Immune Procedure for Optimal Scheduling of Complex Energy Systems - Artificial Immune Systems - page 310

also this characteristic requires that energy is produced in a distributed way
all over the network. The energy management of this system needs to take into
account local loads and generators, with different nominal powers, reliability and
pollution levels and the possible presence of energy storage units. In addition,
all these characteristics and requirements change with time: for instance load
profiles, price of energy bought from or sold to the electrical network etc.. An
accurate scheduling of the system must ensure the use of the most economical
power sources, fulfilling operational constraints and load demand.
The management of the energy system requires the definition of the on/off
status of the machines and the identification of their optimal production profile
of them. When the start-up/shut-down profile is set, the problem can be ap-
proached by means of Linear Programming (LP). The definition of the on/off
status of the sources is referred to as scheduling and it requires the introduc-
tion of logical variables, which define in each time interval (e.g. one hour, one
quarter of an hour etc.) the power source availability. As a consequence, the
complete problem must deal with both continuous (power levels) and integer
(on/off status) variables. This problem can be stated as a Mixed Integer Linear
Programming problem (MILP) [1]. Even if this approach guarantees to find out
the global minimum of the cost function, the use of MILP needs a branch and
bound, or similar approaches, whose computational cost is shown to exponen-
tially increase with the number of branches. Instead of a full LP approach, an
heuristic optimization algorithm can be used to define the on/off status of the
power sources, leaving to an inner LP module the optimization of a particular
configuration. An Artificial Immune System (AIS) algorithm can be eciently
employed in this phase and its use is shown to be quite ecient if all operational
constraints are embedded inside the scheduling interval definition [2].
In this paper, a comparison of the two techniques, MILP and AIS-LP is pre-
sented, both approaches are described and comparisons are carried out in terms
of results accuracy and convergence speed to the optimum.

2 Definition of Energy Management Problem

The outline of the system under study is represented in Fig. 1, where:

- P e is the electrical power produced by the CHP;
- P t is the thermal power produced by the CHP;
- B t is the heat produced by a boiler which fulfills the thermal load when
production of electric power is neither needed nor economically convenient;
- D t is the heat produced in the thermodynamic cycle which is not used by
the thermal load and it is thus released into the atmosphere;
- P p and P s are the electrical power purchased from or sold to the external
network respectively;
- S t is the stored thermal energy;
- U e and U t are the electrical and thermal power required by the load;