Modelling Methodologies to Design and Control Renewables and Hydrogen-Based Telecom Towers Power Supply Systems

Abstract

Proton exchange membrane fuel cell (PEMFCS) and electrolyser (PEMELS) systems, together with a hydrogen storage tank (HST), are suitable to be integrated with renewable microgrids to cover intermittency and fully exploit the excess of electrical energy. Such an integration perfectly fits telecom tower power supply needs, both in off-grid and grid-connected sites. In this framework, a model-based tool enabling both optimal sizing and proper year-through energy management of both the above applications is proposed. Respectively, the islanded optimisation is performed considering two economic indices, i.e., simple payback (SPB) and levelised cost of energy (LCOE), together with two strategies of hydrogen tank management, charge sustaining and depleting, and also accounting for the impact of grid extension distance. On the other hand, the grid connection is addressed through the dynamic programming method, while downsizing PEMELS and HST sizes to improve techno-economic effectiveness, thanks to grid contribution towards renewables curtailment issues mitigation. For both the above introduced HST management strategies, a reduction of more than 70% of the nominal PEMELS power and 90% of the HST size, which will in turn lead to SPB and LCOE being reduced by 80% and 60% in comparison to the islanded case, respectively, is achieved. Furthermore, the charge depleting strategy, relying on possible hydrogen purchase, interestingly provides an SPB and LCOE of 9% and 7% lower than the charge sustaining one.

1. Introduction

Growing energy demand coupled with the need for reducing greenhouse gas emissions, thus improving the living standard in terms of human health, directly leads to the increasing use of renewable energy sources (RESs), such as solar and wind energy. Different RESs can be coupled in response to the energy crisis [1], but a proper techno-economic feasibility study is necessary both to avoid a poor hybrid system efficiency and to obtain advantages from the economic point of view [2]. As the sun and wind are intermittent sources, they are not always available when needed. Consequently, to meet the load request, it is necessary to integrate energy conversion and storage systems. A microgrid is a perfectly suitable solution to couple different RESs, allocating them in the same area, working either in a stand-alone or grid-connected configuration [3]. The above-mentioned RESs’ drawbacks can be addressed and thus solved using fuel cell and electrolyser systems, which can support the plant in case of lack of electricity and produce hydrogen in case of excessive production [4]. The latter is considered as a viable choice for the electrical energy surplus storage since it can be used as a backup system both for short and long periods. Such an outlined aspect is especially valid for places that are harsh to be electrically fed or connected with the national electrical grid, such as the ones considered in this study (i.e., telecom tower applications), where hydrogen can strongly improve the resiliency and self-sustainability of the microgrid. Although the capital expenditures (CAPEX) of hydrogen technologies are higher with respect to competing technologies, the reduced operative expenditures (OPEX) and long lifetime reliability make them a feasible solution for their use in telecom tower applications, namely the subject of the current paper [5]. In this application field, the hydrogen-based technologies turn out to be an effective alternative to diesel generators, normally coupled with batteries in areas characterised by connection instability, in terms of sustainability [6,7]. Furthermore, PEMFCS may be preferrable with respect to long lasting alkaline systems due to their higher power density, efficiency and faster dynamic response [8]. On the other hand, compared to solid oxide systems, used in [9], PEMFCS exhibit a limited round trip efficiency, but their faster dynamic response allows their use in contexts requiring sudden power variations. One promising technology that can be coupled with PEMFCS is metal hydride (MH) storage, which is based on the reversible chemical process in which a crystal structure solid metal and the hydrogen gas are involved and both return to their original phase. Reduced space requirements, high energy density and low operating pressure make this technology very interesting in those applications, reducing personnel risks during maintenance services [10]. Although PEMFCS can replace batteries as energy storage systems, the lack of incentives from the economic point of view may represent a limitation. It is also worth specifying that the latter mentioned drawback can also be faced and partially addressed by plant optimisation procedures as well as effective energy management strategies such as the ones proposed herein, especially in cases where the connection to the electrical grid can be expensive. Against this background, in RES-based microgrids coupled with PEMFCS, two configuration options may be investigated, islanded or grid extended. In the latter case, the grid extension is introduced, and it is defined as the distance between the nearest electric connection and the microgrid site. Ayodele T.R. and al. in [11] analysed the topic by defining a microgrid configuration for health application in rural positions composed by PV panels, wind turbines, a fuel cell system and a hydrogen tank, finally comparing with the grid extended configuration using the break-even grid distance. The latter is here defined as the distance from the nearest network connection at which the net present cost of extending the grid is equal to the net present cost of the stand-alone system, which, in this case, is 8.81 km. This in turn implies that if the grid is far away from this distance, then the stand-alone system is a better option. Although this study is innovative for different reasons, such as the use of hydrogen as an energy storage system instead of batteries and the net present cost to study the investment in long-term periods, the model considers only the distance to determine whether the islanded microgrid is economically convenient or not with respect to the grid-extended one. Luta, D. N., et al. in [12] directly compare the grid-extended configuration and the islanded microgrid in the region of Napier in Africa. Even in this case, a similar simplified model for the break-even distance is used, but a sensitivity analysis on the hydrogen cost is carried out. The other economic metric considered in these studies is the LCOE, which is commonly defined as the average cost of generating one kWh of electrical energy over the lifetime of the most durable investment for the plant element [13,14], and, on the other hand, it is used due to its usefulness to compare different energy production methods, as in [15], where an LCOE-based procedure is used to obtain an economic comparison of a reversible solid oxide cell (rSOC)-based microgrid with other technologies available on the market. It is worth saying that hybridisation among energy systems results in a viable solution to reduce the latter index. In this regard, Taghavifar, H., and Zomorodian, Z. S. in [16] propose a micro-hybrid system installation in on-grid mode (for which the grid extension is equal to 0 since the plant is already grid connected) to sellback the excess electricity and hence economise the building of a high-potential campus site as a source of income using the SPB to analyse the economic feasibility with two scenarios of about 4.6 and 8.11 years. The integration and optimal utilisation of different accessible energy resources into a self-contained micro-grid is examined, and it is mainly focused on the LCOE as an economic index using HOMER as optimisation tool and finding a result of about 0.5151 $/kWh. Moreover, in [17], the connection to the electric grid is considered to obtain better economic results by scaling down the hydrogen-based system used to cover the electrical load given by a fleet of electric and hydrogen vehicles and a residential complex.

The aim of this work is to develop a versatile procedure for the model-based design of a telecommunication green power supply unit consisting of PEMFCS as main supply units and PEMELS to properly exploit available RESs. To clearly outline the wide range of applications of the designed sizing tool, two energy management scenarios leading to different plant sizing, namely charge sustaining and depleting of the HST, have been pursued. Telecom applications that exhibit non-standard geographical positions, loads and energy availability are perfectly suitable to be optimised via such tool. Furthermore, a novel contribution given by this paper is the introduction of improved SPB and LCOE economic indices, which can account for the current hydrogen price and the grid extension distance. Particularly, the latter parameter is crucial to decide whether it is economically convenient to keep a site as a remote one or connect it to the electrical grid. The other interesting innovation introduced in this paper is related to the exploitation of dynamic programming (DP) features to solve the control problem of the grid-connected microgrids, especially for the ones in which it could be advantageous to have a network connection. Indeed, the DP tool, taking as input the already optimised plant, performs a further downsizing of plant components to take full advantage of network connection while managing the power split and complying with applied energy consumption constraints. Exploiting PEMFCS and PEMELS flexibility, plant optimisation and subsequent development of year-through dynamic programming-based energy management strategies allowed achieving relevant techno-economic assessment outcomes. Such results clearly indicate to potential investors the benefit of adopting a well-designed and controlled hydrogen-based microgrid even in the short-term scenario, still characterised by relevant key components cost.

The paper is organised as follows. Section 2 gives a description of the assumed plant and related loads. In Section 3, a mathematical model is presented for each plant component. This allows us to introduce the optimisation procedure performed in Section 4, in which the economic indices, LCOE and SPB, are detailed and the optimal sizing of the islanded microgrid elements is obtained. Then, in Section 5, the DP routine is first introduced and then used as the control strategy for moving towards the grid-connected configuration, finding the best power split between PEMFCS, PEMELS and electrical grid itself. Finally, the main research outcomes, conclusions and follow-ups are provided in the concluding remarks.

2. Plant Description

This work focuses on the study of an islanded microgrid that is grid connected. The selected case study considers an electric load given by telecommunication towers served by the following electricity sources: PV panels and wind turbines. The other plant components, which make it possible to meet the load request, are a PEMFCS, a PEMELS and an HST. It is worth remarking that although the telecommunication tower’s electric load varies over time, in this paper, an average value of 3745W per hour is calculated considering an annual load requirement for the site of 32.85 MWh. Figure 1 points out a qualitative scheme of how the renewable microgrid works, both in the off-grid and grid-connected configuration. During the peaks of renewable electrical production, the energy surplus is used by the PEMELS to produce hydrogen, which is then stored into the tank (PEMELS mode). In case PV panel and wind turbine production is insufficient, the PEMFCS helps meet the load request by consuming hydrogen from the tank (PEMFCS mode). This ensures the self-sufficiency of the microgrid.

Even though various photovoltaic panels are suitable for this application [18], high-performance polycrystalline ones, detailed in [19], were considered in this case. In order to connect the panels to the load net, a DC/AC inverter is necessary. Vertical axis wind turbine technologies were selected for this study for their favourable characteristics, including a minimum speed beyond which it is not possible to generate electricity [20]. Such a wind turbine is composed by a tower, a rotor, an inverter and a grid connection controller.

Table 1. Photovoltaic panel technical parameters.

Parameter	Unit	Value
Maximum power	[W]	270
Efficiency	-	0.16
Dimensions (length × width × height)	[mm]	992 × 40 × 1640

Note: photovoltaic panel model: I’M SOLAR 280P, source [19].

and

Table 2. Wind turbine performance parameters.

Parameter	Unit	Value
Maximum power	[kW]	3.6
Cut-in wind speed	[m/s]	1.5
Nominal wind speed	[m/s]	10
Cut-out wind speed	[m/s]	25

Note: Aeolos-V 3 kW vertical wind turbine, data from [20].

summarise the specifications of those systems.

The RES’s installed power is one of the results of the optimisation of the entire system. The latter optimisation must meet the electric load demand. Once such request is satisfied, the plant will be re-sized for some components and grid connected by adapting different control strategies, comparing results between the islanded microgrid case and the grid connected one. The method for sizing the entire plant is explained in the next paragraphs.

3. Model Description

The model concerns the plant sizing, which requires as inputs the loads that must be satisfied and the power produced by RESs. The insolation and wind profiles depend on the location of the site chosen for the analysis. Therefore, the location has to be defined in terms of latitude and longitude.

3.1. PV and Wind Turbine Calculation Procedure

For this procedure, those chosen in [9] were considered here as well. Once the latitude φ, the inclination of the panel with respect to the south direction γ and the tilt angle of the panel β were defined, it was possible to determine the power of the PV panels in Equation (1):

$$P_{PV}=GA{\eta }_{PV}{n}_{PV}\lambda$$

(1)

where G is the solar incidence, A is the surface of a panel, η_PV is the panel efficiency, n_PV is the number of the installed panels, while λ is a reduction coefficient that is calculated for each month. It is introduced to quantify the difference, in terms of power, when using panels in ideal and in real weather conditions, and it is defined as the ratio between G_{real weather conditions} and G_{without clouding effects}; consequently, λ values lay between 0 and 1. Specifically, the monthly values of G_{real weather conditions} are provided by [21], while those of G_{without clouding effects} are calculated according to [9].

The nominal power of a single wind turbine P_w,n depends on the characteristic speeds of the turbines, and those values are the cut-in V_ci, nominal V_n and cut-out V_co speeds. The working power P_w can be expressed as a function of nominal power P_w,n in Equation (2):

$$P_w=P_{w,n}\frac{V-V_{ci}}{V_n-V_{ci}}, V_{ci}\le V\le V_n$$

$$P_w=P_{w,n}, V_n\le V\le V_{co}$$

$$P_w=0, V\le V_{ci} \mathrm{and} V\ge V_{co}$$

(2)

3.2. PEMFC and PEMEL Systems

This paragraph deals with the explanation of the PEMFCS and PEMELS model, which consists of a series of equations relating key operating values and performance variables (i.e., PEMFCS efficiency vs. net normalised power and PEMELS efficiency vs. gross normalised power). The goal is to find the hydrogen mass necessary in PEMFCS operations and the one produced by PEMELS. As mentioned in the previous section, in PEMFCS mode, the system can fulfil the difference between telecom tower requests and renewable sources’ insufficient production. Therefore, the system consumes hydrogen from the tank. During PEMELS operation, the surplus of renewable production is supplied to the electrolyser in order to produce hydrogen, which is stored in the HST. The energy surplus (or shortage) S is estimated as follows:

$$S=P_{PV}+P_W-TL$$

(3)

The system works in PEMELS mode when S > 0 and in PEMFCS mode when S < 0, and this represents the electric power that the system must provide to the telecom towers. The PEMFCS and PEMELS can operate between a minimum, assumed to be 6% of the maximum power as assessed in [22], and a maximum value, defined in Equations (4) and (5):

$$P_{PEMFCS,nominal}=1.1·\max \left(TL\right)$$

(4)

$$P_{PEMELS,nominal}=P_{PV}+P_W$$

(5)

$P_{PEMFCS,nominal}$ is set to cover intermittency of renewable sources with a 10% excess, whereas $P_{PEMELS,nominal}$ is set equal to the total power of RES in order to make the most of excess electricity. When $S$ is bigger than the minimum power, in absolute value, the working power level is set to be equal to S for one hour (t = 1), while, if this quantity is lower than the respective minimum power, the system works at $P_{min}$ for a time t that is a fraction of one hour, given by the ratio S/P_min. Therefore, the working time is defined as described in Equation (6):

$$t=\mathrm{m}\mathrm{i}\mathrm{n}\{1;\frac{\left|S\right|}{P_{min,PEMELS}}\} \mathrm{or} t=\mathrm{m}\mathrm{i}\mathrm{n}\{1;\frac{\left|S\right|}{P_{min,PEMFCS}}\}$$

(6)

3.3. PEMFCS Mode

In this mode, the power that the system has to produce is equal to the value of S, according to Equation (3). Through this power, which is net as it is the one required by the towers, it is possible to determine the efficiency of the fuel cell system and consequently the hydrogen mass. To determine the efficiency, the equation described in [23] is used. Here, the latter is defined as the ratio between the working power and the maximum available power for the fuel cell system; consequently, it is possible to account for different working conditions for the system, as shown in Figure 2.

Now it is possible to determine, using Equation (7), the mass of hydrogen required in PEMFCS mode at the jth time instant t as a function of the efficiency and the net power:

$$m_{H_2,PEMFCS,j}=\frac{\max \{P_{min},S_j\}}{{\eta }_{PEMFCS,j}LHV}{t}_{PEMFCS,j}$$

(7)

3.4. PEMELS Mode

When S is positive, the renewable production exceeds the demand, so it is possible to store it in the form of hydrogen. In this case, the power needed for the system to produce hydrogen is the gross power, which is related to the efficiency. The latter is defined in [24], and it is related to the ratio between the working power and the maximum power delivered by the electrolyser system, such as in PEMFCS mode. Those values are reduced by about 5% as described in [25,26] because an MH storage system is used that works at about 30 bar [24]. To be more accurate, it is important to remark that the efficiency will drop once the gross power is under 6%, as assessed in [22]. Figure 3 shows its behaviour with the ratio defined before. At low loads, the efficiency of the system drops drastically, as defined [27].

The hydrogen produced in PEMELS mode can be computed using Equation (8):

$$m_{H_2,PEMELS,j}=\frac{{\eta }_{PEMELS,j}\mathrm{m}\mathrm{i}\mathrm{n}\{P_{min},S_j\}}{LHV}{t}_{PEMELS,j}$$

(8)

3.5. Hydrogen Storage Hourly State Calculation

Considering Equations (7) and (8), a mass balance on the HST can be written in Equation (9):

$$m_{H_2,tank}=m_{H_2,PEMELS}-m_{H_2,PEMFCS}$$

(9)

The two terms on the right-hand side represent the hydrogen produced and consumed by the PEMFCS and PEMELS. The daily variation of the HST can be expressed as in Equation (10):

$$\mathit{S}\mathit{O}{\mathit{C}}_{\mathit{H}\mathit{S}\mathit{T},\mathit{j}+1}=\mathit{S}\mathit{O}{\mathit{C}}_{\mathit{H}\mathit{S}\mathit{T},\mathit{j}}+\frac{{\mathit{m}}_{{\mathit{H}}_2,\mathit{t}\mathit{a}\mathit{n}\mathit{k},\mathit{j}}}{\mathit{H}\mathit{S}{\mathit{T}}_{\mathit{s}\mathit{i}\mathit{z}\mathit{e}}}$$

(10)

4. Optimisation Procedure

The SPB, Equation (11), and LCOE, Equation (12), are adopted here as functions to be optimised. It is worth remarking that the SPB and LCOE mathematical formulations are derived by the authors, accounting for the grid extension distance defined in [11].

$$SPB=\frac{\left(TC+IC\right)·\left(1-TD\right)-C_{ge}·D+p_{H_2}·Q_{H_{2_{yr}=0 }}}{ABC+M{C}_{ge}·D-p_{H_2}·{∆}_{H_2}-MC-R} \left[years\right]$$

(11)

$$LCOE=\frac{\left(TC+IC\right)·(1-TD)+{\sum }_{i=1}^n\frac{M{C}_i}{{\left(1+d\right)}^i}+p_{H_2}·\left(Q_{H_{2_{yr}=0}}+{\sum }_{i=1}^n\frac{{∆}_{{H_2}_i}}{{\left(1+d\right)}^i}\right)}{{\sum }_{i=1}^n\frac{{E_y}_i}{{\left(1+d\right)}^i}} \left[\frac{€}{kWh}\right]$$

(12)

Considering the $SPB$, in the numerator, TC is the total microgrid cost (it is given by the sum of costs summarised in

Table 3. Summary of unit costs for each considered key element of the plant.

Components	Unit	Unit Cost
PV plant: panel, inverter	[€/kW]	817 (600, 217)
Wind turbine: tower, rotor, inverter, grid-on controller	[€/kW]	2513 (504, 1108, 635, 266)
HST [30]	[€/kg]	1200
PEMFCS [30]	[€/kW]	1200
PEMELS [30]	[€/kW]	500

), IC is the installation cost (it is about 10% of the TC), MC is the maintenance cost in one year (3% of TC), TD is the tax deduction (50% of the TC, according to the Italian govern policies on green energies [28]), C_ge [11] is the CAPEX for grid extension, D is the grid distance and $Q_{H_{2_{yr}=0 }}$ is the hydrogen mass initially needed (at year 0) to ensure the optimal initial level of the HST (it is a result of the optimisation procedure). In the denominator, ABC is the annual bill cost, which refers to the electricity required by the telecommunication towers. Since the latter is not a cost in case of an islanded configuration, this term is associated with annual savings. MC_ge [10] is the maintenance cost associated with the grid extension, p_H2 is the hydrogen price [29], ${∆}_{H_2}$ is the hydrogen mass that must be purchased year by year to restore the optimal HST initial level, while R is defined as the replacement cost for each main component of the plant (i.e., wind turbines, tanks and so on) and in this analysis it is set equal to 0 since it is assumed that it will be performed once the payback time is reached.

Considering the LCOE, all the terms are the same defined for the SPB except for the fact that the maintenance cost, the cost of hydrogen bought and the annual load E_y are defined over the most durable investment for the plant element (here considered as n = 25 years for PV panels) and reduced by a factor (1 + d)ⁱ that increases with time and where d is defined as the discount rate and it is set equal to 5%. The goal is to minimise the SPB or LCOE; consequently, the variables to be optimised are the number of PV modules n_PV, the number of wind turbines n_w, the capacity of HST HST_size and the quantity of stored hydrogen at the beginning of the year SOC_0,HST. The first two variables are used to satisfy the average electric power request, while the storage system interacts with both PEMFCS and PEMELS to improve their operations, making possible the accumulation of electric power in the form of hydrogen when the production exceeds the demand. Finally, managing SOC_0,HST makes it possible to take full advantage of the fuel cell and the electrolyser systems.

The power of those systems is set as a constraint for the optimisation in order not to waste any electrical energy. All the constraints used are summarised below:

(1)

the state of charge of the hydrogen tank has to lay between 15% and 95%;

(2)

the nominal power of the PEMELS must be equal to the summation of installed PV and wind turbine nominal power, so as to avoid having renewable energy wasted;

(3)

the nominal power of the PEMFCS must be equal to the maximum value of the load oversized by 10% to cover intermittency of renewable sources;

(4)

the final level of the tank must be equal to the initial level in case of charge sustaining strategy. This implies that, considering SPB and LCOE formulas, the term representing the hydrogen bought (${∆}_{{H_2}_i})$ is always negligible. Meanwhile, if the charge depleting strategy is used, the final level of the tank must be equal to half of its initial level.

The first constraint is applied to the entire year, thus avoiding excess and shortage of hydrogen in case of unpredicted surplus or sudden grid unavailability, respectively. The fourth constraint allows us to extend the results of one year for longer periods in both cases, charge sustaining and depleting. In fact, the energy stored in the tank is re-established at the end of the year, in the first case automatically, while in the second case the difference between initial and final level is bought at the end of the year.

Figure 4 shows the model scheme. The orange dashed rectangle block represents the variables that have to be optimised, in this case, the nominal PV and wind turbine power, HST_size and SOC_0,HST initial state. Blue and light blue arrows, respectively, stand for the load demand and renewable production flows, while the green arrows indicate the energy flows in the HST. The balance between the load request and production gives the electric excess/lack, which determines the PEMFCS and PEMELS operating mode, as well as the increase or reduction in terms of HST state of charge. Once the SPB or LCOE, which depend on every component cost, are defined, the optimisation procedure is terminated if one of the parameters reaches the lowest possible value and the constraints are verified, thus the optimal sizing of the plant is achieved. It is worth noting that such a minimisation problem was solved relying on a code developed by the authors in the Matlab^® environment, adopting the ‘interior-point’ optimisation method [31].

5. DP Routine

Dynamic programming is an optimisation method that determines the best arrangement of operating modes to satisfy an objective function during a sliding time frame. In the present work, the time frame (8760 h) is divided into several time steps (1 h each), ranging from the current time to a future time. The applied changes to the system variables lead to certain variation paths during the time frame. The process is performed for all possible paths, and the path with the best result according to the objective function is selected. Finally, the system variables and the operating mode are changed according to the selected path. In this work, the DP routine developed in [32] and used in [17] is applied to find the optimal PEMFCS and PEMELS control policy (i.e., $P_{PEM,j}$) that satisfies the requirements of the telecommunication towers and, in turn, minimises the network connection cost J defined in Equation (17). As it will be seen in this section later, the term J will modify the optimisation objective functions, SPB or LCOE.

DP routine requires as input the sizes of the plant components determined in the previous section, but an appropriate downsizing of PEMELS and HST is performed to take full advantage of the grid connection. Specifically, the PEMELS and the HST are reduced as follows:

$$P_{PEMELS,DP}=3·P_{PEMFCS,optimisation}$$

(13)

$$HS{T}_{size,DP}=10\%HS{T}_{size,optimisation}$$

(14)

Equation (13) refers to the typical value for the electrolyser system when working in combination with a fuel cell system, while Equation (14) is used to obtain the most from the HST [33].

The control system has to decide the amount of energy that can be used in PEMELS mode or can be sold to the grid. At the same time, in case of electricity shortage (related to the intermittency of the renewable sources), the control system must find the best compromise between the amount of energy that has to be supplied by the PEMFCS and the one integrated from the electrical grid.

The variable C_j helps to define hour by hour if wind and solar production from the optimisation can meet the telecommunication tower needs, with the j subscript that is used to refer the balance to the jth hour of the year:

$$C_j=P_{PV,j}+P_{W,j}-T{L}_j$$

(15)

Positive or negative values of $C_j$ define if the system is in a condition of excess or lack of energy, thus determining PEMELS or PEMFCS mode to be activated. In addition, positive and negative $C_j$ values represent the energy stored in the form of hydrogen or sold to the grid and the energy that must be produced through the fuel cell or bought from the grid, respectively. Therefore, the term C_j can be written in Equation (16):

$$C_j=P_{PEM,j}+P_{grid,j}$$

(16)

When P_PEM,j assumes negative values, the system is working in PEMELS mode. In the same way, when P_grid,j assumes negative values, the system is selling electricity to the grid. To this value, P_grid, is associated the cost–function variable J, estimated in Equation (17):

$$J\left(P_{grid}\right)={\sum }_{j=0}^{8760}(P_{bought,j}·C_{el,bought}-P_{sold,j}·C_{el,sold})$$

(17)

Here, P_bought and P_sold are, respectively, the hourly electric power purchased and sold to the grid. In addition, C_el,bought and C_el,sold are the cost for buying electric energy and its selling price, which, here, are considered constantly equal to 0.35 €/kWh and 0.15 €/kWh, respectively [34]. This term will affect the objective function SPB, in Equation (18), or LCOE, in Equation (19), as follows:

$$SPB=\frac{\left(TC+IC\right)·\left(1-TD\right)-C_{ge}·D+p_{H_2}·Q_{H_{2_{yr}=0 }}}{ABC+M{C}_{ge}·D-p_{H_2}·{∆}_{H_2}-MC-R-J}$$

(18)

$$LCOE=\frac{\left(TC+IC\right)·(1-TD)+{\sum }_{i=1}^n\frac{M{C}_i}{{\left(1+d\right)}^i}+p_{H_2}·\left(Q_{H_{2_{yr}=0}}+{\sum }_{i=1}^n\frac{{∆}_{{H_2}_i}}{{\left(1+d\right)}^i}\right)+{\sum }_{i=1}^n\frac{J}{{\left(1+d\right)}^i}}{{\sum }_{i=1}^n\frac{{E_y}_i}{{\left(1+d\right)}^i}}$$

(19)

Once the PEMFCS and PEMELS strategy is found as well as J, the objective function is then calculated, and the aim is to reduce it as much as possible (D in this case is 0).

The state variables X must provide the state of the system in each time step. The most-used state variable in those cases is the state of charge of the tank, as it identifies the state of the system, so the best option for this case is to set SOC_HST as a state variable. The state variable is directly controlled by the control variable U, which, in this case, is P_grid,j. Assumptions on the state and control variable are needed:

(1)

$P_{bought}\le P_{PEMFCS,nominal value}$;

(2)

$P_{sold}\le \max \left(P_{PV}+P_W-TL\right)-P_{PEMELS,nominal value}$;

(3)

$SO{C}_{end,HST}=SO{C}_{0,HST}$, considering charge sustaining strategy;

(4)

$SO{C}_{end,HST}=0.5·SO{C}_{0,HST}$, considering charge depleting strategy.

Where the first hypothesis ensures that the system will not run out of electricity if neither renewable sources or the fuel cell system are available, the second one ensures that the excess of produced electricity will not be wasted, so it can be used by the electrolyser system, which is preferred by the system, or it can be directly sold to the grid.

In order to consider the calculation of SOC_HST, which strictly depends on the hydrogen mass produced and consumed, we considered the same procedure defined in the previous sections. It is worth remarking that in this case, the system will also respect the constraints defined earlier on the fuel cell system and the electrolyser system and the term P_PEM,j, defined in Equation (16). In this case, it will never work under the minimum threshold defined earlier, so the working time in this procedure will always be 1 h. Given the value of the optimal control variable that minimises the cost function over the entire year, it is possible to calculate the SOC_HST trajectory.

6. Results

This section deals with the results obtained from the optimisation procedure, considering the islanded configuration, and those achieved using DP when the plant is grid connected. The latter are summarised in

Table 4. Plant characteristics in the charge sustaining strategy, in terms of renewable, PEMFCS and PEMELS power installed, HST size and initial state, SPB and LCOE results and Capital investment.

Parameter	Unit	P1W1GoffCSd0	P1W1GonCSd0	P1W1GoffCSd5	P1W1GoffCSL	P1W1GonCSL
PV power	[kW]	16.71	16.71	16.71	16.71	16.71
Wind power	[kW]	31.45	31.45	31.45	31.45	31.45
HSTsize	[kg]	104.57	10.457	104.57	104.57	10.457
SOC0,HST	[%]	34.81	34.81	34.81	34.81	34.81
PEMFCS power	[kW]	4.12	4.12	4.12	4.12	4.12
PEMELS power	[kW]	48.16	12.36	48.16	48.16	12.36
SPB	[years]	33.348	6.997	7.397	/	/
LCOE	[€/kWh]	/	/	/	0.520	0.209
Capital invest.	[€]	247,200	116,520	247,200	247,200	116,520

and

Table 5. Plant characteristics in the charge depleting strategy in terms of renewable, PEMFCS and PEMELS power installed, HST size and initial state, SPB and LCOE results and Capital investment.

Parameter	Unit	P1W1GoffCDd0	P1W1GonCDd0	P1W1GoffCDd5	P1W1GoffCDL	P1W1GonCDL
PV power	[kW]	19.80	19.80	19.79	19.79	19.79
Wind power	[kW]	27.11	27.11	27.12	27.13	27.13
HSTsize	[kg]	99.03	9.903	98.96	98.92	9.892
SOC0,HST	[%]	41.51	41.51	41.49	41.47	41.47
PEMFCS power	[kW]	4.12	4.12	4.12	4.12	4.12
PEMELS power	[kW]	46.91	12.36	46.91	46.91	12.36
SPB	[years]	28.533	6.361	5.213	/	/
LCOE	[€/kWh]	/	/	/	0.489	0.195
Capital invest.	[€]	231,540	107,470	231,480	231,450	107,490

.

As it is clearly visible in the tables, the plant sizing is the same for the cases P1W1GoffCSd0 and P1W1GoffCSd5, and it is almost the same for the P1W1GoffCDd0 and P1W1GoffCDd5 cases. Considering the latter, the parameter optimised is the SPB, while if the optimisation is performed by considering LCOE, such as in the P1W1GoffCSL or P1W1GoffCDL cases, the results, in terms of plant sizing, are almost the same with respect to the corresponding SPB-based optimisation. Anyway, the tables show that passing from a charge sustaining to a charge depleting strategy allows levelling the production between PV panels and wind turbines, increasing the number of panels, thus reducing the number of turbines, and as well for the HST_size, which will be slightly reduced, in order to maximise the utilisation of the tank. Its initial state is indeed a bit higher in case of the charge depleting strategy, as it is shown in Figure 5.

Moreover, the main difference showed, among the different scenarios, clearly emerges from the economic point of view: by adopting a charge depleting strategy, there is an SPB reduction of 4.82 years between P1W1GoffCSd0 and P1W1GoffCDd0, and of 2.18 years between P1W1GoffCSd5 and P1W1GoffCDd5. Considering the LCOE, it reduces by about 3 c€/kWh. In the case of grid connection, no matter what strategy was considered, SPB and LCOE display a reduction of about 80% and 60%, respectively, with respect to the off-grid hydrogen microgrid solution. Furthermore, as in the islanded cases, those results will be slightly lower in case of a charge depleting strategy, showing a reduction of about 0.64 years and 1 c€/kWh, respectively. In those cases, the plant has the lowest cost and the best economic return by exchanging energy with the grid. The cost of the plant is reduced by more than half of its corresponding islanded, with a cost decrease of about 150000 €, both in the charge sustaining and charge depleting strategy.

Another analysis is performed considering the grid extension distance in the P1W1GoffCSdx case. Therefore, SPB is expressed as a function of the distance between the microgrid site and the network connection. SPB can vary from its initial value to a more convenient value, and this variation is not affecting the plant that, in terms of components size, is the same anyway. It is composed of 16.71 kW of PV panels, 31.45 kW of wind turbines, 4.12 kW of PEMFCS, 48.16 kW of PEMELS and 104.57 kg of HST. As it can be seen in Figure 6, the SPB decreases with increasing grid extent and reaches a value of 0 when this distance is 6.75 km. On the other hand, the break-even distance of 3.5 km is also calculated by comparing the net present cost of the microgrid solution, considering both CAPEX and OPEX, with the net present cost of extending the grid.

Figure 5a shows the variation over the year of the hydrogen tank level considering the difference between the off-grid optimisation and DP routine when the charge sustaining strategy is adopted. It is visible that the tank level crosses the whole allowed range inside the constraints. During the early days of the year, the stored quantity is exploited, while during spring and summer seasons, a higher level is reached in the tanks due to the increasing power from photovoltaic panels thanks to the higher solar insolation levels. With the optimisation, the curve describes exactly what has been said before. After the DP routine, the HST trajectory is flatter with respect to $SO{C}_{0,HST}$, but a smaller $HS{T}_{size}$ and the connection to the grid can justify it. Figure 5b shows the variation seen in the previous graph but using the charge depleting strategy. It is seen that the tank level varies in the entire allowed range, reaching at the end of the year a final state $SO{C}_{end,HST}$ that is half of the initial one. The latter is the main difference between the two graphs, showing a similar behaviour during the annual timeframe, while, at the beginning and at the end of the year, the slope, in absolute value, is quite higher in the charge depleting case as a result of the optimisation procedure.

Figure 7a displays the energy produced by the PV, wind turbine, consumed by the electric load and the potential energy contained in the hydrogen masses consumed and produced, all expressed in kWh. The difference between the sum of the first two bars and the third one, in each month, represents the power produced or supplied to the PEMFCS and PEMELS in the respective modes, while the difference between the fourth and the fifth bars is the mass of hydrogen taken from or added to the HST. The graph is divided in two parts, putting in evidence of the difference between an islanded and grid-connected microgrid. With this strategy, the renewable production is the same, while adapting a smaller electrolyser and tank and connecting the plant to the grid reduces significantly the hydrogen exchange, as is visible in Figure 7b. In Figure 7c,d, it is possible to see the energy shares in a charge depleting strategy but considering, respectively, the islanded and grid-connected configurations. Those strategies lead to different results in PV production and wind production, which are 24.25 MWh and 37.47 MWh in charge sustaining and 28.72 MWh and 32.32 MWh in charge depleting, but the total production is approximately the same. Furthermore, adapting a charge sustaining or a charge depleting strategy brings a less evident change in HST management (Figure 7b,d) as well as for its trajectory, as it is already possible to see in Figure 5.

Figure 8 shows the distribution of the operating hours over the year of the PEMFCS and PEMELS modes, along with the related efficiencies considering both charge sustaining and depleting strategies (cases P1W1Goffd0, P1W1Goffd5 and P1W1GoffL in Figure 8a,b, and cases P1W1Gond0 and P1W1GonL in Figure 8c,d). The abscissa axis shows the working power that can vary in the entire allowable range, from the minimum allowable power (values under 6% of the nominal power cannot be reachable since it is set as the minimum working power for both) until the nominal value of the respective system. The ordinate on the left shows the hours of operation (on a logarithmic scale, to make a clear comparison between the plots), whereas the axis on the right indicates the efficiency (on a linear scale). In the islanded microgrid (Figure 8a), the PEMFCS works for a total of 4549 h in the charge sustaining strategy and 4611 h in the charge depleting strategy over the year, mainly at mid–high power levels where the efficiency is almost constant, thus resulting in an optimal energy conversion from hydrogen to electricity, apart from the hours and fraction of hours when the system works at minimum power. The PEMELS works for a total of 3640 h in the charge sustaining strategy and 3647 h in the charge depleting strategy over a wider operating range, with maximum power significantly higher than PEMFCS mode, as it can be deduced from Figure 8b. For one year, the total operating time of both systems covers almost 95% of the total hours available, showing just a few differences between the two strategies, with the latter a bit higher. The connection to the grid (Figure 8d) increases the operating time of the PEMELS by 600 h in the charge sustaining strategy and 500 h in the charge depleting one. Even though the nominal power of the electrolyser is significantly reduced, and the plant is grid connected, it operates in a wider range with respect to the power range displayed for PEMFCS, which works mainly at low power (Figure 8c). Thus, by comparing the results obtained in the off-grid configuration (Figure 8a,b) with those obtained in the grid-connected one (Figure 8c,d), it is clear how the grid connection allows a cost-effective resizing and an optimal managing between the power split of PEMFCS and PEMELS and the electric grid itself.

7. Conclusions

The increasing importance of hydrogen as an energy vector and the need for sustainable development inspired this study. Several hydrogen-based technologies, such as proton exchange membrane fuel cells and electrolysers, especially integrated within clean renewable-based microgrids, are increasingly being seen with a great worldwide attention, particularly for telecom applications. This configuration, as seen, is suitable in both islanded and grid-connected configurations and, therefore, this work has the objective of deepening such technologies in both cases, pinpointing major economic and technical aspects. In the present work, the assessment of the islanded microgrid is performed through a constrained optimisation for sizing of plant components, accounting for an annual user demand timeframe, while, when considering the grid connection, it is necessary to find a control logic that governs the power split between the grid, the PEMFCS and PEMELS. A dynamic programming-based algorithm was thus considered, finding the best control policy, while complying with the computational burden constraints. Such a compromise between accuracy and low computation demand is achieved. A normalised modelling approach is introduced for both PEMFCS and PEMELS, which allows interfacing with available renewable sources and the grid in case of network connection. This approach is effective for obtaining the simultaneous optimisation of component sizing and control strategies for telecommunication towers’ requests with good accuracy. The contribution given by this work consists of considering two different strategies, charge sustaining and charge depleting, by means of suitable constraints for hydrogen storage systems, to meet user needs and ensure boundary constraints compliance without affecting the repeatability of the study, since, in case of a charge depleting strategy, the difference between starting and ending state of the tank will be bought. The initial state of the tank has been considered as a design variable to be optimised, which ensures maximising the use of the tank itself throughout the year.

Another relevant contribution is given by the introduction of grid extension, which is the distance between the nearest network connection and the microgrid site. Typically, it is used as a techno-economic index by telecom tower managers when decisions must be made between keeping remote sites as they are or connecting them to the grid itself. Such an inclusion was shown to allow achieving better economic results, comparable with the ones achieved in case of grid connected cases. If the distance considered is compatible with the site analysed, in case of the charge sustaining strategy, a good payback result of about 7.5 years is obtained considering a grid extended to D = 5 km, while, in case of charge depleting, it is about 5 years. The introduction of LCOE and improved SPB index (i.e., by means of the new variables introduced) allows us to have a better overview on the analysed system with respect to previous studies. In fact, the first index is commonly used to determine whether an investment on renewables (especially used in PV panels application) is worth the expense, since it measures the average cost of generating one kWh of electricity over the lifetime of the most durable investment for plant element time.

A PEMFCS- and PEMELS-based microgrid, in order to be truly competitive, requires particular attention to be paid to the optimal usage of hydrogen as a storage mean and energy carrier. Indeed, the results demonstrate that the use of both systems is slightly levelised by passing from an islanded microgrid to a grid-connected one, with a better usage of the electrolyser system, which is downsized according to the typical dimensions with respect to fuel cell system size, (i.e., three times the latter). A reduction of the HST is needed in order to fully exploit the tank itself, thus further lowering the total capital investment. This, in turn, will result in improved economic outcome, in fact, the assessment of the off-grid and grid-connected configurations indicates that SPB and LCOE will reduce by about 25 years and 0,3 €/kWh, respectively, with the total initial cost that is reduced by more than half of the corresponding islanded plant cost. It is worth noting that the above-mentioned high improvements passing from islanded to grid-connected solutions occur when the distance from the grid is zero, thus leading to the ideal condition where no additional costs are to be considered to cover the distance from the grid, when comparing the proposed hydrogen-based microgrid to the conventional grid connected configuration. As recalled above, SPB values greatly reduce when considering the most likely to happen case of relevant distances to be covered, i.e., in remote zones, to find a clean and effective alternative to grid-connected solutions.

Future work will focus on exploiting the dynamic programming algorithm outcomes, for instance, by developing a rule-based control based on fuzzy logic using the results obtained. Another choice can be coupling it with artificial intelligence-based models capable of predicting the demand of energy and production well before, to have a more precise assessment. Thus, a model predictive control architecture can be derived. Finally, to further maximise the PEMFCS and PEMELS advantages, it is possible to consider a hydrogen network as a near-future scenario, where it is possible to buy hydrogen, with a batch of furniture, such as a fixed order, or by ordering the hydrogen needed, and simultaneously it can be sold to this net. This can be done either by adapting an islanded or a grid-connected microgrid. The latter proposal clearly depends on the readiness of the market and can lead to further computational burden by adding another variable to the calculations.