difference in price payed between consumers towards a uniform tariff across customers intra-zone adjustment motivated by political decisions to fix uniform price uniform linear price vs two-part tariff two approaches for two-part tariff: ◮ two-part tariff and service constraint ◮ two-part tariff and marginal cost per kilometer C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 14 / 19

Two-part tariffs (2/4) Service constraint approach: aim is to achieve the first best ⇒ ˘ p , K ∗ ) = � θ ( c , K ∗ ) = ∆ v / c ¯ θ ( ˘ p f , ˘ θ p f , ˘ ˘ p maximizing welfare (under budget constraint) satisfies  � � p = ¯ 1 − A ∗ c ¯ < c ¯ ˘ θ c θ θ per kilometer  (7) � �  A ∗ c ¯ ˘ p f = v ( p e , K ∗ ) − v ( p a ) θ per consumer where A of eq. (5) is evaluated at K ∗ . role of the fixed part: ◮ balancing the operator’s budget ◮ implicit tax to consumers close to the head of the network and a subsidy to consumer far from it C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 15 / 19

Two-part tariffs (3/4) Figure: Two-part tariff under service constraint C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 16 / 19

Two-part tariffs (4/4) Marginal cost of kilometer per customer approach: variable part of the tariff such that: p = c / f ( θ ) fixed part ( p f ) used to balance the budget: � �� � � rK = v ( p e , K ) − v ( p a ) 1 − 2 ¯ � � p f = 1 − θ Ac (8) 2 ˇ F θ ( p f , p , K ) level of installed capital derived from: ∂ K + v ( p e , K f ) − v ( p a ) ∂ v ( p e , K f ) − p f ∂ p f = r (9) c ¯ c ¯ θ 2 θ 2 ∂ K Under this approach, K SB < K f < K ∗ ⇒ slighter distortion than in the non uniform linear tariff case. C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 17 / 19

Summary economic foundations to the pricing of access to electricity distribution networks by consumers first best and drawbacks of implementing it reduction of the network size because of budget constraint with two-part tariff ⇒ implementation of the first best at the cost of “redistributing” the revenue two-part tariff and marginal cost per kilometer ⇒ slighter distortion than in the non uniform linear tariff case C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 18 / 19

Extension relax some assumptions as the number of customers (here normalized to 1) and the distribution of the customers include thermal losses include embedded intermittent sources of electricity explore alternative topological characteristics of the network C. Crampes, M. Laffont (TSE) Distribution network Infraday 2010 19 / 19