The optimal design of energy hubs and CCHP systems consists in determini= ng the energy technologies (i.e., power generation units and energy storage= systems) to be installed and their sizes which minimize a certain cost fun= ction (e.g., the total annual cost given by annualized capital and operatin= g expenditures) while providing electricity, heating and cooling power to a= set of users. In the presence of multiple users and possible installation = sites, it is necessary to determine the units to be installed in each site = and the required energy network connections between sites.

The problem turns out to be a very challenging nonconvex MINLP [1-Elsido= et al, 2017] with a large number of binary variables because it has to inc= lude not only the design variables (units selection and sizes) but also the= operation variables and constraints for the whole system lifetime. Due to = the variable energy demand profiles and electricity prices, the loads of th= e installed units must be continuously adjusted so as to meet the demands a= nd maximize the revenues. Thus, when designing the system, the part-load pe= rformance and the operational flexibility (e.g., ramp constraints) must be = evaluated for the set of expected operating conditions. As a result, in mos= t formulations (see review in [1-Elsido et al, 2017]), the design optimizat= ion problem includes also the operational/scheduling problem (see Section 3= .1.2.2) with a considerable increase of problem size and complexity.

The design problem is more complex than the scheduling problem not only = for the larger number of variables and constraints (design + scheduling var= iables) but also for the nonlinearity of the functions relating units=E2=80= =99 sizes with energy efficiency (larger units feature higher energy effici= ency [1-Elsido et al., 2017]), and investment costs. The approaches propose= d to tackle the resulting nonconvex MINLP problem can be classified in two = main families:

- linearization of all the nonlinear functions so as to obtain a single l= arge scale linear problem (MILP) [2-Yokoyama 2002] and [3-Gabrielli et al 2= 017].
- decomposition of the problem into a design level (upper level or master= problem) and a scheduling level (lower level) [4-Iyer 1998] [5-Fazlollahi = 2014] [1-Elsido 2017]. At the upper level the selection and sizing of the u= nits is optimized by either solving a simplified (and linear) design & = operational problem [4-Iyer and Grossmann 1998] or using evolutionary algor= ithms [5-Fazlollahi 2014] [1-Elsido 2017]. At the lower level, for each fix= ed design solution, the operational scheduling problem is solved.

In order to limit the size of the problem, it is possible to reduce the = number of expected operating periods (i.e., days or weeks) by considering o= nly the most representative ones (i.e., =E2=80=9Ctypical days=E2=80=9D [5-F= azlollahi 2014] or =E2=80=9Ctypical weeks=E2=80=9D [1-Elsido et al 2017]). = Starting from historical data of the users=E2=80=99 energy demand, data clu= stering algorithms, such as the k-means algorithm [6- Hastie et al. 2006], = can be effectively used to group similar operating periods (i.e., days/week= s with similar profiles of energy demands) into clusters and select a few r= epresentative demand profiles to be included in the design problem.

**References**:

[1] Elsido C, Bischi A., Silva P., Martelli E., Two-stage MINLP algorith= m for the optimal synthesis and design of networks of CHP units, Energy 201= 7, 121, 403=E2=80=93426, doi:10.1016/j.energy.2017.01.014.

[2] Yokoyama R, Hasegawa Y, Ito K. A MILP decomposition approach to larg= e scale optimization in structural design of energy supply systems, Energy = Convers Manag 2002;43(6),771-790. Doi:10.1016/S0196-8904(01)00075-9.

[3] Gabrielli, G., Gazzani, M., Martelli, E., Mazzotti, M., 2017. Optima= l design of multi-energy systems with seasonal storage. Accepted for public= ation on Applied Energy (Elsevier).

[4] Fazlollahi, S., Bungener S.L., Mandel P., Becker G., Mar=C3=A9chal F= ., Multi-objectives, multi-period optimization of district energy systems: = I. Selection of typical operating periods, Computers and Chemical Engineeri= ng 2014, 65, 54=E2=80=9366, doi:10.1016/j.compchemeng.2014.03.005.

[5] Iyer R., Grossmann I., Synthesis and operational planning of utility= systems for multiperiod operation, Comput Chem Eng 1998, 22 (7), 979-93, d= oi: 10.1016/S0098-1354(97)00270-6.

[6] Hastie T, Tibshirani R, Friedman J., The elements of statistical lea= rning: data mining, inference and prediction. 2 ed. Springer; 2008.

**Contributors:**

Dr Aldo Bischi, Skolkovo Institute of Science an= d Technology

Dr Tiziano Parriani, Optit

Dr Emanuele Martelli, Politecnico di Milan=
o