Equilibrium on a heat market under network
constraints
Natalia Mikhakhanova
Melentiev Energy Systems Institute Siberian Branch of the RAS, Irkutsk, Russia
[email protected]
The mathematical model of the electricity market and heat is defined as
follows. As the basis the article [1] was used with the addition of the network
structure of the market. Consider power system with I nodes i = 1, . . . , I in which
there are participants of market: various types of plants producing electric power
P and plants producing heat Q, as well as the agents consuming electric power
x and heat y (for details [1]).Each consumer has an utility function FiCE for
agents consuming electricity and FiCH for heat.
FiCE = cei xi − rie x2i ; FiCH = chi yi − rih yi2 ,
(1)
Consider the objective function which is a public welfare of this power system,
so the consumers maximize their utility functions and the producers minimize
their costs. Therefore we are maximizing the welfare:
F =
n
X
FiCE
+
i=1
n
X
FiCH − F COST → max,
(2)
i=1
where:
F COST =
n
X
tec
atec
+ Qtec
i (qPi
i )+
i=1
n
X
kes
akes
+
i Pi
i=1
n
X
kot
akot
i Qi ,
(3)
i=1
We need to write the equations of network balance:
xi =
n
X
Pi +
i=1
yi =
n
X
i=1
Qi +
n
X
dij (1 − δij )vji −
n
X
j=1
j=1
n
X
n
X
dij (1 − δij )wji −
j=1
n
X
i=1
Pitec = b
dij vij ,
(4)
dij wij ,
(5)
j=1
n
X
Qtec
i ,
(6)
i=1
wij ≤ wM axij ; vij ≤ vM axij .
where:
dij is a matrix showing the network structure;
vij is a flow of electric power between nodes ;wij is a flow of heat power;
δij is s the percentage of losses ;
The results of numerical experiments are presented.
(7)
2
Natalia Mikhakhanova
References
1. Molodyuk, V.,V.: A mathematical model of the power plant operation on the
market of electricity and heat. Energy specialist, 12-16 (2014) (In russian)]