**Redispatch-Based Electricity Trading**

Many E=
uropean countries have implemented a system of spot market trading of elect=
ricity that is redispatch-based [1]. Electricity is traded at power exchang=
es like the EEX in Leipzig, Germany. During these auctions, no or only a ce=
rtain part of the technical and physical constraints of electricity transpo=
rt through the transmission network are respected. For instance, in Germany=
, only a market clearing is imposed that yields the balance of traded produ=
ction and consumption. As a result of this drastic simplification, spot mar=
ket results do not have to be feasible with respect to transport through th=
e transmission network. If this turns out to be the case, traded quantities=
have to be redispatched such that the resulting quantities can actually be=
transported. Different systems of redispatch rules are implemented in Euro=
pe, e.g., cost-based redispatch in Austria, Switzerland, and Germany or mar=
ket-based redispatch in Belgium, Finland, France, or Sweden [2]). However, =
and independent of the actual redispatch system, this market design of spot=
market trading and redispatch yields a two-stage model that involves diffe=
rent agents and stakeholders like:

- producers owning conventional power plants or facilities for producing = power from renewables like sun or wind;
- consumers like municipal utilities or large industrial enterprises; and=
- transmission system operators (TSO) that control and maintain the trans= mission network and organize the redispatch.

It is shown in the literature that this system of electricity market des=
ign may yield significant decreases in total social welfare; see [2, 3] and=
the references therein. Thus, the natural question arises if and how diffe=
rent markets can be designed that yield higher welfare outcomes. This quest=
ion is currently an active field of research and involves the investigation=
of alternative systems like the introduction of zonal pricing [3, 4] or no=
dal pricing [3, 5].

**Mathematical Models**

From a =
mathematical point of view, the study of different market designs may intro=
duce the regulator or state as an additional agent that decides on certain =
questions like, e.g., the specification of the actual price zones in zonal =
pricing or the specification or regionally differentiated network fees. Sin=
ce the regulator or state anticipates the influence of his decisions on the=
actions of all other agents, such a rigorous mathematical modeling has imp=
ortant implications on the overall model, since the decisions of the regula=
ting agent couples all other levels of the system, yielding a (typically mi=
xed-integer) multilevel optimization; cf., e.g., [6].

These models =
are extremely hard to solve [7, 8, 9]. Hence, there is a politically and so=
cial need to develop new mathematical theory and algorithms for solving rea=
listic instances of these models.**References**

[1] The European Commission. Commission Regulation (EU) 2015/1222 of 24 J=
uly 2015 establishing a guideline on capacity allocation and congestion man=
agement. 2015.

[2] V. Grimm, A. Martin, M. Schmidt, M. Weibelzahl, =
and G. Zo=CC=88ttl. "Transmission and Generation Investment in Electricity =
Markets: The Effects of Market Splitting and Network Fee Regimes." In: Euro=
pean Journal of Operational Research 254.2 (2016), pp. 493=E2=80=93509. DOI=
: 10.1016/j.ejor.2016.03.044.

[3] P. Holmberg and E. Lazarczyk. "Co=
ngestion management in electricity networks: Nodal, zonal and discriminator=
y pricing." In: (2012). Research Institute of Industrial Economics (IFN). D=
OI: 10.2139/ssrn.2055655.

[4] V. Grimm, T. Kleinert, F. Liers, M. S=
chmidt, G. Z=C3=B6ttl. "Optimal Price Zones of Electricity Markets: A Mixed=
-Integer Multilevel Model and Global Solution Approaches." 2017. Submitted.=
Preprint available at http://www.op=
timization-online.org/DB_HTML/2017/01/5799.html

[5] Joskow, P. =
(2008). "Lessons learned from electricity market liberalization." In: The E=
nergy Journal 29.2, pp. 9=E2=80=9342.

[6] S. Dempe, V. Kalashnikov,=
G. A. Pe=CC=81rez-Valde=CC=81s, and N. Kalashnykova. "Bilevel Programming =
Problems." In: Energy Systems. Springer, Berlin (2015).

[7] X. Deng=
. "Complexity Issues in Bilevel Linear Programming." In: Multilevel Optimiz=
ation: Algorithms and Applications. Ed. by A. Migdalas, P. M. Pardalos, and=
P. Va=CC=88rbrand. Boston, MA: Springer US, 1998, pp. 149=E2=80=93164. DOI=
: 10.1007/ 978-1-4613-0307-7_6.

[8] M. R. Garey and D. S. Johnson. =
Computers and Intractability: A Guide to the Theory of NP-Completeness. New=
York, NY, USA: W. H. Freeman & Co., 1979.

[9] L. Vicente, G. S=
avard, and J. Ju=CC=81dice. "Descent approaches for quadratic bilevel progr=
amming." In: Journal of Optimization Theory and Applications 81.2 (1994), p=
p. 379=E2=80=93399. DOI: 10.1007/BF02191670.

**Contributor**:

Prof. Martin Schmidt, Friedrich-Alexander-Universit=C3=A4t Erlangen-N=C3= =BCrnberg