We consider an IES composed of different production plants that can be allocated in three possible system layouts, i.e., a standard CS, an IES implementing energy hub (IES-DG) and an IES adding bidirectional energy conversion (IES+P2G). In detail, the CS layout considers large-scale plants of either traditional or renewable energy sources, the IES-DG layout contains multiple medium-size prosumers, referred to as energy hubs (EH) [
22], whereas the IES+P2G considers the addition of a storage, in the form of a P2G conversion plant, that converts the excess energy in the grid into natural gas and feeds it into the pipelines. For illustrating purposes, the generic IES considered consists of an NPP (for baseload generation), two CCGT plants (for both baseload and peak regulation), a solar PV field, two WFs, a compression station (to overcome losses in the gas pipes) and a P2G station for energy storage (that can be switched off for simulating the CS layout). The system considered is plotted in
Figure 2, adapting it from previous works, such as [
23,
24]. In particular, we assume that the IES mimics the positioning of a number of realistic plants based in central Italy between Lazio and Campania regions (
Figure 3): for the NPP we assume the data of the Garigliano BWR nuclear reactor, CCGT are Napoli-levante and Teverola power plants, WF consists in fleets of Vesta V90 (2000 kW) turbines and solar PVs are fields of 1 kW PV panels with 35° and 180° of tilt and azimuth angles, respectively, summing up to 200 MW (
Table 1), as a compromise of the results presented in [
25]. In each node, energy can be either injected or absorbed into/from the grid: the six production plants (nodes 1 to 6) and the eight user nodes (nodes 7 to 14) are connected in a ring with nominal voltage of 220 kV, where a radial grid (blue in
Figure 2) distributes gas and feeds the gas plants and gas customers. In
Table 2 and
Table 3, the physical parameters (length, resistance and reactance) of the electric grid connecting the
m-th and the
n-th nodes corresponding to the production plants, and of the pipes connecting the
ϑ-th and
φ-th nodes of the pipeline network (length and frictional factor) are listed, respectively. Notice that a virtual additional node (15) is added to the grid (not shown in
Figure 1) to account for the “import”, when the IES cannot provide enough energy to customers.
Without loss of generality, the power demand of user nodes has been set according to a typical power demand profile during July 2018 [
26], as shown in
Figure 4. This has been taken as a reference demand because it challenges the IES due to the high demand values that must be supplied while complying, at the same time, with the following technical constraints: minimum load for CCGT plants equal to 40% of the nominal power [
27], maximum power for the CCGT equal to 110% of nominal power [
28] and NPP for baseload only with constant power production at nominal power.
The characteristics and models of the EHs that are used in the IES-DG and IES+P2G layouts have been taken from [
22]. The EH internal energy demand is satisfied with a small wind turbine and a combined heat and power station (each EH has a total generation capacity of 1200 kW to satisfy its demand and can exchange power with the grid). In our work, this means that EHs can dispatch power to the grid in case of excess of power production to satisfy normal users demand, and the overall power demand of
Figure 4 must be discounted by the internal demand and the dispatched power, when the eight EHs, each one connected to one load node, are considered.
3.1. The Simulation of the IES Response
A power-flow model is used to calculate voltage
V and phase
at each bus of a power system, for a specified load, generator power and voltage condition [
24]. This entails defining analytical models for each component of the power system, e.g., electric grid, gas pipeline and energy conversion system. In practice, with reference to our case study, the power flow allows computing
Vm and
in each
m-th electric grid node, the active and reactive power
and
, respectively, generated/absorbed power in the
m-th node and, indirectly, pressure
in each
-th gas distribution node and volume flow rate
in each pipeline connecting the
-th and the
-th nodes of the gas network [
29]. The power-flow model provides, at each iteration
τ, the steady state solution of
(hereafter indicated as
and of
F, correspondingly:
where
is the variable matrix composed of voltage phase angle vector (
) at the
m-th electric node, voltage magnitude vector (
), CCGT power generated (
), P2G and gas compressor power demand
,
), pressure at the
-th pipeline node (
) and mass flow rate in the
-th pipeline edge (
);
is the system function matrix composed by active and reactive power (
,
), pressure (
), mass flow rate (
) and compressor power (
).
To simulate the IES of
Figure 2 working in nominal conditions (in all the considered layouts of CS, IES-DG and IES+P2G) when the power demand is as in
Figure 4 [
26], the power-flow model is run 24 times, each one considering the system stationary conditions at each hour of the day (
τ = 1, 2, …, 24). From this, the following quantities can be calculated:
The daily energy exchanged by each
m-th node:
where
(τ) is the active power of the
m-th node at the
τ-th hour;
The overall energy supply
:
The overall energy demand
:
The system energy losses (%)
, due to distribution losses along cables:
Under normal conditions (i.e., neither stochastic nor climate-induced failures are effecting the operation of the production plants and, therefore, the IES) and when the power demand is as in
Figure 4, the energy supplied by each production plant is shown in
Figure 5, where the different shades of colors correspond to the energy supplied by each production plant (CCGT, PV, WF and NPP, respectively, in blue, yellow green and red). In all cases, a difference between the demand curve (dashed line) and the supply can be noticed (and quantified with
as in Equation (11)). In all cases where
, some energy is imported through the virtual node (15) and, in this work, for simplicity, but without loss of generality, the IES is considered failed, because not capable of fulfilling its function of guaranteeing the regional energy independence and security.
We also notice that:
- (1)
For the IES-DG layout, the difference is smaller than for the CS layout, because the EHs produce (locally) part of the required demanded energy, that is actually discounted to the total demand;
- (2)
In the IES+P2G layout, the positive balance of EHs in the central hours of the day and the PV power generation allows CCGT plants “to follow” the demand curve more gradually, independently from renewable energy production oscillation, thanks to the P2G. Indeed, the P2G, in case of high renewable generation, stores energy in the form of gas and avoids large-power demand oscillations.
- (3)
(which increases with the power transmitted by the grid) is the largest for the IES+P2G layout (5.33%), whereas, thanks to local production,
are the smallest for the IES-DG layout (3.51%) and the CS layout (4.28%) (vlues compared with Italian grid average
of 5.7% in 2018 [
26]).
3.2. The IES Reliability Model
The production plants (
γ = 1, 2, 3, 4, 5, 6 of
Table 1) that compose the IES can fail due to both stochastic and climate-induced failures. Stochastic failures usually originate from fatigue and strain of components [
2], and their uncertain failure (or repair) times are, as usual [
15], modeled as exponentially distributed:
where
is the probability that the
γ-th production plant fails (recovers) at time
t (i.e., moves from the nominal state
k to a failed state
(or viceversa)), and
and
are the failure and repair rates, respectively (see
Table 4, where
and
are given for each
γ-th production plant) [
30].
Climate-induced failures are, instead, originated from a natural event that might affect more than one plant at the same time; therefore, climate-induced failures cannot be considered statistically independent (as we assume for the stochastic failures), calling for a different modeling approach. Failures are, indeed, here modeled as “shock” events affecting all plants at the same time that may or may not fail under the shock received, depending on their fragility. For quantitative evaluation, the probability
of failure of the
γ-th plant due to the
δ-th natural event is calculated as:
where
is the probability that the
γ-th plant fails at time
t due to the occurrence of the
δ-th event (i.e., the fragility of the
γ-th plant to the
δ-th event), and
is the probability of
δ-th event occurrence (e.g., a specific
δ-th flooding level occurrence).
is calculated using fragility curves that can be obtained by fitting failure databases. In this work, we assume the following fragility curves; for each
γ-th power production plant:
Solar PV panels (
γ = 1) are assumed to fail with certainty
= 1) when the flooding level exceeds 1 m and to not fail (
= 0) for lower flooding levels, as plotted in
Figure 6 (we conservatively assume that 1 m is the height at which electric equipment is mounted on the PV metal structure and this is the equipment that would be damaged by flooding).
NPP (
γ = 2) is assumed to fail with certainty
= 1) when flooding level exceeds 5.7 m, and to not fail (
= 0) for lower flooding levels, as plotted in
Figure 7 [
31].
CCGT power plants (
γ = 3, 4) are assumed to fail with
as shown in in
Figure 8; different failure probability curves are given for six damage states (negligible, very low, low, medium, relevant and severe) of the concrete walls of CCGT power plants [
32]. In this work, the fragility related with the medium damage state is considered (bold line in
Figure 7).
WF (
γ = 5, 6) are assumed to fail with certainty (
P(
t,
γ = 5, 6|
δ) = 1) when flooding level exceeds 2 m, and to not fail (
P(
t,
γ = 5, 6|
δ) = 0) for lower flooding levels, as plotted in
Figure 9 (we conservatively assume that 2 m is the maximum flooding level withstood by the transformer connecting the plant to the grid, which is the equipment that would be damaged by the flooding).
Flooding occurrence probability
P(
δ) can be obtained from the outcomes of TSUMAPS-NEAM (
http://www.tsumaps-neam.eu/, accessed on June 2019), an international collaborative project aimed at developing tsunami hazard maps for coastal areas in the North-East Atlantic Mediterranean (NEAM) region. As an example, in
Figure 10, we show the
P(
δ) for a flooding return time of 50 years in a generic site of the NEAM region.
It is worth pointing out that, as discussed in [
11], flooding can originate from different threats, such as heavy rainfall, storm surges or tsunamis that, as a chain of events, often overlap each other. For simplicity, but without loss of generality, in this work we assume that floods are modeled independently from each other (i.e., each
δ-th event is completely resolved before the following one is initiated).
3.3. NaTech Events under Climate Change
The climate-induced failures discussed in
Section 3.2 deserve particular care when modeled, due to the variability across space (latitude and longitude) and time (short- or long-time projections). This means working with climate data specific to the IES site (rather than on general worldwide projections) and, also, focusing on specific initiating events (i.e., seismic activity), rather than a multitude of generic sets of natural events. In this work, we tailor the analysis on a specific site (latitude 40° 50′ N, and longitude 14°15′ E, where the IES described in
Section 3.1 is located) and consider different time projections (in the
(year) 2040, 2070 and 2100) for the flooding hazard curves. As flood-driven failures are strongly related to climate change, which induces stronger and more frequent events [
9], we model the flooding severity to increase with the sea level rise that is ultimately dependent on the temperature rise [
33]. In practice, the 8.5 RCP sea-level increase projections
= [0, 0.2003, 0.3889, 0.5970] for
= [2020 2040 2070 2100] are used to fit Equation (15) (corresponding to the flooding hazard curves of
Figure 11), starting from the baseline curve of Equation (14) proposed by [
14] as the probability of flood level in 2020:
It is worth noticing that between 2020 and 2100, the flooding occurrence probability almost doubles (at fixed severity) and that the most frequent events consistently increase in severity, endangering the IES integrity, as long as the climate changes.