ETEM-SG: Optimizing Regional Smart Energy System with Power Distribution Constraints and Options

Abstract

This paper gives a detailed description of the ETEM-SG model, which provides a simulation of the long -term development of a regional multi-energy system in a smart city environment. The originality of the modeling comes from a representation of the power distribution constraints associated with intermittent and volatile renewable energy sources connected at the transmission network like, e.g., wind farms, or the distribution networks like, e.g., roof top PV panels). The model takes into account the options to optimize the power system provided by grid-friendly flexible loads and distributed energy resources, including variable speed drive powered CHP micro-generators, heat pumps, and electric vehicles. One deals with uncertainties in some parameters by implementing robust optimization techniques. A case study, based on the modeling of the energy system of the “Arc Lémanique” region, shows on simulation results, the importance of introducing a representation of power distribution constraints, and options in a regional energy model.

Appendix ETEM shell formulation

1.1 A.1 Sets, Parameters, and Variables

1.1.1 A.1.1 Sets

They provide a nomenclature of all the elements in the energy model.

Θ ::

set of periods

S ::

set of timeslices

C ::

set of commodities

L ::

set of regions

P ::

set of technologies

POL ::

set of emission types

P_PROD[c]⊂P::

set of technologies that are producing commodity c∈C

P_CONS[c]⊂P::

set of technologies that are consuming commodity c∈C

P_MAP[l]⊂P ::

set of technologies that are installed in region l∈L

C_MAP[p]⊂C ::

set of commodities that are input or output for technology p∈P

C_ITEMS[flow_act[p]]⊂C ::

set of commodities in the activity flow

C _s ::

set of storage commodities

SUCC[s] ::

successive timeslice of s∈S used for storage

1.1.2 A.1.2 Parameters

These are values that must be entered by the user. The complete definition of all the parameters constitutes the database of the model.

Economic parameters: they are used to define the objective function.

disc_rate::

Annual discount rate

nb_years [t]::

Number of years in period t∈Θ

cost_icap [t, p]::

Unit cost of capacity increase for technology p at period t

fixom [t, p]::

Fixed maintenance cost per unit of installed capacity for technology p at period t

varom [t, p]::

Variable cost per unit of activity level for technology p at period t

cost_imp [t, s, c]::

Unit cost of import for commodity c in region s at period t

cost_exp [t, s, c]::

Unit cost of export for commodity c in region s at period t

cost_deliv [t, s, p, c]::

Unit cost of delivery for commodity c in technology p in region s at period t

taxe [t, π]::

Unit emission tax for pollutant π at period t

salvage [t, p]::

Salvage value (in %) of technology p that has been installed in period t

avail [p]::

Date of availability of technology p

life [p]::

Life duration of technology p.

Parameters Related to Demands:

network_efficiency [c]::

Global efficiency (≤ 1) of distribution network for commodities other than electricity. The losses in the power distribution networks will be considered in the module representing the activities related to power distribution.

frac_dem [t, s, c]::

Fraction of (useful) demand for commodity c occurring in timeslice s of period t

demand [t, c]::

Useful demand for commodity c in period t.

Parameters Related to Technology Capacities:

avail_factor [t, s, p]::

Availability factor

cap_act [p]::

Capacity factor (translates power into energy)

fraction [s]::

Duration of time slice s in fraction of year

fixed_cap [t, l, p]::

Residual capacity.

Parameters Defining Bounds:

act_bnd_lo [t, s, l, p]::

Lower bound on activity

act_bnd_up [t, s, l, p]::

Upper bound on activity

imp_tot_bnd_lo [t, c]::

Lower bound on import

imp_tot_bnd_up [t, c]::

Upper bound on import

exp_tot_bnd_lo [t, c]::

Lower bound on export

exp_tot_bnd_up [t, c]::

Upper bound on export

cap_bnd_lo [t, l, p]::

Lower bound on capacity

cap_bnd_up [t, l, p]::

Upper bound on capacity

icap_bnd_lo [t, l, p]::

Lower bound on investment

icap_bnd_up [t, l, p]::

Upper bound on investment.

1.1.3 A.1.3 Variables

The decision variables are the following

COST::

System cost (value of objective function)

COM(Θ, S, L, P, C)::

Activity level; production or consumption of commodity C in region L for process P during timeslice S at period Θ

ICAP(Θ, L, P)::

Investment level (increase of capacity) for process P at period Θ and in region L

EXP(Θ, S, C)::

Exports of commodity C during timeslice S at period Θ

IMP(Θ, S, C)::

Imports of commodity C during timeslice S at period Θ

EMI(Θ, POL)::

Emission level of pollutant POL at period Θ resulting from activity levels.

1.2 A.2 Objective Function

The objective function is the total discounted system cost minus the salvage value of the residual life of equipments at the end of the planning period.

$$ \min \mathbf{COST} $$

(27)

with

$$\begin{array}{@{}rcl@{}} \mathbf{COST} & \ge & \sum\limits_{t\in{\Theta}} (1+ \text{disc\_rate})^{-\text{nb\_years}[t]} \left\{\sum\limits_{l \in L, p \in P\_MAP[l]} \text{cost\_icap}[t,p] \mathbf{ICAP}[t,l,p] \right.\\ && +\sum\limits_{l \in L, p \in P\_MAP[l]} \text{fixom}[t,p](\sum\limits_{\begin{array}{c} k\in\{0\dots t\}:\\ \text{life}[p] \ge k+1, \\ t-k\ge \text{avail[p]} \end{array}} \mathbf{ICAP}[t,l,p] \\&& \sum\limits_{s \in S} (\sum\limits_{l \in L, p \in P\_MAP[l]} \text{varom}[t,p] \sum\limits_{c \in C\_ITEMS[\text{flow\_act}[p]]} \mathbf{COM}[t,s,l,p,c] \\&&\left. +\sum\limits_{c \in IMP} \text{cost\_imp}[t,s,c] \mathbf{IMP}[t,s,c] -\sum\limits_{c \in EXP} \text{cost\_exp}[t,s,c] \mathbf{EXP}[t,s,c]\right.\\&& +\sum\limits_{\begin{array}{c} l \in L, p \in P\_MAP[l], \\c \in C\_MAP[p] \end{array}} \text{cost\_deliv}[t,s,p,c] \mathbf{COM}[t,s,l,p,c] )\\&&\left. +\sum\limits_{\pi\in POL}\text{taxe}[t,\pi] \mathbf{EMI}[t,\pi] \right.\\&&\left. - \sum\limits_{\begin{array}{c} l \in L, p \in P_{M}AP[l] : \\t\ge \text{avail}[p] \;\&\; (t+\text{life}[p])\ge T+1 \end{array}} \text{salvage}[t,p]\times \text{cost\_icap}[t,p]\mathbf{ICAP}[t,l,p] \right\} \end{array} $$

1.3 A.3 Constraints

1.3.1 A.3.1 Commodity Balance Equations

For each commodity, or energy form other than electricity, what is produced or imported, at each time slice must be greater or equal to what is consumed or exported. The case of electricity will be treated in the module describing power distribution activities.

$$\forall t \in {\Theta}, s \in S, c \in C$$

$$\begin{array}{@{}rcl@{}} ~\sum\limits_{l \in L, \,p \in P\_PROD[c] \cap P\_MAP[l]}\,(\mathbf{COM}[t,s,l,p,c] + \mathbf{IMP}[t,s,c])\times \text{network\_efficiency}[c]\\ \ge \sum\limits_{l \in L, p \in P\_CONS[c] \cap P\_MAP[l]} \mathbf{COM}[t,s,l,p,c] \\ +\text{frac\_dem}[t,s,c] \times \text{demand}[t,c] + \mathbf{EXP}[t,s,c] \end{array} $$

Capacity Bounds Production For each technology, what is produced is bounded by the available capacity.

$$\forall t \in {\Theta}, s \in S, c \in C, p \in \text{P\_MAP}[l]$$

$$\begin{array}{@{}rcl@{}} ~\sum\limits_{c \in C\_ITEMS[flow\_act[p]]}\mathbf{COM}[t,s,l,p,c]/\mathrm{act_{f}lo}[p,c] \\ < = \text{avail\_factor}[t,s,p]\times \text{cap\_act}[p]\times fraction[s]\times\\ (\sum\limits_{k \in 0 {\dots} t : \text{life}[p]\ge k+1, \; t-k \ge \text{avail}[p]} \mathbf{ICAP}[t-k,l,p]+\text{fixed\_cap}[t,l,p]) \end{array} $$

1.3.2 A.3.2 Balance Equations for Commodity Storage Between Time-Slices

For each storable energy, the amount of stored energy in a given timeslice is transferred to its successive timeslice with a reduction described by a loss factor storage_loss-factor.

$$\forall t \in {\Theta}, c \in C_{s}, s \in S $$

$$\begin{array}{@{}rcl@{}} (\sum\limits_{l \in L, p\in P\_PROD[c] \cap P\_MAP[l]} \mathbf{COM}[t,s,l,p,c])\times \text{storage\_loss-factor}[c] \\ = \sum\limits_{l \in L, p \in P\_CONS[c] \cap P\_MAP[l], \sigma in SUCC[s]} \mathbf{COM}[t,\sigma,l,p,c]; \end{array} $$

1.3.3 A.3.3 Activity bounds

Exogenously defined bounds on activity

$$\forall t \in {\Theta}, s \in S, l \in L, p \in \text{P\_MAP}[l]$$

.

$$\begin{array}{@{}rcl@{}} \text{act\_bnd\_lo}[t,s,l,p] \le \sum\limits_{c \in C\_ITEMS[flow\_act[p]]} \mathbf{COM}[t,s,l,p,c] \le \text{act\_bnd\_up}[t,s,l,p] \end{array} $$

1.3.4 A.3.4 Imports Bounds

Exogenously defined bounds on imports.

$$\forall t \in {\Theta}, s \in S, c \in C$$

$$\begin{array}{@{}rcl@{}} \text{imp\_tot\_bnd\_lo}[t\!,c] \!\le\! \sum\limits_{s \in S} \mathbf{\!IMP}[t\!,s\!,c] \!\le\! \text{imp\_tot\_bnd\_up}[t,c] \end{array} $$

1.3.5 A.3.5 Export Bounds

Exogenously defined bounds on exports.

$$\forall t \in {\Theta}, s \in S, c \in C$$

$$\begin{array}{@{}rcl@{}} \text{e{\kern-.2pt}x{\kern-.2pt}p{\kern-.2pt}\_t{\kern-.2pt}o{\kern-.2pt}t{\kern-.2pt}\_b{\kern-.2pt}n{\kern-.2pt}d{\kern-.2pt}\_l{\kern-.2pt}o}[t\!,\!c] \!\le\! {\sum}_{s \in S} \mathbf{\!EXP}[t,s,c] \!\le \text{exp\_tot\_bnd\_up}[t,c] \end{array} $$

1.3.6 A.3.6 Capacity Bounds

Exogenously defined bounds on capacity.

$$\forall t \in {\Theta}, l \in L, p \in \text{P\_MAP}[l]$$

$$\begin{array}{@{}rcl@{}} \text{cap\_bnd\_lo}[t,l,p] \le \sum\limits_{k \in 0{\dots} t : \text{life}[p]\ge k+1\, \&\, t-k\ge \text{avail}[p]} \mathbf{ICAP}[t-k,l,p]+\text{fixed\_cap}[t,l,p] \le \text{cap\_bnd\_up}[t,l,p] \end{array} $$

1.3.7 Investment Bounds

Exogenously defined bounds on investment.

$$\forall t \in {\Theta}, l \in L, p \in \text{P\_MAP}[l]$$

$$\begin{array}{@{}rcl@{}} \text{icap\_bnd\_lo}[t,l,p] \le \mathbf{ICAP}[t,l,p] \le \text{icap\_bnd\_up}[t,l,p] \end{array} $$

1.3.8 A.3.7 Peak Reserve Equations

Global reserve to cover peak load variations. These constraints impose that the total capacity of all processes producing a commodity at each time period and in each region must exceed the average demand in the time-slice where peaking occurs by a certain percentage. This constraint introduces a safety margin to protect against random events not explicitly represented in the model.

$$\forall t \in {\Theta}, s \in S, c \in C$$

$$\begin{array}{@{}rcl@{}} 1/(1+peak\_reserve[t,s,c])\times (\sum\limits_{l \in L, p \in P\_PROD[c] \cap P\_MAP[l] } \\ cap\_act[p] \times peak\_prod[p,s,c] \times fraction[s] \times avail\_factor[t,s,p] \times \\ (\sum\limits_{k \in 0..t : life[p] \ge k+1 \text{ and } t-k \ge avail[p]} \mathbf{VAR\_ICAP}[t-k,l,p]+fixed\_cap[t,l,p]) \\ + \sum\limits_{l \in L, p \in P\_PROD[c] \cap P\_MAP[l]} peak\_prod[p,s,c]\times \mathbf{VAR\_COM}[t,s,l,p,c]\\ + \sum\limits_{l \in L} \mathbf{VAR\_IMP}[t,s,l,c] ) \times network\_efficiency[c]\\ \ge \\ \sum\limits_{l \in L, p \in P\_CONS[c] \cap P\_MAP[l]} \mathbf{VAR\_COM}[t,s,l,p,c] \\ + \sum\limits_{l \in L} \mathbf{VAR\_EXP}[t,s,l,c] \end{array} $$

Remark 3

This global reserve must be distinguished from the system reserve that we will introduce later on, when modeling the power distribution level, which has a role of coping with production variations intervening, in a fast time scale, due to intermittency of wind and solar generation.