Traditional technical measures for loss reduction in distribution networks primarily involve the replacement of high-energy-consuming distribution transformers, shortening supply radii, balancing three-phase loads, and implementing reactive power compensation. However, these methods are often associated with high investments, construction challenges, and long implementation periods (Zang, 2020).

With the widespread adoption of flexible regulation resources in distribution networks, including energy storage systems (Jiang, 2021), there is a growing emphasis on uncovering the loss reduction potential of existing flexible regulation resources. Modular Mobile Battery Energy Storage (MMBES), representing a novel energy storage technology, possesses the flexibility of both time and space. It can be rapidly deployed at specified locations in response to demand, providing services such as emergency response (Zhang et al., 2020), uninterrupted operations (Li et al., 2022a), and peak load management (Li et al., 2022b; Sun et al., 2023) to distribution networks.

Currently, energy storage deployment in the power system can be broadly categorized into three scenarios:

1) Energy storage deployment on the generation side: In this scenario, energy storage is integrated on the generation side. Literature (Ma et al., 2016) has established a comprehensive economic benefit model for Battery Energy Storage Systems (BESS) participating in wind power ancillary services. It assesses the profitability of the BESS by calculating investment return rates, payback periods, and other economic indicators. Literature (Lü et al., 2015) focuses on the relationship between photovoltaic system and energy storage costs, electricity price models, load characteristics, and the economic feasibility of energy storage systems, aiming to find the optimal economic solution.

In current energy storage systems, a conventional strategy involves deploying these systems at fixed locations, typically at strategically selected sites such as power generation stations, industrial facilities, or substations near residential areas. This deployment strategy is primarily designed based on the geographical location of facilities and the stability of grid demands, enabling efficient energy transmission from storage sites to demand locations. Fixed energy storage systems are advantageous in providing continuous and stable energy output, particularly suitable for grid environments with high predictability and relatively fixed demands.

However, this fixed deployment approach exhibits several significant limitations. First, the flexibility of fixed systems is limited; they cannot rapidly adjust to real-time changes in grid demands. In situations where there are sudden changes in load or emergencies (such as disruptions caused by natural disasters), fixed systems are unable to quickly reposition or adjust their locations to more effectively support specific areas of the grid. Additionally, the installation and maintenance costs of fixed energy storage systems are high, especially in geographically remote or inaccessible areas. This not only increases the economic burden of initial investments but also may affect the long-term sustainability and efficiency of the system. Lastly, fixed systems often require close integration with existing grid infrastructure, which limits their application potential in emerging or slowly upgrading grids where infrastructure may not support efficient energy distribution and management.

To further enhance the flexibility of energy storage applications, both domestic and international research has initiated preliminary studies on mobile energy storage. Literature (Lei et al., 2016), for instance, introduced a two-stage scheduling framework for mobile energy storage based on pre-positioning and real-time allocation. This framework enhances resilience by improving the response to unexpected events. Literature (Lei et al., 2019) proposed a mixed-integer programming model to address challenges related to mobile energy storage scheduling and the disparate time scales of distribution system operation, as well as the coupling of road networks and power grids. By optimizing the dynamic scheduling of mobile power sources, this approach enhances the resilience of the distribution network. To encapsulate, the significance of portable energy storage systems stems from their capacity to manage unforeseen circumstances, including traffic congestion and catastrophic events, alongside securing diverse advantages via adaptable deployments. Hence, the unpredictability of such events and the inclination towards decision-making that accounts for multiple benefits are key elements that affect the setup of energy storage solutions.

This study introduces a refined approach for arranging Modular Mobile Battery Energy Storage (MMBES) within distribution networks, taking into account both overall utility and individual perception. The primary breakthroughs of this research encompass:

1) From the viewpoint of the electric utility company, the research suggests a method for the integrated use of modular energy storage across three situations: standard operation of the distribution network, addressing equipment malfunctions, and managing emergency conditions. In detail, MMBES is utilized for peak shaving in normal operations, providing energy to adaptable loads upon unexpected equipment failures, and allocating power to essential loads in crisis circumstances. This strategy not only improves the comprehensive utility of the energy storage system but also augments the adaptability of the distribution network.

In summary, this research introduces an optimized configuration method for MMBES in distribution networks operated by electric utility companies. It considers comprehensive utility and subjective cognition, addressing various scenarios and benefits. Additionally, it incorporates prospect theory to account for decision-makers’ subjective preferences and handles the uncertainty associated with extreme events. Innovative calculation methods for prospect values related to network reliability and upgrade delay are also presented, enhancing our understanding of energy storage deployment in distribution systems.

The presence of MMBES (Modified Multi-Bus Electrical System) within the substation affects the losses of the upstream power grid and the transformers within the substation. When the operating strategy is fixed and errors are not considered, the reduction in distribution network losses is uniquely correlated with the decision variables. Therefore, the value of distribution network loss reduction, denoted as v E dec , is equivalent to the prospective value of distribution network loss reduction, V dec . The specific expression is as follows: V dec = π + p dec v + E dec + π − p dec v − E dec = v + E dec = E dec − E dec.0 α , E dec ≥ E dec.0 v − E dec = − λ E dec.0 − E dec β , E dec < E dec.0 (10) In the equation: E dec represents the reduction in distribution network losses before and after configuring MMBES; E dec.0 represents the anticipated reduction in losses as expected by the planners. E dec S n , P n , S o c . m i n = ∑ k = 1 N y ∑ j = 1 S ∑ t = 1 24 / Δ T Δ p loss,tj ⋅ Δ T ⋅ n j ⋅ f cost 1 + i 0 k (11) N y = m i n N life , N war (12) In the equation provided: N y represents the operational lifespan of MMBES; S denotes the number of categories into which the daily load profile is divided over the course of a year; n j denotes the quantity of days within a year that are classified under the jth type of standard daily load profiles; Δ p loss.tj signifies the difference in distribution network losses before and after configuring MMBES for the j t h typical daily load category; Δ T represents the time interval per unit, with this paper using a value of 1 h; f cost denotes the unit cost of purchasing electricity from the grid; i 0 represents the baseline rate of return; N life represents the operational lifespan of the battery system, taking into account the impact of discharge depth and the number of cycles. This lifespan can be determined through the rainflow counting method (Wang et al., 2022b); N war stands for the warranty period provided by the MMBES manufacturer.

The effectiveness of distribution network loss reduction is closely related to the operational strategy of MMBES (Modified Multi-Bus Electrical System). Appropriate management of energy storage systems can equalize the flow of electricity in the primary distribution lines and substation transformers across peak and low-demand periods, thereby diminishing losses in the network. In this paper, a peak shaving and valley filling power difference control strategy is employed during normal grid operation, and its performance is illustrated in Figure 4. MMBES undergoes a complete charge-discharge cycle daily, while adhering to Equations 13–15 as the foundation. The start and stop times t g g ≥ 4 for charging and discharging, as well as the power levels ( P 1 and P 2 ), are determined based on the configured capacity and state of charge (SOC) constraints. The difference between P 1 , P 2 , and the actual load represents the charging and discharging power within each time interval.

MMBES Operation Satisfying Equations 13–15: S o c . t = S o c , t − 1 + η p MMBES.t Δ T S n , p MMBES.t ≥ 0 S o c , t − 1 − 1 / η p MMBES.t Δ T S n , p MMBES.t < 0 (13) S o c . m i n ≤ S o c . t ≤ S o c . m a x (14) p MMBES.t ≤ P n (15) In the equation: S o c . t represents the state of charge (SOC) of MMBES at time t ; η denotes the charging and discharging efficiency of MMBES.

In the event of a malfunction on the high-voltage side of the substation or within the substation transformer itself, MMBES can supply energy to the loads within the same island throughout the fault rectification period. This capability significantly boosts the dependability of the distribution system. The dependability traits of the distribution grid are constant, and the advantage of enhancing supply dependability, denoted by v E rel , corresponds to the anticipated benefit of bolstering the distribution grid’s reliability, V rel . The specific formulation is presented below: V rel = π + p rel v + E rel + π − p rel v − E rel = v + E rel = E rel − E rel.0 α , E rel ≥ E rel.0 v − E rel = − λ E rel.0 − E rel β , E rel < E rel.0 (16) In the equation: E rel represents the economic benefits resulting from the enhancement of distribution network reliability; E rel.0 represents the anticipated economic benefits as expected by the planners.

This research utilizes the metric known as Expected Energy Not Supplied (EENS) to assess the dependability of the distribution grid. E rel S n , P n , S o c . m i n = ∑ k = 1 N y Δ E ENS ⋅ f sell + f comp ⋅ R IEA 1 + i 0 k (17) In the equation: Δ E ENS represents the difference in Expected Energy Not Supplied (EENS) before and after configuring MMBES; f sell denotes the average unit selling price of electricity from the grid; f comp represents the production-to-electricity ratio per unit of energy not supplied; R IEA stands for the User Evaluation Coefficient.

Reliability assessment methods can primarily be classified into two major categories: analytical methods and simulation methods. Battery energy storage exhibits temporal characteristics, but Monte Carlo sampling simulations are time-consuming for optimization problems. Therefore, in this paper, we employ the analytical approach known as Fault Consequence Analysis to perform the calculations. The residual energy capacity of MMBES is contingent upon real-world operating conditions and has a direct impact on the outcomes of system failures. Therefore, conducting a statistical analysis of the State of Charge (SOC) in line with the operational strategy is crucial. This analysis enables the determination of the probabilities linked to various SOC levels, which, in turn, facilitates the calculation of the distribution network’s reliability at each SOC level. The comprehensive reliability assessment is achieved by compiling these findings using suitable weighting methods.

The specific formula for calculating EENS is as follows: E ENS = ∑ h = 1 J a h A ∑ b = 1 B E ENSb − m i n E ENSb , S o c . h p rec.b (18) E ENSb = ∑ m = 1 N b λ m μ m P b (19) S o c . h = S n ∑ n = 1 a h b h n a h (20) p rec.b = ∑ m = 1 I s λ m μ m / ∑ m = 1 N b λ m μ m (21) In the equation, J denotes the total number of scenarios corresponding to different SOC levels; A signifies the aggregate count of SOC samples; a h represents the quantity of samples for the h t h SOC scenario; and B indicates the complete number of loads within the distribution network; E ENSb is the annual expected energy not supplied for the b t h load; S o c . h represents the anticipated residual energy of the MMBES for the hth State of Charge (SOC) scenario; p rec.b is the expected ability of MMBES to supply power to the b t h load during a fault; N b represents the elements that can cause a power outage for the b t h load due to a fault; λ m and μ m are respectively the failure rate and repair time for the m t h element; P b is the required power to ensure normal power supply for load b during an outage; b h n represents the n t h sample value for the h t h SOC scenario; I S represents the elements for which MMBES and the load are in the same island after a fault.

The traditional assessment method for delaying power grid upgrades is based on measuring the number of years the expansion can be postponed by evaluating the maximum load reduction before and after energy storage configuration. Despite the potential benefits, the intrinsic likelihood of failures within energy storage systems means they cannot ensure uninterrupted adherence to the N − 1 criterion for grid reliability. This limitation leads to an overestimation of the systems’ advantages. The phrase “credible capacity” for energy storage refers to the volume of supply capacity that can be dependably replaced with a given degree of dependability. It offers a finer assessment of MMBES’s addition to the grid and its replacement worth. The specific expression for the prospective value V del of delaying power grid upgrades is given by (Zhao et al., 2023): V del = π + p del v + E del + π − p del v − E del = v + E del = E del − E del.0 α , E del ≥ E del.0 v − E del = − λ E del.0 − E del β , E del < E del.0 (22) E del S n , P n , S o c . m i n = ∑ k = 1 Δ T y c inv ⋅ 1 − e − i 0 ⋅ Δ T y / Δ T y 1 + i 0 k (23) Δ T y = lg 1 + P rel P max / lg 1 + τ (24) In the equation: E del represents the benefits of postponing distribution network expansion; E del.0 represents the anticipated benefits as expected by the planners; c inv is the required investment for substation and line expansion; Δ T y is the number of years by which MMBES delays power grid upgrades; τ represents the annual rate of load growth; P max signifies the peak load of the system prior to the integration of MMBES; P rel denotes the credible capacity of MMBES.

In this research, following the concept of matching reliability, the credible capacity of MMBES is evaluated using the Effective Load Carrying Capability (ELCC) indicator. The exact correlation is outlined below: R L 0 = R ′ L 0 + Δ L (25) Within the formula, R and R ′ represent the dependability of the distribution grid prior to and subsequent to the deployment of MMBES, respectively. These reliability levels are assessed using the reference Equations 18–21, specifically for the evaluation metric EENS; L 0 and Δ L represent the original total load at various load points within the distribution network and the additional load, respectively. When Equation 25 holds true, the corresponding Δ L represents the credible capacity P rel of MMBES. The step-by-step calculation process is depicted in Figure 5 for reference.

In situations where the electrical power system encounters severe weather phenomena or widespread power interruptions due to military operations, the continuous provision of power to vital loads is essential. MMBES can be divided into various autonomous supply entities depending on the specific nature of the fault, with a focus on guaranteeing power delivery to essential loads should backup power sources fail. If there is surplus capacity, it can then be used to safeguard some of the secondary loads that lack backup support. The prioritization for protection ought to be thoroughly evaluated across three critical dimensions: the safety of human life, the security of the nation, and the potential for economic losses.

Diminishing losses from power outages in critical situations correlates with the likelihood and length of these scenario events. Since both of these factors are uncertain, this attribute follows a certain probability distribution rather than a deterministic value. Its value function should be improved based on Equations 6, 7, as shown specifically in Equation 26. In the weight functions, Equations 8, 9, the probability, denoted as p , for attributes being either gains or losses is no longer 1 or 0. Instead, it is calculated based on the probability density functions as indicated in Equations 27, 28, respectively: v x = ∫ x 0 + ∞ x − x 0 α f x d x , x ≥ x 0 ∫ − ∞ x 0 − λ x 0 − x β f x d x , x < x 0 (26) p = F + ∞ − F x 0 (27) p = F x 0 − F − ∞ (28) Within the formulas: f x denotes the probability density function associated with the attribute, while F x symbolizes the attribute’s cumulative distribution function.

Integrating Equations 8, 9 together with Equations 26 through 28, the prospective model for reducing power outage losses in extreme scenarios, denoted as V ext , can be formulated as follows: V ext = π + p ext v + E ext + π − p ext v − E ext = G + γ G + γ + 1 − F ext + ∞ + F ext E ext.o γ 1 / γ ⋅ ∫ E ext.0 + ∞ E ext − E ext.0 α f ext E ext d E ext + G − δ G − δ + 1 − F ext E ext.0 + F ext − ∞ δ 1 / δ ⋅ ∫ − ∞ E ext.0 − λ E ext.0 − E ext β f ext E ext d E ext (29) In the equation: G + = F ext + ∞ − F ext E ext.0 ; G − = F ext E ext.0 − F ext + ∞ ; E ext represents the benefits of reducing power outage losses in extreme scenarios; E ext.0 represents the anticipated benefits as expected by the planners; p ext represents the probability that E ext is expressed as either gains or losses relative to E ext.0 . E ext S n , P n , S o c . m i n ∼ f ext E ext = ∑ k = 1 N y ∑ b = 1 N imp H − f tra.b ⋅ ζ ext ⋅ f ζ ext ζ ext 1 + i 0 k (30) W sup.b = m i n W rem.b , m a x t fai ⋅ f t fai t fai − t tra.b , 0 ⋅ P b (31) In the equation: H = W sup.b ⋅ f sell + f comp ⋅ R IEA ; N imp represents the number of critical loads to be protected; W sup.b represents the amount of electricity supplied by the energy storage unit to load b during a power outage; f tra.b represents the cost of transporting the energy storage unit to load b ; ζ ext is the probability of extreme scenarios occurring; W rem.b represents the remaining energy of the energy storage unit supplying load b ; t fai is the outage duration, not exceeding 7 days (Zhao et al., 2023); t tra.b represents the duration needed for the energy storage unit to establish a connection with load b .

The full lifecycle cost of configuring MMBES falls under expenditures. When the cost exceeds a reference value, decision-makers perceive it as a loss, and when it is less than the reference value, they perceive it as a gain. The specific expression for the prospective value V c is as follows: V c = π + p c v + C cyc + π − p c v − C cyc = v + C cyc = C cyc.0 − C cyc α , C cyc ≤ C cyc.0 v − C cyc = − λ C cyc − C cyc.0 β , C cyc > C cyc.0 (32) In the equation: C cyc represents the full lifecycle cost of configuring MMBES; C cyc.0 represents the anticipated cost as expected by the planners.

The full lifecycle cost consists of three parts: the initial investment and construction cost C con , the operational and maintenance cost C ope , and the post-disposal recycling and treatment cost C rec . C cyc S n , P n = C con + C ope + C rec (33)

The upfront investment and construction expenses encompass the energy costs for a specified battery capacity and the costs related to energy conversion, monitoring, and management. C con = c s S n + c p P n (34) In the equation: c s represents the unit capacity investment cost of MMBES; c p represents the unit power investment cost.

Operational and maintenance costs include fixed charges based on rated power and variable costs related to energy losses, stemming from the energy storage system’s processes of charging and releasing energy. C ope = ∑ k = 1 N y c ope P n + 1 − η W c h + 1 / η − 1 W dch ⋅ f cost 1 + i 0 k (35) In the equation: c ope represents the unit power annual operational and maintenance cost; W c h and W dch denote the yearly energy quantities for charging and discharging in MMBES.

The post-disposal recycling and treatment cost is the difference between the production cost for decomposing and handling the discarded batteries and the revenue obtained from recovering extracted metal materials. C rec = − c r S n 1 0 3 ⋅ ρ e 1 + i 0 N y = c han − ∑ u = 1 v c u v ρ u v S n 1 0 3 ⋅ ρ e 1 + i 0 N y (36) In the equation: c r represents the unit weight battery recycling price; ρ e represents the particular energy capacity characteristic of the battery; c han represents the cost associated with processing a unit weight of discarded batteries; v indicates the variety of metals contained within the battery; c u v is the recycling value of metal u ; and ρ u v quantifies the proportion of metal u per unit weight present in MMBES.

The paper examines a Class A distribution network in City A, which receives its power from a 220 kV substation connected in a T-shaped configuration to a 66 kV transformer station. The 10 kV output from the 66 kV transformer station is set up in a looped arrangement, as illustrated in Figure 7.

The distribution ratio between substations 1 and 2 stands at 0.55. The schematic displays three outgoing lines, with the main trunk lines designed similarly to the depicted structure. All circuit breakers, with the exceptions of QF5, QF6, and QF12, remain in a normally closed position. MMBES is deployed within substation 1, influencing the electricity flow in the 66 kV and higher voltage networks. Nevertheless, given the urban power grid’s complexity, this study limits its focus to the sectors most impacted, specifically, the alterations in losses for L1, L2, T1, and T2. In the event of a regional network failure, MMBES is activated to segment and reroute power, aiming to reestablish service to vital loads, with S1 and S3 identified as critical loads requiring protection.

1) Distribution system structure parameters: Line L1 and L2 have a length of 5 km, while L3, L4, L5, and L6 are each 3.5 km long. The unit length resistance and reactance are both 0.17 Ω /km and 0.395 Ω /km, respectively. There are 4 transformers with short-circuit losses Δ P k = 88.35 kW, short-circuit voltage percentage U k % = 10.5, no-load losses Δ P 0 = 19.20 kW, and no-load current percentage I 0 % = 0.69.

The population size for the Differential Evolution Algorithm, MNP, is set to 100, and other parameters are referenced from (Liu et al., 2021). The parameters related to prospect theory in the model: α is 0.88, β is 0.88, λ is 2.25, γ is 0.61, δ is 0.69. Through the analysis of significant historical incidents in the area, the probability of extreme scenario occurrence, ζ ext (times/year), follows a uniform distribution U (0.005, 0.1), which corresponds to an occurrence frequency of once every 10–200 years. Setting the outage duration according to guidelines (National Energy Administration, 2018): t fai h ∼ U 12,168 , equivalent to a restoration time of half a day to 7 days.

Given that all attributes are deemed equally significant, we set ω 1 , ω 2 , ω 3 , ω 4 , and ω 5 each at 0.2. After configuring MMBES, the expected benefits for delaying grid upgrade, enhancing reliability, reducing outage losses in extreme scenarios, and reducing network losses are 100, 90, 50, and 50 thousand yuan, respectively. The expected cost expenditure is half of the net benefits, which is 145 thousand yuan, as shown in Table 5.

Based on the parameters mentioned above, conducting simulation calculations using the Differential Evolution Algorithm converges in 200 iterations, with a maximum iteration limit set at 300 iterations. The optimization configuration results for MMBES, along with the benefits/costs and prospects for each attribute, total benefits, and comprehensive prospects, can be found in Table 6.

The data extracted from the table suggests that the optimal configuration for MMBES features a storage capacity of 4986.83 kW-hours (kW ⋅ h), a rated power of 1,600.5 kW (kW), and maintains the operational State of Charge (SOC) at a maximum limit of 0.8. The net profit is 2,793.85 million yuan. The attribute benefits/costs, in descending order, are as follows: Delayed expansion benefit E del , enhanced reliability benefit E rel , configuration cost C cyc , reduced outage loss benefit under disasters E ext , and loss reduction benefit E dec . As the reference point values are relatively small, E del , E rel , E ext , and C cyc are all greater than the reference points, resulting in positive prospects for benefit attributes and negative prospects for cost attributes. E dec is 0, which is less than the reference point, resulting in a negative prospect.

The potential benefits of postponing grid upgrades and renovations are the most significant, particularly when considering MMBES with a substantial capacity of 3,330 kW. In line with the current rate of load growth, this delay can extend the need for expansion by a remarkable 12 years, aligning with the original configuration intent. Following closely is the potential value associated with enhancing the reliability of the distribution network. By doing so, it is possible to reduce the annual electricity deficit by a substantial 2,162.29 kW ⋅ h. The probability of extreme scenarios occurring is relatively low, which explains the smaller prospective value of mitigating outage losses in such circumstances. However, in the unfortunate event of a disaster, MMBES can still contribute to reducing outage losses by a significant 3,989.46 kW ⋅ h. It is essential to note that the chosen study area exhibits minimal load fluctuations, and the cost of reducing losses is tied to the grid’s electricity purchase cost. Consequently, the optimized outcome suggests a relatively high lower limit for state of charge (SOC), which may not be advantageous for minimizing network losses. The outcomes of the optimization distinctly show that, considering the established benchmarks and their relative significance, energy storage systems remain fully charged under normal operational conditions and activate to provide power only during disruptions, leading to the maximum aggregate prospective value ( V ) .

When optimizing with the objective of maximizing net profit, the MMBES configuration results are as follows: S n = 9,043.75 kW ⋅ h, P n = 1712.1 kW, S o c . m i n = 0.8. Both capacity and power are greater than the optimization results when aiming to maximize comprehensive prospects. This is because the positive attribute benefits are weakened while the negative ones are strengthened when aiming to maximize net profit, as decision-makers tend to be more risk-averse, resulting in smaller configuration results. Additionally, when not considering extreme scenarios, the configuration results do not significantly increase, but the net profit decreases by 321.64 million yuan. This suggests that portable energy storage units can improve the overall effectiveness of the configured energy storage system.

Exploring the substantial advantages of postponing grid upgrades while improving reliability, this research delves deeper into the consequences of system sufficiency on the outcomes of the configuration analysis. The substation load rate is increased from 0.50 in a geometric progression to 0.65, and the changes in the prospects of various attributes are shown in Figure 8.

As network adequacy decreases, the system’s demand for MMBES capacity S n and power P n increases continuously, and the optimization configuration results increase monotonically from 0 to 11,019.44 kW ⋅ h and 4,711.5 kW, respectively. The holistic outlook, denoted as value V , demonstrates a pattern characterized by a sharp ascent followed by a gradual decline, reaching its zenith at approximately a load rate of 0.505. This is because at this point, S n and P n are relatively small, leading to lower cost prospect value V c , and the delayed expansion prospect value V del is already ideal. However, as adequacy decreases further, although the reliability prospect value V rel increases significantly, the increase in V c is even greater, resulting in a decrease in the overall prospect value V .

The prospect value V rel for enhancing distribution network reliability and the prospect value V ext for reducing losses in extreme scenarios both exhibit a monotonically increasing trend. The annual deficit in electricity supply and outage losses after disasters that can be reduced increase from 0 to 4778.03 kW ⋅ h and 8,815.55 kW ⋅ h, respectively. The cost prospect V c monotonically decreases, with configuration costs increasing from 0 to 2,665.14 million yuan. The prospect V del for delaying grid upgrade and renovation first increases rapidly and then slightly decreases, with the peak occurring near a load rate of 0.52. This is because when the load rate is greater than 0.5 but less than 0.52, as S n and P n increase, the number of years Δ T y that expansion can be delayed increases rapidly, leading to a rapid increase in V del . However, when the load rate is greater than 0.52, although Δ T y and the total amount of future-year expansion investment still increase with S n and P n , when Δ T y is large, the present value of the profits for the later years is relatively small, resulting in an overall decline in prospects. Furthermore, despite fluctuations in the load rate, the prospect value V dec , aimed at decreasing network losses, invariably holds a steady negative figure, while the optimization results for State of Charge (SOC) consistently stay at the maximum threshold of 0.8 for every load rate scenario.

Recognizing the persistent high level of network loss rate at 6.28% within the distribution system, efforts to enhance this metric entail elevating the significance of the loss reduction attribute ω 1 . This research investigates how cognitive factors related to decision-making, as informed by prospect theory, affect the outcomes of optimization. When ω 1 = 0.95 and ω 2 = ω 3 = ω 4 = ω 5 = 0.0125 , and the reference points are as shown in Table 5, the optimization configuration re-sults differ from Table 6. The configured capacity and power experience a rise from 4986.83 kW ⋅ h and 1,600.5 kW–11,051.02 kW ⋅ h and 1,663.2 kW, correspondingly. Simultaneously, the lower limit of State of Charge (SOC) decreases to 0.20. This adjustment is necessitated by the need for MMBES to achieve reductions in network losses, which entails implementing a strategy of discharging during peak load periods and charging during off-peak periods. This strategy requires a larger capacity and a smaller State of Charge (SOC). Prior to configuring the energy storage system, the network loss stands at 788.17 million kW ⋅ h, and post-configuration, it diminishes to 780.49 million kW ⋅ h, resulting in a network loss rate decrease to 6.22%.Therefore, it becomes clear that by elevating ω 1 , the attribute related to reducing losses is no longer eclipsed by the remaining three attributes, leading to a significant decrease in losses.

If the emphasis is on enhancing the resilience of the distribution network and the importance of reducing losses in extreme scenarios ω 4 is increased, when ω 4 is set to 0.6, and the values of ω 1 , ω 2 , ω 3 and ω 5 are each adjusted to 0.1, the configured capacity and power increase to 9,043.75 kW ⋅ h and 1,712.1 kW, respectively, with an SOC lower limit of 0.8. This is due to the necessity of maintaining the uninterrupted provision of critical loads during extreme scenarios. To achieve this, MMBES requires a larger anticipated surplus energy, which, in turn, demands a larger capacity and State of Charge (SOC). At this level of importance, the reduction in outage losses in extreme scenarios increases from 3,989.46 kW ⋅ h to 7,234.00 kW ⋅ h, significantly enhancing the resilience of the power distribution network.

The decision-maker’s subjective expectations are not constant. When cognitive parameters change, to study their impact on the optimization results, the expected cost expenditure C cyc,0 , which has a significant impact on the comprehensive prospect value V in Figure 8, is increased to 1,500 million yuan. The MMBES configuration capacity and power increase to 6,626.80 kW ⋅ h and 1,646.7 kW, respectively, which is a 32.89% increase for capacity and a 2.89% increase for power compared to Table 6. This phenomenon arises from the fact that when there is an increase in the psychological anticipation of investment, it can shift the prospect value of investment costs from negative to positive. Given the decision-maker’s inclination to be risk-averse when it comes to losses as opposed to gains, a reduction in cost, while keeping other attribute expectations constant, results in an increase in configured capacity and power.

We have conducted a comparative analysis between our proposed scheme for optimizing the configuration of Modular Mobile Battery Energy Storage (MMBES) and existing systems, focusing on several key factors. Our analysis evaluates the performance and effectiveness of our approach in the context of renewable energy integration and grid stability.