Novel Concept of Assessing the Cost of Delivered and Non-Delivered Electricity by Deploying Mobile Electricity Storage Facilities

Abstract

Due to the growing importance of ensuring energy security while using low-carbon sources of electricity, it is necessary to use energy storage technologies. However, sometimes it is not possible to use stationary battery energy storage systems. In such cases, mobile energy storage facilities are an alternative solution. This article presents a methodology for assessing the cost of delivering or not delivering energy to the end user when demand will be covered by mobile electricity storage facilities. It is proposed that financial compensation for the end user should depend on hourly revenues and a bonus coefficient. Next, the cost of delivering energy to the end user was minimized by changing the nominal capacity of the mobile energy storage battery and the number of vehicles, taking into account technical and spatial constraints. The results show that the average cost of delivering energy from mobile energy storage systems can vary from 0.4 EUR/kWh to even 184 EUR/kWh, with an average cost of 9.1 EUR/kWh. However, it should be emphasized that a fleet of vehicles with mobile energy storage facilities can only provide energy for a limited period of time. Out of all the simulations carried out, the best results were achieved for the 1 and 4 h power outages; the level of successful electricity provision was above 80%.

1. Introduction

1.1. Motivation and Background

Current European Union (EU) policies emphasize sustainable development in the electricity generation sector as well as issues of energy security for member states [1,2]. At the same time, it should be remembered that as a society we are completely dependent on electricity, and increasing investment in digitization and moving away from fossil fuels, e.g., in the case of the phase-out of internal combustion engine cars, is causing an increase in demand for electricity [3]. In particular, the transport and IT services sectors are consuming ever-increasing volumes of electricity [4,5]. As our dependence on electricity grows, new challenges arise in ensuring the energy security of facilities, particularly in terms of critical infrastructure. Traditional diesel generators have been supplemented by battery energy storage systems (BESSs) [6] and other hybrid generation units based, for example, on gas combined heat and power or combined solar (PV) power plants with BESSs and wind farms [7]. However, there are doubts as to whether these resources are sufficient. This is because the necessary technical, spatial, economic, and even environmental conditions for investing in stationary power backup resources are not always available. Mobile solutions can therefore be implemented. A popular method is the use of mobile power generators, e.g., distribution system operators (DSOs), in the event of planned or unplanned power outages [8]. When setting new trends in the energy sector, the use of electric vehicles (EVs) for this purpose can be considered [9]. Selected models support vehicle-to-grid (V2G) or vehicle-to-building (V2B) technology, or more broadly, vehicle-to-load (V2L) technology [10,11]. By discharging the EV traction battery using V2G, V2B, or V2L technology, they can provide additional power backup, e.g., during emergencies or natural disasters [12]. However, there are significant limitations regarding their use. Firstly, you need to have an EV that supports this technology; secondly, the vehicle cannot be used for transportation purposes at that moment; and thirdly, you need to take into account the energy reserve needed to continue the movement of the EV. In particular, the latter two operational limitations pose a major barrier to the smooth implementation of this resource for the backup power supply of end users. This has led to the dawn of the concept of mobile energy storage facilities (MESFs) integrated into the cargo space of commercial vehicles, creating custom electric vehicles (CEVs) [13,14]. The authors have already conducted research on scaling the capacity of MESF batteries depending on the services provided and the technical and economic feasibility of load time shifting, and have begun analyses of backup power supply services for end users [13,15,16]. However, during further research, the challenge arose of how to determine the cost of providing such a service, also taking into account the cost of not delivering electricity, normally expressed as the Value of Lost Load (VoLL). It is worth noting, however, that the proposed methodologies for calculating VoLL in the literature refer to the macro scale, showing the diversity between sectors across a large number of entities [17].

The aim of this article is to develop a novel methodology that will provide a comprehensive assessment of the cost of delivering and not delivering electricity from MESFs to the end user. In the first step, the quantification of the rate for the provision of a grid service, comprising the process of discharging a battery in the MESF, is presented. The second phase of this methodology involves an assessment of the cost of not delivering electricity, depending on the hourly revenues recorded by the company. In addition, in order to compare it with existing methodologies, a survey was conducted for three public entities to estimate their individual VoLL values, which will be treated as referenced values. Based on technical and economic constraints, the proposition of power backup services provided by MESFs were shown and the cost of providing this service was calculated. Afterwards, the estimated rates of providing a backup power supply from MESFs were compared to survey-based VoLL values. Furthermore, the possibility of providing such grid services from the DSOs to a group of end users during a power grid failure, supplied from a single medium/low voltage (MV/LV) station, was analyzed.

1.2. State-of-the-Art Services

The backup power services provided by mobile energy storage facilities can be achieved by various techniques—engaging typical electric vehicles to discharge their traction battery (V2G/V2B technology) or calling a fleet of CEVs—that provide additional energy potential. In [18], calculations are presented regarding the number of EVs with V2B technology capabilities that are required for the operation of a local building microgrid, both from a technical and economic perspective. A techno-economic analysis of the V2G system in the JAMALI grid in terms of changes in feed-in tariff schemes, including regular, natural, and demand response tariffs, is described in [19]. Issues related to the optimal scheduling of plug-in hybrid vehicles as mobile power sources in terms of increasing the reliability of microgrids are presented in [20]. The publication [21] describes a solution to the linear programming problem, assuming uncertainties in the process of ensuring optimal energy management in a building microgrid using an EV with V2G technology. In [22], issues are presented in which EVs supplement and stabilize energy production in wind farms and biogas units in terms of off-grid management. The article [23] describes the possibility of using V2G technology in cooperation with local diesel generators at military bases. The publication [24] presents a novel rolling optimization method utilizing EVs and MESFs for dynamic and adaptive load restoration. The research also shows the possibility of using MESFs as additional energy storage devices in the coordination of power systems. In [25], a mobile energy storage dispatch model to minimize load curtailment is presented, through the use of an additional 1 MWh capacity storage unit. The publication [26] focuses on developing a MESF movement strategy to ensure power supply to isolated energy consumers in post-disaster situations, which is critical for research regarding the cost of undelivered energy to consumers. This category of research is also examined in [12,27,28]. On the other hand, [29] presents the possibility of MESF operation in a distribution system, using the IEEE 13-bus test system as an example. Similarly in [30], the possibility of using MESFs in the provision of ancillary services in distribution grids is presented. The second part of the literature review concerns research on the assessment and methodologies of the VoLL indicator. This topic was already a subject of interest among scientists by the end of the 20th century [31,32]. A review of methods for calculating the VoLL indicator is presented in [33]. The article [34] presents a systematic and comparative assessment of the practices of EU member states in calculating VoLL. In [35], detailed research on the VoLL indicator was conducted for 51 sectors of the economy. Meanwhile in [36], research on the VoLL index in Iran was presented. In [37], the VoLL index for Portugal was calculated using a macroeconomic technique, namely the production–function approach. A similar method was used in the study of the VoLL index for the residential sector in Germany [38]. Regional studies were also conducted for Indonesia, where VoLL indices were estimated for outages of 5 min, 1 h, 4 h, 12 h, and 24 h [39], as well as for the industrial sector in South Korea [40]. The publication [41] presents a modified method for calculating the net present cost, taking into account the cost of undelivered energy depending on the VoLL index. More accurate methods of assessing the VoLL index, sensitive to changes in certain economic parameters, were also sought, such as in [42], which presents an approach of using data from choice experiment surveys along with available interruption cost functions. Also, in [43], a modification to the calculation of the VoLL index was presented, taking into account annual savings in energy bills, annualized capital cost, and operating costs of end user backup power resources. The authors of [44] concluded that using more-detailed VoLL data leads to more cost-effective transmission reliability decisions. In [45], on the other hand, the probability of source failure was taken into account in the calculation of the VoLL index.

1.3. Novelty

As the previous literature findings show, there have already been attempts to develop a more accurate method for assessing the costs of delivering or not delivering electricity to end users, including using the principles assigned to the VoLL indicator. In both [41,43], there is a noticeable desire to include a greater number of variables in the assessment of the costs of undelivered energy, particularly for taking into account the investment and operating costs of backup power resources. However, it should be noted that these studies did not address the valuation of the outsourced service of recalling MESFs. In principle, the VoLL indicator could be a good reference value. However, our goal was to propose a simple methodology that would allow us to assess whether calling on an appropriate fleet of MESFs to the place of provision of the grid service would reduce the unit cost of energy delivery or avoid the cost of energy not being delivered. Therefore, a method was proposed in which such a grid service is provided, and the cost to the end user is equal to the deployment of the MESF fleet. The rate for providing the service using MESF was made dependent on whether the energy balance is ensured. If so, i.e., a MESF covers the specified level of electricity demand, then the rate depends on the operating costs and capital expenditures attributable to the resources needed to be run for a single entity, calculated per hour of use, and on the fee associated with the supply of electricity at market price. In the event that the MESF fleet is unable to meet the power demand, it was decided that a premium coefficient should be set, depending on the revenue of a given entity for commercial entities, while for household users it depends on the percentage of the electricity bill, and the rate must be simple and understandable. Our goal was also to move away from treating the sector-based VoLL as the single indicator in the process of assessing the cost of electricity not delivered, as it reflects the behavior of the entire sector, and not a single company, as in [39]. To increase accuracy, it was decided that the unit costs of providing the service in hourly intervals should be determined as a function of time without access to electricity from the grid. Therefore, the following novel contributions were identified as follows:

• A mathematical model for pricing the ancillary service, using a MESF to maintain power supply during power grid failures.
• A change in the approach of linking the cost of electricity non-delivery to the characteristic approach for the VoLL indicator and replacing it with a simpler component dependent solely on the commercial entity’s revenue or the percentage value of the electricity bill for households.
• The application of the developed approach allows for the valuation of services related to the triggering of additional energy resources, such as MESFs, regardless of the VoLL indicator values obtained. This provides flexibility in calculating the cost of delivering or not delivering energy to the end user, e.g., allowing for seasonality to be taken into account.
• The calculation of the technical and economic parameters of the MESF fleet providing ancillary services to end users of a given nature.

The structure of the article is as follows: Section 2 presents the mathematical and simulation models needed to calculate the cost of delivering or not delivering energy to the end user during the provision of grid services using MESFs, Section 3 presents the results of a survey that will allow the VoLL value to be determined in accordance with the approach currently used, Section 4 presents the assumptions for the case study, and Section 5 discusses the results obtained.

2. Materials and Methods

2.1. Modeling the Provision of Grid Services Provided by Mobile Electricity Storage Facilities

The use of mobile energy storage facilities in the distribution grid may provide an opportunity to implement a number of grid services, supporting both the direct functioning of end users and DSOs in creating local energy security resources. Similarly to [13], they are called MESF services, i.e., “services involving the delivery of additional energy capacity from mobile electricity storage, provided by an electricity trading licensed company to service takers or for own purposes on a scheduled or emergency basis” [13]. From the point of view of research on the cost of electricity delivered or not delivered, it is crucial that MESF resources allow for the minimization of the negative financial effect incurred by electricity consumers or indirectly by DSOs. Therefore, providing an additional power source during grid failures could be one of the objectives of using MESF for electricity end users. It can be assumed that the reference value should be the VoLL indicator, which, however, is expressed in the context of the entire sector (production–function) and on an annual basis. In order to assess the feasibility and cost of implementing such a service, taking into account the technical and economic criteria for the operation of CEVs carrying MESF, it is necessary to conduct detailed studies at time intervals characteristic of the analysis of power system operation, i.e., 15 min or 1 h. Based on the aforementioned findings, it is possible to determine a certain hourly volume of electricity that may not be delivered as a result of a power failure to the service taker (end user or DSO). This quantity will be denoted by $E_{DEM,t}$. Such an approach has already been applied in previous studies, especially in relation to VoLL values [40]. Due to the fact that a novel approach methodology adapted to the use of MESFs in the process of providing network services was developed in this study, the VoLL values obtained in the traditional manner will only serve as reference points. However, it is important to note that methodologies for assessing the costs of energy not delivered are often based on annual data, and given the early stage of MESF development, logistical aspects are not taken into account in this study. Therefore, based on annual values, e.g., electricity demand, an attempt was made to express indicators related to the security of supply to service takers, using MESF in hourly intervals by calculating the average hourly volume of electricity as follows:

$$E_{avgh}^{DEM}={\displaystyle \frac{E_{DEM,A}}{8760}}$$

(1)

where $E_{DEM,A}$—the end user’s annual electricity consumption, expressed in kWh, and $E_{avgh}^{DEM}$—average hourly electricity consumption by the service taker, constituting the basis for determining the volume of energy necessary to secure within 1 h, expressed in kWh.

The parameter $E_{avgh}^{DEM}$ will be the base value, which can be modified in further calculations depending on the scenario being examined, as it is only an average value. Therefore, the following formula is applicable:

$$E_{avgh}^{SAF}=E_{avgh}^{DEM}·\sigma ·\tau {\forall }_{\sigma \in <0,1>} {\forall }_{\tau \ge 1}$$

(2)

where $E_{avgh}^{SAF}$—the amount of electricity secured by MESF services, expressed in kWh; $\sigma$—the correction factor determining the degree of electricity secured; and $\tau$—the number of hours of service provision.

As a rule, the energy volume $E_{avgh}^{SAF}$ should be secured by a sufficient number of MESFs with adequate potential. Each MESF will be placed in a custom electric vehicle (CEV), the model of which will be presented in Section 2.2. The basic equation that must be met has been determined as follows:

$$E_{CEV,n}·n_{CEV}{\ge E}_{avgh}^{SAF}$$

(3)

where $E_{MESF,n}$—net electricity supplied by the n-th CEV, expressed in kWh, and $n_{CEV}$—number of CEVs providing the MESF service.

2.2. Modeling the Mobile Electricity Storage Facilities

From Equation (3), it is evident that the electrical energy supplied by n CEVs must cover the demand for MESF services, and therefore it is necessary to first define the amount of this energy and adjust it to the transport capacity of CEVs. The CEV concept has been presented in previous studies [13,15]. It involves the setting up of an additional mobile electricity storage facility in the cargo area of commercial vehicles (both heavy and light). The main idea is that the energy from the MESF does not depend on the traction battery of the electric vehicle that transports it. It depends solely on the state of charge (SOC) of the battery, with the logistical task being the maintenance of the maximum charge level at the start of service. Figure 1 shows a block diagram of energy flows for a CEV vehicle.

Based on Figure 1, it is evident that energy flow to the MESF battery can occur both at the point of service provision and at the recharging capacity spot (RCS), i.e., the CEV stationing base. In this case, the MESF is charged with energy from RES or the grid. Energy also flows to the traction battery at the RCS, and this is the only place where this energy flow can occur. In the reverse direction from the MESF battery to the grid, the main direction of flow occurs at the point of MESF service provision. There may be an exceptional situation in which excess energy from the RES installation cannot be used in other service takers’ facilities, so the energy can be transferred to purpose-built battery energy storage systems at the RCS. Since this article examines new approaches for determining the ratio of delivered and undelivered energy, we will only be interested in the direction from the MESF to the service taker’s installation. We assume that the MESF service provider has made every effort to ensure that at the place of service provision and at the time of its commencement, $SO{C}_{st}=100\%$. Based on this, a general formula for calculating the MESF energy potential can be determined as follows:

$$E_{CEV,n}= {C_{MESF}}_n· SO{C}_{st,n}· DO{D}_n·{\eta }_{BAT}$$

(4)

where ${C_{MESF}}_n$—nominal capacity of the MESF battery of the n-th CEV, expressed in kWh; $SO{C}_{st,n}$—state of charge of the MESF battery for the n-th CEV at the beginning of the MESF service, expressed in %; $DO{D}_n$—depth of discharge of the MESF of the n-th CEV; and ${\eta }_{BAT}$—efficiency of the MESF battery discharge process.

From the perspective of this article, the most important aspect is the appropriate modeling of CEV economic parameters. These should be divided into those that shape the capital expenditure (CAPEX) of the n-th CEV and those that shape the variable and fixed operating costs (OPEX). The methodology used to calculate costs has been previously presented in [15]. Since, in accordance with (2), we are examining the use of CEVs in terms of hourly intervals, it is interesting to calculate the economic parameters per hour of CEV operation. For this purpose, the capital recovery factor (CRF) was used. It is determined as follows [15]:

$$CRF={\displaystyle \frac{p·{\left(1+p\right)}^T}{{\left(1+p\right)}^T-1}}$$

(5)

$$k_{1h}={\displaystyle \frac{CRF}{8760}}$$

(6)

where $k_{1h}$—correction factor determining the financial equivalent for one hour; $CRF$—capital recovery factor; $p$—discount rate; and $T$—number of annuities received equal to exploitation time of CEVs, expressed in years.

Next, economic modeling of CEVs should commence. As shown in Figure 1, this vehicle consists of a battery forming the MESF and the associated power electronics and other devices forming the power circuit, as well as a light or heavy commercial electric vehicle with its own independent traction battery. In addition, the infrastructure must be equipped with a dedicated connection. Therefore, the capital expenditure for a single CEV is determined as follows [15]:

$${\kappa }_{CEV,n}={\kappa }_{CEV,n}^{MESF}+{\kappa }_{CEV,n}^{CON}+{\kappa }_{EV,n}$$

(7)

$${\kappa }_{CEV,n}^{MESF}={\kappa }_{BAT,n}^{MESF}+{\kappa }_{PEL,n}^{MESF}={C_{MESF}}_n·{\kappa }_{BAT,n}^u+{\kappa }_{PEL,n}^{MESF}$$

(8)

$${\kappa }_{EV,n}={\kappa }_{V,n}+{\kappa }_{ADAPT,n}· {\kappa }_{EV,n}$$

(9)

where ${\kappa }_{CEV,n}^{MESF}$—capital expenditure incurred for the building of the MESF in the n-th CEV, expressed in EUR; ${\kappa }_{CEV,n}^{CON}$—capital expenditure incurred for the building or purchase of a dedicated connector for the n-th CEV, expressed in EUR; ${\kappa }_{EV,n}$—capital expenditure for the purchase and adaptation of the n-th EV to serve as a CEV, expressed in EUR; ${\kappa }_{BAT,n}^{MESF}$—capital expenditure on batteries comprising the MESF, expressed in EUR; ${\kappa }_{PEL,n}^{MESF}$—capital expenditure on the purchase of power electronic devices and other power circuit devices for the n-th CEV, expressed in EUR; ${\kappa }_{V,n}$—cost of purchasing an electric vehicle for the CEV, expressed in EUR; ${\kappa }_{ADAPT,n}$—the cost coefficient of adapting the n-th EV to perform the role of a CEV, expressed as a percentage of the capital expenditure for the purchase of the EV; and ${\kappa }_{BAT,n}^u$—the unit cost of the battery comprising the MESF of the n-th CEV, expressed in EUR/kWh.

Hence, in relation to one hour of CEV operation, the following equation applies [15].

$${\kappa }_{CEV,n,t}={\kappa }_{CEV,n}· k_{1h}$$

(10)

where ${\kappa }_{CEV,n,t}$—hourly equivalent of capital expenditure in relation to the n-th CEV, expressed in EUR/h.

After determining the capital expenditures, the next step is to determine the operating costs ${\lambda }_{OP}$ (OPEX) in terms of fixed ${\lambda }_{OP}$ and variable ${\lambda }_{OPv}$. From the point of view of CEV’s operation in the provision of MESF services, fixed costs include all costs that do not depend on the amount of energy transmitted to the service taker, i.e., $E_{CEV,n}$. It is worth noting that these costs include the cost of energy transported along with the cost of charging the traction battery ${\lambda }_{tr,n}$, annual CEV maintenance costs ${\lambda }_{O\&M,n}$, EV battery degradation costs ${\lambda }_{deg,n}$, and CEV driver salary wage ${\lambda }_{wag,n}$. Variable costs include the cost of charging the MESF battery in the RCS and MESF battery degradation costs ${\lambda }_{deg,n}^{MESF}$. It should be noted that in this methodology, variable costs are equivalent to the costs of maintaining energy capacity availability. It is assumed that CEVs providing MESF services perform certain other tasks, and the service taker is required to pay rates resulting from charging the MESF battery in an amount sufficient to perform the service for hours and to cover potential battery degradation costs. In the case of a detailed economic model for establishing MESF services, these should relate to the costs of the electricity actually transferred between the CEV and the service taker. However, for this purpose, it is necessary to develop a logistics model that would illustrate the movement of CEVs in the area and the current SOC for the MESF. As in the case of CAPEX, 1 h intervals are taken into account.

$${\lambda }_{OPf,n,t}={(\lambda }_{tr,n}+{\lambda }_{deg,n}·E_{ch}^{EV})+{(\lambda }_{O\&M,n}· k_{1h}+{\lambda }_{wag,n})$$

(11)

$${\lambda }_{OPv,n,t}={\lambda }_{deg,n}^{MESF}·E_{CEV,n}+{\lambda }_{charg,n}·E_{ch}^{MESF}$$

(12)

where $E_{ch}^{MESF}$—the volume of electricity needed to be replenished in the MESF battery capacity at the RCS, expressed in kWh, and $E_{ch}^{EV}$—the volume of electricity needed to be replenished in the CEV traction battery at the RCS, expressed in kWh.

Therefore, the total hourly cost of using the n-th CEV can be determined by the following equation:

$$C{S}_{CEV,n}^t={\kappa }_{CEV,n,t}+ {\lambda }_{OPf,n,t}+{\lambda }_{OPv,n,t}$$

(13)

where $C{S}_{CEV,n}^t$—total hourly cost of using the n-th CEV as a backup power source providing the MESF service, expressed in EUR/h.

Therefore, the cost of using a fleet consisting of n CEVs during the provision of the entire MESF service can be determined by the following equation:

$$C{S}_{CEV,n}^{FLEET}=\sum _{n=1}^{N}C{S}_{CEV,n}^t·\tau$$

(14)

where $C{S}_{CEV,n}^{FLEET}$—total cost of operating the CEV fleet in the provision of backup power services to the MESF service taker, expressed in EUR.

2.3. Modeling the Cost of Not Delivering Electricity to the End User

The main part of the study is to determine the cost of delivering or not delivering electricity to the service taker, while providing the MESF service related to ensuring a backup power source. The analysis should start with the classic approach to determining the VoLL indicator. According to [33,46], it is determined as follows:

$$VoLL={\displaystyle \frac{GVA}{E_{DEM,A}}}$$

(15)

where $VoLL$—the rate of the cost of electricity not delivered to the end user, expressed in EUR/kWh, and $GVA$—the gross value added, reported for the selected entity, expressed in EUR.

The approach presented in (15) refers to annual values, using economic parameters and energy consumption as benchmarks for determining the average cost per entity operating in economic conditions. The concept of VoLL is also often associated with two indicators provided by end users: (1) willingness to pay (WTP), showing how much the user is willing to pay for maintaining the electricity supply for a given period of time, expressed in EUR/h; and (2) willingness to accept (WTA), which determines the expected level of compensation that the end user should receive for the non-delivery of energy for a given period of time, also expressed in EUR/h. Our goal was to develop an indicator that would respond dynamically to changes in revenue in a given hour and at the same time indicate that the shutdown of economic activity is more related to a temporary loss of revenue than to a reduction in GVA for a given sector, by using a local rather than a global approach. Similarly, the possibility of assessing the cost of electricity outages for a group of end users, in particular households, was analyzed. It should be emphasized that in this case, they were aggregated at the MV/LV station level in order to indicate the cost of not delivering energy to a given area, rather than focusing on sampling individual consumers. This approach will also enable DSOs to assess whether it is worthwhile to invest in their own CEV fleet to secure the energy needs of their customers, e.g., during planned power outages.

2.3.1. Modeling the Cost of Not Delivering Electricity to Commercial End Users

When modeling the cost of not delivering electricity to a commercial end user, the indicator describing the potential financial effect will be a rate based on the hourly revenue that a commercial end user can earn, together with the relevant premium coefficients. As already mentioned, the aim of the article is to propose a new approach to determining the cost of non-delivered energy, taking into account technical and economic criteria, and then securing the end user’s needs with a CEV fleet. Therefore, the hourly revenue recorded by the i-th commercial end user is determined as $R_{i,t}$. The methodology for determining this parameter is not relevant in terms of measuring the cost of delivering or not delivering energy to the end user and can be adjusted by those applying this approach. It is important that the parameter $R_{i,t}$ reflects the potential positive financial impact that will be neglected in case of an electricity supply interruption. Next, it is necessary to estimate the premium coefficient for electricity non-delivery. Our aim is to show that not completing tasks related to the company’s core business, due to a lack of energy supply, is a certain type of penalty, so from the end user’s point of view, we expect an additional benefit for this suspension. Therefore, we decided to set an extra rate, taking into account the multiplication of revenues, instead of using only the estimated revenue function for each hour t. It is proposed that this factor should depend on two components: ${\mu }_i$—a parameter determining the duration of the power outage at the i-th facility, reduced by the number of hours during which energy will be supplied by own generation resources and not contracted by external services $s_i$, as well as $\alpha$—a coefficient determining the severity of the failure, where the maximum value should refer to a severe system failure, and the minimum to local failures, the effects of which are remedied fairly quickly. Therefore,

$$B_i^{COM}=R_{i,t}·(1+{\mu }_i·\alpha )·\tau$$

(16)

$${\mu }_i={\displaystyle \frac{\tau -s_i}{24}} {\forall }_{s_i\ge 0}$$

(17)

where $B_i^{COM}$—the rate of financial compensation for failure to supply electricity during $\tau$ hours to the i-th commercial end user, expressed in EUR.

2.3.2. Modeling the Cost of Not Delivering Electricity to a Group of End Users

The second case involves modeling the cost of not delivering energy to a group of end users who are supplied from a single MV/LV substation. This problem is particularly evident in areas with a high density of households, as it is notoriously difficult to assess the cost of non-delivery of energy to this group of end users. In previously developed methodologies [37,47], monetary rates corresponding to the leisure time of household members were used to assess the cost of non-delivery of energy to households. However, it seems that a more understandable method for end users would be to make the amount of compensation $B_i^{SUB}$ dependent on the percentage of the electricity bill ${\epsilon }_i$, while replacing the revenue component referred to in (16). Therefore,

$$B_i^{SUB}=C{S}_{el,t,i}·{\epsilon }_i·(1+{\mu }_i·\alpha )·\tau$$

(18)

where $C{S}_{el,t,i}$—the cost of electricity purchased by the i-th end user at time t, expressed in EUR; ${\epsilon }_i$—coefficient determining the amount of financial compensation for non-delivery of electricity, depending on the percentage of the value of the electricity bill of the i-th end user, expressed as a percentage; and $B_i^{SUB}$—rate of financial compensation for non-delivery of electricity during hours to the i-th group of end users, expressed in EUR.

2.4. Objective Function

In possessing mathematical models of the costs of not delivering electricity to end users, one can consider determining the alternative cost of delivering electricity to the end users in various operating states of the power system. In the event of a disruption in electricity supply, it is necessary to ensure adequate energy resources through the CEV fleet, in order to balance the amount of energy required by the end user. Thus, the energy balance function of MESF service provision can be determined as follows:

$$E_B\left(\tau \right)=E_{avgh}^{SAF}-E_{CEV,n}·n_{CEV}, {\forall }_{\tau \ge 1}$$

(19)

where $E_B\left(\tau \right)-$ energy balance of the MESF service when providing additional energy supply by the CEV fleet, expressed in kWh.

In order for the MESF service to be provided successfully, i.e., for the facility to receive adequate power supply during a power outage, the parameter $E_B\left(\tau \right)$ should be set to a value greater than or equal to 0. This raises the question of how much and how large of a resource should be allocated to provide the service and what the total cost of avoiding a power outage will be. For this purpose, an electricity supply cost function has been defined, described by $D_{el}\left(\tau \right)$. It indicates the relation in which the cost of supplying electricity to the service taker, when $E_B\ge 0$, is equal to the sum of the costs of using the CEV fleet and the service fee $Fe{e}_i$. It is assumed that this fee during the power outage is equal to the cost of supplying electricity from the grid. In the case where $E_B<0$, i.e., there is an imbalance despite the use of CEV resources, the cost of energy delivery is equal to the sum of the cost of using the CEV fleet and the compensation rate for non-delivery of energy $B_i^{COM}$ or $B_i^{SUB}$, depending on the type of service taker. Our goal is to minimize the cost $D_{el}\left(\tau \right)$, and the decision variables are as follows: the rated capacity of the MESF ${C_{MESF}}_n$, as a component determining the energy potential and CAPEX of single CEV, and the number of CEVs providing the service $n_{CEV}$, defining the total energy potential.

$$\min D_{el}(\tau )=\left\{\begin{array}{c}{CS}_{CEV,n}^t·\tau ·n_{CEV}+Fe{e}_i , for E_B\ge 0 \\ {CS}_{CEV,n}^t·\tau ·n_{CEV}+B_i^{COM}, for E_B<0 \wedge B_i^{COM}>0\\ {CS}_{CEV,n}^t·\tau ·n_{CEV}+B_i^{SUB}, for E_B<0 \wedge B_i^{SUB}>0\end{array}\right.$$

(20)

$$Fe{e}_i=C{S}_{el,i,t}·\tau$$

(21)

$$var({C_{MESF}}_n, n_{CEV})$$

(22)

where $D_{el}\left(\tau \right)$—the cost of delivering electricity to the MESF service taker through the CEV fleet for the $\tau$ hours of the power outage, expressed in EUR; $Fe{e}_i$—the fee for providing the MESF service if the CEV fleet’s energy capacity covers the service taker’s needs, expressed in EUR.

2.5. Constraints

Three types of constraints are introduced, as follows: (1) constraints relating to the rated capacity of the MESF; (2) constraints relating to the maximum number of CEVs assigned to service users; and (3) constraints relating to the need to maintain a positive energy balance for the provision of the MESF service. Therefore, the first constraint means that the calculated MESF capacity cannot be less than a certain assumed value allowing for the minimum provision of MESF services, and cannot be greater than the capacity resulting from the technical possibilities of locating the MESF in the CEV cargo area. For the purposes of this methodology, it is estimated that the ratio ${C_{MESF}^{MIN}}_n/{C_{MESF}^{MAX}}_n$ should not exceed 1:4.

$${{{C_{MESF}^{MIN}}_n \le C}_{MESF}}_n\le {C_{MESF}^{MAX}}_n$$

(23)

where ${C_{MESF}^{MIN}}_n$—minimal nominal capacity of the MESF battery, expressed in kWh; ${C_{MESF}^{MAX}}_n$—maximum nominal capacity of the MESF battery, expressed in kWh.

The second constraint concerns the maximum number of CEVs assigned to a service taker. It is assumed that each of the i-th service takers will have a dedicated number of parking spaces, where CEVs will be able to provide the service. Often, this number results from spatial constraints, e.g., the available number of parking spaces or the capacity to deploy a CEV fleet in the company. For example, a large and dispersed utility, particularly one with high energy demand and importance to society or the economy, will be able to equip itself with a number of CEVs that, based on a simple estimate, should cover demand for a certain period of time. On the other hand, a DSO at a single MV/LV substation does not have the capacity or capability to send a dedicated MESF to each consumer. Therefore,

$$n_{CEV}\le n_{CEV,i}^{MAX} {\forall }_{i\ge 1}$$

(24)

where $n_{CEV,i}^{MAX}$—maximum number of CEVs assigned to the i-th service taker.

The third constraint concerns the need to maintain a positive energy balance for the provision of MESF services. It is assumed that minimizing the cost of energy delivered should not influence the decision of service takers to interrupt the power supply and not use MESF resources. The aim should be to ensure that backup power resources such as CEVs are the first to maintain power supply, if only for technical reasons. Only when it is technically impossible to supply the required volume of energy should the financial impact be considered. Therefore,

$$E_B\left(\tau \right)\ge 0, {\forall }_{\tau \ge 1}$$

(25)

3. Estimation of Survey-Based Value of Lost Load

In order to compare the proposed method of assessing the cost of delivering electricity to an end user contracted to the MESF service, with the potential real costs of WTA and WTP that may be incurred by businesses, we decided to conduct a research survey similar to the standards proposed by ACER and at the national level by the Polish energy regulator [48]. In cooperation with the City of Warsaw, a survey on energy security in public entities was conducted; afterwards, an assessment was made regarding the potential costs of undelivered energy. The entities belong to the following sectors:

• Transport (ENT1): average daily electricity consumption is 32.65 MWh.
• Healthcare (ENT2): average daily electricity consumption is 3.70 MWh.
• Public utilities (ENT3): average daily electricity consumption is 32.48 MWh.

The survey consisted of 26 questions concerning power supply reliability (how satisfied end users are, regarding the continuity of energy delivery), power supply backup methods (available backup resources and their respective capacities, critical loads, etc.), and financial parameters (electricity purchase costs, revenues, operating costs, and gross value added). Due to the need to ensure the security of data processing, the results of this part of the survey will not be presented in this publication, as they involve sensitive data of selected entities. Furthermore, the following questions concern the simulation of two scenarios, in which WTA and WTP indicators had to be determined. To find the aforementioned values, it was necessary to pose questions regarding amount of money that might be spent by end users to maintain the energy supply, as well as any financial compensation to which they might be entitled. Therefore, the following test scenarios were proposed. These tests presented two operating points for the surveyed entities: one in the summer (working day at 1:00 p.m.) and the other in the winter (working day at 6:00 p.m.). Each scenario involved a sudden power outage. The respondents were asked to rate on a scale of 1 (very unlikely) to 10 (very likely) whether they would be willing to pay a given amount to avoid a power outage for a given period of time and whether they would expect appropriate compensation for such an outage.

Table 1. Analyzed scenarios and cases in proposed research survey, based on [48].

Scenario	Cases
Summer, weekday 13.00	WTP: PLN 10,000 (EUR 2326) 1 h interruption (S_CAS_1) 4 h interruption (S_CAS_2) 24 h interruption (S_CAS_3) PLN 100,000 (EUR 23,256) 1 h interruption (S_CAS_4) 4 h interruption(S_CAS_5) 24 h interruption (S_CAS_6) PLN 1,000,000 (EUR 232,558) 1 h interruption (S_CAS_7) 4 h interruption (S_CAS_8) 24 h interruption (S_CAS_9)
	WTA: PLN 10,000 (EUR 2326) 1 h interruption (S_CAS_10) 4 h interruption (S_CAS_11) 24 h interruption (S_CAS_12) PLN 100,000 (EUR 23,256) 1 h interruption (S_CAS_13) 4 h interruption (S_CAS_14) 24 h interruption (S_CAS_15) PLN 1,000,000 (EUR 232,558) 1 h interruption (S_CAS_16) 4 h interruption (S_CAS_17) 24 h interruption (S_CAS_18)
Winter, weekday 18.00	WTP: PLN 10,000 (EUR 2326) 1 h interruption (W_CAS_1) 4 h interruption (W_CAS_2) 24 h interruption (W_CAS_3) PLN 100,000 (EUR 23,256) 1 h interruption (W_CAS_4) 4 h interruption(W_CAS_5) 24 h interruption (W_CAS_6) PLN 1,000,000 (EUR 232,558) 1 h interruption (W_CAS_7) 4 h interruption (W_CAS_8) 24 h interruption (W_CAS_9)
	WTA: PLN 10,000 (EUR 2326) 1 h interruption (W_CAS_10) 4 h interruption (W_CAS_11) 24 h interruption (W_CAS_12) PLN 100,000 (EUR 23,256) 1 h interruption (W_CAS_13) 4 h interruption (W_CAS_14) 24 h interruption (W_CAS_15) PLN 1,000,000 (EUR 232,558) 1 h interruption (W_CAS_16) 4 h interruption (W_CAS_17) 24 h interruption (W_CAS_18)

presents a summary of the analyzed scenarios and the cases considered.

As already mentioned, respondents rated each of the 36 cases on a scale of 1 to 10. This is a new feature compared to the survey conducted at the national level by the Polish Energy Regulatory Office (ERO), presented in [48]. Thanks to the approach of a scale-based assessment of a given case, it is possible to set a dynamic cut-off threshold that determines which responses should be considered acceptable from the point of view of the survey creator. Therefore, it is considered that the respondent has expressed a positive willingness to pay to avoid energy supplies or to receive adequate compensation when the parameter ${\zeta }_{WTP}$ or ${\zeta }_{WTA}$ takes a value of 1. Thus,

$${{\forall }_{x, c{t}_{WTP} \in \{\mathrm{1,2},\dots ,10\}} \zeta }_{WTP}=\left\{\begin{array}{c}0, if x<c{t}_{WTP}\\ 1, , if x\ge c{t}_{WTP}\end{array}\right.$$

(26)

$${{\forall }_{x, c{t}_{WTA} \in \{1,2,\dots ,10\}} \zeta }_{WTA}=\left\{\begin{array}{c}0, if x<c{t}_{WTA}\\ 1, , if x\ge c{t}_{WTA}\end{array}\right.$$

(27)

where $c{t}_{WTP}$—cut-off point for positive responses for cases related to WTP; $c{t}_{WTA}$—cut-off point for positive responses for cases related to WTA; and $x$—response selected by the interviewee.

Next, WTP and WTA were separately assessed in terms of each scenario, and a matrix of coefficients ${\zeta }_{WTP}$ and ${\zeta }_{WTA}$ was created. In this research survey, thresholds $c{t}_{WTP}=3$ and $c{t}_{WTA}=3$ were assumed. Low cut-off values were chosen to reflect uncertainties in the responses. It seems that in subsequent studies, these indicators should be equal to 5 or more.

Table 2. Positive and accepted responses regarding WTP and WTA factors for the separately analyzed cases.

Value|Interruption Time [h]	1	4	24	1	4	24	1	4	24	1	4	24
	ENT1: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Summer			ENT1: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Summer			ENT1: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Winter			ENT1: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Winter
EUR 2326	1	1	1	0	0	0	1	1	1	0	0	0
EUR 23,256	1	1	1	0	0	0	1	1	1	0	0	0
EUR 232,558	0	0	1	1	1	1	0	0	1	1	1	1
	ENT2: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Summer			ENT2: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Summer			ENT2: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Winter			ENT2: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Winter
EUR 2326	0	1	1	0	0	1	0	0	1	0	0	0
EUR 23,256	0	0	1	0	1	1	0	0	1	0	0	1
EUR 232,558	0	0	0	1	1	1	0	0	0	0	0	1
	ENT3: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Summer			ENT3: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Summer			ENT3: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{P}}$, Winter			ENT3: ${\mathit{\zeta }}_{\mathit{W}\mathit{T}\mathit{A}}$, Winter
EUR 2326	1	1	1	1	1	1	1	1	1	1	1	1
EUR 23,256	0	1	1	1	1	1	1	1	1	1	1	1
EUR 232,558	1	1	1	1	1	1	1	1	1	1	1	1

presents a summary of cases where ${\zeta }_{WTP}$ and ${\zeta }_{WTA}$ are greater than 0.

As can be seen from Table 2, for a given power supply interruption time, more than one positive response may occur. Therefore, in order to calculate the VoLL indicator values, the results from Table 2 were divided into two additional tables (

Table 3. Maximal values of WTP and WTA factors for surveyed end users.

Case|Interruption Time [h]	1	4	24
ENT1
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	23,256	23,256	232,558
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	232,558	232,558	232,558
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	23,256	23,256	232,558
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	232,558	232,558	232,558
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{a}\mathit{x}}}^{\mathit{E}\mathit{N}\mathit{T}1}$ [EUR]	127,907	127,907	232,558
ENT2
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	0	2326	23,256
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	232,558	23,2558	232,558
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	0	0	23,256
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	0	0	232,558
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{a}\mathit{x}}}^{\mathit{E}\mathit{N}\mathit{T}2}$ [EUR]	58,140	58,721	127,907
ENT3
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	232,558	232,558	232,558
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, summer [EUR]	232,558	232,558	232,558
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	232,558	232,558	232,558
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}$, winter [EUR]	232,558	232,558	232,558
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{a}\mathit{x}}}^{\mathit{E}\mathit{N}\mathit{T}3}$ [EUR]	232,558	232,558	232,558

and

Table 4. Minimal values of WTP and WTA factors for surveyed end users.

Case|Interruption Time [h]	1	4	24
ENT1
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	2326	2326	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	232,558	232,558	232,558
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	2326	2326	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	232,558	232,558	232,558
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{i}\mathit{n}}}^{\mathit{E}\mathit{N}\mathit{T}1}$ [EUR]	117,442	117,442	117,442
ENT2
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	0	2326	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	232,558	23,256	2326
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	0	0	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	0	0	23,256
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{i}\mathit{n}}}^{\mathit{E}\mathit{N}\mathit{T}2}$ [EUR]	58,140	6395	7558
ENT3
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	2326	2326	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, summer [EUR]	2326	2326	2326
$\mathit{W}\mathit{T}{\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	2326	2326	2326
$\mathit{W}\mathit{T}{\mathit{A}}_{\mathit{m}\mathit{i}\mathit{n}}$, winter [EUR]	2326	2326	2326
${\mathit{W}}_{\mathit{a}\mathit{v}{\mathit{g}}_{\mathit{m}\mathit{i}\mathit{n}}}^{\mathit{E}\mathit{N}\mathit{T}3}$ [EUR]	2326	2326	2326

), which present the highest and lowest WTP and WTA indicator values for each scenario. This time, monetary values were assigned to them.

Based on the values $W_{av{g}_{max}}^{ENT1}$, $W_{av{g}_{max}}^{ENT2}$, and $W_{av{g}_{max}}^{ENT3}$, the maximum VoLL levels were determined for end users ENT1, ENT2, and ENT3, respectively, for each interruption time. Similarly, for the indicators $W_{av{g}_{min}}^{ENT1}$, $W_{av{g}_{min}}^{ENT2}$, and $W_{av{g}_{min}}^{ENT3}$, the minimal VoLL values were determined, also for each end user and each interruption time. The VoLL values were determined as follows:

$$VoL{L}_{sur}^{max}={\displaystyle \frac{W_{av{g}_{max}}^{ENTi}}{E_{avgh}^{DEM}·\tau }}={\displaystyle \frac{\frac{\sum _{sc=1}^{N_{sc}} WT{P}_{max,sc}+ WT{A}_{max,sc}}{N_{sc}}}{E_{avgh}^{DEM}·\tau }}$$

(28)

$$VoL{L}_{sur}^{min}={\displaystyle \frac{W_{av{g}_{min}}^{ENTi}}{E_{avgh}^{DEM}·\tau }}={\displaystyle \frac{\frac{\sum _{sc=1}^{N_{sc}} WT{P}_{min,sc}+WT{A}_{min,sc}}{N_{sc}}}{E_{avgh}^{DEM}·\tau }}$$

(29)

$$VoL{L}_{sur}^{avg}={\displaystyle \frac{VoL{L}_{sur}^{max}+VoL{L}_{sur}^{min}}{2}}$$

(30)

where $VoL{L}_{sur}^{max}$—the value of the VoLL indicator, assuming the highest WTA or WTP values assigned to a given end user, expressed in EUR/kWh; $VoL{L}_{sur}^{min}$—the value of the VoLL indicator, assuming the lowest WTA or WTP values assigned to a given end user, expressed in EUR/kWh; $VoL{L}_{sur}^{avg}$—the value of the VoLL indicator, assuming the average value of the indicators $VoL{L}_{sur}^{max}$ and $VoL{L}_{sur}^{min}$, expressed in EUR/kWh; $sc$—subsequent scenarios; and $N_{sc}$—the number of scenarios taken into account.

The results of the calculated indicators for ENT1, ENT2, and ENT3 end users are presented in

Table 5. Results of VoLL index estimation, based on a research survey.

VoLL Values|Interruption Time [h]	1	4	24	1	4	24	1	4	24
	ENT1			ENT2			ENT3
$\mathit{V}\mathit{o}\mathit{L}{\mathit{L}}_{\mathit{s}\mathit{u}\mathit{r}}^{\mathit{m}\mathit{i}\mathit{n}}$ [EUR/kWh]	8.63	2.16	0.36	376.89	10.36	2.04	1.72	0.43	0.07
$\mathit{V}\mathit{o}\mathit{L}{\mathit{L}}_{\mathit{s}\mathit{u}\mathit{r}}^{\mathit{m}\mathit{a}\mathit{x}}$ [EUR/kWh]	9.40	2.35	0.71	376.89	95.16	34.55	171.80	42.95	7.16
$\mathit{V}\mathit{o}\mathit{L}{\mathit{L}}_{\mathit{s}\mathit{u}\mathit{r}}^{\mathit{a}\mathit{v}\mathit{g}}$ [EUR/kWh]	9.02	2.25	0.54	376.89	52.76	18.29	86.76	21.69	3.61
VOLL CEPA [EUR/kWh]	3.13			N/A			2.19
VOLL PL_ERO [EUR/kWh]	18.93			30.02			19.88
Total VoLL average [EUR/kWh]	3.94			149.32			37.35

. Additionally, they were compared with the values published in [48].

Based on Table 5, it can be seen that the recorded VoLL values are most often similar to the values obtained in [47] for VOLL CEPA and [48] for VOLL PL_ERO, but only for extended power outages. It should be emphasized that in the aforementioned publications, it was not always possible to assign the relevant economic sectors for which the VoLL indicators were determined. Therefore, the best approximation was made to reflect the diversity of sectors (as much as possible). The VoLL indicators recorded in the survey are, in most cases, several times higher than the current average electricity prices on the retail market. In extreme cases, this difference can be several hundred times greater. The average VoLL value was also calculated from the indicators, taking into account all the electricity supply interruptions considered. It should also be noted that as the number of hours without an electricity supply increases, the unit VoLL indicator decreases. This means that respondents rated a 1 h power outage as the most troublesome, by setting high WTP and WTA rates. In the [47,48] studies, the survey was conducted on a larger number of entities. It is also worth noting that reading the index for a given sector of the economy may not be representative in assessing the costs of energy failure in one’s own company. Therefore, it is necessary to conduct one’s own analyses, which in the long term will allow for the selection of an appropriate strategy to mitigate the negative effects of power outages. The final element of the research related to the survey was to perform a sensitivity analysis of the WTA and WTP indicators on the size of the cut-off threshold, using ENT1 as an example. Therefore, a case where the cut-off threshold was increased from three to seven was analyzed. The results are presented in

Table 6. Sensitivity analysis of the cut-off threshold on the values of WTP and WTA indicators for ENT1.

Ct = 3	Time Without Energy Supply [h]			ct = 7	Time Without Energy Supply [h]
	1	4	24		1	4	24
WTP [EUR]				WTP [EUR]
EUR 2326	✓	✓	✓	EUR 2326	✓	✓	✓
EUR 23,256	✓	✓	✓	EUR 23,256	✗	✗	✓
EUR 232,558	✗	✗	✓	EUR 232,558	✗	✗	✗
WTA [EUR]				WTA [EUR]
EUR 2326	✗	✗	✗	EUR 2326	✗	✗	✗
EUR 23,256	✗	✗	✗	EUR 23,256	✗	✗	✗
EUR 232,558	✓	✓	✓	EUR 232,558	✗	✓	✓

.

Based on Table 6, it can be concluded that in the proposed methodology for calculating the VoLL index using the approach to assessing the realism of WTP and WTA rates, an important element is the selection of the appropriate cut-off value, which will determine the estimated VoLL values. It can be noted that in some cases the maximum VOLL values will decrease (e.g., WTP, 24 h break). When estimating VoLL indicators, from an operational point of view, a thorough analysis of the relationship between ${\zeta }_{WTP}\left(ct\right)$ and ${\zeta }_{WTA}\left(ct\right)$ should be performed. It should be noted that in order to increase the accuracy of the results, it would be advisable to survey a larger number of entities in a given sector. However, the research team had limited capacity to conduct such surveys. In Poland, the national regulator conducted a survey in which it obtained responses from 2402 respondents, 1007 of whom belong to households. It should also be emphasized that the aforementioned study did not use a 1–10 scale for each financial level. In subsequent surveys, the intervals between responses should be narrowed, as this would enable a thorough analysis of the sensitivity of the cut-off value to define acceptable ranges for end users.

4. Case Study

4.1. General Assumptions

In order to implement the proposed research methodology, a case study was conducted for three entities that had previously been approached in a research survey on the costs of electricity non-delivery. Each entity was characterized by three statistical parameters: average hourly electricity consumption $E_{avgh}^{DEM}$, average hourly business revenue $R_{i,t}$, and average hourly electricity cost $C{S}_{el,i,t}$. In addition, the maximum number of CEVs $n_{CEV,i}^{MAX}$ that can provide MESF services was determined for each facility. It is worth mentioning that, as in [13,15], two types of CEVs were simulated as follows: smaller CEVs comparable to electric light commercial vehicles (ELCVs) and larger ones comparable to electric heavy commercial vehicles (EHCVs).

Table 7. Key technical and economic parameters of the analyzed facilities.

Parameter	Entity 1	Entity 2	Entity 3
Functionality	Transport	Healthcare	Public Utilities
Average hourly energy demand [kWh]	13,604.76	154.26	1353.68
Average hourly business revenue [EUR]	23,203.54	2805.59	688.44
Average hourly cost of electricity [EUR]	2134.64	27.63	162.97
Power backup time- own sources [h] *	0	0	0
Maximal number of CEV to provide the service	ELCV: 1500 EHCV: 100	ELCV: 5 EHCV: 2	ELCV: 50 EHCV: 5

* Assumed for the purpose of this study.

presents the aforementioned parameters for the analyzed entities and other relevant parameters needed for use in this methodology.

Based on Table 7, it can be seen that the selected facilities vary in terms of both the amount of electricity consumed and the revenues generated or costs incurred for electricity. The purpose of this practice was to demonstrate the versatility of the methodology developed. For each facility, it was assumed that the following degree of energy security values would be examined, and are represented by the term $\sigma$:

• $\sigma =20\%$;
• $\sigma =40\%$;
• $\sigma =60\%$;
• $\sigma =80\%$;
• $\sigma =100\%$.

This diversity will allow for a more accurate analysis of the number of CEVs that should provide services, and will also provide information for facilities that want to secure their needs through CEV services, and if they should first prioritize their consumption from the point of view of maintaining continuity of supply. In addition, a set of technical and economic parameters necessary for the implementation of further steps of the methodology was established. Therefore, the most important parameters are as follows [15]:

• Discount rate $p=6\%$;
• Expected lifetime $T=10 years$;
• Correction factor $k_{1h}=0.0016\%$;
• Hourly wage for CEV driver ${\lambda }_{wag,n}=10{\displaystyle \frac{EUR}{h}}$;
• Unit electricity cost for EV charging ${\lambda }_{charg,n}=0.12{\displaystyle \frac{EUR}{kWh}}$;
• Depth of Discharge $DOD=0.8;$
• State of charge in starting time of the service provision $SO{C}_{st,n}=100\%$;
• Battery efficiency ${\eta }_{BAT}=90\%$;
• The severity of the failure $\alpha =1$.

It should also be added that one additional simulation was performed, in which the secured facility was an MV/LV power station (ENT4). This is a typical substation characteristic of an urban area, supplying 207 end users, 160 of which are households. The following parameters were assumed.

• Average hourly energy demand [kWh]: 123.35;
• Average hourly cost of electricity [EUR]: 23.75;
• Compensation fee as percentage of electricity cost: 20%, 50%, 100%;
• Power backup time- own sources [h]: 0;
• Maximal number of CEV to provide the service: ELCV—5; EHCV—2.

4.2. Modeling of Custom Electric Vehicles and Mobile Electricity Storage Facilities

In terms of modeling CEVs and the MESFs installed within them, they were divided into two categories of vehicles: ELCVs and EHCVs. The reason for this division is the need to check whether it is profitable to invest in a fleet of less energy-efficient vehicles, or whether it is better to equip a smaller fleet of heavy-duty vehicles, taking into account their mobility limitations. It was estimated that fixed operating costs would be marginal in terms of the total cost of energy supply from MESF, so to simplify the calculations, the decision was made to use average values for selected parameters, such as the purchase cost of an electric vehicle ${\kappa }_{V,n}$, traction battery capacity, unit electricity consumption of an EV traction battery, number of traction battery cycles, and MESF (needed to calculate battery degradation costs). It was also assumed that the cost of adaptation would be ${\kappa }_{ADAPT,n}=10\%$ of capital expenditure for the purchase of EVs. Maintenance costs ${\lambda }_{O\&M,n}$ were defined as 2.5% of the total CAPEX for CEVs. Thus, the basic technical and economic parameters of CEVs were defined and are presented in

Table 8. Key technical and economic parameters of CEVs, based on [15].

Parameter	Value
Capital Expenditure for Electric Vehicle ${\mathrm{\kappa }}_{\mathrm{V},\mathrm{n}}$ [EUR]	29,122
Nominal traction battery capacity [kWh]	35
Unit energy consumption for traction battery [kWh/km]	0.35
Transport costs with charging EV battery [EUR/service]	0.78
Degradation cost of the battery [EUR/kWh]	0.12
CEV operating and maintenance cost [EUR/h]	2.5% of total CAPEX/8760
Distance to service provision facility MESF [km]	8

.

Additionally, it was assumed that the costs of the converter connecting the CEV to the end user’s installation would amount to ${\kappa }_{CEV,n}^{CON}=3000 EUR$ [15]. Next, the technical parameters of the MESF, dedicated to each EV category, were modeled. To increase the diversification of calculations, two options for the maximum rated capacity of the MESF battery were adopted for each vehicle category. These are presented in

Table 9. Simulation parameters of MESF inside CEVs.

Parameter	ELCV		EHCV
Option	A	B	C	D
Maximal battery capacity [kWh] ${C_{MESF}^{MAX}}_n$	120	192	800	1000
Minimal battery capacity [kWh] ${C_{MESF}^{MIN}}_n$	40	60	200	250
Discharge/charge power [kW]	80
Maximal weight of battery pack [kg]	500.4	801.9	3336.0	4170.0
Nominal DC voltage [V]	600 V–800 V DC
Unit cost of MESF battery ${\kappa }_{BAT,n}^u$ [EUR/kWh]	350
Cost of power electronic and auxiliary circuit [EUR] ${\kappa }_{PEL,n}^{MESF}$	20,000
Unit cost of battery degradation ${\lambda }_{deg,n}^{MESF}$ [EUR/kWh]	0.12

.

5. Results and Discussion

This section presents the results of the simulations regarding the securing of the power demands of ENT1-ENT3 and the ENT4 substation using CEV, and determines the cost of delivering or not delivering electricity for each case. The presentation of the results will be divided according to the individual facilities. Finally, a synthetic comparison of all optimization results and survey results will be made. It is worth noting that for ELCV, the baseline option is “A,” while for EHCV, it is option “C.”

5.1. ENT1 Service Taker

The first entity to be analyzed is ENT1. It consists of many dispersed facilities throughout the city and concerns the transport sector. Due to high electricity consumption and considerable dispersion of facilities, the decision was made to simulate a very large CEV fleet. Figure 2 shows the simulation results for option A as a function of the number of hours without electricity supply.

Based on Figure 2, it can be seen that through the optimization of the number of CEVs in option A for different levels of facility security, it is not necessary to use the full permissible number of CEVs available. It is worth noting that increases in this value are recorded in terms of steps (Figure 2a). In terms of battery capacity, it can be observed that most simulation cases oscillated around the maximum permissible MESF rated capacity. One may also ask how to assess the number of hours without power supply from the power grid for which the energy balance using the MESF service is positive (demand coverage). This question can be answered by analyzing Figure 2b. When the cost of electricity supply $D_{el}\left(\tau \right)$ begins to rise sharply, this means that positive values appear for the parameter $B_i^{COM}$. Based on Figure 2b, it can be estimated that for up to approximately 10 h, the provision of the MESF service allows the power supply to the facilities of entity ENT1 to be maintained. Therefore, the next step is to check how increasing the upper limit of the MESF battery capacity would affect the provision of services and possibly extend the power supply backup time for the facility. Tests were carried out for option “B”, i.e., MESF with a maximum capacity of 192 kWh. Figure 3 shows a comparison of options A and B for two edge cases of ENT1 entity security level, i.e., 20% and 100%.

Based on Figure 3, it can be seen that in the case where 100% of the demand was secured using the MESF service, the potential service and power maintenance time increased from 10 to 15 h. However, the large energy potential was represented by the fleet of 1500 CEVs. When covering 20% of energy demand with the MESF service, there is no significant difference between using a MESF with a capacity of 120 kWh and using one with a capacity of 192 kWh (options A and B). Next, the possibility of providing the same service using EHCVs (options C and D) was examined. Figure 4 and Figure 5 show the same considerations that were applied to ELCVs.

Based on Figure 4 and Figure 5, it can be seen that constraints on the number of large MESFs result in the power supply backup time for $\sigma =100\%$ being even shorter than in the case of ELCV. It is worth noting that in the case of $\sigma =20\%$, there is also a situation where the assumed number of EHCVs generates too little energy potential for the energy balance of the service to be positive (sudden increase in cost in 21 h without power). To improve the results, it is necessary to consider increasing the limit on the number of CEVs. However, it is worth remembering that such an operation generates additional costs related to capital expenditure. Such additional analyses were carried out during the study. Based on these analyses, it was calculated that for ELCVs in option A (maximum MESF capacity of 120 kWh), the vehicle fleet would have to consist of more than 6000 vehicles to cover 100% of the demand for MESF service provision. For option C and EHCVs (maximum MESF capacity of 800 kWh), this number would be almost 600. These fleets are 4 and 6 times larger, respectively. In such a situation, it would be necessary to consider covering the demand with other backup power sources or prioritizing consumption in order to secure 20% of the demand with MESFs. The final step in the analysis for ENT1 was to calculate the unit cost of supplying electricity under the MESF service. This cost will also allow the marginal rate for the service to be determined and compared to the VoLL indicator. It is determined as the ratio of the function $D_{el}\left(\tau \right)$ to the amount of electricity secured by CEV $E_{avgh}^{SAF}$.

Table 10. Average cost of delivering electricity to service taker ENT1 during MESF service provision.

Hours Without Energy Supply [h]	Option	Average Cost of Delivering Electricity in MESF Service [EUR/kWh]
		$\mathit{\sigma }=20$%	$\mathit{\sigma }=40$%	$\mathit{\sigma }=60$%	$\mathit{\sigma }=80$%	$\mathit{\sigma }=100$%
1	A	1.17	0.78	0.65	0.58	0.54
	B	1.12	0.73	0.60	0.53	0.49
	C	1.06	0.66	0.53	0.47	0.43
	D	1.06	0.66	0.53	0.46	0.42
4	A	1.59	1.20	1.22	1.00	1.17
	B	1.39	1.00	0.87	0.80	0.83
	C	1.14	0.75	0.62	0.55	0.51
	D	1.18	0.78	0.60	0.54	0.50
24	A	4.39	12.11	8.07	6.05	4.84
	B	3.21	3.73	2.69	6.19	4.95
	C	17.87	8.94	5.96	4.47	3.57
	D	1.65	8.98	5.99	4.49	3.59

presents the results of calculations of this index for three periods without power supply from the grid: 1 h, 4 h, and 24 h.

Based on Table 10, it can be seen that the unit cost of providing MESF service decreases with the length of the power outage. It can be concluded that the use of a large amount of energy resources for a short period of time will involve higher costs. Comparing the values obtained in Table 10 with the VoLL indicators from the survey, one can observe similar values. In the survey, the VoLL indicator for a 1 h power outage was 9 EUR/kWh, which means that the MESF service is much more cost-effective, with a cost of approximately 1 EUR/kWh. In the case of a 4 h power outage, the MESF service is again more cost-effective, and is approx. 1 EUR/kWh compared to approx. 2 EUR/kWh. Only in the case of a 24 h outage does the MESF service cease to be a cost-effective solution, i.e., the end user, bearing the cost of non-delivery of energy, would pay less than for the MESF service, which would not fully balance their energy needs anyway. The total average cost of electricity supply using MESF was 2.56 EUR/kWh, which is better than the average VoLL recorded in the ENT1 survey of 3.94 EUR/kWh. It is worth noting that there is a slight anomaly in the results presented in Table 10. In the case of a 24 h power outage and MESF in option C, there is a rapid spike in the unit cost of electricity delivered from this energy source. This was caused by reaching the limitations of the implemented algorithm. This result should be considered insignificant in the context of the other results obtained.

5.2. ENT2 Service Taker

The second entity analyzed will be ENT2. It is an entity with one facility in the healthcare sector. Given its spatial limitations, the decision was made to model a CEV fleet that could be used in parking spaces in front of such a facility. Figure 6 shows the simulation results for option A as a function of the number of hours without electricity supply.

Based on Figure 6, it can be seen that MESF in option A will cover 100% of demand for approximately 2 h, while the maximum value for MESF is reached in 3 h and the cost of delivery increases rapidly, which indicates the need to pay compensation for failure to deliver electricity. As in the case of ENT1, prioritization of consumption will become crucial. When the security level of the facility is reduced to 20%, the power supply retention time under the MESF service increases to 14 h. It should be emphasized that a very small number of acceptable MESFs were used, as ENT2 has only one facility, with limited parking space. In terms of MESF battery capacity, the vast majority of results hovered around the maximum acceptable capacity in option A, i.e., 120 kWh. Simulations were then performed for option B. Figure 7 shows a comparison of options A and B for two edge cases of ENT2’s security level, i.e., 20% and 100%.

It can therefore be noted that, as in the case of ENT1, the use of MESF with a higher permissible battery capacity allows for a significant extension of the power supply time in the MESF service. By prioritizing consumption and securing 20% of energy demand with the MESF service, it is possible to achieve 22 h of service time. These are promising results, considering how long power generators are designed to last. Next, the possibility of providing the same service using EHCVs (options C and D) was examined. Figure 8 and Figure 9 show similar considerations to those for ELCVs, with the maximum number of CEVs for EHCVs being two.

Based on Figure 8 and Figure 9, it can be seen that thanks to the use of a large permissible MESF battery capacity, the power backup time for the ENT2 facility has increased significantly, from 2 h to 7 h, in a case where it was necessary to secure 100% of the energy needs. In the case of the lowest level of facility protection, i.e., $\sigma =20\%$, it can be seen that the involvement of CEVs for EHCVs allows the 24 h energy demand of the ENT2 facility to be covered. Increasing the capacity of the EHCV battery from 800 kWh to 1000 kWh allowed for an additional extension of the MESF service time from 7 h to 9 h. The cost of supplying electricity to the service recipient does not exceed EUR 1500 per service when the energy balance is positive. In the event of an imbalance, the value increases to EUR 100,000. Next, the unit cost of providing the MESF service was compared with the VoLL indicator.

Table 11. Average cost of delivering electricity to service taker ENT2 during MESF service provision.

Hours Without Energy Supply [h]	Option	Average Cost of Delivering Electricity in MESF Service [EUR/kWh]
		$\mathit{\sigma }=20$%	$\mathit{\sigma }=40$%	$\mathit{\sigma }=60$%	$\mathit{\sigma }=80$%	$\mathit{\sigma }=100$%
1	A	1.53	0.89	0.80	0.66	0.54
	B	1.55	0.89	0.68	0.57	0.58
	C	1.67	0.96	0.72	0.60	0.53
	D	1.71	0.98	0.73	0.61	0.53
4	A	1.92	1.28	1.19	27.23	21.78
	B	1.55	1.10	0.95	0.97	0.83
	C	1.59	0.96	0.72	0.60	0.63
	D	1.60	0.98	0.73	0.61	0.53
24	A	183.98	91.99	61.32	45.99	36.80
	B	184.14	92.07	61.38	46.03	36.83
	C	2.20	91.66	61.10	45.83	36.66
	D	2.29	91.75	61.16	45.87	36.70

presents the results of calculations for the unit cost of providing the service for ENT2 for three periods without power supply from the grid for 1 h, 4 h, and 24 h.

Based on Table 11 and the survey results, it can be concluded that the reported unit cost of energy delivery under the MESF service is significantly lower than the VoLL indicator obtained in cases where the energy balance is positive. The average VoLL indicator value for the survey was 149.32 EUR/kWh, which means that the values were only higher in two simulation cases (24 h interruption, options A and B). It is worth noting that none of the results obtained from the survey approach to calculating the VoLL index were lower than 2.04 EUR/kWh. Therefore, it seems entirely reasonable to use MESF services to secure the energy needs of the ENT2 facility.

5.3. ENT3 Service Taker

The third entity analyzed will be ENT3. It is an entity that owns several facilities and operates in the public utilities sector. After a preliminary analysis of the facilities’ electricity demand, the maximum number of ELCVs in the CEV vehicle fleet was set at 50, while no more than 5 EHCVs are planned to be used. Figure 10 shows the simulation results for option A as a function of the number of hours without electricity supply.

Based on Figure 10, it can be seen that the maximum number of CEVs set for ENT3 will cover 100% of its energy needs for approximately 3 h. It is worth noting that the function curve for 80% and 100% coverage is the same. If consumption is prioritized and the level of secured energy demand is reduced to 20%, the power supply can be maintained for approximately 15 h. It should also be emphasized that the recorded MESF battery capacities were not less than 60 kWh for cases with a high share of consumption prioritization and gradually approached 120 kWh. Simulations were then performed for option B. Figure 11 shows a comparison of options A and B for two extreme cases of the ENT3 entity’s security level, i.e., 20% and 100%.

Based on Figure 11, it can be seen that the effect of increasing the maximum MESF capacity to 192 kWh during the provision of the MESF service for ENT3 is not very significant when 100% of the energy demand needs to be covered. It is visible at a much lower level of demand for the service (20%), where it allows for 24 h continuous provision of the MESF service consisting in the supply of electricity from a backup power source, assuming a limited number of CEVs. Due to the fact that the effect of increasing capacity within the ELCV was not significant, the possibility of providing the same service using EHCVs (options C and D) was examined. Figure 12 and Figure 13 present similar considerations to those for ELCV.

Based on Figure 12 and Figure 13, it can be seen that due to the small size of the CEV fleet classified as EHCVs, the results of the MESF service provision process are worse than those of ELCVs; the time is shorter by about 5 h for the case $\sigma =20\%$ and the time is the same for $\sigma =100\%$. However, the total maximum cost of delivering electricity to the ENT3 service recipient is lower when using an MESF fleet built on EHCVs and amounts to EUR 35,000 for CEVs in options C and D, compared to almost EUR 50,000 for options A and B. Next, the unit cost of providing the MESF service was compared with the VoLL indicator.

Table 12. Average cost of delivering electricity to service taker ENT3 during MESF service provision.

Hours Without Energy Supply [h]	Option	Average Cost of Delivering Electricity in MESF Service [EUR/kWh]
		$\mathit{\sigma }=20$%	$\mathit{\sigma }=40$%	$\mathit{\sigma }=60$%	$\mathit{\sigma }=80$%	$\mathit{\sigma }=100$%
1	A	1.06	0.74	0.69	0.58	0.52
	B	0.94	0.66	0.56	0.49	0.50
	C	0.90	0.57	0.48	0.42	0.40
	D	0.91	0.57	0.48	0.42	0.39
4	A	1.59	1.25	1.18	1.54	1.23
	B	1.22	1.15	0.81	0.85	0.82
	C	0.96	0.69	1.30	0.98	0.78
	D	0.97	0.67	0.55	1.02	0.82
24	A	7.48	3.74	2.49	1.87	1.50
	B	3.07	3.83	2.55	1.92	1.53
	C	5.50	2.75	1.83	1.37	1.10
	D	5.55	2.77	1.85	1.39	1.11

shows the results of the calculations for the unit cost of providing the service for ENT3 for three periods without a main power supply for 1 h, 4 h, and 24 h.

Based on Table 12 and the survey results, it can be seen that the average costs of providing the MESF service are significantly lower than those obtained for estimating the VoLL indicator. The average VoLL indicator was 37.35 EUR/kWh, while the highest unit cost of provision was only 7.5 EUR/kWh. However, it should be emphasized that for the minimum acceptable WTA and WTP values determining the VoLL index, lower values were obtained than those resulting from the cost of providing the MESF service. In the best cases, this cost is only twice as high as the current energy price, which leaves room for further optimization, for example, in the area of logistics.

5.4. Synthetic Comparison of Entities ENT1-ENT3

Two comparative tables were prepared in order to contrast the results for the feasibility and cost of implementing the MESF service for entities ENT1-ENT3.

Table 13. Technical feasibility of MESF service provision for ENT1-ENT3—positive energy balance.

Hours Without Energy Supply [h]	Option	ENT1					ENT2					ENT3
		$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$	$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$	$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$
1	A	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
	B	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
	C	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
	D	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
4	A	✓	✓	✓	✓	✓	✓	✓	✓	✗	✗	✓	✓	✓	✗	✗
	B	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
	C	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✗	✗	✗
	D	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✗	✗
24	A	✓	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗	✗
	B	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	✗	✗	✗	✗
	C	✗	✗	✗	✗	✗	✓	✗	✗	✗	✗	✗	✗	✗	✗	✗
	D	✓	✗	✗	✗	✗	✓	✗	✗	✗	✗	✗	✗	✗	✗	✗

shows the cases in which a positive energy balance was recorded, i.e., the use of MESF allowed the service recipient’s target electricity volume to be covered, while

Table 14. Average cost of delivering electricity to service takers ENT1-ENT3 during MESF service provision.

Hours Without Energy Supply [h]	Option	Average Cost of Delivering Electricity in MESF Service [EUR/kWh]
		ENT1					ENT2					ENT3
		$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$	$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$	$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$
1	A	1.17	0.78	0.65	0.58	0.54	1.53	0.89	0.80	0.66	0.54	1.06	0.74	0.69	0.58	0.52
	B	1.12	0.73	0.60	0.53	0.49	1.55	0.89	0.68	0.57	0.58	0.94	0.66	0.56	0.49	0.50
	C	1.06	0.66	0.53	0.47	0.43	1.67	0.96	0.72	0.60	0.53	0.90	0.57	0.48	0.42	0.40
	D	1.06	0.66	0.53	0.46	0.42	1.71	0.98	0.73	0.61	0.53	0.91	0.57	0.48	0.42	0.39
4	A	1.59	1.20	1.22	1.00	1.17	1.92	1.28	1.19	27.23	21.78	1.59	1.25	1.18	1.54	1.23
	B	1.39	1.00	0.87	0.80	0.83	1.55	1.10	0.95	0.97	0.83	1.22	1.15	0.81	0.85	0.82
	C	1.14	0.75	0.62	0.55	0.51	1.59	0.96	0.72	0.60	0.63	0.96	0.69	1.30	0.98	0.78
	D	1.18	0.78	0.60	0.54	0.50	1.60	0.98	0.73	0.61	0.53	0.97	0.67	0.55	1.02	0.82
24	A	4.39	12.11	8.07	6.05	4.84	183.98	91.99	61.32	45.99	36.80	7.48	3.74	2.49	1.87	1.50
	B	3.21	3.73	2.69	6.19	4.95	184.14	92.07	61.38	46.03	36.83	3.07	3.83	2.55	1.92	1.53
	C	17.87	8.94	5.96	4.47	3.57	2.20	91.66	61.10	45.83	36.66	5.50	2.75	1.83	1.37	1.10
	D	1.65	8.98	5.99	4.49	3.59	2.29	91.75	61.16	45.87	36.70	5.55	2.77	1.85	1.39	1.11

presents a summary of the costs of implementing the MESF service, previously presented in Table 10, Table 11 and Table 12.

According to Table 13 and Table 14, when a positive energy balance is recorded for the provision of MESF backup power services using CEV, the cost of provision does not exceed 1.5 EUR/kWh in the vast majority of cases, which is consistent with the results achieved in [15] for load time shifting services. The maximum cost of providing the MESF backup power service, for which a positive energy balance is recorded, is 3.73 EUR/kWh, which is still significantly lower than the VoLL indicators for the entities studied. This confirms the viability of using MESF as an additional energy resource when it is necessary to provide backup power to the service taker. It is also worth noting that the proposed CEV fleet limits make it practically impossible to provide the analyzed MESF service for a 24 h power outage. Only in 13% of cases for a 24 h power outage was a positive energy balance recorded. For a 1 h power outage, all cases allowed for the technical implementation of the MESF service. For a 4 h power outage, 82% of cases are technically feasible for the service. In terms of the costs of implementing the MESF service, the highest are recorded for ENT2. This may be due to the need to keep the CEV fleet in operation, with a relatively low level of demand for the service, which from the point of view of unit cost generates a high value for the service. In [16], it was estimated that the unit cost of diesel generators in emergency mode is 0.66 EUR/kWh. In 24% of cases for all ENT1-ENT3 entities, values lower than the unit cost of electricity generation and supply from a diesel generator were recorded. In order to verify and recalculate the unit costs of diesel generator operation, the methodology described in [16] was used to estimate this cost for the conditions applicable to ENT1-ENT3.

The unit cost of energy generation from a diesel generator is particularly sensitive to changes in fuel prices. Therefore, we analyzed cases where the fuel price varies from 1 EUR/L to 1.6 EUR/L, with the fuel price in [16] being 1.2 EUR/L.

Table 15. Average cost of delivering electricity to service takers ENT1-ENT3: comparison of MESF and diesel generator.

Hours Without Energy Supply [h]	MESF				Diesel Generator
	Option	ENT1	ENT2	ENT3	Fuel Price for Diesel GEN [EUR/L]	ENT1	ENT2	ENT3
		$\mathit{\sigma }=100$%	$\mathit{\sigma }=100$%	$\mathit{\sigma }=100$%		$\mathit{\sigma }=100$%	$\mathit{\sigma }=100$%	$\mathit{\sigma }=100$%
1	A	0.54	0.54	0.52	1	1.57	91.00	10.86
	B	0.49	0.58	0.50	1.2	1.68	91.11	10.96
	C	0.43	0.53	0.40	1.4	1.79	91.22	11.07
	D	0.42	0.53	0.39	1.6	1.90	91.33	11.18
4	A	1.17	21.78	1.23	1	0.80	23.16	3.12
	B	0.83	0.83	0.82	1.2	0.91	23.27	3.23
	C	0.51	0.63	0.78	1.4	1.02	23.38	3.34
	D	0.50	0.53	0.82	1.6	1.13	23.49	3.45
24	A	4.84	36.80	1.50	1	0.59	4.32	0.98
	B	4.95	36.83	1.53	1.2	0.70	4.43	1.09
	C	3.57	36.66	1.10	1.4	0.81	4.54	1.20
	D	3.59	36.70	1.11	1.6	0.92	4.64	1.31

presents a summary of the costs of delivering energy to service takers ENT1-ENT3, comparing MESF and diesel generator technologies for cases where 100% of the electricity in the facilities is secured.

Based on Table 15, it can be seen that in the case of shorter power outages (1 h or 4 h), MESF technology has an advantage over diesel generators as a backup power resource. Only in the case of a 24 h power outage is the use of a generator more cost-effective. In Table 15, cases where the unit cost of energy supplied from a backup source such as a diesel generator is lower than for MESF technology, are marked in red. It should be noted that the impact of fuel price changes on the unit cost of electricity production in a diesel generator is quite significant and can change its unit cost by up to several dozen percent. This may again suggest that securing energy needs with MESF should be the first line of defense, and that diesel generators will need to be started in the event of lengthy outages.

At this point, it is worth discussing the logistical aspects of using CEVs with MESFs in real-world conditions. Although this study did not analyze any logistical aspects, the authors are aware of the particular importance of this branch of MESF mechanism design, especially in urban areas. Proper management of the CEV fleet can help deliver the required energy capacity faster and, thanks to the use of advanced forecasting tools, accurately estimate the number of vehicles that need to be deployed. It is important to correctly define the functions that CEVs will perform in the logistics model, i.e., whether they will remain on standby to provide backup power services or whether they will function as vehicles optimizing the operation of the local power system, e.g., by collecting surplus production from RES. It is worth noting that not only is the number of CEVs important, but so is the number of available parking spaces. Logistics algorithms will need to be able to manage the deployment of MESFs to specific locations in order to maximize the number of occupied parking spaces. CEV fleet management also involves a number of decision-making issues. For example, should a CEV complete the discharging or charging process despite the occurrence of a second service with better economic parameters? These and other issues will pose a huge logistical challenge for future CEV fleet managers.

A brief sensitivity analysis of other key parameters such as discount rate and battery efficiency was also performed. In terms of the efficiency of the MESF battery discharge–charge process for the analyzed option A, a change in efficiency of +/−5% would affect the MESF energy potential by 4.8 kWh, which in the case of the inclusion of maximal ELCV fleet for ENT1 would change (both up and down) the resource potential by 7.2 MWh, for ENT2 by 24 kWh, and for ENT3 by 240 kWh. The assessment of the impact of the change on the discount rate was performed only for ENT1 and option A of the CEV vehicle. The CRF ratio, which translates into the value of capital expenditure per vehicle, was analyzed. The base discount rate was 6%, and cases where the discount rate was 4% and 8% were examined. The results of the sensitivity analysis showed a change in the amount of capital expenditure per hour of operation of +0.84% for an 8% discount rate and −0.81% for a 4% discount rate. Due to the marginal changes, the other simulation cases were omitted. The remaining technical and economic parameters have a negligible impact on the simulation results and have therefore also been skipped. The key factor is the change in the number of CEVs providing MESF services, as presented in Section 5.1, Section 5.2 and Section 5.3.

5.5. Service Taker ENT4—MV/LV Substation

In previous cases, the cost of delivering electricity using MESF for individual commercial entities ENT1-ENT3 was analyzed. They could involve dispersed locations, with each facility belonging to a given entity performing the same type of economic activity. The problem noted by the authors of the publication is the need to analyze whether, as part of the energy transition process, the DSO could equip itself with a CEV fleet to power entire areas of the distribution network, e.g., MV/LV stations, in the event of power outages. In addition, Section 2 already addressed the problems of valuing the cost of electricity outages when households are the predominant type of end users. Therefore, it seems that in such cases, the DSO would take over jurisdiction over the CEV fleet operation, replacing mobile diesel generators with mobile electricity storage facilities. The analysis selected a power station supplying 207 end users, 160 of which are households with an average hourly energy consumption of 123 kWh. It was assumed that the DSO could deploy 5 CEVs in options A or B, or 2 vehicles in options C or D. To simplify the analysis, the assessment was limited to the unit cost of supplying electricity to end users at the ENT4 station for two edge cases of compensation, for 20% and 100% of the electricity bill. All MESF configuration options (A, B, C, D) and all levels of electricity security were analyzed.

Table 16. Average cost of delivering electricity to service taker ENT4 during MESF service provision.

Hours Without Energy Supply [h]	Option	Average Cost of Delivering Electricity in MESF Service [EUR/kWh]—20% of Electricity Bill					Average Cost of Delivering Electricity in MESF Service [EUR/kWh]—100% of Electricity Bill
		$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$	$$\mathit{\sigma }=20\mathbf{\%}$$	$$\mathit{\sigma }=40\mathbf{\%}$$	$$\mathit{\sigma }=60\mathbf{\%}$$	$$\mathit{\sigma }=80\mathbf{\%}$$	$$\mathit{\sigma }=100\mathbf{\%}$$
1	A	0.93	0.58	0.63	0.54	0.48	1.70	0.97	0.73	0.73	0.63
	B	0.74	0.47	0.51	0.43	0.38	1.37	0.78	0.59	0.58	0.51
	C	0.77	0.48	0.39	0.34	0.31	1.50	0.79	0.59	0.52	0.45
	D	0.80	0.48	0.39	0.34	0.31	1.54	0.87	0.64	0.53	0.67
4	A	1.45	1.09	0.97	0.91	0.75	2.19	1.46	1.37	1.10	0.93
	B	1.15	0.69	0.66	0.64	0.55	1.36	0.99	0.86	0.69	0.75
	C	0.80	0.51	0.40	0.47	0.42	1.41	0.84	0.62	0.52	0.45
	D	0.81	0.51	0.40	0.47	0.42	1.42	0.86	0.64	0.53	0.91
24	A	3.02	1.51	1.00	0.75	0.60	4.56	2.28	1.52	1.14	0.91
	B	2.51	1.28	0.85	0.64	0.51	2.98	1.90	1.27	0.95	0.76
	C	1.48	0.86	0.57	0.43	0.34	2.03	1.47	0.98	0.75	0.60
	D	1.50	0.89	0.63	0.47	0.38	1.54	1.15	1.05	0.79	0.60

presents the results of calculations for the unit cost of service provision for ENT3 for the following three periods without a main power supply: 1 h, 4 h, and 24 h.

Based on Table 16, it can be seen that the unit cost of delivering electricity to end users as part of the MESF backup power supply service ranges from 0.35 EUR/kWh to 4.56 EUR/kWh. These values are similar to those recorded for commercial entities. Comparing these values with the VoLL value obtained for households in [47] (6.26 EUR/kWh), a positive effect of using the MESF service can be observed, as it is lower than the VoLL index.

The DSO should certainly consider the possibility of using CEVs as an alternative to mobile diesel generators. As with ENT1-ENT3 entities, the cost-effectiveness of the MESF service was checked against the unit costs of labor and energy supply from a diesel generator. In 71 out of 120 cases (59%), the unit operating cost of CEVs was lower than that of diesel generators, which is a better result than in the combined analysis for ENT1-ENT3.

6. Conclusions

This article presents a novel approach to determining the cost of electricity delivered or not delivered to end users, especially in situations where mobile electricity storage facilities were used as backup power resources. Different types of MESF battery capacity were modeled, in order to validate the feasibility of MESF service provision in smaller (ELCV) or larger (EHCV) CEVs. The methodology for calculating the unit cost of delivering or not delivering energy was based on hourly parameters, with modifications proposed for calculating the lost costs resulting from the cessation of business activity due to a power outage in the event of electricity not being delivered. The VoLL parameter was used as a reference index. Usually, this is determined for a given sector of the economy in terms of annual energy consumption and gross value added or from surveys conducted by energy regulators. On the contrary, the proposed methodology made it possible to determine the potential cost of energy failure more accurately, making it dependent on the hourly revenue of the company and the duration of the power outage. In addition, such an indicator was determined for areas with a high density of households, making the lost cost dependent on the percentage of the electricity bill. Next, the cost of energy non-delivery was taken into account in the form of an economic benefit for the end user (in the event of an imbalance) as a function of the cost of electricity delivery from the MESF for the end user’s backup power service. The obtained results allow us to conclude that CEVs with built-in MESFs can serve as a backup power source for commercial entities and for DSOs in supporting the power supply of the MV/LV station area, provided that the cost of providing this service is lower than the cost of starting a diesel generator. The research found that MESFs perform better as a backup power source during shorter power outages (1 h and 4 h), in which 100% and 82% of all cases, respectively, prove their technically feasible for the service. On the other hand, for outages lasting 24 h, only 13% of cases show a positive energy balance. The same findings apply to economic viability. The maximum cost of providing the MESF backup power service, for which a technical feasibility is proven, is 3.73 EUR/kWh. For longer outages it is more cost-effective to start a diesel generator, as the premium for covering lost revenue during the grid failure, rapidly increases the cost. While analyzing the possibilities of using MESFs as a backup power source, the availability of space for discharging them could be a major constraint and the demand should be carefully chosen. Future and ongoing research in the area of MESF service mechanism design will focus on the optimal use of the CEV fleet and the allocation of suitable services to them, using the logistics model that is currently being developed. This will make it possible to assess whether CEVs providing backup power services will be able to provide other energy services, as well as their response times and availability. In summary, mobile electricity storage facilities can be a future-oriented, cost-effective method of backing up the electricity demand of end users, and a more accurate method of estimating the cost of delivering or not delivering energy will allow for the optimal selection of resources to carry out such an operation.