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14 February 2024

Synergism of Fuzzy Leaky Bucket with Virtual Buffer for Large Scale Social Driven Energy Allocation in Emergencies in Smart City Zones

and
1
Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USA
2
Department of Computer Science, Kennesaw State University, Marietta, GA 30060, USA
*
Author to whom correspondence should be addressed.
Electronics2024, 13(4), 762;https://doi.org/10.3390/electronics13040762
This article belongs to the Special Issue Big Data and Large-Scale Data Processing Applications
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Abstract

Smart cities can be viewed as expansive systems that optimize operational quality and deliver a range of services, particularly in the realm of energy management. Identifying energy zones within smart cities marks an initial step towards ensuring equitable energy distribution driven by factors beyond energy considerations. This study introduces a socially oriented methodology for energy allocation during emergencies, implemented at the zone level to address justice concerns. The proposed method integrates a fuzzy leaky bucket model with an energy virtual buffer, leveraging extensive data from diverse city zones to allocate energy resources during emergent situations. By employing fuzzy sets and rules, the leaky bucket mechanism distributes buffered energy to zones, aiming to maximize energy utilization while promoting social justice principles. Evaluation of the approach utilizes consumption data from simulated smart city zones during energy-constrained emergencies, comparing it against a uniform allocation method. Results demonstrate the socially equitable allocation facilitated by the proposed methodology.

1. Introduction

The progress in information and communication technologies has facilitated the rise and conceptualization of smart cities systems. Within smart cities, cyber and physical infrastructures coalesce and engage in mutual interaction, aiming to optimize the utilization of physical resources through data and information [1]. The implementation of a smart city embodies significant complexity due to the intricate interplay among diverse infrastructures, including but not limited to energy, transportation, and lighting [2].
Significantly, the energy infrastructure, particularly the electrical grid, stands as the cornerstone of a smart city, as the entire digital framework relies on electricity consumption [3]. Consequently, it can be argued that the functionality of a smart city hinges on the seamless flow of electricity throughout its premises. The integration of electrical grids with information technologies has birthed the concept of smart grids, which serves as the foundational technology for the development of smart cities. Citizens, who are also consumers, interface with the grid through smart meters equipped with intelligent algorithms designed to act in their best interests [4]. Through digital connectivity facilitated by communication networks, smart meters employ algorithms to make optimal purchasing decisions based on real-time data. Given the scale and population density of cities, coupled with the proliferation of smart meters and digital systems, a vast amount of data is generated within the smart city ecosystem [5]. Consequently, the concept of big data and its subsequent processing become integral components of smart city operations.
Efforts to promote efficient electricity consumption have facilitated the division of urban areas into distinct electricity zones, as noted in [6]. These zones bear resemblance to microgrids, as they may house their own generation sources, such as renewables, alongside their consumer base [7]. Generally, when a zone integrates generation units, it is advisable to prioritize the allocation of generated electricity to local consumers. Consuming electricity locally offers the advantage of optimizing grid usage, as power lines are not tasked with transmitting electrical energy over long distances. This effectively reduces the strain on the grid, lowering the risk of blackouts and overloads [8].
The Texas outage case of 2021 [9] provided us several lessons with regard to the management of energy resources, while also raising concerns about the most efficient strategy for allocating available energy during emergencies. Particularly, utilities are faced with difficult decisions during such crises regarding where and for how long to allocate the limited electrical power to meet citizens’ needs to the greatest extent possible. One approach often taken is to implement scheduled power outages in specific city zones for a predetermined period, resulting in certain zones having access to power while others do not. This challenge becomes especially daunting when dealing with large-scale and densely populated cities.
In this context, the fundamental question under scrutiny is how to allocate available electrical power within the various areas (zones) of a city in a manner that is efficient for the grid while also fostering a feeling of justice to the citizens [10]. The management of electricity at the zone level is still in its infancy, although there are ongoing efforts primarily leveraging artificial intelligence. In summary, the existing efforts [11,12,13,14,15,16] indicate a limited exploration of zone-based allocation in smart cities, particularly concerning emergency scenarios. Furthermore, none of the proposed methods thus far consider social factors as part of their decision-making process, thereby failing to provide a sense of "allocation justice" to the affected citizens.
The present paper addresses this gap by introducing a novel method that leverages artificial intelligence to develop a zone-based, socially driven allocation strategy for emergency electricity supply in smart cities. The proposed approach integrates a synergistic framework encompassing the concept of the leaky bucket [17], employing tools of fuzzy logic [18], and incorporating the concept of energy virtual buffer [19]. By employing fuzzy inference, the proposed method enables the representation of information in the form of fuzzy sets, which in turn facilitates rapid computation at a low cost. The utilization of fuzzy sets accommodates the representation of large data streams using simple functions, while fuzzy rules implicitly support decision-making based on various factors, such as electricity signals and social considerations [20].
The roadmap of this manuscript is as follows: In the next section, the concept and relater work on smart city zones is introduced, while the proposed approach is presented and discussed in Section 3. In Section 4, the fuzzy leaky bucket approach is applied for allocation of electricity in a simulated smart city and the results are discussed, while in Section 5 the main points of the paper are summarized.

3. Socially Driven Energy Allocation Approach

This section outlines the proposed approach for allocating electrical energy during emergencies within the zones of a smart city. The approach entails making decisions regarding the quantity of energy to be supplied to each specific zone.

3.1. Problem Statement

Emergency scenarios such as heavy snowfall or extensive rainfall can pose significant challenges to electrical systems and, consequently, to the overall energy supply of a city. Among the most common issues encountered in such situations is the grid’s inability to meet the full demand of consumers. This shortfall may arise from either an exceptionally high demand exceeding the capacity of generated electricity or technical difficulties impairing the grid’s delivery capacity. These challenges are particularly prevalent in densely populated areas, such as large metropolitan cities.
Up to this point, utilities typically address the aforementioned challenge by implementing selective shutdowns of electricity supply to various areas within the city, which entails providing a uniform supply of energy per area. These shutdowns remain in effect for a predetermined duration, after which electricity flow is restored. However, simultaneously, shutdowns occur in zones located in other areas of the city. It’s important to note that critical facilities such as hospitals and universities are exempt from these shutdowns unless there is a complete grid failure. However, the strategy of employing uniform shutdowns described above often leads to a sense of injustice among citizens, particularly those from lower social strata who lack access to modern generation technologies. This sense of injustice is heightened within the context of smart cities.

3.2. Leaky Bucket

The leaky bucket is an algorithm that has been successfully applied to several engineering domains aiming at controlling a process. Its main concept comes from the everyday life and more specifically from leaking water filled buckets. The algorithm is driven by the simple idea that the bucket may overflow when the leakage rate is lower than the incoming water rate. The algorithmic leaky bucket aims at limiting the actions associated with occurred events (in most cases discrete ones). Well-known applications of the leaky bucket entail controlling of the data packet transmission in communication networks [36], and the flow in service networks [37].
Figure 2 presents a graphical representation of the leaky bucket algorithm. We observe that the bucket takes one of the two states: (i) overflown state when the incoming flow rate (F) is higher than the leakage (L), i.e., F > L, and (ii) non-flown state when the leakage (L) is higher than the incoming flow, i.e., F < L.
Figure 2. Visualization of a leaky bucket and its states, s, where F and L denote the incoming and outcoming flow respectively.
An alternative rendition of the leaky bucket is the token-driven leaky bucket, primarily employed to regulate the rate of leakage from the bucket. The block diagram of this version is depicted in Figure 3. The fundamental concept revolves around two buffers: the data buffer and the token buffer. The data buffer receives input data packets, while the token buffer receives tokens. A data packet is released from the buffer only if the number of buffered tokens surpasses a predefined threshold. Importantly, the threshold is determined by the modeler based on the requirements of the specific application in question.
Figure 3. Token Driven Leaky Bucket approach.
The token driven algorithm allows the control of data release from the buffer. The higher the threshold (T), the higher the number of tokens that need to arrive before a data packet is released.

3.3. Fuzzy Leaky Bucket and Energy Virtual Buffer

In this section, we introduce the proposed fuzzy leaky bucket algorithm designed to allocate the available energy—significantly reduced compared to normal conditions—during emergencies. The primary objective of the algorithm is to ensure a fair distribution of the limited energy supply during emergencies, wherein the capacity of the electricity grid is constrained by non-normal conditions. The algorithm aims to determine the amount of energy allocated to each city zone. To achieve this, we propose a token-driven fuzzy leaky bucket algorithm that incorporates social factors into the token definition process. By doing so, the algorithm promotes a sense of justice in the allocation of energy during emergencies.
The block diagram illustrating the fuzzy leaky bucket algorithm for energy allocation is provided in Figure 4. It’s important to note that this method involves the utilization of a fuzzy logic inference system to determine the number of tokens in the leaky bucket, consequently influencing the release of energy from the buffer. Another innovative aspect is the introduction of energy packets, which integrate with the concept of the virtual buffer [38]. The term "energy virtual buffer" refers to the data structure that “virtually stores” energy amounts. This data structure is crucial since energy is a commodity that must be consumed in real time and cannot be stored on a large scale [39,40].
Figure 4. Synergistic approach of the fuzzy leaky bucket with energy virtual buffer for energy allocation.
Central to executing the energy allocation process is the availability of knowledge, typically obtained through forecasting, regarding the generated energy, and its structuring into “packets” [41,42]. It’s important to highlight that in practical terms, energy cannot be physically divided into packets. However, since this division is forecasted data—representing energy that has not yet been generated but is scheduled—artificially splitting it into packets becomes feasible [43,44]. The objective of the fuzzy leaky bucket algorithm is to allocate an appropriate number of energy packets stored in the virtual buffer to the respective zones. This proves invaluable during emergencies, where the unique conditions necessitate special handling of energy allocation.
The cornerstone of the proposed bucket type lies in the creation of a fuzzy inference engine. The architecture of the engine, including all input and output variables, is depicted in Figure 5. Notably, the fuzzy inference system comprises four socially related variables and two energy variables. The input variables associated with the zone are as follows:
Figure 5. Fuzzy Inference System for token rate determination.
  • Average Income (Social): This social variable reflects the average wealth of the zone’s citizens. It helps gauge the economic status of a zone, with “non-wealthy” zones potentially requiring more energy compared to affluent zones, which may rely on individual generators like diesel generators.
  • City Population Percentage (Social): This variable indicates the percentage population density of the zone as the ratio of zone’s population residing within the geographical area of the zone.
  • Disability Percentage (Social): This variable represents the percentage of the zone’s population officially registered as disabled. It supports zones with citizens with declared disabilities, considering their vulnerability and potential need for energy to operate essential equipment and instruments.
  • Number of Critical Buildings (Social): This variable denotes the count of critical buildings within the zone. Critical buildings may include hospitals, airports, and schools, among others.
  • Zone Forecasted Generation (Energy): This variable signifies the forecasted generation within the zone from its resources, such as renewables.
  • Percentage of Diesel Generators (Energy): This variable indicates the percentage of zone residents who possess secondary electricity generation using diesel generators. Diesel generators can serve as auxiliary suppliers, operating independently of the main power grid or microgrid.
  • Token Number (Output Variable): This variable represents the token number determined by the fuzzy system.
As illustrated in Figure 5, the aforementioned variables are transformed into fuzzy variables through fuzzification, with each variable depicted in Figure 6 as fuzzy sets. It’s important to note that fuzzy sets enable the expression and large-scale representation of multiple values within the variables using simple linguistic terms [45,46,47,48]. Furthermore, fuzzy logic facilitates the fusion of fuzzy variables into a single output, which takes the form of token numbers in this manuscript. Selection of the type of the fuzzy sets, which take the form of triangles, is based on past experience of the modelers; furthermore, triangular fuzzy sets is a common choice in fuzzy inference systems.
Figure 6. Fuzzy Sets for fuzzification of input and output variables.
In our study, information fusion is achieved through a set of 62 fuzzy rules that correlate social and energy inputs to the number of tokens. The fuzzy rules, presented in Table 1, encapsulate the variables 1-7, succinctly denoted as (in Table 1):
Table 1. Fuzzy Inference Rules for determining the number of tokens.
–
“Income,” refers to Average Income (Social)
–
“Population,” refers to City Population Percentage (Social)
–
“Disability,” refers to Disability Percentage (Social)
–
“Building,” refers to Number of Critical Buildings (Social)
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“Forecast,” refers to Zone Forecasted Generation (Energy)
–
“Diesel,” refers to Percentage of Diesel Generators (Energy)
–
“Tokens” refers to Token Number (Output Variable)
To enhance clarity in the decision-making process, we have outlined the steps for obtaining the final token number in Figure 7.
Figure 7. Block diagram of the token evaluation process.
The fuzzy leaky bucket is employed synergistically with a First-in-First-out (FiFo) queue [49] to allocate energy packets to the zones. The zones are placed in the queue and await the fuzzy leaky bucket to provide the number of tokens for a specific cycle. Subsequently, the number of generated tokens is compared with the bucket’s threshold T. If the number of tokens exceeds the threshold, the energy packet is released [50]. This mechanism ensures an orderly and efficient allocation of energy packets based on the fuzzy logic-driven token determination process.
At this point, it’s essential to emphasize that the virtual buffer holds the entire available energy for the upcoming hour. However, it’s crucial to understand that the buffered energy is constrained due to emergency conditions, significantly less compared to what would be available under normal circumstances (where socially fair allocation is not necessary) [51,52,53,54]. In summary, the allocation process unfolds through the following steps:
  • The available energy for the next hour is placed in the virtual buffer.
  • Zones are organized in a first-in-first-out (FIFO) structure, with the sequence of zones selected randomly.
  • The available buffered energy is divided into a set of energy packets, with the number of packets determined by the system operator.
  • The fuzzy leaky bucket is invoked, and the number of tokens is obtained for the first zone in the FIFO.
  • The number of tokens is compared with a predetermined threshold T.
  • If the number of tokens is below the threshold, no energy packet is released.
  • If the number of tokens is above the threshold, one energy packet is released.
  • If the number of tokens is above 2*T, then 2 energy packets are released.
  • If the number of tokens is above N*T, then N energy packets are released.
  • The zone is then removed from the list, and the next zone is selected.
  • The process returns to step 4.
  • Steps 4-11 are repeated for all zones until no energy packets remain or all zones have been allocated energy packets.
  • If there are residual energy packets—i.e., all zones have been processed but there is still available energy—then the remaining packets are distributed uniformly among all zones.
It’s important to emphasize that the process outlined in steps 1-13 occurs every hour to allocate the available energy on an hourly basis. In order to ensure fairness across all zones, the order in which the zones are placed in the FIFO structure is determined randomly. This means that the sequence of zones is randomized each hour, for instance, using a randomizer, to prevent any bias or favoritism in the allocation process.

4. Test Results

4.1. Simulation Setup

This section presents the test results obtained from an emergency scenario in a smart city comprising 1000 residents distributed across various social and energy variable combinations [55,56]. Our simulations involved the use of a randomizer to generate diverse scenarios based on the social and energy values of our city, allowing us to explore different conditions [57,58,59]. Moreover, the buffered energy was also randomized, providing values in the range of 0-100 MW. The available energy was divided into 100 virtual energy packets to be allocated among zones, with the city partitioned into 10 zones. For benchmarking purposes, we implemented a simple uniform round-robin method where each zone received an equal amount of energy. Additionally, the threshold for the Fuzzy Leaky Bucket to release an energy packet was set to 10 tokens, meaning that 84 tokens would release 8 packets. These parameters and methods enabled us to conduct comprehensive tests and analyze the effectiveness of the proposed allocation approach in emergency situations within smart cities.

4.2. Results

The simulated results have been meticulously recorded and are presented to showcase the social justice aspect of the proposed approach. We simulated 10 different scenarios, the values of which are detailed in Table 2. The allocated energy for each scenario is depicted as a function of the social variables outlined in the preceding section. The results obtained are illustrated in Figure 8, where the energy allocation using the Fuzzy Leaky Bucket is compared to that obtained with the uniform round-robin method in terms of the percentage of available energy allocated to each zone. These comparisons provide valuable insights into the effectiveness and fairness of the proposed approach, offering a clear evaluation of how energy is distributed across different zones under varying social and energy conditions within the smart city.
Table 2. Smart city scenarios and values per simulated zone.
Figure 8. Results obtained with fuzzy leaky bucket in the form of the percent of available energy allocated to each of the city’s zones and compared with the uniform distribution.
Table 2 illustrates a wide array of simulated scenarios, each reflecting distinct social differences within the city zones. For instance, in scenario 10, we observe a significant disparity between zones, with one zone having an average income of approximately $83,000 and another zone with an average income of around $19,000. Income is a primary social criterion that profoundly influences everyday life, and our simulated scenarios vividly showcase the diverse social levels present within the city. This disparity becomes even more apparent as one examines the detailed social values presented in Table 2, emphasizing the significant variations across different zones within the smart city environment.
The obtained results shed light on the allocation of limited available energy, constrained by emergency conditions, across the smart city zones. While the uniform allocation of energy packets to all zones may appear fair at first glance, it fails to account for the individual characteristics of each zone. This limitation becomes evident in Figure 8, where the available energy is consistently distributed equally to all zones, resulting in a constant 10% allocation rate per zone. Essentially, the uniform distribution method provides a flat allocation rate, disregarding any zone-specific features. Although this approach may be quick and computationally inexpensive, it lacks a sense of social fairness.
In contrast, the proposed fuzzy leaky bucket approach, in synergy with the virtual buffer, allocates energy packets differently by considering the social features of each zone. As depicted in Figure 8, the fuzzy leaky bucket does not provide a uniform allocation in any of the tested scenarios, indicating its distinct behavior compared to the uniform approach. Moreover, by accounting for the social characteristics of the zones, the allocation varies while ensuring that all zones are satisfactorily supplied with energy. Importantly, no zone receives zero energy allocation, underscoring the fuzzy leaky bucket’s consideration of individual zone characteristics.
A closer examination of the decisions in Figure 8 reveals that zones with lower values in their social characteristics receive higher energy allocations. This validates the design of our algorithm, which leverages social variables and developed fuzzy rules to support zones with lower social variables. Scenario 8 serves as a notable example of this strategy: zones 1 and 7, with lower average incomes, receive higher energy allocations compared to zone 6, which has a higher income rate and self-generation capacity. This trend is consistent across all scenarios, emphasizing the algorithm’s commitment to justice for all city citizens through equitable energy allocation.
Finally, the distribution of each variable in scenario 1 is illustrated in Figure 9. Additionally, the distribution allocation derived from the fuzzy leaky approach is presented in the same graph. It’s evident from this graph that the final allocation does not perfectly resemble any of the other distributions. Consequently, we conclude that all variables contribute to the final allocation, indicating that the proposed approach can be deemed fair to all zones.
Figure 9. Graph representing the distribution per variable for scenario 1. We observe that the energy allocation has a non-uniform distribution that does not resemble any of the rest implying that all variables have their effect on allocation distribution.
It is noteworthy that zone 1 has received the minimum allocation of energy, whereas Zone 10 has received the maximum amount. Consequently, the energy disparity between these two zones is the most significant among all pairs within the simulated city. This variance in energy allocation is primarily driven by the social factors considered by the fuzzy inference system. Zones 1 and 10 exhibit the highest disparity across the variables ’Income,’ ’Population,’ ’Disability,’ and ’Building,’ whereas this disparity is not as pronounced in the two energy-related variables. This observation underscores the impact of social variables on the final energy allocation. Thus, we can confidently assert that the proposed method ensures social justice of energy allocation in emergencies.

5. Conclusions

This work introduces a novel approach to allocating available energy during emergencies within the framework of smart cities. At its core, the approach leverages digital connectivity capabilities and advanced data processing techniques to facilitate more efficient and equitable decision-making processes. To achieve this goal, the proposed approach integrates a fuzzy leaky bucket mechanism in conjunction with an energy virtual buffer to regulate the allocation of energy during emergency situations.
The limitation in energy distribution during emergent situations often leads to perceptions of unfair treatment among residents, fostering feelings of marginalization and social injustice. This paper addresses this gap by introducing an approach that allocates energy while considering the social characteristics of smart city residents. By dividing the city into consumption zones and assigning virtual energy packets to each zone, the approach aims to mitigate disparities in energy distribution.
Central to this approach is the use of fuzzy logic-based leaky bucket, which enables the processing of large volumes of data and subsequent decision-making through fuzzy sets and rules. These fuzzy tools facilitate the transformation of diverse residential data into an efficient and socially equitable decision-making framework. Additionally, the strength of fuzzy logic lies in its ability to represent large datasets using linguistic terms, thereby enabling the integration of both energy and social variables into the decision-making process.
The presented approach has undergone testing using a set of 10 large-scale scenarios within a smart city, incorporating diverse values for social and energy variables. Results from these tests are compared with the uniform distribution of energy and highlight three main observations: (i) Our approach consistently deviates from uniform allocation across all test scenarios. (ii) It ensures that no zone receives zero energy allocation. (iii) It prioritizes support for lower social strata consumers while ensuring adequate energy provision to all zones.
In summary, the variation in allocation patterns achieved by the fuzzy leaky bucket, in contrast to the uniform pattern, demonstrates an acceptable social allocation that fosters a sense of “social justice” among residents.

Author Contributions

Conceptualization, M.A. (Miltiadis Alamaniotis); methodology, M.A. (Miltiadis Alamaniotis) and M.A. (Michail Alexiou); software, M.A. (Miltiadis Alamaniotis); validation, M.A. (Miltiadis Alamaniotis) and M.A. (Michail Alexiou); formal analysis, M.A. (Miltiadis Alamaniotis); data curation, M.A. (Michail Alexiou); writing—original draft preparation, M.A. (Miltiadis Alamaniotis); writing—review and editing, M.A. (Michail Alexiou); All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The data are available upon request to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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