The Process of Using Power Supply Technical Solutions for Electronic Security Systems Operated in Smart Buildings: Modelling, Simulation and Reliability Analysis

Abstract

This article presents selected issues related to the reliability of the power supply for electronic security systems (ESSs) used in smart buildings (SBs). ESSs operate in diverse environmental conditions and are responsible for the safety of lives, property and the natural environment of SB users. The operational tasks of ESSs in SBs require a continuous power supply from various sources, including renewable energy sources. The authors conducted an analysis of the power supply for selected ESSs used in SBs, which enabled the development of a power supply model. For the proposed model, the authors designed a proprietary graph of the ESS operational process, taking into account power supply implementation. Considering the operational indicators for the analysed ESSs, such as repair and failure rates, a computer simulation was performed. The simulation allowed the determination of the reliability of the ESS power supply within the considered redundancy configuration of additional energy sources, which can be utilised during the design phase. The reliability analysis of the power supply and the determination of rational parameters conducted in the article are crucial for achieving all the functionalities of ESSs in SBs, as envisioned during the design process. The article is divided into six chapters, structured to address the topics sequentially: an introduction to the state of the issue, a critical literature review, an analysis of the power supply for selected ESSs, implementation of renewable energy sources, the development of a proprietary model and operational graph, a computer simulation and conclusions.

1. Introduction

ESSs are employed in buildings and over vast areas (e.g., airfields, logistic hubs, seaports, etc.) for the purpose of ensuring internal and external security [1,2]. Integrating ESSs with other systems within the aforementioned facilities enables additional functionalities to be obtained that may be utilised to optimise SB control. In this case, the so-called BMS (Building Management Systems) enable effective monitoring and management of all elements and equipment within an SB, such as heating, air-conditioning and security [3,4,5]. Safety requirements for SBs or other construction facilities are always paramount. In such cases, ensuring the reliability of the energy supply through the use of various redundancies and technical or organisational solutions is of utmost importance. The costs of implementing such initiatives are not taken into account, as the protection of human life (e.g., passengers at airports or on railways) and health is always the top priority. A failure in the energy supply leading to an ESS alarm may result in the suspension of operations on land, air, sea or rail transport routes.

Safety Management System (SMS), in accordance with the definitions and applicable European and Polish standards, refers to the appropriate organisation, technical measures and established procedures adopted by an infrastructure manager in a smart building (SB) to ensure the safe management of its operations in specific internal and external environments exposed to adverse threats, such as assault, burglary, fire, robbery, etc.

Energy management system (EMS) describes the fundamental concept and introduces management practices related to the efficient utilisation of electrical energy in all its forms. It encompasses the specific technical and organisational requirements for an energy system that enable an energy-distributing enterprise to systematically pursue continuous improvements in energy efficiency, taking into account legal and other requirements imposed in the context of power supply for SBs, including ensuring the reliability and continuity of the supply.

Heating and Climate Management Systems (CHMS) are responsible for the continuous monitoring and management of the living comfort of individuals within SBs. Key systems utilised in SBs include heating and air-conditioning systems. The reliability and effectiveness of these systems directly impact the quality of life and work environments within SBs. The operation of these technical systems depends on the reliability of the power supply.

ICTMS (Communication and Telecommunication Information for ESS Transmission Modules and Systems) represents a specific category of information and communication technologies that collect, process and transmit information in electronic form using, for example, digital techniques and all electronic communication tools, both wired and wireless, within SBs.

The integration of these independent electrical, electronic and power systems responsible for the power supply into a single common building control system (BCS) enables optimal control and operation of structures [6,7,8]. SBs and vast areas employ various transmission buses and systems that may be classified as one of three following systems [9,10,11]:

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Building automation system (BAS), responsible for managing the technical functions of the facility—heating, lighting, air-conditioning, etc.;

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Security management system (SMS) in an ESS, e.g., a Fire Alarm System (FAS), IDS, ACS, closed-circuit television (CCTV) or an audio warning system (AWS) [12,13,14];

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Energy management system (ECS), which monitors the consumption of electricity powering the building [15,16].

The authors of the available source literature related to SB-related issues have additionally distinguished stand-alone management-related technical systems, i.e., CHMS (air-conditioning and comfort heating) and the ICTMS responsible for electronic communication and information exchange via available telecom channels—Figure 1 [17,18,19].

In addition to the systems employed in SBs, as shown in Figure 1, integration covers other crucial technical subsystems, including ESSs—Figure 2. Ensuring SB security involves the following additional technical systems [20,21,22]:

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SB HVAC systems also based on renewable energy;

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Automatic control and management systems for lighting in apartments, passageways and garages employing CCTV cameras [23,24];

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Smart control for shutters, entrance gates, building entrances involving CCTV, ACSs and AWSs;

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Management systems for ICT employed by SB technical systems and users, e.g., TV, Internet, information notification to the State Fire Service (SFS) or the Alarm-Receiving Centre (ACR) [25,26,27].

The correct operation of all of the technical systems above requires a power supply with appropriate technical parameters. Facilities that are classified as so-called state-critical infrastructure (SCI) implement tasks that are key from the perspective of a given country’s functioning. Modern SCI buildings are usually intended as facilities that employ artificial intelligence throughout the entire operation process. This also includes power supply reliability, particularly in the case of ESSs that are responsible for the security, health and life of persons [28,29,30]. Guaranteeing power supply reliability involves the implementation of specific activities that enable ESS task continuation under conditions with a malfunctioning primary power supply source (e.g., battery bank, UPS, generator, etc.) [31,32,33].

Figure 1 and Figure 2 symbolically illustrate the role of the energy supply system for other technical subsystems used in smart buildings (SBs). Internal power lines and energy supply (both primary and backup) are distributed to, for example, the SMS, CHMS and ICTMS via automatic power backup switches (Figure 1), as well as to other technical subsystems of the SB, i.e., branch nos. 1 to 8 (Figure 2).

Automation, security and management systems employed in SBs require appropriate control and information exchange algorithms. This is for information acquisition and external communication—e.g., with an ACR, SFS or the Police. Information exchange inside an SB is coded and encrypted [34,35,36]. This particularly applies to ESS messages. Please see branches 1 and 7 of the SB management tree—Figure 3. An important issue associated with proper security management in an SB is ensuring power supply. It is implemented by the energy management system PSFPG (branch 3). An SB employs electricity from two independent power plants, UPSs, battery banks (BA), etc., as shown in Figure 3. The available source is designated R. In the event of unfit source G, the automatic backup power switch (ABPS) automatically switches to power supply using an existing backup source R (Figure 3). Renewable energy sources (PRES) are employed within the power system to supply SBs. Branch 2 is responsible for controlling artificial lighting sources. Available lighting control methods are used. These include, e.g., motion sensors (CIL), CCTV (ELC and LCMD) and control software (SSL and SCLC). The SB employs heating and conditioning (HC) control—branch 4. This involves using recuperation (AHR), water consumption control and management (WDHC), comfort ventilation (VC) and room opening/closing (BC, COW, WCCHF). The entire SB security management control process also involves window opening/closing control and management (WC)—branch 5 [37,38,39]. This is also room functional monitoring—branch 6 and door entry/exit security management (CHF) at different building floors [40,41].

Achieving power supply continuity and reliability is indispensable within an SB operation process. Therefore, this objective is achieved by employing various known methods of ensuring SB electricity supply continuity and functionality. The primary goal of this research paper is to present the issue of power supply reliability, with particular focus on ESSs operated and employed within the SB operation process. Therefore, the entire article has a well-defined structure, preceded by an introduction discussing the state of the art, which synthetically discusses the implementation and use of technical systems in SBs. The second chapter is a critical review of the state of the art related to power supply implementation. The next chapters give an overview of the implementation of the power supply system for different ESSs operated in SBs. The research paper summary includes an implemented simulation of power supply reliability for a selected ESS, and limited conclusions.

An important research issue that the authors of this article address in the manuscript is the reliability of the ESS power supply—see branch no. 1 in Figure 3.

The notations adopted by the authors of this article in Figure 3 correspond to the following full descriptions: 1, 2, …, 7 branches of the control management tree. 1—(ESS) electronic security systems, 2— (LC) lighting control, 3— (PSFFPG) electricity management system, 4—(HC) heating and air-conditioning control, 5—(WC) window closing/opening control, 6—(CHF) entry/exit security management, 7—(ARC) alarm-receiving centre, L1, L2, L3—power supply phases. Designations of individual blocks are shown in the figure (e.g., Police (P), Border Guards (BG), Fire Brigade (FB), etc.). t(s)—timeline in seconds, PF—photovoltaic panels, BA—battery bank, SP—industrial grid power supply, AP—power generator, R—allowed power supply backup for the ESS, Zb—IDS power supply, Zt—CCTV power supply, Zc—ACS power supply, Za—AWS power supply, Ze—electronic lock power supply, Zp—FAS power supply.

For the sake of figure legibility, Figure 3 does not illustrate all the power supply connections to all SB subsystem branches (1, 2, 3, …, 7). However, all elements are powered from an industrial grid or using R—Figure 3.

All operational signals of the ESS usage process are encoded and encrypted. Additionally, two independent telecommunication channels are used for reliability, most often via a wireless telecommunications network, and transmitted to the ARC, as symbolically shown in Figure 3. In some cases, a wired telecommunication link (leased telephone line) is used. In this case, the link is also secured (encoded and encrypted) and additionally monitored by the alarm centre to detect issues such as line replacement, short circuits or disconnections, etc.

All ESSs employed in SBs are technically and functionally interconnected with other systems operated at a given time. However, according to the applicable regulations regarding providing security in SBs, two systems—the FAS and AWS—cannot be integrated with other technical objects, e.g., CHMS or ICTMS. Only information exchange is possible. All systems operating within an SB (including the ESS) require ensuring electricity supply continuity. Power supply continuity is implemented in accordance with a well-known principle of ensuring reliability, i.e., employing redundancy. In addition to power supply continuity, the implementation of assumed functionalities within an SB requires ensuring appropriate supply voltage parameters, e.g., amplitude, harmonic content, decays, etc.

2. Literature Review

All systems employed within an SB are operated under different environmental conditions. Their operation depends on the continuity of power supplied from the primary source SP, and other R sources, as shown in Figure 3, in the event of unfitness. SB functioning requires electricity [42,43]. A power supply system should exhibit high reliability throughout its service period. This reliability may be achieved by applying various technical solutions, such as redundancy or the fail-safe principle. Such solutions not only relate to the technical issues associated with power supply but also to the operation of all systems employed in SBs (branches 1, 2, 3, … 7—Figure 3) [44,45,46]. ESS operation (branch 1) is responsible for SB security and depends on the electrical power supply.

Figure 3 presents, in a simplified manner using the tree branches from nos. 1 to 7, the individual technical subsystems used in an SB. Each branch represents a specific technical subsystem used for controlling and managing comfort and safety in an SB. Since the article discusses the reliability of the energy supply for the ESS, the branch to which these systems are attached in the diagram is labelled as no. 1. The article then focuses solely on the role of energy supply for the ESS. At the same time, the operation of selected ESS subsystems, such as the FAS, AWS, CCTV, ACS, etc., is described.

Each of the ESS subsystems has its own emergency power supply determined based on the energy balance, taking into account specific operation times—i.e., monitoring and alarms. Any post-execution changes in connections and controls, as well as the upgrading of individual ESSs, should not affect (deteriorate) reliability, the so-called R₀(t) initial reliability assumed already by the system designer [47,48,49].

2.1. Overview of SB System Operational Issues and Conditions Related to Processes Associated with the Occurrence of Natural Environment Interference

The operation of electronic equipment, components and systems employed in SBs depends on broadly understood environmental conditions. A particular requirement is related to the operation of components susceptible to environmental impact. These components include ESS sensors responding to changes in the physical quantities present within the protected rooms—e.g., temperature, motion, smoke, etc. One of the issues that requires particular attention in all facilities constituting an SB is electromagnetic compatibility [50,51,52]. The authors believe that electromagnetic environment studies in an SB are not duly executed by ESS designers across the entire spectrum. This issue is crucial throughout the entire service life of systems operated in SBs, especially if the initial conditions of the electromagnetic environment have changed, e.g., installation of a cellular telephony transmitter, radio and television transmitters, etc. The permissible changes in the parameters of certain elements, e.g., the ESS, should be taken into account already at the engineering stage of the operation process of electronic components with low susceptibility, strength and resistance to interference, not only electromagnetic interference, but also mechanical interference, wall (building partition) vibrations, dust and changes in humidity, pressure or temperature [53,54,55]. According to the authors, there are no regulations and legal requirements applicable to this issue. Preliminary electroclimate testing should always be conducted prior to the initial design process. This includes testing of vibrations, dust, humidity and noise. The measurements and initial assessment of the environment pertaining to an SB have an impact, e.g., reduced probability of false ESS alarms, which is particularly important in the case of FASs [56,57].

2.2. Issues Related to the Continuous Online Diagnosis Process for Electronic Systems Operated in SBs, ESSs in Particular

Diagnosing technical parameters is crucial in relation to the operation of electronic systems, including wireless systems. The response to the partial, e.g., a single monitoring circuit, or total (catastrophic) unfitness of these systems is an issue of particular significance in the context of ESSs, which are responsible for safety, including fire-related safety. Diagnosing should be automatic, and concurrent with all working signals for all of the systems employed within an SB [58,59,60]. This process should be implemented in real time. Diagnostic information forwarded as part of the process should be sent to, e.g., an ARC, or employed locally by service staff. It should be encrypted and additionally modulated by an interference-resistant signal. According to the authors, the technical systems employed in SBs should also develop forecasts regarding the future technical condition of these facilities, which is not the case in all subsystems. There is currently an absence of technical elaborations taking this prediction process into account [61,62].

2.3. Operation Process of Sensors and Activators Employed in SB Electronic Systems—Overview of Issues Related to the Operation Process

Sensors, which respond to different, variable physical phenomena, e.g., temperature, smoke, humidity, water or electromagnetic radiation, are responsible in electronic systems employed in SBs for control processes. These are the elements that always, if used within an ESS, determine the detection of a hazard [2,5]. A primary detector (sensor) signal is decisive for the transition of a system from the state of monitoring to the state of alarming [15,25,39]. This process significantly impacts the so-called false alarm signals. It is particularly important in FASs, since such a change in the state always generates maintenance-related economic expenditures, e.g., at railway stations or relating to airport traffic [63,64,65]. The authors believe that such issues should be taken into account already at the initial system engineering stage. They should always be minimised in the source itself—sensors in the detector in this case. The potential state-of-the-art technical solutions that can be employed include, e.g., dual multisensors. Another option is to apply neural networks in modern detectors to include a process to track changes in amplitude, fluctuations and rate of change of the physical factors [66,67]. All detectors, as well as activators used within SBs and ESSs, must come with appropriate resistance, strength and susceptibility to interference within the natural environment where they are employed throughout their service life.

2.4. Overview of Operation-Related Issues and Operation Processes Regarding Power Supply in SB Facilities

The issue of SB power supply is overriding in relation to, e.g., water, gas or heat supply. Without electricity, SB electronic systems cannot operate and implement their operational tasks. Therefore, the power supply, as well as the quality of the electricity fed to an SB, is extremely important [2,45,51]. Power supply reliability and the operation of electronic systems without a so-called critical failure are most often ensured via the application of the redundancy and fail-safe principles [68,69,70]. Power generators and UPS devices are most usually designated as redundant power supply equipment, as shown in Figure 3. In the case of ESSs, these are battery banks hooked up to alarm control panels (ACP), which constitute power sources for the entire system. However, such redundancy and technical solutions require additional financial outlays. According to the authors, investors are not always eager to incur such costs and implement a construction project at the lowest cost [71,72]. This translates to the absence of backup devices or backup devices with inadequate technical parameters [1,15,26]. Power supply units in all electronic systems employed in SBs are always equipped with anti-destructive and failure-protection components, which respond to, e.g., surges within the power grid [73,74,75]. However, the authors of this paper, when conducting their research, particularly focusing on ESSs, have not always encountered such elements within these systems. This especially applies to the protection of long buses, monitoring circuits or transmission lines over vast areas against atmospheric discharges in an electromagnetically distorted natural environment [2,15].

An operation-related issue that is equally important to power supply reliability is related to technical parameters and power supply quality—e.g., amplitude, harmonic content, blackouts, decays, dips, etc. An ESS is always powered by smart power supplies monitored (diagnosed) and located in alarm control panels. The current capacity of ESS power supplies should cover the entire demand of security systems under two operating modes, i.e., monitoring and alarming. ESS power supplies are equipped with EMC filters, stabilisers, and anti-destructive safeguards, tasked with feeding power to actuators (usually sensors within detection loops or circuits) with specific technical parameters.

3. Power Supply in Selected ESSs in Smart Buildings and over a Vast Area

Electronic security systems (ESSs) constitute a particular group of subsystems employed in smart buildings (SB) [2,9,12,28,34,36]. The power supply, backup and emergency power supply in particular, in such systems is the foundation of their reliable operation in the event of primary power failure and plays one of the crucial roles in the process of ensuring security within a protected facility. In addition to taking the power supply of the systems themselves into account, an issue that has become important recently is also ensuring power to auxiliary equipment that increases the range of such sensors, e.g., through installing them onboard a UAV (drone). If we classify ESS power supply systems, we can distinguish four characteristic system groups, namely, Visual Supervision Systems (VSSs), Fire Alarm Systems (FAS), Intrusion Detection Systems (IDSs) and access control systems (ACS), based on the advantages of the IDS and VSS power supply.

3.1. Implementation of Power Supply for Selected Unmanned Aerial Vehicles Monitoring a Vast Forest Area and an Airfield

The wide range of applications for unmanned aerial vehicles (UAVs) in numerous industry segments and scientific fields also includes electronic security systems. The mobility of aerial platforms has made UAVs a system that enables the monitoring of vast critical infrastructure areas in real time. The movement velocity of UAVs and their range allow them to detect fires and wanted persons and monitor facilities with increased intrusion risk, contamination, etc. It should be noted, however, that the range of drones, directly correlated with the detection efficiency associated with selected objects, is impacted by the type of employed power supply. So, how to supply power to unmanned aerial vehicles?

Greatly simplified, a turbine engine is a miniature aircraft engine system. The operating principle of such an engine is based on drawing air, compressing it and mixing it with fuel to be combusted, followed by releasing high-speed exhaust gases to generate thrust [76]. However, their optimum performance is limited to within high-power ranges, which makes such a solution uncommon in UAVs [77].

One of the most popular UAV power supply types is a technology based on battery power. Battery power is employed in small unmanned aerial vehicles since it offers a relatively straightforward and flexible system architecture. Battery-based UAVs most usually employ lithium systems such as LiPo. The battery life of battery-powered unmanned aerial vehicles is restricted by battery pack weight. The maximum flight time in such a configuration is approximately 90 min when using a LiPo battery. One of the main challenges to overcome for battery-powered electric vehicles, including unmanned aerial vehicles, is their limited autonomy. Great effort has been devoted to improving battery efficiency to extend battery life and enable longer missions for electric vehicles. Despite the progress in electric cell technology, the specific energy of modern batteries still limits the battery life and range of unmanned aerial vehicles, which may fail to meet the requirements of numerous UAV applications [78].

The battery replacement algorithm is a technique employed for in-mission UAV charging. Elements that are required to extend the range when applying this method include ground stations that implement UAV battery replacement autonomously or with human intervention. Such a method based on ground stations effectively expands the possibilities related to the fire monitoring of vast, e.g., forest, areas. There are numerous concepts and prototypes that represent the actual embodiment of such a system. One of the research papers describes a designed and deployed automatic refuelling station system for small UAVs, to enable prolonged autonomous missions with swarm-type UAV systems. The study involved developing a planning and learning algorithm, and testing it throughout a 3 h continuous flight involving three unmanned aerial vehicles and more than 100 battery replacements [79].

Laser-based in-flight charging is an approach to UAV power supply that also, like the previously described technology, ensures effective flight time extension—Figure 4. The operating principle of such a system is based on deploying independent ground stations that power UAVs by generating a laser beam. A UAV traversing the airspace is equipped with a lens and an electronic system that enables the conversion of laser light energy into electricity used to power the drone. Wireless charging allows a UAV to remain in the air indefinitely, without the need to land and charge the battery. The described UAV charging strategy reduces the risk of a crash associated with the take-off and touch-down procedures. LaserMotive has developed a working prototype capable of transferring power of up to hundreds of Watts [80]. The presented method offers numerous benefits; however, laser-based power supply entails certain limitations. The main one is flight altitude, which, due to finite laser power and the UAV receiving system, must be reduced compared to in the case of conventional battery power.

UAV power supply based on hydrogen fuel cells offers significant benefits compared to traditional batteries. Given the flight range and refuelling speed, this method is far superior over conventional UAV-powering techniques. The specific energy of LiPo batteries, commonly employed in UAVs, is 250 [Wh/kg], whereas the specific energy of a fuel cell system with a compressed hydrogen tank is up to 1000 [Wh/kg], which enables a considerably longer flight time [81]. Hydrogen power allows the UAV to move for several hours, not just several minutes. However, given the complexity of such a UAV design and the location of refuelling stations, as well as the safety of such a process, it is not a perfect method.

Hybrid UAV power supply is the combination of traditional battery power and fuel cells. The roles of both systems are clearly different. Owing to their rapid energy transmission properties, these batteries play a crucial role during energy-intensive manoeuvres, i.e., touch-downs and fast climbs. A fuel cell takes over as the primary power source during cruise and descent phases, providing constant power, and also charging the battery to maintain its charged state.

Relying solely on a single power source may lead to UAV restrictions. Each of the UAV power supply technologies described exhibits different efficiency characteristics under different environmental conditions. The selection of an appropriate UAV power supply is determined by the features of the electronic security system within which the unmanned vehicle will operate.

The most effective method of powering a UAV for integration with a smart building involves LiPo cells. Drone charging management in a smart building requires employing advanced systems that not only enable charging the UAVs alone, but also have the capability to monitor their battery status and integration with other building systems and ensure energy stability. A charging station is the main component of such a system. Drone charging stations are specially designed devices that can automatically charge UAV batteries. They can be designed in different forms, e.g., static and automatic charging stations or inductive chargers. In the case of charging stations in a smart building, it is crucial to ensure an uninterrupted power supply. Uninterruptible power supply (UPS) systems can be employed to maintain charger operation in the event of a mains power failure. Energy management systems in a smart building are able to monitor energy consumption by drone charging stations, and to monitor energy distribution within the entire facility. An energy management system guarantees energy use optimisation depending on available resources, e.g., solar power or other renewable sources, monitors drone battery status and provides information on required charging or energy load management.

3.2. Power Supply of Selected Fire Alarm Systems and Fixed Extinguishing Devices Monitoring Civil Structures

While UAV power supply systems have not been standardised and their development is an innovative process, the Fire Alarm System (FAS) power supply is defined in standards such as [82]. Pursuant to standard requirements, the FAS panel power supply should be a power grid—Figure 5. The power source should be separate from other consumers. If impossible, and the power source must be common, the power supply system must satisfy the requirements of FAS power supply circuit overriding and independence. This means that a failure in the power supply circuits of other consumers cannot impact FAS power supply operation [82].

The primary power of a control panel should have isolating protection for the power connection and upstream of the circuit breaker. The protection should be specially marked, and its access restricted to prevent unauthorised isolation of the primary FAS power.

An FAS must have backup power, in case of a primary power source failure. It is required for the FAS backup power source to be batteries. Backup power supply battery bank capacity should enable the powering of a system under monitoring operation for 72 h, after which the battery should also have sufficient energy to enable operation in an alarm state for at least 30 min. However, it should be noted that, if a guaranteed time to repair is less than 24 h, the minimum battery capacity can be reduced to 30 h. This time can be cut to 4 h if there are service personnel, spare parts and an emergency generator available 24/7 locally [76].

Battery bank capacity (in Ah) at 20 °C should be calculated as per the following formula [83]:

$$Q_{min}=k\ast [\left(D_1\ast I_1\ast t_1\right)+\left(D_2\ast I_2\ast t_2\right)]$$

(1)

where

• $I_1$—current drawn from the batteries in the event of primary power failure in the monitoring state. It is the power consumption by all active FAS elements;
• $I_2$—current drawn from the batteries in the event of primary power failure in the alarm state;
• $t_1$—backup power supply time in the monitoring state;
• $t_2$—backup power supply time in the alarm state;
• k—coefficient of 1.25. It takes into account the battery ageing process;
• $D_1$—coefficient associated with reducing battery capacity due to I1 power consumption in the monitoring state;
• $D_2$—coefficient associated with reducing battery capacity due to I2 power consumption in the alarm state.

In practice, D1 = 1 is assumed for FASs. In the case of the D2 coefficient, a value of D2 = 1 can be adopted for typical operating conditions; however, this value can reach 1.5 for certain control panels, e.g., one with an expanded audio warning system.

The backup power battery charging device should offer charging of the batteries to at least 80% of their rated capacity within 24 h and to 100% within the next 48 h.

Fire equipment power supplies must be equipped with a system to signal the maximum resistance of the battery and connected circuit elements, e.g., fuses. If an FAS has several batteries connected in parallel, these systems should monitor each battery circuit separately. Resistance in each circuit should not exceed a specific value, as expressed by relationship (2) [83]:

$$R_{imax}<n\ast k\ast {\displaystyle \frac{U_n}{I_2}}$$

(2)

where

• n—number of battery strings;
• k—coefficient of 0.1;
• $U_n$—rated supply voltage;
• $I_2$—current drawn from the batteries in the event of primary power failure in the alarm state.

The k coefficient takes into account the maximum possible drop in rated supply voltage at current consumption I2, caused by increased battery circuit resistance. The resistance value should not result in a supply voltage drop of more than 10% in the alarm state with backup power.

The basic power source for fire-fighting equipment, such as an FAS, should be a power grid. Fixed Extinguishing Devices (FEDs) constitute fire-fighting equipment that operate upon alarm triggering. Fire-fighting equipment that is to operate during an alarm should be supplied upstream of the fire circuit breaker, preferably via a separate switchgear [84].

Similarly to before, FEDs require a backup power source. Pumps with water demand below 20 dm³/s are an exception. Battery banks, power generators independent of primary power or a power supply line independent of the main power can be employed as a backup power source. When employing a power generator as a backup power source, the minimum fuel stock should be sufficient for 4 h of full-load operation. In the event of using batteries, the requirements are the same as for an FAS. Pumps with an electric drive should be able to reach maximum capacity within 15 s upon start-up [84].

3.3. Power Supply of Access Control Systems Monitoring a Vast Area and State-Critical Infrastructure Facilities

Technical solutions in the field of supplying power to access control systems (ACSs), as well as time and attendance systems (T&ASs) monitoring vast areas and critical infrastructure facilities, significantly differ from the ones applied in facilities of lesser complexity (in terms of area as well as functions and organisation) [85]. In the case of the latter of the groups, these are primarily area solutions of concentrated topology, which include a single central power supply node in the form of a buffer power supply unit, feeding electricity to all devices and modules making up an ACS and T&AS (in an extreme case, integrated on a PCB of an ACS control unit). The concept behind such a solution is illustrated in Figure 6.

In this case, phase supply voltage, before it reaches the ACS and T&AS, passes through an overcurrent and surge protection module, sometimes fitted with additional filtering circuits. It is then subject to reduction through a step-down transformer. Thus, a processed power signal is supplied to a power supply unit integrated on a PCB of the most fundamental ACS and T&AS module—an access controller. In this case, it is the integrated power supply unit system that is responsible for monitoring the operating status and charging process of a backup secondary power source, namely, a gel battery, and for converting a phase AC mains voltage into VDC, which is the primary power supply of the system. The role of the module in question is also to automatically switch between the distinguished power sources, depending on the situation. In addition, the access module has to also generate a number of voltages supplied to the modules and devices making up the ACS and T&AS. Most often, it is a control signal for electromechanical interlocks (electric strikes, electric door openers, etc.)—usually 12 [VDC]. Moreover, such modules have at least one bus that enables numeric keypads equipped with proximity element readers (cards, key rings, etc.) to be connected. It is simultaneously a bus powering the elements in question (in practice, 5 or 12 [VDC]). It should be emphasised that buses for exchanging data between expansion modules, low-current outputs, etc., represent a load from the perspective of a power supply unit, the current capacity of which is limited. A significant system expansion or retrofitting it with modules exhibiting high electricity demand requires the application of a distributed power supply topology for the access control and time and attendance systems. An example of such a solution concept is illustrated in Figure 7.

When analysing Figure 6, one can notice that all ACS or T&AS modules form a whole from the perspective of information exchange. Individual expansion modules form links with their master access controllers via a communication bus (Com_bus), which, depending on its configuration, may power individual modules. Similarly, individual proximity card readers with built-in keypads communicate with their master access controllers via a dedicated bus (12V_5V_Prox_bus). Communication between individual access controllers via a communication bus (usually one that employs the RS-485 protocol) completes the integration of all the components into a coherent system.

From the perspective of an electricity distribution system, it can be noted that a DC1 access controller is supplied via an external SPS1 source, which employs the B1 battery as a backup power supply. In addition, the ExM1 extension module is powered via a DC1 access controller via a Com_bus1 bus. In this scenario, the ExM1 also supplies electricity to hooked-up proximity card readers with built-in keypads and electric door openers, while the DC1 additionally supplies electric door strikes.

However, the ExM2 module, through an appropriate Com_bus1 bus connection, will exchange data with the DC1 module, but electricity will be supplied via it to the SPS buffer power supply and the backup power supply (B3 battery). In addition, SPS3 and B3 will be responsible for providing electricity to the high-current elements of the ACS and T&AS in the form of a parking barrier and the swing gate of a controlled passage. Moreover, the ExM2 module will be responsible for supplying proximity card readers with a built-in keypad.

The DC2 access controller employs a power supply system integrated on its PCB, which supplies energy also to proximity card readers with an integrated keypad and electric door openers.

The ExM3 extension module is powered via an external SPS4 buffer power supply and a backup power source in the form of a B4 battery, whereas the data are exchanged with its master module via a Com_bus2 data bus. In turn, it is responsible for controlling the lift. It should be stressed that, in practice, the lift drive mechanism backup power supply employs diesel generators, which have not been included in the figure to maintain clarity, such as access monitoring systems (reed switches fastened to door leaves).

In the case of vast and critical infrastructure areas, the case is not only a complex engineering issue but also that of a normative and legal nature [85,86,87]. Military facilities are a particular example of critical infrastructure sites. Their electronic technical security systems (including ACSs and T&ASs) are subject to separate requirements, which currently are set out in temporary Operational and Technical Requirements for Military Equipment Group 19—Specialized systems and equipment for facility protection, dated 8 May 2020 [88]. The requirements applicable to power supply include:

• A primary (single-phase) AC power supply system must be operating under 230 [V], with a tolerance of (+10 ÷ −15)% and a frequency of 50 [Hz] ± 2%;
• A primary power supply point must be clearly separated and equipped with individual overcurrent and overvoltage protection;
• A primary power supply point must be located inside a protected area;
• An electronic technical protection system must be equipped with a backup power source that ensures the operation of the entire system for 15 min in the alarm state and, depending on more specific requirements and the technical potential of the facility itself, operation in normal mode for 12, 36 or 72 h;
• A process of switching between primary and backup power should be automatic in both directions, depending on the circumstances, and the transitions themselves must be indicated at a local control centre of the protected facility.

The document also refers to the issue of facilities employing diesel generators. It should be emphasised that the devices and modules making up an ACS or T&AS include actuators with elevated electricity consumption. These are, among others, turnstiles, rotating barriers, road barriers, controllers and motors of vertical and horizontal entrance gates, key depositories, parking and anti-terrorist entrance-parking blocks and barriers, spikes, etc. Therefore, it would be difficult to expect all of the aforementioned components to be supplied from a common power supply unit. As a result, the document specifies situations where such elements are required to have their own independent power source satisfying analogous conditions.

The document also refers to a very important aspect which is often overlooked in the context of implementing an ACS in private (consumer) facilities. The entire system (and hence its power supply system) stands out with its resistance to electromagnetic interference. It should be stressed that they may be of both natural and artificial origin, and can be generated unintentionally (e.g., as a manufacturing process side-effect or intentionally [13,40,50,89,90], as a factor that deliberately disrupts the operation of electronic technical protection systems. They can even be the source of their failure. Similar wording is applied in the context of static discharges (including atmospheric).

Given the requirements above and the features of the ACS and T&AS operated in expanded facilities, and facilities classified as critical infrastructure, and taking into account the number of elements within the system, the limitations on the capacity of batteries sold that make up backup power supply systems and the required operation time of a system based on them, as well as the required recharging times, it should be concluded that the leading concept in such cases will be a distributed power supply system.

Electronic security systems, as well as their power supply systems, have a significant scope of responsibility compared to consumer building automation systems. The systems under consideration are responsible for the security of property (both material and immaterial). In extreme situations, they are responsible for the health and lives of individuals and personnel in areas under the surveillance of these systems. For this reason, ESSs as well as their electrical power distribution systems should be characterised by a high level of reliability. One of the most common approaches is modelling the operation process of the considered systems. This ensures an objective comparison of the reliability of different models and provides significant benefits in situations where the operation process of the actual system will meet the assumptions of the more favourable model.

4. Alternative ESS Power Sources: Studies and an Analysis of the Technical Feasibility of Implementing Alternative Power Sources in Visual Surveillance Systems

Above all, issues related to alternative power sources in electronic security systems (ESSs) are associated with the application of emergency power in the form of electric batteries, usually with gel electrolyte, whereas the development of, among others, PV technologies and the continuous process of reducing energy demand by electric components, e.g., processors in VSS cameras, lead to ESS solutions equipped with small-size PV panels appearing on the market [91]. In addition to photovoltaic panels, a particularly interesting technology seems to be miniature wind turbines, which could also be employed as protection system power sources, especially in areas with unstable insolation conditions, such as Central European countries. Such sources could have a primary and supplementary role relative to photovoltaic panels; however, the authors of this paper attempted to analyse the possibilities of using photovoltaic panels only, owing to the lower risk of mechanical damage which is inherent to solutions based on wind turbines [92]. Furthermore, wind turbines would require frequent maintenance inspections, thus reducing the time the system remains in a state of full technical fitness. In light of the above, the authors attempted to construct a test bench based on photovoltaic solutions, static and dynamic, equipped with a tracking system, adjusting panel position relative to the current position of the sun. An additional aspect in favour of employing PV panels instead of small-size wind turbines concerns the issue of noise generated by rotating turbine components [93].

Because backup power supply issues have long been associated with ESSs, it seems natural to additionally employ this power source as energy storage. The research involved studies aimed at determining the total extractable electricity at a selected Central European location originating from the process of converting solar energy from small-size photovoltaic panels.

Yet another aspect in favour of applying alternative power sources is the issues associated with the monitoring areas often making up critical infrastructure with no access to standard power supply [22,27]. Examples include border crossing areas on mountain peaks, mountain dams, the areas of the so-called green border, railway lines, bridges, dams, oil and gas infrastructure, etc. Environmental monitoring is an additional related aspect. Such solutions could contribute to tackling the problem of, among others, illegal waste disposal. An important feature is also the application of such a solution; however, its mobile nature enables associated hazards, e.g., exposure to natural disasters, to be counteracted, such as through monitoring areas at risk of fires, floods or landslides, etc.

In order to verify the application aspects in practice that would enable employing photovoltaic solutions for the purposes of powering, e.g., VSS cameras, the authors analysed the available hardware solutions related to photovoltaic panels, as well as the power parameters of VSS cameras. Because it would be beneficial to install such a panel above a camera fixed on, e.g., a mast, the dimensions of the panel itself should be as small as possible. An oversized photovoltaic panel placed above a camera could obscure a section of its field of view, in the case of wide-angle cameras in particular, and lead to its shading and thus, e.g., incorrect operation of automatic day and night algorithm operation. Shading would obscure the detection zone of the photoresistor built into the camera, which is used to trigger the day/night operation algorithm of the camera. In addition, IR illuminators, usually located in the cameras, could cause reflections from the lower panel surface if its size is too large. Therefore, the authors attempted to design and experimentally test under actual conditions a VSS power supply in the form of small-size photovoltaic panels. The test bench shown in Figure 8 was designed and constructed for this purpose. Depending on the season, such a panel would have to be repositioned over the range from approx. 20° to approx. 50°. In turn, it is widely accepted that, for a latitude corresponding to central Poland, the optimum inclination angle is approx. 30–35° for ground-mounted photovoltaic panels, and its minimum value should be 15°. However, photovoltaic panel inclination could differ depending on technical and environmental conditions, as well as latitude. The optimum positioning of photovoltaic panels is easier to achieve in the case of ground-mounted units on a large, open area of ground.

Figure 9 shows the results of the conducted studies, demonstrating a comparison of the power generated by a static panel on a cloudless day and the following day with slight cloud cover for the same longitude and latitude. By numerically integrating the area under the graphs, it could be concluded that the achievable power reduction for this case was 21%.

In addition, Figure 10 illustrates a comparison of the power generated by a static panel and a dynamic panel on the same day, and for the same longitude and latitude. Based on the above, the authors determined a potential energy gain when using a tracking system which amounted to 37% in this case, and reached 10% in January in a similar situation.

The visual surveillance systems currently installed within critical infrastructure facilities are mostly IP based. Such systems are characterised by two primary power supply possibilities—12 V or 24 V direct current (DC) or alternating current (AC)—and according to the Power over Ethernet (PoE) technology, as per the IEEE802.3af or PoE+ (IEEE802.3at) standards [94]. In light of their high electricity demand relative to other ESSs, video surveillance systems (VSS) are characterised by the non-standard architecture of their backup power supply- Figure 11. The reason for such a high electricity demand is primarily the IR illuminator elements in the cameras, PTZ camera automation elements and sometimes the systems improving camera reliability in so-called harsh conditions, such as anti-icing heaters and rain wipers.

PoE-based power supply systems have one major advantage—they eliminate the need to apply additional AC power, which greatly reduces installation costs and increases their reliability through cutting the number of elements (power supply units mainly) that can fail [95]. Such a technology also increases the system security level owing to the fact that it relies on lower voltage levels.

A PoE circuit is composed of three primary components, namely, power sourcing equipment (PSE), cabling and a powered device (PD)-Figure 12.

In most cases, the role of the PSE in VSSs is a switch/router or a monitoring recorder expanded with such POE-compatible devices.

In IEEE standards applicable to PoE, power is supplied via PSE only when the PD requires it. If a PD is disconnected, the PSE will isolate the power supply. This enables PoE technology to be significantly safer than a typical AC power supply, such as regular electrical sockets. PoE also involves lower voltage, namely, from 43 to 57 V DC.

The studies conducted confirm the feasibility of this solution in practice. The solution with a tracking panel could, in particular, reduce the capacity of reserved power sources. Long-term tests with the bench are currently underway, the results of which will be presented in future publications.

5. Power Supply Reliability Models for Integrated ESSs Based on Conventional and Alternative Energy Sources

ESSs utilise the industrial power grid as a power supply. Various forms of redundancy are employed due to the implementation of crucial functionalities related to the security and protection of civil structures, and for the purposes of ensuring the reliability and continuity of the electricity supply. ESS redundancy is achieved through implementing various alternative power sources available on the market. The most common ones are battery banks (capacity based on energy balance for each system separately), power generators and a UPS emergency power supply unit. Alternative, eco-friendly power sources such as photovoltaic panels and wind turbines of various capacities are also used. Such power supply solutions based on eco-friendly power sources enable electricity to be supplied to ESSs operating over vast areas—railway sites, airfields or logistic hubs. Supplied electricity is used for the house-load of ESS elements, while the surplus is accumulated in battery banks. Such a power supply solution requires the application of battery bank charge online diagnostic equipment. Due to the ESS element–alarm control panel (ACP) distance, the information on the technical status is always transmitted wirelessly. Battery bank capacity is determined for each of the discussed ESSs separately, taking into account the time of operation under two of the basic technical states—i.e., monitoring and alarm. ESSs usually employ 12 V power. However, two systems, the FAS and AWS (related to fire hazards), employ 24 V and 48 V power, respectively. A higher rated voltage value is associated with significantly larger rated supply currents for certain FAS and AWS components—e.g., acoustic and optical signalling devices (AOSD), smoke damper drives, power amplifiers, power supplies or the speakers broadcasting evacuation and fire hazard messages.

5.1. Fundamental Technical Assumptions Related to the Operation of an ESS Within an SB and over a Vast Area Associated with the Modelling of Such Systems

By applying all available reliability methods, ESSs aim to ensure the electricity supply continuity required for these systems to operate under all technical states—monitoring, alarm and failure. This is implemented via different power supply methods, as illustrated in Figure 13. The following power supply sources (1 to 5) are employed, as shown in Figure 13: The primary power source is the industrial power grid, designated as No. 1. State-critical infrastructure (SCI) facilities usually employ an independent power supply from two different power plants (A and B). In the event of unfitness, e.g., power from A, the ABPS automatically switches to power from source B. Figure 13 does not show any variants of this power source for the sake of its legibility. Each separate ESS operated within an SB or over a vast area has its own power supply with a specific current output, usually located in an ACP—marked as PS in Figure 13. An ESS ACP acts as a power supply unit for all elements and devices hooked up to the main board input connectors, i.e., detection lines and circuits, transmission buses or coaxial cables used in CCTV and AWS—Figure 13. Each power supply (PS) located in an ACP uses electricity from an industrial grid—ES—Figure 13. Individual elements within detection lines—in the case of an AWS, it is the (CR₁₁, CR₁, …, CR_n−11, CR_n−1, CR_n and CR_n1) and, for an FAS, (S₁₁, S₁₂, S₁₃, S_1R—first detection line and S₂₁, S₂₂, S₂₃, S_2R—second detection line)—are supplied via a PS, which adapts grid voltages to the rated values of that equipment—Figure 13. All ESSs operated in an SB have their own battery with a specific capacity, e.g., AB_ACS, AB_FAS, AB_CCTV, AB_AWS and AB_BASS—Figure 13. The battery output voltage value and its technical state are continuously monitored by a diagnostic module fitted within an ACP, and the diagnostic information is available online at the operation site of a given ESS (LCD panel available on the ACP front). Such information is also transmitted via radio to a service and maintenance centre located at the operation site of a given system (building) or to an ARC. These signals are concurrent with information originating from detectors or other ESS elements within detection circuits or lines, and are generated separately for each of the systems, as shown in Figure 13 (D_ACS, D_FAS, D_CCTV, D_AWS and D_BASS). The two eco-friendly power sources shown in Figure 13—photovoltaic panels and low-power wind turbines—can be employed when powering ESS elements and devices located at a large distance from the ACP, due to permissible voltage drops within detection lines and transmission buses, or in the event of no consent from the investor (owner of adjacent land) regarding the possibility of a hardwired connection. Such a power supply type can also be used to feed electricity to unmanned aerial vehicles (UAV) operated for the purpose of fire surveillance in a vast area.

The following tactical and technical assumptions to be used to develop the models were adopted for the discussion on the operation process of ESSs operated in SBs:

• The μ recovery (repair) rate of individual ESS components and devices depends on the availability of service personnel within an SB or ARC. Reducing ESS unfitness time is a crucial issue. This means the implementation of proper organisation and the functioning of the so-called on-site storage. This storage houses components, which usually lead to ESS unfitness.
• The λ failure rate of components and devices employed for ESS operation is at a constant level throughout the entire modelling time of these systems. Adopting such an assumption for the calculations takes the so-called initial ageing process into account. This process is executed for all ESS components. Components should operate as in an actual ESS, i.e., implement all assumed functionalities, such as the permissible maximum current load of a power supply or UPS. These components should be located within detection lines and be powered with rated voltage from a power supply consuming electricity from an EPS—Figure 13. Implementing this process leads to elimination of the so-called infancy period in the course of the normal operation of all ESS components, including power supply equipment. ESS components and power supply equipment are not operated until they are completely worn out. They are replaced with other units in the course of retrofitting or expansion. Such a process is taken into account in ESS modelling.
• If the components and devices are incorrectly stored in warehouses (e.g., at the wrong temperature or humidity level), this should be taken into account in the change of λ rates.
• The ESS operation process in an SB is ahistorical. The technical state of a given ESS is a function of the history of the previous operation process for this system. Current technical state(s) of an ESS is (are) always a state (set of states) wherein these systems are at time t₀.
• The operation process of ESSs in SBs does not include the so-called absorbing states, which prevent the complete functioning of a given system. Anti-destructive systems and proper ESS organisation enable this issue to be implemented.
• All technical states within the process of operating ESSs in an SB—e.g., monitoring, alarm, blocking, etc., are permissible and mutually communicated.
• The process of operating ESSs in SBs does not involve catastrophic failures.

5.2. Developing Assumptions for the Modelling Process Involving ESSs Operated in SBs

Given the aforementioned assumptions for the operation process of ESSs employed in SBs and over vast areas, the authors developed a power supply model for integrated security systems—Figure 14. Individual security systems operated in civil structures are based on different power supply solutions. Due to the key role of FASs and AWSs, there are extensive power supply (redundant) systems that ensure power supply continuity for all components and devices within these technical objects. An FAS and AWS have power sources as unloaded (cold) backup, which enable continued operation of these systems. These include a low-power generator (FAS, AWS), UPS (AWS, FAS) and, additionally, in the case of the FAS, photovoltaic panels (PP₁) and low-power wind turbines (WWP₁). All ESSs shown in Figure 14 have their own battery banks from AB₁, AB₂, AB₃ and AB₄ to AB₅, the capacity of which is determined based on the energy balance of the respective systems. Fire hazard monitoring systems in smart buildings employ an FAS powered with 24 V, while the AWS operates on 48 V power (appropriately connected serial battery banks with a rated 12 V). An increasing supply voltage in these systems is imposed by the high current load of the detection lines and circuits, particularly in the AWS, where the end components are broadcast speakers powered by voltages of up to 100 V and more. The operation process of ESSs employed in SBs and over a vast area is always an ordered trio that can be expressed as (3):

$$\mathrm{M}=⟨\mathrm{S}\mathrm{B},\mathrm{R}\mathrm{E},\mathrm{F}\mathrm{R}⟩$$

(3)

where SB means the respective technical states of ESSs operated in SBs, described through (4).

$$SB=\left\{\mathrm{SPZ},\mathrm{SZB},\mathrm{SB}\right\}$$

(4)

SB is a set of the following ESS operating states, interpreted as follows:

• SPZ—state of full fitness of all integrated ESSs operated within an SB and over a vast area. ESSs implement all pre-planned operational tasks, and power is supplied from an industrial power grid—Figure 14 (marked in green, S₀ state, all redundant power sources are functional and ready to accept house-load associated with, e.g., ACS, FAS, AWS, etc.). Redundant power systems are always diagnosed online.
• SZB—state of ESS safety hazard (industrial grid primary power failure, redundant power sources), where, e.g., the UPS, power generator (PG), battery banks (AB), etc., take over an appropriate power supply system role. All ESSs in a technical state (SZB) implement operational tasks with a preset functionality, and the information on unfitness detected by diagnostic modules is forwarded via alarm control panels (ACP) to local service groups and the alarm-receiving centre (ARC). Operational tasks—and security monitoring by individual ESSs—are implemented further down the road. These states are also marked with partially filled green in Figure 14 due to the partial unfitness of one, two or more power sources, for example, an FAS (SZB is the following distinguished hazard states: S_D21 (industrial power supply and PG failure), S_D22 (UPS unfitness), S_D23 (wind power plant unfitness) and S_D24 (PP1 panel failure)). ESB—BASS (Figure 14) has only two SZB states—i.e., S_D51 and S_D52. The available local service personnel immediately take remedial actions associated with the recovery of all power supply systems, whereas the service personnel in the ARC receive remote information on unfitness and have a preset time frame to intervene in order to check the entire redundant power supply system.
• SB—state of safety unreliability for ESSs operated in IBs. States belonging to the SB set can be interpreted as follows: ESS full fitness and safety hazard for FAS (1,2,3,4), ACS (1,2), AWS (1,2), CCTV (1) and BASS (1,2), respectively; and safety unreliability (Figure 14, states marked in red—S_D1, S_D2, S_D3, S_D4 and S_D5). Marking individual states in an operation process graph enables technical discussions related to ESS operation within an SB and the security model in terms of its functioning and the implementation of assumed operational tasks.
• The second element, RE, found in Expression (1) for the ordered M triple is always a set of the following pairs with elements interpreted as follows (Figure 14):
• $\left(\mathrm{SPZ},\mathrm{SZB}\right)$ is always the information on the possible transition of SB-operated ESSs from the SPZ state to the SZB (S_D21, S_D22, S_D23, S_D24) state for the FAS or for the AWS (S_D31, S_D32), BASS (S_D51, S_D52), etc. ESSs implement their assigned operational tasks; however, these systems are powered from backup power sources, which are characterised by a specified, finite current capacity. Security systems are fully fit, and building or SB rooms have functional motion detectors for, e.g., smoke, flame or unauthorised motion. At an appropriate μ recovery rate, the service personnel located in the SB restore full functionality of the power supply systems—e.g., in an FAS, it is μ_D21—PG2 fitness restoration, μ_D22—UPS2 fitness restoration, etc. Power supply repair rate (μ) is a function dependent on numerous variables, e.g., time of repair, replacement, failure identification, delivery of repair parts, etc.
• $\left(\mathrm{SZB}; \mathrm{SB}\right)$ is the information on the potential transition of ESSs operated in SBs from the SZB state to the SB state. All power supply systems—primary and redundant (Figure 13)—have failed. ESSs not powered by electricity fail to ensure security within an entire SB-type facility. This described event related to power supply, wherein all sources are subject to failure, is very unlikely, and the operation time of a given ESS on AB1, AB2, AB3, …, AB5 is sufficiently long to enable selected power sources to be improved—restoring the fitness state. All ESSs operated in SBs are appropriately protected against, e.g., atmospheric discharge pulses or surges occurring within a power grid. Such safeguards, associated with the impact of interference on an ESS, are implemented already at the ESS engineering stage and it is impossible to switch from the state S₀ to, e.g., S_D2 (FAS), S_D3 (AWS), S_D4 (CCTV), etc. However, failure to undertake ESS recovery results in a transition to the safety unreliability state. Therefore, the RE element can be described with Expression (5):

  $$RE=\left\{\left(\mathrm{SPZ},\mathrm{SZB}\right),\left(\mathrm{SZB},\mathrm{SB}\right),\left(\mathrm{SPZ},\mathrm{SB}\right)\right\}$$

  (5)

i.e., the RE element can be determined with Expression (6):

$$RE\subset \mathrm{SxS}$$

(6)

Relationship (6) is a mathematical notation of relationship (5) and means that the RE set of relationships is a subset of the Cartesian product for the set of S states. Let the considerations assume that FR is always a set of functions, each of which is described using a given RE set. The function always adopts values from a set of positive real numbers, i.e., R⁺. All functions of the λ failure intensities for given ESSs operated in an SB always have a specific form. It can always be described using Expression (7):

$$\lambda : RE \to R^{+}$$

(7)

In such a case, each of the elements in set RE is accordingly assigned a number from set R⁺. This function is always interpreted as the transition intensity within a given operational graph for a given ESS—Figure 13. In particular, example relationships that describe the operation process can be written for ESSs operated in SBs:

• $\lambda \left(\mathrm{SPZ},\mathrm{SZB}1\right)\equiv {\lambda }_{D21}, {\lambda }_{D12},{\lambda }_{D31},{\lambda }_{D41},{\lambda }_{D5 }, itd.$ is interpreted as a transition rate for a given ESS from a state of full fitness (SPZ) to a state of safety hazard—SZB (unfitness of individual redundant power sources, e.g., PG2, UPS2, WPP1, PP1 or AB2 in the case of an FAS);
• $\left(\mathrm{SZB}1,\mathrm{SB}\right)\equiv {\lambda }_{D25},{\lambda }_{D32}, {\lambda }_{D41}, {\lambda }_{D52}, {\lambda }_{D1}$ is interpreted as the intensity of SB-operated ESS transitions from a state of safety hazard (SZB) to a state of safety unreliability—S_B (fully unfit FAS, AWS, ACS, CCTV or BASS). All ESSs operated in an SB are fully unfit, i.e., they do not implement tasks associated with ensuring security within a facility. Security in this case can be guaranteed by physical guards within the facility or relevant uniformed services;
• λ is the overall intensity of the ESS transition from a state of full fitness (S_PZ) to a state of safety unreliability (S_B). All ESSs in an SB are fully unfit. This unfitness case was not taken into account in Figure 14 since all power sources—primary and backup—have extensive anti-destructive protections. Only deliberate actions, e.g., at time t₀, via a strong pulse, e.g., of an electromagnetic weapon, can lead to the transition in the graph shown in Figure 14.

Designations in Figure 14:

-

S_O(t)—probability function for ESSs operated in an SB staying in a state of full fitness (the t variable indicates time). All security systems execute a complex and in-house operational task programmed into the ACP, and associated with facility protection.

-

[S_D21(t), S_D22(t), S_D23(t), S_D24(t)—FAS], [S_D11(t), S_D12(t)—ACS], …, [S_D51(t), S_D52(t)—BASS] is the probability function for an ESS staying in a state of safety hazard. It is the unfitness of the primary or redundant power supply source—Figure 14. In this technical state, local service staff, at the SB site or remote in an ACR, immediately undertake improvement activities—recovery of damaged power sources or replacement with new equipment;

-

S_D1(t), S_D2(t), S_D3(t), S_D4(t), S_D5(t) is the probability function required for ESSs operated in an SB to stay in a safety unreliability state. Unfitness of all power sources—primary and redundant—prevents the implementation of basic tasks, i.e., monitoring, throughout the entire civil structure. The battery bank—the last backup power source in all ESSs—is also discharged by currents flowing in the monitoring circuits, lines and loops of these systems. In such a case, the recovery process to be implemented within an ESS operated in an SB will always be first conducted within an FAS. It is the security system that is responsible for life, health and property, as well as internal and external environments.

The transition graph shown in Figure 14 will be described by the following Kolmogorov–Chapman equations, in order to determine the probabilities of the complex system in question staying in individual states (8):

$$\begin{gathered} R_0^{\prime }\left(t\right)=-{\lambda }_{D11}\cdot R_0\left(t\right)+{\mu }_{D11}\cdot Q_{D11}\left(t\right)-{\lambda }_{D21}\cdot R_0\left(t\right)+{\mu }_{D21}\cdot Q_{D21}\left(t\right)-{\lambda }_{D3}\cdot R_0\left(t\right)+{\mu }_{D3}\cdot Q_{D31}\left(t\right)-{\lambda }_{D4}\cdot R_0\left(t\right)+{\mu }_{D4}\cdot Q_{D41}\left(t\right)-{\lambda }_{D5}\cdot R_0\left(t\right)+{\mu }_{D5}\cdot Q_{D51}\left(t\right) \\ {Q}_{D11}^{\prime }\left(t\right)={\lambda }_{D11}\cdot R_0\left(t\right)-{\mu }_{D11}\cdot Q_{D11}\left(t\right)-{\lambda }_{D12}\cdot Q_{D11}\left(t\right)+{\mu }_{D12}\cdot Q_{D12}\left(t\right) \\ {Q}_{D12}^{\prime }\left(t\right)={\lambda }_{D12}\cdot Q_{D11}\left(t\right)-{\mu }_{D12}\cdot Q_{D12}\left(t\right)-{\lambda }_{D1}\cdot Q_{D12}\left(t\right)+{\mu }_{D1}\cdot Q_{D1}\left(t\right) \\ {Q}_{D1}^{\prime }\left(t\right)={\lambda }_{D1}\cdot Q_{D12}\left(t\right)-{\mu }_{D1}\cdot Q_{D1}\left(t\right) \\ {Q}_{D21}^{\prime }\left(t\right)={\lambda }_{D21}\cdot R_0\left(t\right)-{\mu }_{D21}\cdot Q_{D21}\left(t\right)-{\lambda }_{D22}\cdot Q_{D21}\left(t\right)+{\mu }_{D22}\cdot Q_{D22}\left(t\right) \\ {Q}_{D22}^{\prime }\left(t\right)={\lambda }_{D22}\cdot Q_{D21}\left(t\right)-{\mu }_{D22}\cdot Q_{D22}\left(t\right)-{\lambda }_{D23}\cdot Q_{D22}\left(t\right)+{\mu }_{D23}\cdot Q_{D23}\left(t\right) \\ {Q}_{D23}^{\prime }\left(t\right)={\lambda }_{D23}\cdot Q_{D22}\left(t\right)-{\mu }_{D23}\cdot Q_{D23}\left(t\right)-{\lambda }_{D24}\cdot Q_{D23}\left(t\right)+{\mu }_{D24}\cdot Q_{D24}\left(t\right) \\ {Q}_{D24}^{\prime }\left(t\right)={\lambda }_{D24}\cdot Q_{D23}\left(t\right)-{\mu }_{D24}\cdot Q_{D24}\left(t\right)-{\lambda }_{D25}\cdot Q_{D24}\left(t\right)+{\mu }_{D25}\cdot Q_{D2}\left(t\right) \\ {Q}_{D2}^{\prime }\left(t\right)={\lambda }_{D25}\cdot Q_{D24}\left(t\right)-{\mu }_{D25}\cdot Q_{D2}\left(t\right) \\ {Q}_{D31}^{\prime }\left(t\right)={\lambda }_{D3}\cdot R_0\left(t\right)-{\mu }_{D3}\cdot Q_{D31}\left(t\right)-{\lambda }_{D31}\cdot Q_{D31}\left(t\right)+{\mu }_{D31}\cdot Q_{D32}\left(t\right) \\ {Q}_{D32}^{\prime }\left(t\right)={\lambda }_{D31}\cdot Q_{D31}\left(t\right)-{\mu }_{D31}\cdot Q_{D32}\left(t\right)-{\lambda }_{D32}\cdot Q_{D32}\left(t\right)+{\mu }_{D32}\cdot Q_{D3}\left(t\right) \\ {Q}_{D32}^{\prime }\left(t\right)={\lambda }_{D32}\cdot Q_{D32}\left(t\right)-{\mu }_{D32}\cdot Q_{D3}\left(t\right) \\ {Q}_{D41}^{\prime }\left(t\right)={\lambda }_{D4}\cdot R_0\left(t\right)-{\mu }_{D4}\cdot Q_{D41}\left(t\right)-{\lambda }_{D41}\cdot Q_{D41}\left(t\right)+{\mu }_{D41}\cdot Q_{D4}\left(t\right) \\ {Q}_{D4}^{\prime }\left(t\right)={\lambda }_{D41}\cdot Q_{D41}\left(t\right)-{\mu }_{D41}\cdot Q_{D4}\left(t\right) \\ {Q}_{D51}^{\prime }\left(t\right)={\lambda }_{D5}\cdot R_0\left(t\right)-{\mu }_{D5}\cdot Q_{D51}\left(t\right)-{\lambda }_{D51}\cdot Q_{D51}\left(t\right)+{\mu }_{D51}\cdot Q_{D52}\left(t\right) \\ {Q}_{D52}^{\prime }\left(t\right)={\lambda }_{D51}\cdot Q_{D51}\left(t\right)-{\mu }_{D51}\cdot Q_{D52}\left(t\right)-{\lambda }_{D52}\cdot Q_{D52}\left(t\right)+{\mu }_{D52}\cdot Q_{D5}\left(t\right) \\ {Q}_{D5}^{\prime }\left(t\right)={\lambda }_{D52}\cdot Q_{D52}\left(t\right)-{\mu }_{D52}\cdot Q_{D5}\left(t\right) \end{gathered}$$

(8)

By adopting initial conditions for the complex system in form of (9),

$$\begin{gathered} R_0\left(0\right)=1 \\ {Q}_{D11}\left(0\right)=Q_{D12}\left(0\right)=Q_{D1}\left(0\right)=Q_{D21}\left(0\right)=Q_{D22}\left(0\right)=Q_{D23}\left(0\right)=Q_{D24}\left(0\right)=Q_{D2}\left(0\right)=Q_{D31}\left(0\right)=Q_{D32}\left(0\right) \\ =Q_{D3}\left(0\right)=Q_{D41}\left(0\right)=Q_{D4}\left(0\right)=Q_{D51}\left(0\right)=Q_{D52}\left(0\right)=Q_{D5}\left(0\right)=0 \end{gathered}$$

(9)

and applying the Laplace transform to the system of Equation (8), the probability function for an ESS staying in a state of full fitness in symbolic terms is expressed by the relationship (10):

$${\mathrm{R}}_0\left(\mathrm{s}\right)={\displaystyle \frac{\begin{array}{c}-\left(0.01+0.17·s+0.8·{\mathrm{s}}^2+{\mathrm{s}}^3\right)·\left(0.0025+0.0525 ·s+0.38·{\mathrm{s}}^2+1.22· {\mathrm{s}}^3+1.8 ·{\mathrm{s}}^4+{\mathrm{s}}^5\right)·\\ \left(0.01+0.17 ·s+0.8·{\mathrm{s}}^2+{\mathrm{s}}^3\right)·\left(-0.02-0.3 ·s-{\mathrm{s}}^2\right)·\left(\begin{array}{c}-1.6 · {10}^{-8}·\left(0.5+s\right)-\\ \left(0.1+s\right)·\left(4·{10}^{-9}-\left(0.2+s\right)·\left(0.5+s\right)\right)\end{array}\right)\end{array}}{\begin{array}{c}5.0002·{10}^{-11}·s+4.35016·{10}^{-9}·{\mathrm{s}}^2+{1.73005·{10}^{-7}·\mathrm{s}}^3+{4.17062·{10}^{-6}·\mathrm{s}}^4+\\ 0.0000681449·s^5+0.00079952·s^6+0.0.00696241·s^7+0.0458756·s^8+\\ 0.231035·s^9+0.892·s^{10}+2.63123·s^{11}+5.86862·s^{12}+\\ 9.70605·s^{13}+11.515·s^{14}+9.25002·s^{15}+4.5·s^{16}+s^{17}\end{array}}}$$

(10)

The aforementioned calculations were based on the following adopted intensities of transitions between distinguished states, arising from studying the ESSs operated in civil structures. The studies covered n = 20 ESSs operated under different environmental conditions, and involved the determination of average λ failure and recovery μ rates. These parameters were subject to a computer simulation and the grounds for the determination of basic ESS characteristics—e.g., probability of systems staying in a state of full fitness—Figure 15.

$$\begin{gathered} {\lambda }_{D11}={\lambda }_{D21}={\lambda }_{D3}={\lambda }_{D4}={\lambda }_{D5}=0.8·{10}^{-6} \\ {\lambda }_{D12}={\lambda }_{D22}={\lambda }_{D31}={\lambda }_{D41}={\lambda }_{D51}=0.8·{10}^{-7} \\ {\lambda }_{D1}={\lambda }_{D23}={\lambda }_{D24}={\lambda }_{D25}={\lambda }_{D32}={\lambda }_{D52}=0.8·{10}^{-8} \\ {\mu }_{D11}={\mu }_{D21}={\mu }_{D3}={\mu }_{D4}={\mu }_{D5}=0.1 \\ {\mu }_{D12}={\mu }_{D22}={\mu }_{D31}={\mu }_{D41}={\mu }_{D51}=0.2 \\ {\mu }_{D1}={\mu }_{D23}={\mu }_{D24}={\mu }_{D25}={\mu }_{D32}={\mu }_{D52}=0.5 \end{gathered}$$

A solution to Equation (10) in the time domain is Expression (11):

$$R_0\left(t\right)=0.99996+0.00775945·{\mathrm{e}}^{-4.49764· t}·\left(\begin{array}{c}-0.293853·{\mathrm{e}}^{3.99118· t}+2.85106·{\mathrm{e}}^{3.99456· t}-\\ 5.43294·{\mathrm{e}}^{3.99653· t}+6.79814·{\mathrm{e}}^{3.99959· t}-\\ 4.45591·{\mathrm{e}}^{4.00121· t}+0.533391·{\mathrm{e}}^{4.00417· t}-\\ 0.653783·{\mathrm{e}}^{4.29587· t}+6.37597·{\mathrm{e}}^{4.29697· t}-\\ 6.41002·{\mathrm{e}}^{4.29725· t}+1.6978·{\mathrm{e}}^{4.2993· t}-\\ 1.01017·{\mathrm{e}}^{4.29977· t}+0.16018·{\mathrm{e}}^{4.39698· t}-\\ 0.787204·{\mathrm{e}}^{4.39737· t}+1.28874·{\mathrm{e}}^{4.39769· t}-\\ 1.65648·{\mathrm{e}}^{4.39806· t}+{\mathrm{e}}^{4.39817· t}\end{array}\right)$$

(11)

Figure 15 shows the waveform of the probability function for a complex security system staying in a state of full fitness. In such a state, all components and devices making up a complex system are operational, and power is supplied from an industrial power grid. A battery bank is always a backup power source for all ESSs operated in civil structures. For an ESS operation time equal to t = 50 h, Figure 15 shows a slight decrease in the probability function for a complex security system staying in a state of full fitness (R₀(t = 0) = 1, do R₀(t = 50 h) = 0.99996). Such a small change in the value of this R₀(t) function is determined by the so-called ESS infancy. After starting up and commissioning an ESS within an SB, unfitness states most commonly arise from design or installation errors—e.g., mechanical sensor connections (sensor–housing connections), all kinds of electronic element soldering or link or address errors of individual devices within monitoring circuits or lines. These are the most common errors in the early service life of an ESS.

In order to precisely map the variability waveform for the probability function related to a complex security system staying in a state of full safety shown in Figure 7, the authors developed a graph for $t=〈\mathrm{0,100}〉 \left[h\right]$. This is illustrated in Figure 16.

In the case of such μ, λ values adopted for the calculation of the R₀(t) probability function related to a complex system staying in a state of full fitness, we can calculate the change rate (reduced initial R₀(t) value) for a preset time interval of the ESS operation within an SB. This can be expressed using Expression (12):

$$K_{g1}\left(t\right)={\displaystyle \frac{R_0(dla t=10 h)}{Dt}}={\displaystyle \frac{{0.17·10}^{-4}}{10}}={0.17·10}^{-5}\left[{\displaystyle \frac{{∆R}_0\left(t\right)}{h}}\right]$$

(12)

The R₀(t) probability function change rate during the initial ESS operation process is K_g1(t) = 0.17·10⁻⁵, which is very low. However, taking into account the crucial security systems, such as the FAS or AWS, operated within an SB, the aim for the value of this function during this period is to be as low as possible, i.e., K_g1(t) ≅ 0. In such a case, all monitoring lines or circuits for the aforementioned systems are fit at the initial stage of the operation process, resulting in no failures associated with the start-up and commissioning of all ESSs monitoring SB security.

In order to determine the impact of the operation intensity of individual systems on the value of probability for a complex system staying in a state of full fitness, the authors adopted variability of the intensities describing the functioning of an access control system. The following values of the ACS transition between distinguished states were adopted for further calculations, resulting from operation process studies within the SB. These are the λ failure rate values (maximum values obtained during the study process were adopted for the calculations):

$$\begin{gathered} {\lambda }_{D11}=100·{10}^{-5} \\ {\lambda }_{D12}=50·{10}^{-6} \\ {\lambda }_{D1}=400·{10}^{-5} \end{gathered}$$

Figure 17 shows the waveform of the probability function for a complex security system staying in a state of full fitness, taking into account the adopted new transition intensity values for an access control system operated in an SB.

The value of the R₀(t) function showing the probability of an ACS staying in a state of full fitness for time t = 50 h is 0.9901, which is significantly lower than for the case in question, as shown in Figure 16, where this value was R₀(t = 50 h) = 0.99996.

In order to precisely illustrate the variability waveform for the functions depicting the probability of a complex security system (taking into account the new ACS transition intensities adopted) staying in a state of full fitness shown in Figure 17, the authors developed a graph for $t=〈\mathrm{0,100}〉 \left[h\right]$. This is illustrated in Figure 18.

The initial function change rate for a preset SB ESS operation time interval can be also calculated for the adopted μ, λ to calculate the R₀(t) function for the probability of a complex system staying in a state of full fitness. This can be expressed using Expression (13):

$$K_{g2}\left(t\right)={\displaystyle \frac{R_0(dla t=43 h)}{Dt}}={\displaystyle \frac{{0.72·10}^{-2}}{43}}={1.67·10}^{-4}\left[{\displaystyle \frac{{∆R}_0\left(t\right)}{h}}\right]$$

(13)

The R₀(t) function change rate at the initial stage of the operation process in the case of an AWS is K_g2(t) = 1.67·10⁻⁴. If we assume the functionalities implemented by an AWS in an SB, particularly during a fire (e.g., releasing the locks, electric strikes, interlocks, etc.), the value of this function during the initial evacuation of people from a smart building should be as low as possible, i.e., K_g2(t) ≅ 0. Then, all ACS-implemented functions will be executed as planned during a fire, i.e., the complete release of all door interlocks when evacuating people from a building upon an alarm being raised by an FAS and its sounding by the AWS. In such a case, all ACS transmission lines and devices are fit at the initial operation stage. There are no failures resulting from the start-up and commissioning stage.

Figure 19 shows the comparison of the R₀(t) function for the probability of a complex system staying in a state of full fitness for $t=〈\mathrm{0,100}〉 \left[h\right].$

6. Conclusions

The process of operating electronic security systems, and the reliability of these technical systems (i.e., AWSs, ACSs, IDSs) operated in smart buildings in particular, is crucial in the context of the entire assumed service life. Therefore, all modules, components and devices employed to construct them should be subject to an initial ageing process already at the manufacturing plants. This should take into account the so-called device infancy. During that period, all ESS components exhibit high susceptibility to failures, even in the case of a good design and installation. Therefore, FAS, AWS or ACS manufacturing plants should implement and take the initial ageing process into account already at the stage of manufacturing all ESS components. The site visits of the authors at selected manufacturing plants in Poland indicated that such a process is being implemented. The authors do not have any information related to other ESSs manufactured globally. The initial ageing time is always ‘secret/confidential’ information for a given manufacturer/company. The issue of ESS power supply reliability is extremely important. Therefore, all security systems are fitted with their own ‘battery banks’, treated as backup power sources, regardless of the remaining power infrastructure of the entire facility or the vast area where such security systems are operated. This article discusses an SB power supply reliability computer simulation. The attached graphs 15 to 19 illustrating the waveform of the R₀(t) probability function for a complex power supply system staying in a state of full fitness show that the maximum value always declines at the initial operation process stage. The change rate of the R₀(t) in the initial ESS operation period was calculated for the purposes of the simulation for two operational scenarios of such objects with adopted μ, λ intensities. The change rate (reduction in the initial R₀(t) value) for a preset time interval is higher for the second case since the ACS system was included in the considerations and calculations of the ESS operation process parameters. The change rate of the R₀(t) probability function at the initial stage of the operation process for the entire ESS is K_g1(t) = 0.17·10⁻⁵. When considering the operation of a different ACS, with inferior technical parameters, the change rate of the R₀(t) function at the initial operation process stage is K_g2(t) = 1.67·10⁻⁴. The ACS implements very important functions in the event of a declared fire phenomenon within a facility and is always controlled by the FAS. An ACS includes mechanical and electromechanical parts, such as locks, electric strikes, tripods or interlocks. These are devices that are usually damaged in the event of heavy traffic within protected buildings. However, with high power supply reliability being the aim of the operation process, the value of this function should be as low as possible, i.e., K_g2(t) ≅ 0. This prevents failures associated with the ESS start-up and commissioning stage, which are related to the SB power supply. All ESSs operated in an SB exhibit expanded power supply redundancy. This issue is also crucial in the case of buildings, facilities and areas classified as so-called state-critical infrastructure.

Since the technical standards and regulations applicable in Poland that the article has been based on are consistent with EU legislation, this approach may also be implemented in relation to ESSs operated within the European Union.