Dynamic Spatial Auction Market Models with General Cost Mappings

Abstract

The deregulation of electricity markets in Europe has deeply changed the organization of this sector. Vertically integrated generating companies have been unbundled to create competition and to increase the competitiveness of electricity markets. Directive 96/92/EC was issued by the European Commission to liberalize electricity markets and to pave the way for the creation of the Internal Electricity Market. In particular, this Directive aimed at promoting the competition in the activities of electricity generation and wholesale through the creation of a “marketplace” and the maximization of transparency and efficiency. Competition in European day-ahead electricity markets has been established through auction markets where electricity producers and consumers offer/bid prices and volumes. This paper suggests a dynamic equilibrium model for a system of auction markets linked by transmission lines and subject to energy balance and transmission constraints, such as those characterizing restructured electricity markets. This model is treated as a system of variational inequalities with arbitrary monotone mappings. An inexact splitting type method is proposed to find its solution. Numerical experiments are conducted on the Italian day-ahead electricity market.

Appendices

Appendix

1.1 A Definitions

In this Appendix, we explain the meaning of some abbreviations used throughout the paper.

1.2 A.1 Power Exchange (PX)

As indicated at page 15 of Directorate-General for Directorate-General for Energy and Transport ( 2008), “Electricity Power Exchanges (PXs) are voluntary trading platforms pro- posing standardized instruments and clearing services to their members. The range of the products traded on a power exchange varies from a single hour delivery of electricity on a predefined high voltage grid for the next day (or even the intra day) to an elaborate contract covering periods stretching to a couple of years. PX are organised in two interrelated parts - the physical and the forward segments. The physical segment covers the trade with contracts that are closest to maturity. The forward segment of the power exchange provides the platform for trading derivative contracts”

1.3 A.2 Transmission System Operator (TSO)

As indicated by the UCTE Operation Handbook-Glossary (2014), “a Transmission System Operator is a company that is responsible for operating, maintaining and developing the transmission system for a control area and its interconnections”. A control area usually coincides “with the territory of a company, a country or a geographical area, physically demarcated by the position of points for measurement of the interchanged power and energy to the remaining interconnected network, operated by a single TSO, with physical loads and controllable generation units connected within the control area (See pages G-4 and G-14).

B Notation

• $t=\{1, \dots , T\}$: Set of time subintervals;

• $i=\{1, \dots , N\}$: Set of auction markets (zones). In each zone, there are traders and buyers that participate to the auction mechanism. We define with S _i and Q _i the set of traders and buyers that respectively offer and bid in market i;

• $\alpha _{s,t}^{\prime }$: Lower bound imposed on the (electricity) offer submitted by trader (power producer) s at time t;

• $\beta _{s,t}^{\prime }$: Upper bound imposed on the (electricity) offer submitted by trader (power producer) s at time t;

• $\alpha _{q,t}^{\prime \prime }$: Lower bound imposed on the (electricity) bid submitted by buyer (power consumer) q at time t;

• $\beta _{q,t}^{\prime \prime }$: Upper bound imposed on the (electricity) bid submitted by buyer (power consumer) q at time t;

• $a_{s,t}^{g}$, $b_{s,t}^{g}$: Intercept and slope of the offer price function of power producer s participating to the auction organized in zone i at time t;

• $a_{i,t}^{h}$, $b_{i,t}^{h}$: Intercept and slope of the bid price function of consumers participating to the auction organized in zone i at time t;

• x _s,t : Offer submitted to the auction by trader s at time t;

• y _q,t : Bid submitted to the auction by buyer q at time t;

• u _i,t : Excess of (electricity) supply (u _i,t ≥0) or excess of (electricity) demand (u _i,t ≤0) in zone i at time t;

• f _{i j,t} : Electricity flow from zone i to zone j at time t;

• v _i,t : Electricity stored in zone i at time t;

• p _i,t : Electricity price resulting from the auction clearing in zone i at time t.

C Additional Data

In this section, we report additional data that have been used in our numerical experiments.

Table 4 Power transfer limits F _{i j} between zone i and zone j in nighttime and daytime

Table 5 Reference congestion costs c _{i j,t(f)} between zone i and zone j

Table 6 Values of parameters $\beta _{s,t}^{\prime }$ corresponding to the total available capacity owned by power producer s in zone i at time t

Table 7 Values of parameters $a_{s,t}^{g}$ and $b_{s,t}^{g}$ of the offer price function g _s,t

Table 8 Average generation level per power producer s and zone i

Table 9 Reference marginal production costs per power producer s and zone i

Table 10 Marginal production cost per zone i and technology

Table 11 Available capacity per power producer s, zone i, and technology

Table 12 Reference demand per time segment t and zone i

Table 13 Reference price per time segment t

Table 14 Values of parameters $\beta ^{\prime \prime }_{i,t}$ corresponding to the peak demand throughout 2012 at time t in market i (Case 1)

Table 15 Values of parameters $\alpha ^{\prime \prime }_{i,t}$ corresponding to average bid demand values submitted by consumer in zone i at time t to the Italian day-ahead market (Case 2)

Table 16 Operating costs r _i,t (v) and available capacity of pumped-storage hydro plant in zone i