Reliability and Maintenance Prioritization Analysis of Combined Cooling, Heating and Power Systems

energies

Article Reliability and Maintenance Prioritization Analysis of Combined Cooling, Heating and Power Systems

Jinming Jiang 1, Xindong Wei 2, Weijun Gao 1,*, Soichiro Kuroki 1 and Zhonghui Liu 1

1 Faculty of Environmental Engineering, the University of Kitakyushu, Kitakyushu 808-0135, Japan; [email protected] (J.J.); [email protected] (S.K.); [email protected] (Z.L.) 2 School of Environmental and Municipal Engineering, Jilin Jianzhu University, Changchun 130118, China; [email protected] * Correspondence: [email protected]; Tel.: +81-093-695-3234

Received: 5 May 2018; Accepted: 7 June 2018; Published: 11 June 2018

Abstract: A combined cooling, heating, and power (CCHP) system is a complex and repairable system containing a large number of components and series of subsystems. When a failure occurs in one component, it might cause a failure of a subsystem or whole system. Traditional maintenance methods might lead to the waste of maintenance resources and a high cost of maintenance. The reliability and maintenance prioritization analyses can help managers optimize maintenance strategies and reduce the total cost. A reliability importance index is one of the factors in maintenance prioritization analysis. This paper aims at selecting the component reliability importance indices to identify the priority of component maintenance of a CCHP system from the perspective of maintenance cost. Failure cost importance index (FCI) and Potential failure cost importance index (PI) are developed for the maintenance prioritization analysis of a CCHP system. A Markov model based on the state–space method (SSM) is used to analyze the reliability and availability of a CCHP system. A set of actual survey reliability data of CCHP systems is used to support the validity of the reliability importance indices. The results indicate that the FCI and PI might lead to different rankings of maintenance prioritization. The FCI and PI will help managers make a reasonable decision for maintenance on a cost basis.

Keywords: reliability analysis; maintenance prioritization; state-space method; Markov process; CCHP system

1. Introduction Combined cooling, heating, and power (CCHP) systems produce electricity and available heat from one generation site and the conversion efficiency of primary energy to useful energy is approximately 70–80% [1,2]. Due to the high conversion efficiency and greater environmental benefit, CCHP systems have attracted more attention in the past few decades [3] and are widely used in buildings or regional energy systems [4]. The CCHP system, also known as the tri-generation system, can be applied in a stand-alone microgrid (MG) or combined with the city power grid. Recent research is focused on system management, operation, system optimization, size optimization, energy management, renewable energies, and more [5]. Some renewable energies and technologies have been applied in the CCHP system, such as fuel cells, heat pumps [6], photovoltaics (PV), wind turbines, and more [7,8]. Integrating renewable energy into the CCHP system can further improve the system’s energy efficiency and reduce carbon dioxide emissions; the renewable energies integrated into CCHP (RECCHP) systems can be used when the power grid is unavailable, for example, on islands, and in deserts [9]. Chen et al. [10] proposed a multi-objective optimization model of energy management for the integrated electrical and natural gas network

Energies 2018, 11, 1519; doi:10.3390/en11061519 www.mdpi.com/journal/energies Energies 2018, 11, 1519 2 of 24 with CCHP plants. Lo Basso et al. [6] analyzed the thermal management and off-design operation of coupling of combined heat and power (CHP) and heat pump for the energy retrofitting of residential buildings. Wang et al. [11] presented a comprehensive operation model to enhance the economic and environmental benefits through the improved CCHP strategy of MG. The main objective of optimization is to improve energy efficiency, maximize environmental benefits, and reduce the expense of the system. Some previous studies on system design and optimization of a CCHP system were often set to a constant, or assumed that the reliability and maintenance of the system were completely unfailing for operation [12]. The cost of operation and maintenance of a system account for more than 50% of the total cost of the whole life cycle [13] in fact. Thus, a reasonable maintenance strategy can improve the reliability of a system and reduce the maintenance cost. Some articles on the operation, reliability, and maintenance of a CCHP system or microgrid are related to facilities’ distribution and system optimization design. Ou [14] proposed an unsymmetrical faults analysis method to deal with the unsymmetrical faults of microgrid distribution systems adopting hybrid compensation. Ting-Chia Ou et al. studied the operation and control strategies for a microgrid which used renewable energies and fuel cells as power generators [15]; a technology was developed to improve the transient stability in the hybrid power multi-system [16]. Noussan et al. [17] proposed an optimization tool to enhance the operation of a CHP system combined with a heat pump. Zamani-Gargari et al. [18] proposed a method which combined the Monte Carlo Simulation (MCS) method to assess the reliability of a wind power system with energy storage. Yang et al. [19] proposed an approach to analyzing how the wind farm electrical system influenced the system when the electrical system faulted. Wang [20] presented a reliability and availability analysis of a redundant and non-redundant BCHP (building, cooling, heating, and power) system, but did not consider the component reliability of the system. Haghifam, and Manbachi [21] proposed a reliability and availability modeling of CHP systems to analyze the impact of CHP system reliability with improved gas-delivery, water-delivery, and hot water-delivery subsystems but did not model the reliability of individual components. Frangopoulos [22] analyzed the effect of optimization on the synthesis, design, and operation of a cogeneration system based on reliability considerations, but did not consider the effect of component reliability. El-Nashar [23] presented an optimal design model of a cogeneration system using the thermoeconomic theory to carry out the design optimization. Only a few articles to date have studied the component reliability of the power generation plant, cogeneration system, and CCHP system. Sabouhi et al. [24] mentioned a reliability model to assess the combined cycle power generation plants and applied it to a reliability analysis for gas turbine power plants and steam turbine power plants. The reliability of components was used to compute the system availability and the study compared the availability, but did not mention the importance of maintenance regarding the components in one system. Carazas et al. [25] presented an availability analysis for component maintenance policies of a gas turbine, but did not assess the reliability of the whole power generation system. A CCHP system is a complex system, however, containing a large number of components and a series of subsystems. When a failure occurs on one component, it might cause a failure of a subsystem or the whole system. The reliability of the whole system is dependent on the reliability of each component of the system. Traditionally, the maintenance of components in a system is managed by specifying a fixed schedule. Each component of a system has its own maintenance schedule performed according to the manufacturer’s recommendations. It might lead to the waste of maintenance resources and a high cost of maintenance. To comprehensively evaluate the degree of maintenance importance regarding the components of a whole system and propose a reasonable maintenance strategy is a vital way to avoid the wastage of maintenance resources and reduce the total costs, therefore, the reliability and maintenance prioritization analysis of components of a whole system is necessary. A reliability importance index is one of the methods to identify system weaknesses and provide a numerical value to determine which components are more important for the improvement of system reliability [26]. The reliability importance index can be used to assess which components Energies 2018, 11, 1519 3 of 24 are needing maintenance and which components are needing more attention to reduce maintenance costs [27]. It can provide a reference for system designers and managers to optimize the design plan and operation strategy for future design, redesign, and operation to reduce the total cost and improve reliability. Conventional reliability importance indices are a function of component reliability, however; they cannot be used directly to optimize maintenance costs. Two new reliability importance indices are developed in this study based on the component failure cost for the identification of component maintenance priorities from the perspective of maintenance cost. A comparative analysis is performed between the new reliability importance indices and conventional reliability importance indices. Additionally, a Markov model based on the state–space method (SSM) is used to analyze the reliability and availability of components and subsystems of a CCHP System. This study is validated by actual survey reliability data of the CCHP system in Kitakyushu Science and Research Park (KSRP), Kitakyushu, Japan; the system has been operational since July 2001. This paper is organized as follows: Section2 introduces the main components of a CCHP system and the CCHP system at Kitakyushu Science and Research Park, the applied objective; Section3 describes the methodologies of reliability analysis and reliability importance analysis; Section4 analyzes the reliability of a CCHP system; Section5 presents the numerical calculations and dissection of the case; Section6 outlines the conclusions.

2. Main Components of CCHP Systems Several technologies have been applied to CCHP systems for power generation, waste heat recovery, thermal storage, and thermal energy conversion such as an Absorption chiller. The main components of technologies are the keys to system reliability. The main components and subsystem technologies of a CCHP system are listed in Table1[ 7,28]. Some auxiliaries and components are not listed in this table, such as cooling pumps, cooling towers, control panels and so on, but these components also have an inﬂuence on the subsystem or system reliability. Hence, auxiliaries and components will be considered in the reliability analysis of the system.

Table 1. The main components of the CCHP system technologies.

Technology Function Main Components/Subsystems Power generation; Fuel processor, air processor, power section, power conditioner and Fuel cell (FCs) Waste heat supply so forth. Power generation; Reciprocating engines Engine, fuel processor, generator, cooling system, and so forth. Waste heat supply Power generation; Engine/turbine, generator, compressor, fuel compressor, power Gas turbines/engines Waste heat supply conditioner, cooling system, and so forth. Photovoltaic system (PVs) Power generation Solar cells, power conditioner, DC/AC generator and so forth. Wind energy conversion Power generation Winder turbines, generator, gearbox, yaw motor and so forth. system (WECS) Small hydro-turbines Power generation Turbine, generator, power conditioner and so forth. Burner, heat exchanger, supply lines, return lines, ﬁrebox, circulator Boiler Thermal supply pumps, deaerators/condenser and so forth. Thermal compressor, condenser, evaporator, cooling tower, solution Absorption chiller Thermal supply pump and so forth. Heat pump Thermal supply Compressor, condenser, expansion valve, evaporator and so forth.

The CCHP system at Kitakyushu Science and Research Park (KSRP) [29] is the analysis objective. The Kitakyushu Science and Research Park is located in Kitakyushu, Japan. The generation of electricity and thermal form of the CCHP system are used to meet the electricity load, space cooling load, space heating load, and hot water load of several buildings on the campus. The system scheme of the CCHP system at KSRP is shown in Figure1[30]. The fuel cells and gas engines fueled by natural gas Energies 2018, 11, 1519 4 of 24 are used to drive the power generation units to generate electricity. Every power generation unit has an independent cooling water system. The waste heat from the power generation unit is recovered by the heat recovery steam generator (HRSG), and the 50% recovered heat from the fuel cell is used to drive the absorption chiller to meet the space cooling load in summer and the space heating load in winter. The 50% recovered heat from the fuel cell and all recovered heat from the gas engine are used to drive the heat exchanger to meet the hot water load. Since the electricity generation of the system cannot meet the electricity load of the campus, it is necessary to purchase electricity from the electricityEnergies grid. 2018, The11, x FOR available PEER REVIEW gas-fired absorption chiller fueled by natural gas meets the shortage4 of 25 of space cooling and space heating. An auxiliary boiler fueled by natural gas is used to complement the Burner, heat exchanger, supply lines, return lines, firebox, Boiler Thermal supply shortage of hot water. Details of the power generationcirculator pumps, units deaerators/condenser of the CCHP system and so forth. in KSRP is shown in Thermal compressor, condenser, evaporator, cooling tower, Table2[30].Absorption chiller Thermal supply The research flow of reliability and maintenancesolution pump prioritization and so forth. analysis is shown in Figure2. Heat pump Thermal supply Compressor, condenser, expansion valve, evaporator and so forth. Reliability and maintenance prioritization analyses will be applied to the components and subsystems of the CCHPThe system research at flow KSRP. of reliability The following and maintenance points of systemprioritization reliability analysis are is assumedshown in forFigure the 2. CCHP systemReliability at KSRP: and maintenance prioritization analyses will be applied to the components and subsystems of the CCHP system at KSRP. The following points of system reliability are assumed for (1) Thethe CCHP failure system of a componentat KSRP: or a subsystem is independent of each other. This analysis only considers(1) The failure one component of a component failure or a and subsystem how it is affects independent the system of each status other. and This operation; analysis only multiple failuresconsiders of components one component in the failure system and will how not it beaffect considereds the system at status this time. and operation; multiple (2) Whenfailures a failure of components occurs in ain power the system generation will not be unit, considered the outage at this of time. electricity will be satisfied by the(2) electricity When a failure grid andoccurs the in failurea power of generation the electricity unit, the grid outage is not of considered. electricity will Similarly, be satisfied the by outage of spacethe electricity cooling/heating, grid and the and failure hot water of theis electric consideredity grid satisfiedis not considered. when the Similarly, corresponding the outage system has failed.of space cooling/heating, and hot water is considered satisfied when the corresponding system has failed.

Grid electricity Electricity

CWS1

Natural gas FC HRSG1 ACS Space cooling Space heating

Natural gas GE HRSG2 Natural gas

CWS2

Natural gas AB HE Hot water

Figure 1. The system scheme of the CCHP system at KSRP. Figure 1. The system scheme of the CCHP system at KSRP. Table 2. The details of the power generation units of the CCHP system at KSRP. Table 2. The details of the power generation units of the CCHP system at KSRP. Type Fuel Cell Gas Engine TypeCapacity Fuel 200 CellkW 160 Gas kW Engine Power generation Capacity 200 kW 160 kW efficiency 40% 28.7% Power generation efﬁciency 40% 28.7% (with(with 100% 100% load) load) 20%, Collecting heat for hot water 47.7% HeatHeat release release efﬁciency efficiency 20%, Collecting heat for hot water 47.7% 20%, Collecting heat for space cooling and Collecting heat for hot (with(with 100% 100% load) load) 20%, Collecting heat for space cooling and heating Collecting heat for hot water heating water Run for 24 h over time Run for 14 h Operational mode Run for 24 h over time Run for 14 h Operational mode Priority to run Run for 8:00~22:00 Priority to run Run for 8:00~22:00

Energies 2018, 11, 1519 5 of 24 Energies 2018, 11, x FOR PEER REVIEW 5 of 25

Start reliability and maintenance analysis process.

Investigate and review the system information and base data. (e.g. maintenance records, inspection records, failure records; repair records etc. )

Identify the main components and subsystems; draw the Reliability Block Diagrams.

Perform the reliability analysis Calculate reliability factors of components and systems by (e.g. failure rate, repair rate, the SSM and Markov process. MTTR etc.)

Results of reliability and Analyze the reliability availability of components and importance indices. systems.

Validation of the reliability importance indices. To formulate or reformulate the maintenance strategy in the cost basis.

Figure 2. The research flowchart of reliability and maintenance prioritization analysis. Figure 2. The research flowchart of reliability and maintenance prioritization analysis. 3. Methodology 3. Methodology 3.1. Reliability Analysis Methods 3.1. Reliability Analysis Methods Reliability is defined as the ability of an item to perform a required function under given Reliability is defined as the ability of an item to perform a required function under given conditions conditions for a stated period. Reliability analysis methods are applied during any phase of a system’s for a stated period. Reliability analysis methods are applied during any phase of a system’s lifetime lifetime to enhance the system’s safety, quality, and operational availability [31]. Reliability and to enhance the system’s safety, quality, and operational availability [31]. Reliability and availability availability analyses are widely performed in various fields, for instance, engineering and medical analyses are widely performed in various fields, for instance, engineering and medical science, since it science, since it was proposed in the 1960s, and the most reliability analysis models and methods are was proposed in the 1960s, and the most reliability analysis models and methods are proposed and proposed and applied [32]. Some widely used system reliability analysis methods, for instance, applied [32]. Some widely used system reliability analysis methods, for instance, failure tree analysis, failure tree analysis, FMEA (failure modes, effects, and criticality analysis) and event tree analysis, FMEA (failure modes, effects, and criticality analysis) and event tree analysis, are used to analyze are used to analyze the failures, failure modes, and failure effects [33]. Those analysis methods are all the failures, failure modes, and failure effects [33]. Those analysis methods are all based on the based on the assumption that the components or the system are only in either a functioning state or assumption that the components or the system are only in either a functioning state or failed state. failed state. Therefore, the analysis models are rather static and not well suited for analysis of Therefore, the analysis models are rather static and not well suited for analysis of repairable systems. repairable systems. The reliability problems of a complex system can be described by the state of the The reliability problems of a complex system can be described by the state of the system, and a system, and a complex system can exist in one of the multiple states. The states of a system are complex system can exist in one of the multiple states. The states of a system are discrete, identifiable, discrete, identifiable, and continuous in time. Some reliability analysis methods with stochastic and continuous in time. Some reliability analysis methods with stochastic processes are used to analyze processes are used to analyze the reliability of a repairable system, such as the Homogeneous Poisson the reliability of a repairable system, such as the Homogeneous Poisson Processes, Renewal Processes, Processes, Renewal Processes, and the Markov Processes which is the most widely used analysis and the Markov Processes which is the most widely used analysis method since it can be used to method since it can be used to model systems with several states and transitions between the states [20]. model systems with several states and transitions between the states [20]. Reliability assessment methods of multistate systems are based on two different approaches: Reliability assessment methods of multistate systems are based on two different approaches: analytical stochastic process and the Monte Carlo simulation method [21]. The Markov process is the analytical stochastic process and the Monte Carlo simulation method [21]. The Markov process is the main analytical stochastic process [31] since it can be used to perform the reliability analysis of a main analytical stochastic process [31] since it can be used to perform the reliability analysis of a system system that has changed continuously or discretely with the passage of time and space. The SSM is that has changed continuously or discretely with the passage of time and space. The SSM is applicable applicable for the assessment of reliability, availability, and maintainability of large and complex systems, and it is considered an irreplaceable method for evaluating repairable and complex systems [20,22]. The frequency-balance method is one of the analytical stochastic continuous Markov

Energies 2018, 11, 1519 6 of 24 for the assessment of reliability, availability, and maintainability of large and complex systems, and it is considered an irreplaceable method for evaluating repairable and complex systems [20,22]. Energies 2018, 11, x FOR PEER REVIEW 6 of 25 The frequency-balance method is one of the analytical stochastic continuous Markov solutions used to evaluate the state probability [21]. A CCHP system is a complex and repairable system, where the solutions used to evaluate the state probability [21]. A CCHP system is a complex and repairable function of components or systems can be restored to a certain state through repair, maintenance system, where the function of components or systems can be restored to a certain state through repair, or replacement activities. Therefore, the Markov process, based on the state–space method (SSM), maintenance or replacement activities. Therefore, the Markov process, based on the state–space is suitable to analyze the reliability of a CCHP system. method (SSM), is suitable to analyze the reliability of a CCHP system. The state of a system depends on the state of its individual components; each component has The state of a system depends on the state of its individual components; each component has two states: functioning (1) and failed (0). Since each component has two states (functioning or failed), two states: functioning (1) and failed (0). Since each component has two states (functioning or failed), when a system has n quantity of components, the system will still have, at most, 2n possible states. when a system has n quantity of components, the system will still have, at most, 2 possible states. The state of a system is transferred randomly with time in those states. A Markov model based on a The state of a system is transferred randomly with time in those states. A Markov model based on a state–space method (SSM) is performed for the reliability analysis of a system with two components. state–space method (SSM) is performed for the reliability analysis of a system with two components. The Markov model and possible states of the system are shown in Figure3 and Table3, respectively. The Markov model and possible states of the system are shown in Figure 3 and Table 3, respectively. The failure rate (λ) is represented by the transition rate of one component from a functioning state to The failure rate () is represented by the transition rate of one component from a functioning state to failed state. Similarly, the repair rate (µ) is represented by the transition rate of one component from a failed state. Similarly, the repair rate () is represented by the transition rate of one component from failed state to a functioning state. Thus, the failure rate and repair rate of a component are used to a failed state to a functioning state. Thus, the failure rate and repair rate of a component are used to describe the transition rate between two states of the system. The reliability and availability analysis describe the transition rate between two states of the system. The reliability and availability analysis model using the Markov process and SSM can be decomposed into the following steps: model using the Markov process and SSM can be decomposed into the following steps: (1) List and classify all system states; the same state should be merged, and the non-related state (1) List and classify all system states; the same state should be merged, and the non-related state should be removed. should be removed. (2) ConstructConstruct the the state state space space diagram diagram of of the the syst system;em; confirm conﬁrm the the transition transition rate between states. (3) CalculateCalculate the the probabilities probabilities of of the the states states during during a a lifetime. lifetime. (4) CalculateCalculate the reliability andand availabilityavailabilityindices, indices, such such as as the the failure failure rate rate (generally (generally represented represented by bythe the mean mean time time to failure),to failure), repair repair rate rate (generally (generally represented represented by theby the mean mean time time to repair) to repair) and and the theavailabilities availabilities of theof the components. components.

Figure 3. TheThe Markov Markov model of a sy systemstem with two components.

TableTable 3. The possible states of a system with two components. Items Component 1 Component 2 Items Component 1 Component 2 Failure rate Failure rate λ1 λ2 Repair rate Repair rate µ1 µ2 StateState 1 1 1 1 1 1 StateState 2 2 0 0 1 1 StateState 3 3 1 1 0 0 State 4 0 0 State 4 0 0 There are two states for every component: a functioning state (1) and a failed state (0). There are two states for every component: a functioning state (1) and a failed state (0).

A steady-state distribution system is used to limit the Markov processes. Generally, a set of linear, order differential equations is established to determine the probability distribution of the system. The probability distribution equation is shown below:

() = (),(),…,() (1)

Energies 2018, 11, 1519 7 of 24

P(t) = [P1(t), P2(t),..., Pn(t)] (1) where the Pi(t) is the probability of the system in state i at time t and P(t) is the state probability matrix at time t. A density matrix, Q, is deﬁned as the following:   q11 q12 ... q1n    q21 q22 ... n  Q =   (2)  . . .. .   . . . .  qn1 qn2 ... qnn where qij = λij(i 6= j) and qii = − ∑i6=j λij. The following state equations are presented for the steady-state probability of the system: ( P·Q = 0 (3) ∑ Pi = 1

Thus, for a system with two components, as shown in Figure2 and Table3, the state transition density matrix is presented as follows:   −(λ1 + λ2) λ1 λ2 0  − +   µ1 (µ1 λ2) 0 λ2  Q =   (4)  µ2 0 −(µ2 + λ1) λ1  0 µ2 µ1 −(µ1 + µ2)

Based on Equation (3), the following equations can be acquired:  −(λ + λ )P + µ P + µ P = 0  1 2 1 1 2 2 3  λ P − (µ + λ )P + µ P = 0  1 1 1 2 2 2 4 λ1P1 − (µ1 + λ2)P2 + µ1P4 = 0 (5)  P + P − ( + )P =  µ2 2 µ1 3 µ2 µ1 4 0  P1 + P2 + P3 + P4 = 1

The state probabilities of the system are obtained through solving the Equations in (5), with the following results: µ1µ2 P1 = (6) (λ1 + µ1)(λ2 + µ2)

λ1µ2 P2 = (7) (λ1 + µ1)(λ2 + µ2)

λ2µ1 P3 = (8) (λ1 + µ1)(λ2 + µ2)

λ1λ2 P4 = (9) (λ1 + µ1)(λ2 + µ2) where the availability of component 1 is written as follows:

Acomponent 1 = P1 + P3 (10) Energies 2018, 11, 1519 8 of 24 where the availability of component 2 is written as follows:

Acomponent 2 = P1 + P2 (11) where the availability of the whole system (both component 1 and component 2 are functioning) is written as follows: Awhole system = P1 (12) where the availability of the system (whole system or part of the system are functioning) is written as follows: Asystem = P1 + P2 + P3 (13) Generally, a complex system consists of multiple series and parallel subsystems, thus, the reliability calculation methods for a series subsystem and parallel subsystem are different [34]. The reliability of a series system with n components is presented as follows:

Rseries = R1R2R3 ··· Rn (14)

The reliability of a parallel system with n components is presented as follows:

Rparallel = 1 − [(1 − R1)(1 − R2) ··· (1 − Rn)] (15)

3.2. Component Importance Indices Reliability importance indices can be used to determine project prioritization of components in a system. Several reliability importance measures (RIM)—Birnbaum’s measure [35], Fussell–Vesely’s measure [36], Criticality importance measure [37] for instance—have been proposed in previous studies. Based on those reliability importance measures, several importance indices were developed. Reliability importance is a function of maintenance results like operation time, failure, and repair characteristics of components in a system [38]. There are many techniques to evaluate reliability importance measures (RIM), an example of which are the Monte Carlo Simulation, Markov Methods, Petri Nets, Fault Tree Analysis (FTA), and Reliability Block Diagrams (RBD) [39]. Marcantonio Catelani et al. described two metrics for the component reliability importance assessment on complex systems—credible importance potential (CIP) and improvement potential (IP) [26]. Rong Gao and Kai Yao presented some formulas for the calculation of the importance index of components of uncertain reliability systems [40]. Patrik Hilber and Lina Bertling presented two indices which evaluated the total interruption cost and those indices were applied and simulated on an electricity distribution network [41]. The Birnbaum’s measure was developed in 1969, and it is deﬁned as follows:

B ∂Rsys(t) Usys(t) Ik (t) = = (16) ∂Rk(t) Uk(t)

B where Ik is the Birnbaum importance (BI) of the kth component, Rsys(t) is the reliability of system at time t, Rk(t) is the reliability of kth component at time t, Usys(t) is the unreliability of the system, Uk(t) is the unreliability of the kth component at time t. Birnbaum’s reliability importance measure presented that a component would be failed at time t. Component criticality importance (CI) [37] can be used to determine the probability that the component would be failed before time t:

C ∂Rsys(t) Uk(t) B Uk(t) Ik (t) = · = Ik (t)· (17) ∂Rk(t) Usys(t) Usys(t)

This paper presents new reliability importance indices based on Birnbaum’s measure and Patrik Hilber’s research. The failure cost of components has been used as an assessment factor for a reliability Energies 2018, 11, 1519 9 of 24 importance measure of a CCHP system. The component reliability importance index based on failure cost is deﬁned as follows: F ∂CTF Ik = (18) ∂λk F F where Ik is the reliability importance index that is considered the failure cost. The unit Ik is failure cost per failure (failure cost/f). F Reliability importance index of failure cost (Ik ) is affected by the repair cost of the component and the repair rate, but is not related to the failure rate. The second reliability importance index is related to failure rate and proposes a maintenance prioritization with comprehensive consideration of failure rate, repair rate and required repair cost. Potential failure cost importance index deﬁnes the expected cost of failure before the failure occurs. It is presented as the following:

P F Ik = Ik λk (19)

P where Ik is the potential failure cost importance index of k component, and the unit of this index is failure cost per unit time (cost/unit time). The failure cost of a component of a CCHP system is deﬁned as the total cost of the system during the failure time, including the component repair cost and the added cost for an unserved load (electricity or space cooling and heating, or hot water). The total failure cost is deﬁned as the following:

CTF(k) = ∑[CR,n(k) + CA,n(k)] (20) n where CTF is total failure cost of component k’s failure, CR is the repair cost for k component, and the CA is the added cost of the outage (electricity or space cooling and heating, or hot water). The added cost during an outage is defined as the cost that should be paid in order to meet the insufficiency of the energy load when the failure occurred, such as when the power generator experiences a failure leading to an outage-state; the insufficient electricity will be met by the electrical grid and the insufficient heat from the waste heat will be met by gas boiler or gas-fired absorption chiller, thus, the total cost of electricity and natural gas for meeting the insufficiency are the added cost of the unserved load. The added cost of the outage (electricity or space cooling and heating, or hot water) is calculated as the following: CA = u × Lu × MTTR (21) where u is the unit price of electricity or city gas; and Lu presents the amount of electricity or city gas are purchased , and MTTR is the mean time to repair. Generally, MTTR is defined as the total amount of time spent performing all corrective or preventative maintenance repair divided by the total number of those repairs. The mean time between failure (MTBF), the mean time to failure (MTTF), and the mean time to repair (MTTR) are the basic categories of failure rates [42]. A failure rate can be presented as follows: λ = 1/MTBF (22)

3.3. Comparisons of Component Reliability Importance Indices Failure cost importance and potential failure cost importance indices are developed to provide accurate cost indicators for managers to optimize the maintenance strategy to reduce the total maintenance cost and improve the system reliability. Comparisons of the four component importance indices are presented in Table4. IB and IC are related to failure rate, and they show the probability of components that would fail at time t or before time t, respectively. However, the failure rate only depends on the component’s properties and shows the maintenance results. IB and IC cannot accurately reﬂect the component’s importance of maintenance when the maintenance costs are considered for Energies 2018, 11, 1519 10 of 24 the maintenance strategy. Thus, the failure cost should be used as a factor to evaluate the component importance index when the economics of maintenance are considered, due to the failure cost being related to the repair rate and component repair cost. Therefore, IF and IP as the importance indices, which are the comprehensive consideration of failure rate, repair cost, and repair rate, are developed in this paper.

Table 4. The comparisons of the component reliability importance indices.

Importance Index Description Relation of Maintenance Factors IB The probability of a component failing at time t Failure rate IC The probability of a component failing before time t Failure rate IF The expect failure cost if the component fails. Repair rate, component repair cost. The expect failure cost in a unit time caused by Failure rate, repair rate, component IP Energies 2018, 11, x FOR PEER REVIEW component failure. repair cost. 10 of 25

4.4. ReliabilityReliability AnalysisAnalysis ofof CCHPCCHP SystemSystem ReliabilityReliability andand availabilityavailability analysesanalyses ofof componentscomponents andand subsystemssubsystems areare appliedapplied inin thethe CCHPCCHP systemsystem at at KSRP.KSRP. The The CCHP CCHP system system is is a a complexcomplex system system whichwhich cancan provideprovide thethe electricityelectricity andand thermalthermal energiesenergies (cooling,(cooling, heating,heating, andand hothot water)water) toto meetmeet customercustomer load,load, andand isis combinedcombined withwith aa seriesseries ofof subsystemssubsystems consistingconsisting ofof aa powerpower generationgeneration system,system, citycity gasgas supplysupply system,system, waterwater supplysupply system,system, coolingcooling waterwater system,system, thermalthermal supplysupply system,system, andand transfertransfer system.system. Therefore,Therefore, thethe reliabilityreliability ofof thisthis CCHPCCHP systemsystem mustmust considerconsider seriesseries subsystemsubsystem reliability,reliability, whichwhich isis tootoo complexcomplex andand difﬁcultdifficult toto bebe analyzed,analyzed, hence,hence, thethe reliabilityreliability ofof thisthis CCHPCCHP systemsystem waswas simpliﬁedsimplified asas customer-orientedcustomer-oriented reliability;reliability; onlyonly the the reliability reliability of of electricity, electricity, space space cooling cooling and and heating, heating, and and hot waterhot water delivery delivery to the to customer the customer were considered.were considered. The Markov The Markov processes processes and SSM and were SSM selected were to selected analyze to the analyze reliability the and reliability availability and ofavailability the electricity of the subsystem, electricity subsystem, space cooling space and co heatingoling and subsystem, heating subsyste hot waterm, hot subsystem water subsystem and the wholeand the system. whole system. AA simplesimple customer-oriented customer-oriented reliability reliability model model of of the the CCHP CCHP system system is shownis shown in Figurein Figure4. Based 4. Based on thison model,this model, the electricity the electricity subsystem, subsystem, space cooling space andcooling heating and subsystem,heating subsystem, and hot water and subsystemhot water aresubsystem described are as described a series connection. as a series This connection. is because This the is whole because system the whole reliability system should reliability be considered should frombe considered the perspective from ofthe the perspective customer. Thus,of the the custom reliabilityer. Thus, of the the whole reliability system of is the written whole as: system is written as: RCCHP = Relectricity·Rcooling & heating·Rhot water (23) = ∙ & ∙ (23) WhenWhen oneone ofof thethe subsystems fails but but the the other other subs subsystemsystems still still function, function, it itcreates creates a asituation situation of ofavailability availability of ofthe the functioning functioning su subsystemsbsystems but but not not the the availability availability for the wholewhole system.system. WhenWhen aa componentcomponent or or subsystem subsystem has has stopped stopped operating operating according according to a schedule, to a schedule, its reliability its reliability is not cemented is not incemented the whole in system’sthe whole reliability. system’s According reliability. to According the schedule, to the for schedule, instance, for the instance, space cooling the space and heatingcooling subsystemand heating will subsystem stop in the will spring stop or autumnin the spring due to or lack autumn of need due resulting to lack from of temperatureneed resulting changes, from therefore,temperature the wholechanges, system’s therefore, reliability the whole is only system’s dependent reliability on the electricityis only dependent and hot water on the subsystem’s electricity reliability.and hot water Even subsystem’s though parts reliability. of the systemEven though are no pa longerrts of the functioning, system are the no restlonger of thefunctioning, system can the continuerest of the to system function. can continue to function.

Customer

FigureFigure 4.4. AA simplesimple customer-orientedcustomer-oriented reliabilityreliability model model of of a a CCHP CCHP system. system.

4.1. Electricity Subsystem 4.1. Electricity Subsystem The subsystem of electricity generation of the CCHP system of KSRP consisted of two generation The subsystem of electricity generation of the CCHP system of KSRP consisted of two generation units, a fuel cell unit (E1) and a gas engine unit (E2). The main components of the electricity subsystem units, a fuel cell unit (E1) and a gas engine unit (E2). The main components of the electricity subsystem of the CCHP system are presented in Table 5. The main components of the fuel cell unit included the of the CCHP system are presented in Table5. The main components of the fuel cell unit included the fuel cell, cooling power1, and cooling pump1. The main components of the gas engine unit included the gas engine, cooling tower2, and cooling pump2. A simplified reliability block diagram of the electricity subsystem of the CCHP system is shown in Figure 5. Generally, the two generation units were regarded as having a parallel relationship, where at least one of them would be functioning, and the system was considered reliable and available. However, when one of the units failed, it caused the electricity supply to be in a lacking state. Thus, the situation where one of the units failed was considered as unavailable or partially available. The reliability of the whole system or a subsystem of the CCHP system was defined as all of the components of the system functioning under given conditions for the stated period. This system, considering customer-oriented reliability, could be described as all subsystems were reliable since the system can be viewed as a series system.

Energies 2018, 11, 1519 11 of 24 fuel cell, cooling power1, and cooling pump1. The main components of the gas engine unit included the gas engine, cooling tower2, and cooling pump2. A simpliﬁed reliability block diagram of the electricity subsystem of the CCHP system is shown in Figure5. Generally, the two generation units were regarded as having a parallel relationship, where at least one of them would be functioning, and the system was considered reliable and available. However, when one of the units failed, it caused the electricity supply to be in a lacking state. Thus, the situation where one of the units failed was considered as unavailable or partially available. The reliability of the whole system or a subsystem of the CCHP system was deﬁned as all of the components of the system functioningEnergies 2018, 11 under, x FOR given PEER conditionsREVIEW for the stated period. This system, considering customer-oriented11 of 25 reliability, could be described as all subsystems were reliable since the system can be viewed as a series system. Table 5. The electricity subsystem of CCHP system. Generation Unit Main Component Function of Electricity Table 5. The electricity subsystem of CCHP system. Produce E1 Fuel cell (FC), Cooling tower1 (CT1), and Cooling pump1 (CP1). Generation Unit of Electricity Main Component Functionelectricity E1 Fuel cell (FC), Cooling tower1 (CT1), and Cooling pump1 (CP1). Produce electricityProduce E2 E2 Gas engineGas engine(GE), (GE),Cooling Cooling tower2 tower2 (CT2), (CT2), and and CoolingCooling pump2 pump2 (CP2). (CP2). Produce electricity electricity

FC CT1 CP1

GE CT2 CP2

Figure 5. The reliability block diagram of an electricity subsystem of the CCHP system. Figure 5. The reliability block diagram of an electricity subsystem of the CCHP system.

Based on reliability analysis methods introduced in Section 3.1, the operation states and Based on reliability analysis methods introduced in Section 3.1, the operation states and reliability reliability data for the electricity subsystem of the CCHP system is shown in Table 6. The operation datastates for of the the electricity electricity subsystem subsystem of theincluded CCHP system4 states, is shownthe completely in Table6 .available The operation state states(State1), of thethe electricitypartially available subsystem states included (State2, 4 states, State3), the and completely the completely available unavailable state (State1), state the (State4). partially The available failure statesrate and (State2, repair State3), rate of and E1, the E2, completely and the subsystems unavailable are state symbolized (State4). The in Table failure 6. rate The and reliability repair rateof the of E1,electricity E2, and subsystem the subsystems was dependent are symbolized on the in reliability Table6. The of State1, reliability thus, of the electricityreliability of subsystem the electricity was dependentsubsystem onwas the determined reliability ofby State1, both E1 thus, and the E2. reliability of the electricity subsystem was determined by both E1 and E2. Table 6. The operation states and reliability data for the electricity subsystem of the CCHP system. Table 6. The operation states and reliability data for the electricity subsystem of the CCHP system. Items E1 E2 Electricity Supply State Reliability Items E1 E2 Electricity Supply State Reliability Failure rate ----

RepairFailure rate rate λE1 λE2 λelectricity —----- Repair rate µ µ µ —- State 1 1 E1 1 E2 E1 + E2electricity State 1 1 1 E1 + E2 RE1RE2 State 2 0 1 E2 (lacking) State 2 0 1 E2 (lacking) RE2 StateState 3 3 1 1 0 0 E1 (lacking) E1 (lacking) RE1 StateState 4 4 0 0 0 0 0 0 0 0

AA seriesseries system’s system’s reliability reliability was was expressed expressed by Equation by Equation (14), thus, (14), the thus, reliability the reliability of E1 is presented of E1 is aspresented follows: as follows: R = R R R (24) E1 =FCCT1 CP1 (24) AA reliabilityreliability cancan bebe expressedexpressed byby thethe failurefailure raterate asas inin thethe followingfollowing equation:equation:

() −λ (t) () = k (25) Rk(t) = Rt (25) Therefore, if the failure rates are constant, then Equation (24) can be expressed as

() = = = (26) Thus, the following equation is obtained from the above equation:

= + + (27) Similarly, the failure rate of E2 is obtained using

= + + (28) Moreover, the availability of the electricity subsystem is equal to the probability of State1, and it also is defined as ⁄ + , therefore, the availability of the electricity subsystem is expressed as

Energies 2018, 11, 1519 12 of 24

Therefore, if the failure rates are constant, then Equation (24) can be expressed as

−λE1 −λFC −λCT1 −λCP1 −(λFC+λCT1+λCP1) RE1 = e = e e e = e (26)

Thus, the following equation is obtained from the above equation:

λE1 = λFC + λCT1 + λCP1 (27)

Similarly, the failure rate of E2 is obtained using

λE2 = λGE + λCT2 + λCP2 (28)

Moreover, the availability of the electricity subsystem is equal to the probability of State1, and it also is deﬁned as µ/λ + µ, therefore, the availability of the electricity subsystem is expressed as

µelectricity µE1µE2 Aelectricity = = (29) λelectricity + µelectricity (λE1 + µE1)(λE2 + µE2)

Therefore, the repair rate of the electricity system is solved as

λelectricityµE1µE2 µelectricity = (30) λE1λE2 + λE1µE2 + λE2µE1

Let rE1 = 1/µE1, rE2 = 1/µE2, relectricity = 1/µelectricity, and then

1 relectricity = (λE1rE1 + λE2rE2 + λE1λE2rE1rE2) (31) λE1 + λE2

Usually, µE1 λE1, µE2 λE1 and then, Equation (32) is written as

1 relectricity ≈ (λE1rE1 + λE2rE2) (32) λE1 + λE2

Thus, the repair rate of the electricity subsystem is obtained by the following:

1 λ + λ µ = = E1 E2 (33) electricity λ λ relecricity E1/µE1 + E2/µE2

Hence, for a series system consisting of n components, the failure rate and repair rate are presented as the following, respectively: n λn = ∑ λk (34) k=1 n ∑k=1 λk µn = (35) n λ ∑k=1 k/µk Thus, the main reliability parameters of E1, E2, and the electricity subsystem are expressed as the following: Failure rate of E1: λE1 = λFC + λCT1 + λCP1 (36) Failure rate of E2: λE2 = λGE + λCT2 + λCP2 (37) Failure rate of electricity subsystem:

λelectricity = λFC + λCT1 + λCP1 + λGE + λCT2 + λCP2 (38) Energies 2018, 11, 1519 13 of 24

Repair rate of E1: λFC + λCT1 + λCP1 µE1 = (39) λFC/µFC + λCT1/µCT1 + λCP1/µCP1 Repair rate of E2: λGE + λCT2 + λCP2 µE2 = (40) λGE/µGE + λCT2/µCT2 + λCP2/µCP2 Repair rate of electricity subsystem:

λFC + λCT1 + λCP1 + λGE + λCT2 + λCP2 µelectricity = (41) λFC/µFC + λCT1/µCT1 + λCP1/µCP1 + λGE/µGE + λCT2/µCT2 + λCP2/µCP2

TheEnergies availability 2018, 11, x ofFOR the PEER electricity REVIEW subsystem: 13 of 25

1 Aelectricity = = (42) λFC µ + λCT1 µ + λCP1 µ + λGE µ + λCT2 µ + λCP2 µ + (42) ( / FC /CT 1 /CP1 / GE / CT2 / CP2) 1 ( + + + + + )+1 The reliabilityThe reliability of the of electricity the electricity subsystem: subsystem:

= = (43) −λelectricity Relectricity = Rs1 = e (43)

4.2. Space Cooling and Heating Subsystem 4.2. Space Cooling and Heating Subsystem The space cooling and heating subsystem of the CCHP system at KSRP consisted of three space Thecooling space and cooling heating and generation heating units, subsystem the generation of the units CCHP that system used the at waste KSRP heat consisted from the fuel of three cell space coolingunit and (CH1), heating and generation the generation units, units thethat generationassisted the absorption units that chiller used fueled thewaste by natural heat gas from (CH2 the fuel cell unitand (CH1), CH3). and More the details generation of the space units cooling that and assisted heating the subsystem absorption are shown chiller in Table fueled 7. The by main natural gas (CH2 andcomponents CH3). Moreof CH1 details included of the the fuel space cell coolingunit (E1), andthe heat heating recovery subsystem steam generator1, are shown and inthe Table 7. absorption chiller1. CH2 and CH3 only had one component, an absorption chiller fueled by natural The main components of CH1 included the fuel cell unit (E1), the heat recovery steam generator1, gas. and the absorptionA simplified chiller1. reliability CH2 block and diagram CH3 only of the had space one cooling component, and heating an absorptionsubsystem of chillerthe CCHP fueled by natural gas.system is shown in Figure 6. The space cooling and heating for customers came from three ways. The A simpliﬁedCH2 and CH3 reliability each used block the same diagram component. of the The space operation cooling states and and heating reliability subsystem data for the of space the CCHP system iscooling shown and in heating Figure subsystem6. The spaceof the CCHP cooling system and are heating presented for in customers Table 8. Due came to CH2 from and three CH3 ways. The CH2only and having CH3 one each component, used the the same failure component. rate and repair The rate operation of CH2 and states CH3 and units reliability were expressed data for the by the component’s failure rate and repair rate. The reliability and availability of the space cooling space cooling and heating subsystem of the CCHP system are presented in Table8. Due to CH2 and and heating subsystem were equal to the reliability and availability of State 1. CH3 only having one component, the failure rate and repair rate of CH2 and CH3 units were expressed by the component’s failureTable rate 7. The and space repair cooling rate. andThe heating reliability subsystem and of the availability CCHP system. of the space cooling and heating subsystem were equal to the reliability and availability of State 1. Generation Unit of Main Equipment Function Cooling and Heating Table 7. The space cooling and heating subsystem of the CCHP system. Fuel cell unit (E1), Heat recovery steam Supply cooling or heating by using CH1 generator1 (HRSG1), Absorption chiller the heat from heat recovery steam Generation Unit of Main Equipment Function Cooling and Heating 1 (AC1). generator 1 Fuel cell unit (E1), Heat recovery steam SupplySupply heating cooling or or cooling heating using by using the heat CH1 CH2 Absorption chiller 2 (AC2). generator1 (HRSG1), Absorption chiller 1 (AC1). naturalfrom heatgas recovery steam generator 1 CH2 Absorption chiller 2 (AC2). Supply heating or cooling using natural gas Supply heating or cooling using CH3 Absorption chiller 3 (AC3). CH3 Absorption chiller 3 (AC3). naturalSupply gas heating or cooling using natural gas

E1 HRSG1 AC1

AC2

AC3

Figure 6. The reliability block diagram of the space cooling and heating subsystem of the CCHP Figure 6. The reliability block diagram of the space cooling and heating subsystem of the CCHP system. system.

Energies 2018, 11, 1519 14 of 24

Table 8. The operation states and reliability data for the space cooling and heating subsystem of the CCHP system.

Items CH1 CH2 CH3 Space Cooling and Heating Supply State Reliability

Failure rate λCHI λAC2 λAC3 λcooling & heating —- Repair rate µCH1 µAC2 µAC3 µcooling & heating —- State 1 1 1 1 CH1 + CH2 + CH3 RCH1RCH2RCH3 State 2 1 0 1 CH1 + CH3 (lacking) RCH1RCH3 State 3 1 1 0 CH1 + CH2 (lacking) RCH1RCH2 State 4 1 0 0 CH1 (lacking) RCH1 State 5 0 1 1 CH2 + CH3 (lacking) RCH2RCH3 State 6 0 1 0 CH2 (lacking) RCH2 State 7 0 0 1 CH3 (lacking) RCH3 State 8 0 0 0 0 0

According to Equations (34) and (35), the main reliability parameters of the CH1 unit and space cooling and heating subsystem are expressed as the following: Failure rate of CH1: λCH1 = λE1 + λHRSG1 + λAC1 (44) Repair rate of CH1: λE1 + λHRSG1 + λAC1 µCH1 = (45) λE1/µE1 + λHRSG1/µHRSG1 + λAC1/µAC1 Failure rate of the space cooling and heating subsystem:

λcooling & heating = λE1 + λHRSG1 + λAC1 + λAC2 + λAC3 (46)

Repair rate of the space cooling and heating subsystem:

λCH1 + λAC2 + λAC3 µcooling & heating = (47) λCH1/µCH1 + λAC2/µAC2 + λAC3/µAC3

The availability of the space cooling and heating subsystem:

1 Acooling & heating = (48) (λCH1/µCH1 + λAC2/µAC2 + λAC3/µAC3) + 1

The reliability of the space cooling and heating subsystem:

−λcooling & heating Rcooling & heating = e (49)

4.3. Hot Water Subsystem The hot water subsystem of the CCHP system at KSRP consisted of three hot water generation units and a heat exchanger unit. The generation unit (HW1) used the recovery heat from E1, the generation unit (HW2) used the recovery heat from E2, and an auxiliary boiler (HW1) fueled by natural gas produced the hot water when the heat from HW1 and HW2 was not enough. A heat exchanger unit (HE) was used to exchange the heat to hot water. More details of the main components of the hot water subsystem are shown in Table9. The main components of HW1 included the fuel cell unit and heat recovery steam generator1. The main components of HW2 included the gas engine unit and heat recovery steam generator2, while HW3 had only one component, the auxiliary boiler. Energies 2018, 11, 1519 15 of 24

Table 9. The hot water subsystem of the CCHP system.

Generation Unit of Hot Water Main Equipment Function Fuel cell unit (E1), Heat recovery steam HW1 Supply heat for hot water from HRSG1 generator 1. (HRSG1) Gas engine unit (E2), Heat recovery steam HW2 Supply heat for hot water from HRSG2. generator 2 (HRSG2). HW3 Auxiliary boiler (AB). Supply heat for hot water using natural gas. HE Heat exchanger (HE). Exchanged the heat for hot water.

A simpliﬁed reliability block diagram of the hot water subsystem of the CCHP system is shown in Figure7. The hot water subsystem was regarded as a series system consisting of the three hot water generation units and a heat exchanger unit. When the heat exchanger unit failed, the hot water supply was interrupted and the hot water subsystem was unavailable. The operation states and reliability data for the hot water subsystem of the CCHP system is shown in Table 10. There were 9 states of the hot water subsystem. The reliability and availability of the hot water subsystem were equal to the reliability and availability of State1. Thus, the main reliability parameters of HW1, HW2, and the hot water subsystem were obtained as follows: Failure rate of HW1: λHW1 = λE1 + λHRSG1 (50) Repair rate of HW1: λE1 + λHRSG1 µHW1 = (51) λE1/µE1 + λHRSG1/µHRSG1 Failure rate of HW2: λHW2 = λE2 + λHRSG2 (52) Repair rate of HW2: λE2 + λHRSG2 µHW2 = (53) λE2/µE2 + λHRSG2/µHRSG2 Failure rate of the hot water subsystem:

λhot water = λHW1 + λHW2 + λAB + λHE (54)

Repair rate of the hot water subsystem:

λHW1 + λHW2 + λAB + λHE µhot water = (55) λHW1/µHW1 + λHW2/µHW2 + λAB/µAB + λHE/λHE Energies 2018, 11, x FOR PEER REVIEW 16 of 25 The availability of the hot water subsystem: 11 A hot water == (56) (λHW1/µ + λHW2/µ + λAB /µ + λHE/λHE ) + 1 (56) ( HW1 + HW2 + AB + )+1 The reliability of the hot water subsystem: The reliability of the hot water subsystem: R = e−λhot water (57) hot water = (57)

E1 HRSG1

E2 HRSG2 HE

Figure 7. The reliability block diagram of the hot water subsystem of the CCHP system. Figure 7. The reliability block diagram of the hot water subsystem of the CCHP system. Table 10. The operation states and reliability data for the hot water subsystem of the CCHP system.

Hot Water Items HW1 HW2 HW3 HE State Reliability Supply

Failure ---- rate

Repair ---- rate

+ State 1 1 1 1 1 +

+ State 2 1 1 0 1 (lacking)

+ State 3 1 0 1 1 (lacking)

+ State 4 0 1 1 1 (lacking)

State 5 1 0 0 1 (lacking)

State 6 0 1 0 1 (lacking)

State 7 0 0 1 1 (lacking) State 8 0 0 0 1 0 0

State 9 1 1 1 0 0 0

5. Numerical Calculation and Discussion The numerical calculation and analysis of the CCHP system at KSRP is discussed in this section. All the base reliability data (failure rate, MTTR and so forth.) were obtained from actual records, such as operation records, maintenance records, repair records, and more.

Energies 2018, 11, 1519 16 of 24

Table 10. The operation states and reliability data for the hot water subsystem of the CCHP system.

Items HW1 HW2 HW3 HE Hot Water Supply State Reliability

Failure rate λHW1 λHW2 λAB λHE λHot water —- Repair rate µHW1 µHW2 µAB µHE µHot water —- State 1 1 1 1 1 HW1 + HW2 + HW3 RHW1RHW2RHW3RHE State 2 1 1 0 1 HW1 + HW2 (lacking) RHW1RHW2RHE State 3 1 0 1 1 HW1 + HW3 (lacking) RHW1RHW3RHE State 4 0 1 1 1 HW2 + HW3 (lacking) RHW2RHW3RHE State 5 1 0 0 1 HW1 (lacking) RHW1RHE ate 6 0 1 0 1 HW2 (lacking) RHW2RHE State 7 0 0 1 1 HW3 (lacking) RHW3RHE State 8 0 0 0 1 0 0 State 9 1 1 1 0 0 0

5.1. Reliability Calculation Based on the actual investigation, the failure rate and MTTR of the main components of the CCHP system at KSRP are shown in Table 11. The failure rate and MTTR were the actual data gathered from inspection and repair records of the CCHP system at KSPR from April 2002 to March 2011. During this investigation, the repair data of the cooling pumps of the cooling water system, the heat recovery steam generators, and the absorption chillers were difﬁcult to separate because the same components were maintained and repaired at the same time, generally. Therefore, the three components assumed the same failure rate and MTTR even though they were in different generation units. The failure rate and MTTR of the tree type components were obtained based on the total number of failures and the number of components. Table 11 shows that the gas engine had the highest failure rate and that the fuel cell had the second highest failure rate, thus, the power generation unit had a higher failure rate than other units. The auxiliary boiler and heat exchanger had the lowest failure rate. The fuel cell and absorption chiller had the highest MTTR in this system. All the reliability data were a true reﬂection of the actual situation of the system under the current operation and maintenance strategies. Each component had an independent maintenance strategy according to the manufacturer’s recommendations.

Table 11. The failure rate and MTTR of the main component of the CCHP system in KSRP.

Failure Rate Main Components Component Symbol MTTR (Days) (Failure/Day) Fuel Cell FC 0.002982 2.0 Cooling tower for fuel cell CT1 0.001210 1.0 Cooling pump for fuel cell CP1 0.001534 1.0 Gas engine GE 0.008037 1.4 Cooling tower for gas engine CT2 0.001143 1.0 Cooling pump for gas engine CP2 0.001534 1.0 Heat recovery steam generator for fuel cell HRSG1 0.001217 1.5 Heat recovery steam generator for gas engine HRSG2 0.001217 1.5 Absorption chiller AC1 to 3 0.005265 2.0 Auxiliary boiler AB 0.000930 1.0 Heat exchanger HE 0.000846 1.0

The reliability and availability of the CCHP system at KSRP was analyzed in Section 3.1. Based on that analysis, the calculation results are present here. The reliability of all components in the CCHP system is shown in Figure8. The reliability of each component was related to failure rate. The reliability of the electricity generator and absorption chiller was lower than other components in this system, and the heat exchanger and auxiliary boiler had the higher reliability. Energies 2018, 11, x FOR PEER REVIEW 17 of 25

gathered from inspection and repair records of the CCHP system at KSPR from April 2002 to March 2011. During this investigation, the repair data of the cooling pumps of the cooling water system, the heat recovery steam generators, and the absorption chillers were difficult to separate because the same components were maintained and repaired at the same time, generally. Therefore, the three components assumed the same failure rate and MTTR even though they were in different generation units. The failure rate and MTTR of the tree type components were obtained based on the total number of failures and the number of components. Table 11 shows that the gas engine had the highest failure rate and that the fuel cell had the second highest failure rate, thus, the power generation unit had a higher failure rate than other units. The auxiliary boiler and heat exchanger had the lowest failure rate. The fuel cell and absorption chiller had the highest MTTR in this system. All the reliability data were a true reflection of the actual situation of the system under the current operation and maintenance strategies. Each component had an independent maintenance strategy according to the manufacturer’s recommendations.

Table 11. The failure rate and MTTR of the main component of the CCHP system in KSRP.

Failure Rate MTTR Main Components Component Symbol (Failure/Day) (Days) Fuel Cell FC 0.002982 2.0 Cooling tower for fuel cell CT1 0.001210 1.0 Cooling pump for fuel cell CP1 0.001534 1.0 Gas engine GE 0.008037 1.4 Cooling tower for gas engine CT2 0.001143 1.0 Cooling pump for gas engine CP2 0.001534 1.0 Heat recovery steam generator for fuel cell HRSG1 0.001217 1.5 Heat recovery steam generator for gas engine HRSG2 0.001217 1.5 Absorption chiller AC1 to 3 0.005265 2.0 Auxiliary boiler AB 0.000930 1.0 Heat exchanger HE 0.000846 1.0

The reliability and availability of the CCHP system at KSRP was analyzed in Section 3.1. Based on that analysis, the calculation results are present here. The reliability of all components in the CCHP system is shown in Figure 8. The reliability of each component was related to failure rate. The reliability of the electricity generator and absorption chiller was lower than other components in this Energiessystem,2018, 11 and, 1519 the heat exchanger and auxiliary boiler had the higher reliability. 17 of 24

FigureFigure 8. The8. The reliability reliability of of all all componentscomponents in in the the CCHP CCHP system. system.

TheEnergies reliabilityThe 2018 reliability, 11, x FOR of thePEERof the electricity, REVIEW electricity, space space cooling cooling andand heating, and and hot hot water water generation generation units18 unitsof are 25 are shownshownEnergies in Figure 2018in Figure, 119, .x FOR Comparing 9. Comparing PEER REVIEW the the reliability reliability of of two two electricity electricity generation generation units, units, the fuel the cell fuel unit18 cell wasof 25 unit higher than the gas engine unit because the gas engine had a higher failure rate than the fuel cell, was higher than the gas engine unit because the gas engine had a higher failure rate than the fuel whilehigher the than cooling the gas water engine system’s unit becausefailure rates the gas were engi similar.ne had The a higher reliability failure of therate space than coolingthe fuel andcell, cell, whileheatingwhile the generation cooling water unit water (CH1) system’s system’s that failure combined failure rates rateswith were the were similar. waste similar. Theheat reliability recovery The reliability ofunit the was space of lower the cooling space than andthe cooling and heatingreliabilityheating generation of the generation unit unit (CH1) (CH1) units, that that which combined combined only withhad with the gas-firedwaste the waste heat absorption recovery heat recovery unitchiller. was unit Comparing lower was than lower thethe than the reliabilitythreereliability hot water ofof thethe generation generation units, units, units, the which reliability which only only of had the had thehot thegas-firedwater gas-ﬁred generation absorption absorption units chiller. (HW1, chiller. Comparing HW2), Comparing which the the threecombinedthree hot hot water waterwith thegeneration generation waste heat units, units, recovery the thereliability unit, reliability were of the lower of hot the water than hot thegeneration water reliability generation units of the(HW1, unitsauxiliary HW2), (HW1, boiler. which HW2), whichFigurescombined combined 10 andwith with 11 the show thewaste wastethe heat reliability heatrecovery recovery and unit, availability were unit, lower were of the than lower subsystems the thanreliability theand reliability theof thewhole auxiliary system. of the boiler. auxiliaryThe boiler.spaceFigures Figures cooling 10 and 10 and 11and heating show 11 theshow system reliability the was reliability more and availability unreliable and availability than of the other subsystems subsystems of the and subsystems because the whole the system. andabsorption the The whole space cooling and heating system was more unreliable than other subsystems because the absorption system.chiller’s The reliability space cooling was lower. and heatingThe results system show wasthat the more reliability unreliable of the than CCHP other system subsystems depended becauseon eachchiller’s component’s reliability reliability was lower. due The to results it being show a series that system. the reliability of the CCHP system depended on the absorption chiller’s reliability was lower. The results show that the reliability of the CCHP system each component’s reliability due to it being a series system. depended on each component’s reliability due to it being a series system.

Figure 9. The reliability of the generation units of the CCHP system. FigureFigure 9. The 9. The reliability reliability of of the the generationgeneration units units of of the the CCHP CCHP system. system.

Figure 10. The reliability of the systems of the CCHP system at KSRP. Figure 10. The reliability of the systems of the CCHP system at KSRP. Figure 10. The reliability of the systems of the CCHP system at KSRP.

Energies 2018, 11, x FOR PEER REVIEW 19 of 25 Energies 2018, 11, 1519 18 of 24 Energies 2018, 11, x FOR PEER REVIEW 19 of 25

Figure 11. The availability of the systems of the CCHP system at KSRP. FigureFigure 11. 11.The The availability availability of of the the systems systems of thethe CCHP CCHP system system at KSRP.at KSRP. 5.2. Component Importance Calculation 5.2. Component5.2. Component Importance Importance Calculation Calculation The Birnbaum importance (BI) and criticality importance (CI) methods were applied in this The BirnbaumThe Birnbaum importance importance (BI) (BI) and and criticality criticality importance (CI) (CI) methods methods were were applied applied in this in this systemsystem to evaluate to evaluate the the subsystem subsystem and and components’ components’ importance importance levels levels over over the the whole whole system system and to and to system to evaluate the subsystem and components’ importance levels over the whole system and to give agive maintenance a maintenance prioritization prioritization of of components components with withinin this this system. system. Simultaneously, Simultaneously, the failure the failure cost cost give a maintenance prioritization of components within this system. Simultaneously, the failure cost importanceimportance index index (FCI) (FCI) described described in in Section Section 3.23.2 was calculated calculated in in this this section, section, and and the results the results of the of the importancefailurefailure cost cost reliabilityindex reliability (FCI) importance described importance arein are Section compared compared 3.2 towasto BIBI calculatedand CI. CI. in this section, and the results of the failureThe cost BIThe reliability values BI values of importance theof the components components are compared of of the the CCHPCCHP to BI system and CI. are are shown shown in inFigure Figure 12. 12The. Themaintenance maintenance prioritizationTheprioritization BI values of the of of componentsthe the components components using using of the the BI BI CCHP values values system isis GEGE > areAC AC shown> > FC FC > >CP2 in CP2 Figure > CP1 > CP1 > 12. HRSG1 > The HRSG1 >maintenance HRSG2 > HRSG2 prioritization> CT1> CT1 > CT2 > CT2 of > the> AB AB components > > HE. The The reliability reliability using the importance importanceBI valu esof theis GE of power the > ACpower generation > FC generation> CP2 unit > and CP1 absorption unit > HRSG1 and absorptionchiller > HRSG2 was higher than the other components. Figure 13 shows the CI values of the components of the CCHP >chiller CT1 > wasCT2 > higher AB > HE. than The the reliability other components. importance Figureof the power 13 shows generation the CI unit values and of absorption the components chiller system. The order of the priority maintenance actions is the same as the BI analysis results. However, wasof the higher CCHP than system. the other The components. order of the Figure priority 13 sh maintenanceows the CI values actions of is the the components same as the of BIthe analysis CCHP system.the The criticality order importanceof the priority of the maintenance gas engine is actions much larger is the than same other as the components, BI analysis for results. instance, However, the results.cooling However, pump, thecooling criticality tower, auxiliary importance boiler, of theheat gas exchanger, engine and is much heat recovery larger than steam other generator. components, the criticality importance of the gas engine is much larger than other components, for instance, the for instance,The failure the cooling cost importance pump, cooling indices tower,were introduced auxiliary in boiler, Section heat 3.2. The exchanger, failure cost and includes heat recovery the cooling pump, cooling tower, auxiliary boiler, heat exchanger, and heat recovery steam generator. steamrepair generator. cost of the failure component and the cost of the outage due to component failure. The cost of TheTheoutage failure failure can costbe cost calculated importance importance by Equationindices indices were were(21), introducedand introduced the outage in in Section Sectiondata of 3.2.3.2electricity,. The The fa failure ilurespace cost costcooling includes includes and the the repairrepairheating, cost cost of of andthe the hotfailure failure water component component due to the componentand and the the cost cost failure of of the the is shownoutage outage in due due Table to to 12.component component The failure failure. failure. of the fuel The The cell cost cost of of outageoutageunit can (E1) bebe led calculatedcalculated to the outage by by Equation ofEquation electricity, (21), (21), space and and the cooling outagethe outageand data heating, data of electricity, and of electricity,hot water. space The coolingspace failure cooling and of the heating, and heating,and hotgas and waterengine hot dueled water to to the the due outage component to the of electricitycomponent failure and is failure shownhot water. is in shown TableSince AC2in12 .Table The and failure AC312. The do of not failure the use fuel waste of cellthe heat, unitfuel cell (E1) their failure can be equated to no added cost of failure. The repair cost of each component is calculated unitled to(E1) the led outage to the of outage electricity, of electricity, space cooling space and cooling heating, and and heating, hot water. and hot The water. failure The of the failure gas engineof the according to the actual data from April 2002 to March 2011. gasled engine to the outage led to the of electricity outage of andelectricity hot water. and Sincehot water. AC2 andSince AC3 AC2 do and not AC3 use wastedo not heat, use theirwaste failure heat, theircan be failure equated can tobe noequated added to cost no a ofdded failure. cost Theof failure. repair The cost repair of each cost component of each component is calculated is calculated according accordingto the actual to the data actual from data April from 2002 April to March 2002 2011.to March 2011.

Figure 12. The BI values of the components of the CCHP system.

Figure 12. The BI values of the components of the CCHP system. Figure 12. The BI values of the components of the CCHP system.

Energies 2018, 11, 1519 19 of 24 Energies 2018, 11, x FOR PEER REVIEW 20 of 25

FigureFigure 13. 13. TheThe CI CI values values of of the the compon componentsents of of the the CCHP CCHP system.

Table 12. The outage data of electricity, space cooling and heating, and hot water due to Table 12. The outage data of electricity, space cooling and heating, and hot water due to component component failure. failure.

OutageOutage Main Component ComponentComponent Symbol Main Component ElectricityElectricity Hot WaterHot Water Heat/CoolingHeat/Cooling Symbol (kWh/day) (kWh/Day) (kWh/Day) (kWh/day) (kWh/Day) (kWh/Day) Fuel Cell FC 4800 2280 2280 CoolingFuel tower Cell for fuel cell FC CT1 4800 4800 2280 2280 2280 2280 CoolingCooling tower pump for for fuel fuel cell cell CT1 CP1 4800 4800 2280 2280 2280 2280 Heat recovery steam generator for fuel cell HRSG1 — 2280 2280 Cooling pumpGas enginefor fuel cell CP1 GE 4800 1600 2280 2520 2280 — Heat recoveryCooling tower steam for gasgenerator engine CT2 1600 2520 — Cooling pump for gas engineHRSG1 CP2 --- 16002280 2520 2280 — Heat recoveryfor steam fuelgenerator cell for gas engine HRSG2 — 2520 — Gas engine GE AC1 1600 — 2520 — --- 2280 Absorption chiller AC2 — — — Cooling tower for gas engine CT2 AC3 1600 — 2520 — --- — Cooling pumpAuxiliary for gas boiler engine CP2 AB 1600 — 2520 463 --- — Heat recoveryHeat steam exchanger generator HE — 5263 — HRSG2 --- 2520 --- for gas engine The failure cost importance index valuesAC1 of the components--- of the CCHP--- system are2280 shown in Figure 14Absorption. The order chiller of prioritized maintenanceAC2 is GE > HRSG2--- > HRSG1--- > FC > AB > HE--- > CT1 > CT2 > CP > AC. The gas engine had the higherAC3 failure cost than--- other components.--- The failure--- cost of the absorptionAuxiliary chiller boiler was lowest in the CCHP AB system. Potential --- failure cost 463 importance index --- values of the componentsHeat exchanger of the CCHP system are HE presented in Figure --- 15. This 5263 result shows the --- potential failure cost before the failure occurred. It presents the importance of the component maintenance from the perspectiveThe failure ofcost operation importance and index maintenance values of costs. the components The order of of prioritized the CCHP maintenance system are shown based onin Figurepotential 14. failure The order cost of importance prioritized index maintenance values is GEis GE > FC> HRSG2 > AC > > HRSG2 HRSG1 > > HRSG1 FC > AB > > CP HE > > CT1 CT1 > > CT2 CT2 > >AB CP > > HE. AC. Comparing The gas engine the failure had the cost higher importance failure co indexst than and other potential components. failure costThe importancefailure cost index,of the absorptionthe gas engine chiller was was the lowest most important in the CCHP component system. Potential of this CCHP failure system. cost importance The reliability index importance values of theof thecomponents fuel cell andof the heat CCHP recovery system steam are generatorpresented werein Figure second 15. in This importance result shows to the the gas potential engine. failureThe difference cost before between the failure the failure occurred. cost importance It presents indexthe importance and the potential of the failurecomponent cost importancemaintenance is fromthat the the failure perspective rate is of considered operation in and the maintenance potential failure costs. cost The importance. order of prioritized The auxiliary maintenance boiler and based heat onexchanger, potential for failure instance, cost hadimportance the highest index failure values cost is GE of one > FC component, > AC > HRSG2 but had > HRSG1 the lowest > CP potential > CT1 > CT2failure > AB cost > HE. due Comparing to the low failurethe failure rate. cost This importance point should index be consideredand potential in failure the system cost importance design and index,maintenance the gas strategies. engine was the most important component of this CCHP system. The reliability importanceThe four of the reliability fuel cell importance and heat recovery indices havesteam been generator applied were in second this system, in importance and the resultsto the gas are engine.presented. The Comparing difference thebetween four reliability the failure importance cost importance indices, theindex BI andand CIthe were potential only related failure to cost the importancefailure rate, is generally, that the failure which canrate beis considered reduced by in improving the potential the maintenancefailure cost importance. level and optimizing The auxiliary the boilermaintenance and heat strategy exchanger, for repairs for instance, of a complex had system.the highest Reducing failure the cost system of one operation component, and maintenancebut had the lowestcosts is potential one of the failure main cost goals due of to maintenance the low failure optimization. rate. This point Thus, should the reliability be considered importance in the system indices design and maintenance strategies.

Energies 2018, 11, x FOR PEER REVIEW 21 of 25 Energies 2018, 11, x FOR PEER REVIEW 21 of 25 The four reliability importance indices have been applied in this system, and the results are The four reliability importance indices have been applied in this system, and the results are presented. Comparing the four reliability importance indices, the BI and CI were only related to the presented. Comparing the four reliability importance indices, the BI and CI were only related to the failure rate, generally, which can be reduced by improving the maintenance level and optimizing the failure rate, generally, which can be reduced by improving the maintenance level and optimizing the maintenance strategy for repairs of a complex system. Reducing the system operation and maintenance strategy for repairs of a complex system. Reducing the system operation and maintenance costs is one of the main goals of maintenance optimization. Thus, the reliability Energiesmaintenance2018, 11, 1519costs is one of the main goals of maintenance optimization. Thus, the reliability20 of 24 importance indices that consider the repair and outage costs were applied to assess the priority of importance indices that consider the repair and outage costs were applied to assess the priority of component maintenance within the system. The failure cost importance index was related to the component maintenance within the system. The failure cost importance index was related to the thatMTTR consider and the the repair repair cost and of outage each costscomponent. were applied The potential to assess failure the priority cost ofimportance component index maintenance was not MTTR and the repair cost of each component. The potential failure cost importance index was not withinonly related the system. to the TheMTTR failure and costrepair importance cost, but indexto the wasfailure related rate. toTherefore, the MTTR the and failure the repair cost importance cost of each only related to the MTTR and repair cost, but to the failure rate. Therefore, the failure cost importance component.and potential The failure potential cost importance failure cost importanceindices can indexprovide was a comprehensive not only related analysis to the MTTR measure and for repair the and potential failure cost importance indices can provide a comprehensive analysis measure for the cost,component but to themaintenance failure rate. optimization Therefore, the. failure cost importance and potential failure cost importance indicescomponent can providemaintenance a comprehensive optimization analysis. measure for the component maintenance optimization.

Figure 14. The failure cost importance index values of components of the CCHP system. Figure 14.14. The failure cost importance indexindex valuesvalues ofof componentscomponents ofof thethe CCHPCCHP system.system.

Figure 15. The potential failure cost importance index values of components ofof thethe CCHPCCHP system.system. Figure 15. The potential failure cost importance index values of components of the CCHP system. 6. Conclusions and Prospects 6. Conclusions and Prospects This paperpaper focusesfocuses onon thethe reliabilityreliability andand availabilityavailability analysisanalysis andand componentscomponents maintenancemaintenance This paper focuses on the reliability and availability analysis and components maintenance prioritizationprioritization analysisanalysis ofof thethe CCHPCCHP system.system. Failure cost importance index (FCI) and potential failure prioritization analysis of the CCHP system. Failure cost importance index (FCI) and potential failure costcost importanceimportance indexindex (PI)(PI) werewere developeddeveloped forfor thethe maintenancemaintenance prioritizationprioritization analysisanalysis ofof thethe CCHPCCHP cost importance index (PI) were developed for the maintenance prioritization analysis of the CCHP system.system. A A Markov model based on a state–space method was used to analyze the reliabilityreliability andand system. A Markov model based on a state–space method was used to analyze the reliability and availability of the the CCHP CCHP system. system. The The reliability reliability and and availability availability of the of thecomponents, components, subsystems, subsystems, and availability of the CCHP system. The reliability and availability of the components, subsystems, and andwhole whole system system were were deduced. deduced. whole system were deduced. This paperpaper aimed aimed at at selecting selecting the the component component reliability reliability importance importance indices indices to identify to identify the priority the This paper aimed at selecting the component reliability importance indices to identify the ofpriority the component of the component maintenance maintenance from the from perspective the perspective of maintenance of maintenance cost. The cost. BI The and BI CI and were CI usedwere priority of the component maintenance from the perspective of maintenance cost. The BI and CI were toused compare to compare to FCI to andFCI and PI. ItPI. was It was observed observed that that the the FCI FCI and and PI PI might might lead lead toto differentdifferent rankings. used to compare to FCI and PI. It was observed that the FCI and PI might lead to different rankings. FCI enabledenabled the the system system managers managers to knowto know the the cost cost of a one-timeof a one-time failure failure of each of component each component in a system. in a FCI enabled the system managers to know the cost of a one-time failure of each component in a PI enabled the system managers to know the cost before the failure occurred for a one-time failure of each component in a system. The two indices would help managers to make a reasonable decision for maintenance on the cost basis, and also help designers to optimize the system on the cost basis. The reliability of the CCHP system is the product of the reliability of each component when the reliability is considered the energy supply. The system reliability can be ensured by improving the Energies 2018, 11, 1519 21 of 24 components’ failure rates. The auxiliary boiler (low failure rate with high failure cost) can improve the reliability of the subsystem. The reliability and availability analysis method is the only study on how one component failure can affect the system as a whole or in part; the reliability of multiple failure states and the time-variances were ignored. Moreover, the CCHP system is a complex and repairable system, generally with high maintenance and reliability, where failure data is difﬁcult to obtain, thus, the degradation data can be used to optimize the maintenance strategy based on the component reliability importance indices. The proposed component reliability importance indices of the maintenance prioritization analysis in this paper can be applied to other cogeneration systems or to other maintenance problems. The reliability importance indices will be further validated in CCHP systems which use renewable energies and other technologies like PV, wind power, or heat pumps.

Author Contributions: J.J. analysis the data and wrote paper; Z.L. contributed materials; X.W., W.G. and S.K. provided revised suggestions and editing. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Abbreviations

Nomenclature CCHP Combined cooling heating and power SSM State-space method KSRP Kitakyushu science and research park R Reliability A Availability U Unavailability P Probability f Number of failure λ Failure rate (f/unit time) µ Repair rate e Napier’s constant MTBF Mean time between failure MTTF Mean time to failure MTTR Mean time to repair t Time u Unit price of grid electricity or city gas Lu Purchases of electricity or city gas I Importance index BI Birnbaum importance CI Criticality importance FCI Failure cost importance index PI Potential failure cost importance index CTF Total failure cost (total cost/unit time) CR Repair cost CA Add cost during outage JPY Japanese yen Subscript sys System k Component number i, j Number of state n Failure numbers of one component in a certain period Energies 2018, 11, 1519 22 of 24

Superscript B Birnbaum importance index C Criticality importance index F Failure cost importance index (cost/f) P Potential failure cost importance index (cost/unit time) Main units and components E Generation unit of electricity CH Generation unit of space cooling and heating HW Generation unit of hot water FC Fuel cell GE Gas engine CT Cooling tower CP Cooling pump HRSG Heat recovery steam generator AC Absorption chiller AB Auxiliary boiler HE Heat exchanger CWS Cooling water system ACS Absorption chiller system

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