Local Energy Community to Support Hydrogen Production and Network Flexibility

Abstract

This paper deals with the optimal scheduling of the resources of a renewable energy community, whose coordination is aimed at providing flexibility services to the electrical distribution network. The available resources are renewable generation units, battery energy storage systems, dispatchable loads, and power-to-hydrogen systems. The main purposes behind the proposed strategy are enhancement of self-consumption and hydrogen production from local resources and the maximization of the economic benefits derived from both the selling of hydrogen and the subsidies given to the community for the shared energy. The proposed approach is formulated as an economic problem accounting for the perspectives of both community members and the distribution system operator. In more detail, a mixed-integer constrained non-linear optimization problem is formulated. Technical constraints related to the resources and the power flows in the electrical grid are considered. Numerical applications allow for verifying the effectiveness of the procedure. The results show that it is possible to increase self-consumption and the production of green hydrogen while providing flexibility services through the exploitation of community resources in terms of active and reactive power support. More specifically, the application of the proposed strategy to different case studies showed that daily revenues of up to EUR 1000 for each MW of renewable energy generation installed can be obtained. This value includes the benefit obtained thanks to the provision of flexibility services, which contribute about 58% of the total.

1. Introduction

Hydrogen can provide energy to otherwise difficult sectors to decarbonize through electrification. While nowadays over 95% of current hydrogen production is fossil-fuel based, renewable energy sources (RESs) can be easily used to produce hydrogen through electrolyzers, thus helping mitigate the problems related to the variability of renewable sources and allowing a further source of storage for electricity generated from RESs. Electrolyzers can then assume the role of a “flexible load” that is able to provide balancing services to the power system while producing hydrogen for mobility and industrial applications or injection into the gas grid [1]. In [2], the need to supplement electric power system flexibility from the typical sources with new sources was identified, and the role hydrogen production plays in providing flexibility in future electric power systems was analyzed. Particularly, it was concluded that hydrogen production needs to be more deeply integrated into power system planning and operation. In [3], the potential grid services that hydrogen might provide include: regulation, load following, providing an operating reserve, and seasonal energy arbitrage. The inclusion of hydrogen in the optimization of grid management is therefore a critical issue that requires proper strategies in order to enhance the efficient and rational use of the various resources of the grid.

While the topic of integrating several resources, including both the electrical and hydrogen vectors, has been treated in the technical literature, only a few papers have dealt with their integration into a grid considering the technical problems related to grid operation. In [4], a transactive energy-based model is presented for optimal stochastic scheduling of renewable-based microgrids ($\mu$Gs) to maximize economic benefits in the day-ahead market. In the paper, hydrogen energy storage is used for alleviating the intermittence of the RESs. Ref. [5] focuses on the resilience of $\mu$Gs based on power-to-hydrogen and on its ability to operate independently. A comprehensive multi-energy $\mu$G model representing the interaction between electrical, natural gas, and hydrogen subsystems is presented in [6]. Particularly, the proposed model is aimed at maximizing the economic profit for the $\mu$G operator. In [7], a control approach is proposed to schedule the resources of a multi-energy system; it includes the conversion of renewable energy into hydrogen. Particularly, the inclusion of the electrolyzer into a demand response service helps mitigate voltage violations and overloads in an MV distribution network. In [8], a day-ahead security-constrained unit commitment is proposed to integrate a power-to-hydrogen facility in the power system to reduce the violation of load flow constraints due to large wind power penetration. The integration of hydrogen into energy systems through unit commitment is also discussed in [9]. A management approach is proposed in [10] that includes voltage-VAR optimization functionality and ensures hydrogen production while compensating for voltage fluctuation due to renewable generation.

With specific reference to renewable energy communities (RECs), several resources can contribute to flexibility provision, particularly by applying demand response services. Regarding RECs, a survey of the flexibility provision from local energy communities in the context of electricity markets is proposed in [11]. An energy community managed by a local energy controller is proposed in [12]; it includes price-based demand response programs to motivate end-users to modify their consumption patterns, thus allowing the provision of flexibility services to the electrical grid. A demand-response-based strategy for the energy management of a smart grid community is proposed in [13]; it coordinates the distributed resources to balance loads and to reduce the grid consumption cost.

The use of power-to-hydrogen for improving energy self-consumption of renewable power generation has been treated in the technical literature. Particularly, in [14], the optimal configuration of energy systems serving a mixed-use district equipped with an electrolyzer for green hydrogen production was identified. In [15], advanced energy management strategies were proposed to enhance energy flexibility and grid stability through a hybrid electricity–hydrogen sharing system. In [16], a security-constrained multi-period optimal power flow model is proposed with the aim of coordinating generators and power-to-hydrogen units in the presence of large-scale renewable energy sources. Concerning RECs in particular, this topic has been treated in [17,18]. Both papers consider the renewable generation plant to be directly connected to an electrolyzer.

Based on the idea of filling the current gaps in the technical literature by integrating the potential of hydrogen and multi-energy systems in RECs and also considering grid interactions, this paper proposes a new operation strategy for RECs that includes sector coupling resources. Particularly, in this paper, a new formulation is proposed wherein the main objective is to enhance self-consumption and support local hydrogen production while maximizing the economic benefit derived from both selling hydrogen and the subsidies given to the community for the shared energy. For this purpose, the REC considered in this paper includes RES generation systems, battery energy storage systems (BESSs), and electrolyzers, which are all connected to the grid through power converters. Among the various distributed resources, controllable loads are also considered; they can provide demand response service [19]. In addition, another ancillary service is deemed to be provided to the electrical distribution grid: a reactive power service for voltage regulation. This service is supposed to be remunerated, thus guaranteeing a further economic benefit to the community members. To include the remuneration of reactive power in the optimization procedure, we considered ref. [20], wherein a pricing model for joint power and ancillary services was developed. Finally, the multivector approach used in the paper does not ignore all of the technical aspects related to grid operation. Particularly, the electrical power flows in the grid are considered, and all of the constraints related to the BESSs, the distributed generation (DG) systems, and the loads are considered as well.

The remainder of the paper is organized as follows. Section 2 describes the problem formulation; the results of the numerical applications are shown and discussed in Section 3; in Section 4, some conclusions are drawn.

2. Problem Formulation

The proposed control strategy applies to an REC and to the MV distribution network to which its resources are connected. The resources of the REC include photovoltaic (PV) systems, BESSs, electrolyzers, and controllable loads—all connected to the grid through power converters—and non-controllable loads. Regarding the controllable loads, based on their behavior and requirements, they are divided into three types [21]:

• Type I loads: They consume a fixed amount of total energy during the scheduling period and can switch between on and off states. While turned on, their output is a fixed value. Also, the required total energy must be provided within a given operating time window. Examples are water pumps, washing machines, and electric vehicles.
• Type II loads: They also need to consume a fixed amount of total energy, can be switched on and off during a given operating time window, and operate with a fixed power value. However, they also cannot be turned off consecutively for more than a few hours. Examples are refrigerators and freezers.
• Type III loads: Differently from the previous two, they only have a lower boundary for the energy to be provided within the assigned operating time window. They can be switched on and off and can adjust their power consumption continuously. However, their power supply must be above a certain threshold for them to be turned on.

As will be discussed further, the electrolyzer is managed as a controllable load of type III.

The control strategy aims to coordinate these resources to increase REC self-consumption while supporting hydrogen production and guaranteeing flexibility services to the distribution grids. The proposed approach is formulated as an economic problem accounting for the perspectives of both REC members and the distribution system operator (DSO). From the REC members’ point of view, the revenue related to the local self-consumption of PV energy and that provided by the selling of the hydrogen produced are taken into account. From the DSO’s point of view, the cost sustained for the flexibility service in terms of reactive power support is considered. Since the proposed approach aims to increase the self-consumption, the BESS and the electrolyzer are supposed to be allowed to absorb a quantity of energy not exceeding that produced by the RES. Thus, for the assessment of the incentivized energy, the power discharged by the BESS is evaluated as that produced by the RES.

2.1. Objective Function

The control is formulated as day-ahead scheduling aimed at providing the active and reactive power profiles of the BESSs, the reactive power profile of the PV units, the active power of the controllable loads, and the active power of the electrolyzer. Inputs of the scheduling procedure are the forecasts of the daily profiles of the non-controllable loads and of the PV production, the requirements of the controllable loads, the prices for the remuneration of the hydrogen sold, and the incentives related to the shared energy and the reactive power support service. The problem is formulated as a mixed-integer constrained non-linear optimization problem. Each day is divided into $n_t$ time intervals of length $\mathsf{\Delta }t$. The objective function that has to be maximized is formulated in terms of revenues of the REC related to the hydrogen production and to the shared energy and the cost sustained by the DSO for the reactive power support:

$$f_{obj}=\sum _{k=1}^{n_t}\left(m_{H_2,k}{P}_{r,H_2}+E_{sh,k}{P}_{r,sh}-Q_{rec,k}\mathsf{\Delta }t{P}_{r,Q}\right),$$

(1)

where with reference to the time interval k, $m_{H_2,k}$ is the mass and $P_{r,H_2}$ is the sell price of the produced hydrogen, $E_{sh,k}$ is the shared energy, $P_{r,sh}$ is its incentive price, $Q_{rec,k}$ is the sum of the reactive powers provided by all the resources of the REC (taken as positive values), and $P_{r,Q}$ is the reactive energy price.

Regarding $m_{H_2,k}$, it can be evaluated as:

$$m_{H_2,k}={\dot{m}}_{H_2,k}\left(P_{el,k}\right)·\mathsf{\Delta }tk=1,\dots ,n_t,$$

(2)

where ${\dot{m}}_{H_2,k}\left(P_{el,k}\right)$ is the rate of hydrogen production in kg/h, which, in turn, strictly depends on the electric power $P_{el,k}$ absorbed by the electrolyzer at time interval k.

The problem of linking ${\dot{m}}_{H_2,k}$ to the optimization variable $P_{el,k}$ is developed in what follows and refers to the use of a proton exchange membrane (PEM) electrolyzer. In the time domain, the rate of production is given by [22,23]:

$${\dot{m}}_{H_2}\left(t\right)={\eta }_F{M}_{m,H_2}3600{\displaystyle \frac{n_{cell}{i}_{cell}\left(t\right)}{2F}},$$

(3)

where ${\eta }_F$ is Faraday’s efficiency, $M_{m,H_2}$ is the molar mass of molecular hydrogen, which is used to convert mol/s to kg/s, F = 96,487 C/mol is Faraday’s constant, $i_{cell}$ is the current in each cell, and $n_{cell}$ is the total number of cells composing the electrolyzer.

The steady-state electrical behavior of the electrolyzer is represented using the following model for the polarization curve [24,25]:

$$V_{cell}(T,p)=E_{rev}(T,p)+R_i(T,p)·i_{cell},$$

(4)

where $V_{cell}$ is the electrolyzer’s single-cell voltage, p and T are the working pressure and temperature values, respectively, for the cell, $E_{rev}$ is the reversible voltage, and $R_i$ is the equivalent internal cell resistance. The reversible voltage and the internal resistance are evaluated using the following expressions [26]:

$$E_{rev}=e_{rev0}+{\displaystyle \frac{RT}{2F}}·ln\left({\displaystyle \frac{p}{p_0}}\right)$$

(5)

$$R_i=R_{i0}+k_p·ln\left({\displaystyle \frac{p}{p_0}}\right)+d{R}_t(T-T_0),$$

(6)

where $e_{rev0}$ is the reversible cell potential in standard conditions, R = 8.3144 J/(molK) is the universal gas constant, $p_0$ and $T_0$ are the standard pressure and temperature, respectively, $R_{i0}$ is the internal resistance at standard pressure and temperature, $k_p$ is a curve-fitting parameter, and $d{R}_t$ is the internal resistance temperature coefficient of the cell.

Since $P_{el}\left(t\right)=n_{cell}·V_{cell}\left(t\right)·i_{cell}\left(t\right)$, by combining this equation with (4), $i_{cell}\left(t\right)$ can be derived as:

$$i_{cell}\left(t\right)={\displaystyle \frac{-E_{rev}+\sqrt{E_{rev}^2+4{\displaystyle \frac{P_{el}\left(t\right)}{n_{cell}}}{R}_i}}{2R_i}},$$

(7)

which can be used in (3) to obtain ${\dot{m}}_{H_2}\left(t\right)$ as a function of $P_{el}\left(t\right)$. Relation (3) can then be brought back to the discrete-time domain, obtaining the function ${\dot{m}}_{H_2,k}\left(P_{el,k}\right)$.

Regarding $E_{sh,k}$, in accordance with the Italian policy to incentivize the self-consumption in RECs [27], it is given by the minimum value between the overall energy the REC absorbs from the network and the overall energy the REC injects into the network. In our case, the load power also includes the power absorbed from the network by the electrolyzer, while the injected power includes the power generated by the RES and that discharged by the BESS minus the energy charged by the BESS. The shared energy can be then defined as:

$$E_{sh,k}=min\left\{P_{L,rec,k}+P_{el,k};P_{dg,rec,k}+P_{b,dch,k}-P_{b,ch,k}\right\}\mathsf{\Delta }t,$$

(8)

where referring to the k-th time interval, $P_{L,rec,k}$ is the overall active power absorbed by all the members’ loads, $P_{b,ch,k}$ ($P_{b,dch,k}$) is the overall charging (discharging) power of all the BESSs, and $P_{dg,rec,k}$ is the overall active power generated by all the DG units. They are given by:

$$P_{L,rec,k}=\sum _{i=1}^{N_{rec}}\left(P_{L,i,k}+P_{L,i,k}^I+P_{L,i,k}^{II}+P_{L,i,k}^{III}\right)$$

(9)

where $P_{L,i,k}$ is the non-controllable load power, $P_{L,i,k}^I$, $P_{L,i,k}^{II}$, and $P_{L,i,k}^{III}$ are the powers of the three types of controllable loads mentioned above [21], and where

$$P_{dg,rec,k}=\sum _{i=1}^{N_{rec}}{P}_{dg,i,k}$$

(10)

$$P_{b,ch,k}=\sum _{i=1}^{N_{rec}}{P}_{b,ch,k,i}$$

(11)

$$P_{b,dch,k}=\sum _{i=1}^{N_{rec}}{P}_{b,dch,k,i},$$

(12)

with $N_{rec}$ being the number of REC members, and where with reference to the i-th REC member and the k-th time interval, $P_{dg,i,k}$ is the power generated by the DG unit, and $P_{b,ch,k,i}$ ($P_{b,dch,k,i}$) is the power charged (discharged) by the BESS.

The maximization of the above function is subject to equality and inequality constraints that are defined in what follows for each component they refer to.

2.2. Grid Constraints

Equality constraints related to the active and reactive power balances at each bus i of the network are imposed:

$$P_{i,k}=V_{i,k}\sum _{j=1}^{n_t}{V}_{j,k}[G_{i,j}cos\left({\delta }_{i,j,k}\right)+B_{i,j}sin\left({\delta }_{i,j,k}\right)]$$

(13)

$$Q_{i,k}=V_{i,k}\sum _{j=1}^{n_t}{V}_{j,k}[G_{i,j}sin\left({\delta }_{i,j,k}\right)-B_{i,j}cos\left({\delta }_{i,j,k}\right)],$$

(14)

where concerning the time interval k$(k=1,\dots ,n_t)$, $P_{i,k}\left(Q_{i,k}\right)$ is the active (reactive) power injected at bus i of the network, $G_{i,j}$$\left(B_{i,j}\right)$ is the conductance (susceptance) of the nodal admittance matrix related to buses i and j, $V_{i,k}$ is the voltage magnitude at bus i, and ${\delta }_{i,j,k}$ is the phase angle between voltages at buses i and j.

Inequality constraints are imposed on the voltage magnitude at all the network buses, which must fall within a permissible range:

$$V_{min}\le V_{i,k}\le V_{max}i=1,\dots ,nk=1,\dots ,n_t,$$

(15)

where $V_{min}$ and $V_{max}$ are the minimum and maximum voltage values, respectively.

2.3. DG Constraints

The DG units are connected to the grid through power converters. Constraints are thus imposed on the reactive power, which cannot exceed a range of values. In this case, it is assumed that the range is based on the performances required by the DG in the distribution network [20]:

$$Q_{dg,min,i}\le Q_{dg,i,k}\le Q_{dg,max,i}i=1,\dots ,n_{d}k=1,\dots ,n_t,$$

(16)

where $Q_{dg,min,i}$ and $Q_{dg,max,i}$ are the minimum and maximum reactive powers, respectively, that can be provided by the i-th DG, $Q_{dg,i,k}$ is the reactive power provided, and $n_d$ is the number of DG units. It is worth noting that constraint (16) is related to the mechanism of reactive power pricing. The values of $Q_{dg,min,i}$ and $Q_{dg,max,i}$ are imposed, respectively, based on the lagging and leading power factors the DG unit can work with [20].

2.4. BESSs Constraints

A constraint similar to that reported in (16) must be imposed on the converters interfacing with the batteries:

$$Q_{b,min,i}\le Q_{b,i,k}\le Q_{b,max,i}i=1,\dots ,n_{b}k=1,\dots ,n_t,$$

(17)

where $Q_{b,min,i}$ and $Q_{b,max,i}$ are the minimum and maximum reactive powers that can be provided by the i-th BESS, $Q_{b,i,k}$ is the reactive power provided, and $n_b$ is the number of BESSs.

Differently from that of DG units, the active power of BESSs is a control variable [28]; therefore, it also has to be limited:

$$P_{b,ch,k,i}\le P_{b,ch,max,i}i=1,\dots ,n_{b}k=1,\dots ,n_t,$$

(18)

$$P_{b,dch,k,i}\le P_{b,dch,max,i}i=1,\dots ,n_{b}k=1,\dots ,n_t,$$

(19)

where $P_{b,ch,max,i}$ and $P_{b,dch,max,i}$ are the maximum charging and discharging active powers, respectively, allowed for the i-th BESS.

Moreover, a constraint is imposed on the batteries’ state of charge (SoC), which must fall within an admissible range:

$$So{C}_{min,i}\le So{C}_{b,i,k}\le So{C}_{max,i}i=1,\dots ,n_{b}k=1,\dots ,n_t,$$

(20)

where $So{C}_{b,i,k}$ is the i-th battery’s SoC at the end of time interval k, whereas $So{C}_{min,i}$ and $So{C}_{max,i}$ are its minimum and maximum values, respectively. These values are assessed based on the state of health and the preservation of battery lifetime. The SoC can be evaluated as:

$$So{C}_{b,i,k}=So{C}_{b,i,k-1}+\left[{\eta }_{ch,i}{P}_{b,ch,k,i}-{\displaystyle \frac{1}{{\eta }_{dch,i}}}{P}_{b,dch,k,i}\right]\mathsf{\Delta }ti=1,\dots ,n_{b}k=1,\dots ,n_t,$$

(21)

where ${\eta }_{ch,i}$ and ${\eta }_{dch,i}$ are the i-th BESS’s charging and discharging efficiencies, respectively. A further constraint on the SoC is related to its value at the end of the day, which must be the same as the value it had at the beginning of the day:

$$So{C}_{b,i,0}=So{C}_{b,i,n_t}i=1,\dots ,n_b,$$

(22)

where $So{C}_{b,i,0}$ is the initial SoC, and $So{C}_{b,i,n_t}$ is the SoC at the end of the day. It is also imposed that batteries cannot charge and discharge at the same time:

$$P_{b,ch,k,i}·P_{b,dch,k,j}=0i,j=1,\dots ,n_{b}k=1,\dots ,n_t.$$

(23)

Note that in (23), the product of the charging and discharging powers can refer to the same battery or distinct batteries. In the latter case, this constraint imposes that, at the same time interval, all the BESSs must either charge or discharge. This allows for obtaining efficient use of the BESSs.

2.5. Controllable Load Constraints

The controllable load constraints refer to their specific behavior, and the requirements and are defined as follows [21].

Type I loads:

The operative characteristics of type I loads translate into the following constraints, to be imposed on their power values:

$$\begin{array}{cc}\hfill & \sum _{k\in {\mathsf{\Omega }}_I}{P}_{L,i,k}^I\mathsf{\Delta }t={\overline{E}}_{L,I,i}\hfill \\ \hfill & P_{L,i,k}^I\in \{0,{\overline{P}}_{L,I,i}\}\hfill \\ \hfill & k\in {\mathsf{\Omega }}_{I,i}\hfill \end{array}$$

(24)

where ${\mathsf{\Omega }}_{I,i}\subseteq [1,\dots ,n_t]$ is the subset of time intervals within which the load must be scheduled, ${\overline{E}}_{L,I,i}$ is the total energy required by the load, and ${\overline{P}}_{L,I,i}$ is the load power when it is turned on.

Type II loads:

The behavior of type II loads was modeled using the following constraints:

$$\begin{array}{cc}\hfill & \sum _{k\in {\mathsf{\Omega }}_{II,i}}{P}_{L,i,k}^{II}\mathsf{\Delta }t={\overline{E}}_{L,II,i}\hfill \\ \hfill & \sum _{k=t}^{t+q_{II,i}}{P}_{L,i,k}^{II}\mathsf{\Delta }t\ge n_{II,i}{\overline{P}}_{L,II,i}\mathsf{\Delta }t\hfill \\ \hfill & P_{L,i,k}^{II}\in \{0,{\overline{P}}_{L,II,i}\}\hfill \\ \hfill & k\in {\mathsf{\Omega }}_{II,i},\hfill \\ \hfill & t={\overline{p}}_{1,i},\dots ,{\overline{p}}_{2,i}-q_{II,i},\hfill \end{array}$$

(25)

where ${\mathsf{\Omega }}_{II,i}=[{\overline{p}}_{1,i},{\overline{p}}_{2,i}]\subseteq [1,\dots ,n_t]$ is the subset of time intervals within which the load must be scheduled, ${\overline{E}}_{L,II,i}$ is the total energy required by the load, ${\overline{P}}_{L,II,i}$ is the load power when it is turned on, and $n_{II,i}$ is the minimum number of time intervals during which the load must be turned on for every operating period lasting $q_{II,i}$ time intervals.

Type III loads:

The behavior of type III loads was modeled using the following constraints:

$$\begin{array}{cc}\hfill & \sum _{k\in {\mathsf{\Omega }}_{III,i}}{P}_{L,i,k}^{III}\mathsf{\Delta }t\ge {\overline{E}}_{L,III,i}\hfill \\ \hfill & P_{L,i,k}^{III}\in \{0,p_{L,aux,i,k}\}\hfill \\ \hfill & P_{L,III,min,i}\le p_{L,aux,i,k}\le P_{L,III,max,i}\hfill \\ \hfill & k\in {\mathsf{\Omega }}_{III,i},\hfill \end{array}$$

(26)

where ${\mathsf{\Omega }}_{III,i}\subseteq [1,\dots ,n_t]$ is the subset of time intervals within which the type III loads must be scheduled, ${\overline{E}}_{L,III,i}$ is the minimum energy to be supplied within this period, $P_{L,III,min,i}$ and $P_{L,III,max,i}$ are the minimum and maximum powers, respectively, that the load can absorb when it is turned on, and the auxiliary variable $p_{L,aux,i,k}$ is the continuously varying power value of the load while turned on.

Outside of their respective scheduling windows ${\mathsf{\Omega }}_{\alpha ,i}$ ($\alpha =I,II,III)$, all controllable loads are turned off.

2.6. Electrolyzer Constraints

Regarding the electrolyzer, it is managed as a controllable load of type III, where in (26), $p_{L,aux,i,k}$ is limited by the rating of the electrolyzer $P_{el}^{rtd}$ as the maximum value and by the turndown power as the minimum value. Regarding the latter, this lower boundary exists to prevent excessive crossover of hydrogen into the oxygen-rich anode region, which would create hazardous conditions [29]. Also, it has to be noted that at a low load level, the efficiency is low due to relatively higher consumption from the system’s auxiliaries. Proper models are available in the literature to evaluate the conversion efficiency at low-power operating points [30]. However, to avoid working at a low efficiency level, in practical applications, the minimum working power is set to be a little higher than the turndown level. Thus, the implementation of more accurate models that take into account the relatively higher consumption from the system’s auxiliaries was not performed. Regarding the first constraint of (26), $E_{L,III,i}$ can be assumed to be equal to a value imposed by the storage tank, which was not considered in this paper.

A constraint is also placed on the power balance, preventing both the electrolyzer and the BESSs to be powered by the grid. This means that the power used to charge the BESSs can only be generated by the DG units, and the power supplied to the electrolyzer can be provided only by the DG units or the discharging BESSs:

$$P_{el,k}+P_{b,ch,k}\le P_{b,dch,k}+P_{dg,rec,k}.$$

(27)

2.7. Solution Method

As stated at the beginning of Section 2.1, the proposed strategy is formulated as a mixed-integer constrained non-linear minimization problem, for which the scheme is shown in Figure 1. In this paper, however, the problem was solved through mixed-integer linear programming (MILP). For this reason, some expedients and techniques were used to adjust the non-linear functions and constraints detailed in the previous sections to a linear framework.

Figure 1. Flowchart of the proposed procedure.

The electrolyzer’s model described by (3)–(7) results in a non-linear relation between ${\dot{m}}_{H_2,k}$ and $P_{el,k}$. Assuming constant temperature and pressure, the model can be linearized as follows [31]:

$${\dot{m}}_{H_2,k}=a·P_{el,k}+bk=1,\dots ,n_t,$$

(28)

where a and b are the linear regression parameters. With reference to an electrolyzer with a power of 1 MW, which was used in the numerical application, the comparison between the rigorous model and (28) is shown in Figure 2. The resulting mean error relative to the electrolyzer’s actual hydrogen production rate is a little above 1%.

Figure 2. Comparison between the original electrolyzer model and its linearization (28).

The function to be minimized in (8) is also non-linear. To circumvent this problem, a vector of $n_t$ auxiliary optimization variables was introduced to represent the shared energy $E_{sh,k}$ for $k=1,\dots ,n_t$. By including it in the objective function as a term to be maximized and, at the same time, imposing through constraints that it be less than or equal to each of the arguments in curly brackets in (8), it coincides with the shared energy as defined in the same equation.

Moreover, the reactive power $Q_{rec,k}$, which appears in (1), requires the evaluation of absolute values. This was handled by considering distinct optimization variables for the capacitive and inductive reactive power contributions in (16) and (17). This approach required the use of the big-M method [32] to make sure that each resource is modeled so it can output only positive or only negative reactive power at any given time step.

The power flow Equations (13) and (14) were linearized through the Newton–Raphson function.

The constraint (23) was implemented using the big-M method, imposing that the variables related to the charging and discharging powers of any singular BESS or belonging to distinct BESSs cannot be contemporaneously different from zero. This solution requires the introduction of auxiliary boolean variables representing the charging/discharging states of each BESS at each time step.

In a slightly different form, the big-M method was also used to linearize the model (26) of the type III controllable loads. In this case, two sets of $n_t$ auxiliary variables are needed for each load. At each time step k, one auxiliary variable is a boolean representing the on/off state of the load, and the other corresponds to $p_{L,aux,i,k}$. The product of these two results is the actual power absorbed by the load. Since the electrolyzer is modeled similarly to type III loads, it also requires the use of the big-M method.

3. Numerical Application

The proposed scheduling procedure was applied to the test MV distribution network of Figure 3 [33]. This network is composed of two feeders connected to an upstream HV network through two 25 MVA, 110/20 kV transformers. The REC members are customers connected to buses #4, #5, #9, #12, #14, and #15 and include some non-controllable loads for which the overall rated power is about 100 kW. The REC includes two PV systems connected to buses #12 and #14, which are both characterized by 1 MW rated power, two BESSs connected to buses #4 and #9, with each having 0.5 MW rated power and 2 MWh capacity, and an electrolyzer having 1 MW rated power connected at bus #7. A minimum value equal to 10% of the rated power was assumed for the electrolyzer [34]. These data are reported in Table 1. A group of controllable loads are also considered and are connected to bus #15; their details are reported in Table 2. The PV power generation profile was adapted starting from a set of available measured data referring to the GECAD N PV power plant installed at the Instituto Superior de Engenharia do Porto/Politécnico do Porto [35]. In particular, a typical summer day PV power production profile was chosen for the numerical application. It is shown in Figure 4 together with an example of a non-controllable load power profile. Regarding the reactive power support provision of BESSs and PV units, both are assumed to be able to work within lagging and leading power factors of $0.9$.

Figure 3. Scheme of the test network.

Table 1. Data of the REC resources.

	N.C. Load	PV 1	PV 2	Electrolyzer	BESS 1	BESS 2
Bus	#4, #5, #9, #12, #14, #15	#12	#14	#7	#4	#9
Rating	100 kW	1 MW	1 MW	1 MW	0.5 MW 2 MWh	0.5 MW 2 MWh

Table 2. Controllable load details.

	Type I	Type II	Type III
${\overline{P}}_{L,\alpha }$ (kW)	200	100	-
${\overline{E}}_{L,\alpha }$ (kWh)	800	600	400
${\mathsf{\Omega }}_{\alpha }$	08:00–16:00	06:00–18:00	08:00–16:00
$P_{L,\alpha ,min}$	-	-	10
$P_{L,\alpha ,max}$	-	-	100
$n_{\alpha }$	-	2	-
$q_{\alpha }$	-	4	-

$\alpha =\mathrm{I},\mathrm{II},\mathrm{III}.$

Figure 4. Active power profiles of (a) the PV system connected to node #12 and (b) the load at node #10.

Each resource is supposed to have a different point of delivery. According to [27], the price for the shared energy for generation units with rated power greater than 600 kW is evaluated as (60 + max (0; 180 − zonal price)) EUR/MWh. However, this value cannot be higher than 100 EUR/MWh. Based on the current value of the Italian market price, the resulting shared energy price has been assumed to be equal to 100 EUR/MWh. The selling price for the hydrogen is assumed 2.3 EUR/kg [36], and the tariff for the remuneration of the reactive power support is 3 EUR/MVarh [20]. The proposed method was implemented using the Optimization Toolbox provided by MATLAB^®, version R2020b.

3.1. Case Studies

The test of the procedure was carried out by considering three case studies. Initially, it is supposed (case study 1) that there is no coordination between REC members and the DSO: the perspective of the REC is considered and its revenue from shared energy and hydrogen production is maximized without considering the network constraints.

Then (case study 2), a simulation performs a scheduling procedure that includes coordination between the DSO and REC. The resources adapt their active power exchanges to maximize the REC revenue while simultaneously supporting the DSO, guaranteeing that the network constraints are satisfied.

Finally, the third case study (case study 3) also includes the reactive power support provided by the BESSs and PV systems. The perspectives of both the REC members, which aim to maximize their revenue, and the DSO, which requires minimizing the expenditure sustained for voltage support, are considered.

3.2. Results

The results in terms of shared energy, hydrogen production, and overall REC revenue are reported in Table 3.

Table 3. Simulation results.

	Case 1	Case 2	Case 3
Produced H2 [kg]	262.9	74.0	262.9
Shared energy [MWh]	14.123	6.767	14.123
Revenue [EUR]	2015	847	2035

The results of case 1 are the best in terms of shared energy and H₂ production since, in this case, network constraints are not considered. Including the network constraints without considering any reactive power support (case 2), the shared energy and H₂ production decrease. This is due to the limitation of active power flows between PV units, loads, and the electrolyzer. When reactive power support is considered (case 3), constraint violations are avoided without impacting the active power flow. This allows us to get the same results in terms of shared energy and H₂ production of case 1 thanks to the reactive power support.

In terms of revenues, the worst results appear for case 2. The revenue for case 3 is slightly higher than that of case 1 since, while the revenue from H₂ production and shared energy are the same as that of case 1, a further contribution is obtained from the reactive power provision, whose amount is, however, a little less than a 1% increase. It is worth noting that while the reactive power service is an additional cost for the DSO, it is also a benefit that allows an increase to both H₂ production and shared energy.

In Figure 5, the voltage profiles for some hours of the day are shown with reference to the three case studies. Figure 5a refers to case 1 and shows the voltage constraint violation at hour 12. This violation is clearly due to the increased load power of bus #7 due to the electrolyzer power demand at this hour. As shown in Figure 5b, which refers to case 2, the constraint violation is avoided thanks to the reduction in the electrolyzer’s power demand. In case 3, the reactive power support allows for avoiding the voltage violation (Figure 5c), even with the higher power demand by the electrolyzer. This is confirmed by Figure 6, where the active power demand profile of the electrolyzer is reported for all the cases.

Figure 5. Voltage levels for all nodes for hours 8 and 12 for (a) case 1, (b) case 2, and (c) case 3.

Figure 6. Electrolyzer active power profiles for (a) case 1, (b) case 2, and (c) case 3.

Further results from the numerical application of the proposed procedure are reported in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12. The contributions of both BESSs are shown in Figure 7 and Figure 8 in terms of charging and discharging power and SoC. The power profiles of controllable loads in all three cases are reported in Figure 9, Figure 10 and Figure 11. The reactive power of some resources is reported in Figure 12.

Figure 7. (a) Active power and (b) SOC of the BESS connected to node #4 (case 3).

Figure 8. (a) Active power and (b) SOC of the BESS connected to node #9 (case 3).

Figure 9. Active power profiles of (a) type I, (b) type II, and (c) type III controllable loads (case 1).

Figure 10. Active power profiles of (a) type I, (b) type II, and (c) type III controllable loads (case 2).

Figure 11. Active power profiles of (a) type I, (b) type II, and (c) type III controllable loads (case 3).

Figure 12. Reactive power profiles for case 3 for: (a) the BESS connected to node #4, (b) the BESS connected to node #9, and (c) the PV system at node #12.

As is shown in Figure 7 and Figure 8, both BESSs are used to shift the energy provision in the hours of low PV generation, thus increasing the self-consumption and the production of H₂. Similarly, controllable load scheduling appears properly coordinated with the other resources (Figure 9, Figure 10 and Figure 11). The profiles vary from case to case. More precisely, cases 1 and 3 show identical behavior for the type I load, while cases 2 and 3 are identical for the type II load profile. The type III load instead behaves differently in all three cases. This is likely due to its greater flexibility compared to the other controllable loads. Finally, Figure 12 reveals that the contributions of BESSs and PV units mainly appear when large power is absorbed from the electrolyzer. The reactive power profile of the PV unit installed in node #14 is not shown, as it is null during the whole day. All figures show that the imposed constraints are satisfied.

Numerical results also show that the linearization techniques discussed in Section 2.7 had low effects on the accuracy of the results. In terms of total daily hydrogen production, the error caused by the use of the linearized model (28) in place of the original one described by (3)–(7) amounts to about 0.55% in case 1, 0.68% in case 2 and 0.64% in case 3. The error related to the Newton–Raphson-based approximation of the load flow equations was also evaluated. Referring, for example, to case 3: the maximum voltage error across all nodes and all hours of the day is approximately 0.0012 pu; the maximum error relative to each node voltage is about 0.135%; the mean relative error across all nodes and all hours of the day is around 0.022%.

Comparing the results of the numerical application with those obtained in other papers published in the technical literature, some observations can be made. The use of the proposed procedure allows for incrementing the production of hydrogen through the exploitation of the resources of an REC, as shown in [17]. Also, it can be observed that the essential contribution of the reactive power support to the production of hydrogen recognized in [16] is confirmed, and the procedure proposed in this paper allows for consideration of the reactive provision from all of the resources of the REC. Compared to the results of [31], the proposed procedure allows for increasing the share of renewable energy through the proper coordination of the storage systems and controllable loads instead of using fossil-based energy absorbed from the network.

4. Conclusions

In this paper, optimal scheduling of the resources of a renewable energy community is proposed to enhance self-consumption, increase the production of hydrogen from local resources, and provide flexibility services to the electrical distribution network. The flexibility service considered in this paper consists of reactive power provision to the grid operator for voltage regulation. The proposed scheduling strategy is formulated in terms of a mixed-integer non-linear optimization problem. The results of the numerical applications show the importance of the proposed strategy to enhance both the economic and environmental benefits obtainable from the proper use of the distributed resources of a renewable energy community. Though they are not analytically evaluated in this paper, environmental benefits deriving from the proposed procedure are related to the maximization of the self-consumption derived from renewable energy sources and the exploitation of green hydrogen produced from local non-fossil sources. The contribution of hydrogen to the decarbonization of sectors such as transport, buildings, and industry is further increased by the possibility of decoupling generation and consumption through the production of transportable hydrogen. Also, the results allowed for analyzing the potential of hydrogen to support power system decarbonization by complementing batteries and other providers of grid services and flexibility. It has to be noted that, in this paper, the electrolyzer is assumed to be working at a fixed temperature and pressure. Future works could take into account the thermal balance and pressure dynamics of the electrolyzer. Uncertainty could also be taken into account by using a probabilistic approach, as it is becoming a more and more important factor in the context of power systems featuring deeper penetration of variable energy resources.