CHEMICAL ENGINEERING TRANSACTIONS VOL. 81, 2020 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Qiuwang Wang, Min Zeng, Panos Seferlis, Ting Ma, Jiří J. Klemeš Copyright © 2020, AIDIC Servizi S.r.l. ISBN 978-88-95608-79-2; ISSN 2283-9216 Operation Optimisation of Combined Cooling, Heating and Power Systems Ke Chena, Haoqin Fanga, Jianzhao Zhoua, Yue Lina, Chang Heb, Bingjian Zhangb, Qinglin Chenb, Yi Manc, Ming Pana,* aSchool of Chemical Engineering and Technology, Sun Yat-Sen University, Zhuhai, China bSchool of Materials Science and Engineering, Sun Yat-Sen University, Zhuhai, China cState Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou, China panm5@mail.sysu.edu.cn Improving the overall performance of combined cooling, heating, and power (CCHP) systems have received great attention from both industry and academia. Due to the high amount of nonlinearities involved in detailed CCHP operations, it has to be formulated as a complex nonlinear programming (NLP) model. The existing work usually uses stochastic algorithms, such as the Genetic Algorithm (GA), which in general have difficulty obeying equality constraints for solving large-scale NLP problems. This paper presents an effective deterministic algorithm to satisfy all equality constraints and find optimal solutions in acceptable computation time. A case study has been carried out to compare our method with GA. The solution given by GA has large deviations in the constraints of cooling. Our optimal solution based on the deterministic algorithm can achieve the same energy-saving but satisfies all operational constraints, which demonstrated the validity and efficiency of our proposed method. 1. Introduction A typical combined cooling, heating, and power (CCHP) system consist of a power generator unit (PGU), cooling components, and heating components. PUG consumes fuel to produce electric energy and the heat from exhaust gas (Orre et al., 2018). This exhaust heat splits into two parts, one provides heat to a heating system, and another is utilised to drive chillers (cooling system), converting around 75 % of the fuel source into useful energy. The efficiency of a CCHP system depends on its operations greatly. Operation optimisation has been widely studied for improving CCHP performances. Due to the nonlinearities required for formulating detailed CCHP operations, including the nonlinear coefficients of PGU efficiency and cooling unit efficiency, CCHP operations have to be modelled as a nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) problems, namely nonconvex optimisation. Stochastic and deterministic methods constitute two classes of methods for nonconvex global optimisation (Cho et al., 2014). The stochastic methods such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are often recommended for solving complex nonlinear problems. Ebrahimi et al. (2012) used GA to optimise a CCHP cycle to provide energy to a residential building. They stated that the energy-saving ratios could achieve more than 69 % in summer and 25 % in winter. Wang et al. (2010) employed GA to optimise a building cooling heating and power (BCHP) system to maximise energy saving and environmental impact reduction, where the optimal ratio of electric cooling to cool load balances the relationship between the waste heat and the generated electricity from the PGU. Even many stochastic methods have been reported for optimising CCHP operations, and their main drawback is the difficulty to handle constrained problems as the stochastic search operators frequently produce infeasible solutions. Deterministic approaches generate a sequence of points that converge to a globally optimal solution based on the analytical properties of the problem. Hashemi (2009) proposed an offline (MINLP) model for optimal operation of CCHP systems, and also used LINGO to find optimal energy flow regarding both the amounts of electric, thermal and cooling loads in each time interval and the prices of electricity and utilities. Lu et al. (2015) used the MINLP approach to solve the optimal scheduling DOI: 10.3303/CET2081031 Paper Received: 17/04/2020; Revised: 31/05/2020; Accepted: 31/05/2020 Please cite this article as: Chen K., Fang H., Zhou J., Lin Y., He C., Zhang B., Chen Q., Man Y., Pan M., 2020, Operation Optimisation of Combined Cooling, Heating, and Power Systems, Chemical Engineering Transactions, 81, 181-186 DOI:10.3303/CET2081031 181 problems of energy systems in building integrated with energy generation and thermal energy storage. Their results showed that the strategy could reduce operational energy costs greatly (about 25 %) compared with a rule-based strategy. Based on the above discussion, compared with deterministic methods, stochastic methods are less mathematically complicated, contain randomness in the search procedure, but converge to a solution much slower. This paper presents a deterministic approach for optimising an industrial CCHP problem and compares our method with the most popular stochastic method, namely GA. 2. Problem statement The problem addressed for comparing the GA method and the deterministic method is an industrial problem (Li et al., 2018). It is a CCHP-CHR system composed of a power generator unit (PGU), a PGU heat recovery unit (PGUHRU), a heat pump (HP), a hot water unit (HWU), exchangers, an absorption chiller (AC), and a condensation heat recovery unit (CHRU). As presented in Figure 1, both the electric grid (Egrid) and PGU (Epgu) provide the electricity to the building. The cooling system generates cool air with the use of the HP (Qhp) driven by electricity (Ehp) and the absorption chiller (Qab) driven by the heat from the PGUHRU (Qhre,ab). The heating provided to the building are mainly from the hot water unit (Qhwu) driven by electricity (Ehwu), the heat (Qhwe) exchanged from the PGU heat recovery unit (Qhre,hwe), and the heat (Qch) from the condensation heat recovery unit. The PGUHRU collects the waste heat from PGU jacket water and exhaust gas. CHRU includes two heat exchangers since the energy equality of HP and AC is different, and some low-grade heat (Qex,ch) from AC should be abandoned. The temperatures of CHRU are shown in Table 1. This CCHP-CHR system performs much better than the traditional CCHP system as it utilises the condensation heat from the heat pump and absorption chiller. Figure 1: A CCHP-CHR structure 3. Modelling of the CCHP-CHR system Modelling the CCHP-CHR system includes formulating the energy balance and efficiency in each unit, the relationships among the units, and the satisfactions of energy requirements. The whole system is divided into three sub-systems, an electricity system, a cooling system, and a heating system. And the system planning period consists of several independent time intervals (t). 3.1 Modelling of the electricity system In each operating time interval (t), the electricity from the electric grid (Egrid (t)) and power generation unit (Epgu(t)) provides the electricity to the building (Eload (t)), heat pump (Ehp (t)) and hot water unit (Ehwu (t)), as shown in Figure 1. )()()()()( tEtEtEtEtE hwuhploadgridpgu ++=+ (1) 182 Eq(2) describes that the electricity produced by the power generation unit (Epgu(t)) is affected by the fuel consumption (Fpgu (t)), electricity efficiency (ŋel) and thermal efficiency (ŋth) of the power generator. Thermal efficiency is the energy efficiency of an internal combustion engine, and electricity efficiency is the mechanical efficiency of the generator. thelpgupgu tFtE ηη ⋅⋅= )()( (2) This electricity efficiency (ŋel) and thermal efficiency (ŋth) of the power generator are obtained by polynomial fitting of statistic data from American Society of Heating, Refrigerating and Air-Conditioning Engineers(Wu et al., 2016), shown as Eq(3) and (4). 2 210 pgupguel PLRaPLRaa ++=η (3) 2 210 pgupguth PLRbPLRbb ++=η (4) PLRpgu is the part-load ratio of the power generator, which is defined in Eq(5), where Epgu, rated (t) is the rated capacity of the power generator. )( )( , tE tE PLR ratedpgu pgu pgu = (5) Similar to the power generation unit, the electricity bought from the electric grid (Egrid (t)) is constrained as follows: gridptgridpggridgrid tFtE ,,)()( ηη ⋅⋅= (6) where Fgrid (t) is the fuel consumed by the grid, ŋpg,grid and ŋpt,grid are the power generation efficiency and transmission efficiency of the grid. Since the range of ŋpg,grid and ŋpt, the grid is not very large, they are taken as constant here. As shown in Eq(1), the heat pump and hot water unit also require electric energy. The electricity consumed by the heat pump (Ehp (t)) and hot water unit (Ehwu (t)) is related to their supplying thermal energy (Qhp (t) or Qhwu (t)) and the relevant coefficients (COPhp or COPhwu), as expressed in Eq(7) and Eq(8). hp hp hp COP tQ tE )( )( = (7) hwu hwu hwu COP tQ E )( = (8) 3.2 Modelling of the cooling system As presented in Figure 1, the cooling load of the building (Qload,c (t)) is the sum of the cooling from the absorption chiller (Qab (t)) and heat pump (Qhp (t)). )()()( , tQtQtQ cloadhpab =+ (9) Eq(10) and Eq(11) describe the cooling from the absorption chiller (Qab (t)), where Qhre,ab (t) is a part of the heat recovered from the power generator and used to drive the absorption chiller, COPab is the cooling coefficient of the absorption chiller simulated by polynomial fitting, c is the coefficient of the formulation of COPab, and PLRab is the part-load ratio of the absorption chiller similar to Eq(5). ababhreab COPtQtQ ⋅= )()( , (10) 3 3 2 210 abababab PLRcPLRcPLRccCOP +++= (11) In order to determine the heat recovered from the power generator to drive the absorption chiller (Qhre,ab (t)), the heat recovered from the power generator (Qhre (t)) must be calculated as follows: hrethpguhre tFtQ ηη ⋅−⋅= )1()()( (12) where ŋhre is the efficiency of the heat recovery unit which represents the heat loss of the recovered heat from PGU, Fgrid (t)·(1- ŋth) means the waste heat recovered from the power generator. The part of recovered heat of power generator used to drive the absorption chiller (Qhre,ab (t) in Eq(10) can be expressed in Eq(13). α(t) is the ratio of recovered heat from the power generator sent to the absorption chiller. 183 )()()(, tQttQ hreabhre ⋅= α (13) 3.3 Modelling of the heating system The energy balance of the heating system in Figure 1 shows that the sum of the hot water load of the building (Qload,hw(t)) and the waste heat from the condensation heat recovery unit (Qex,ch (t)) is equal to the summation of a part of heat recovered from the power generator to produce hot water (Qhwe (t)), the heat from hot water unit (Qhwu), and the heat recovered from the condensation heat recovery unit (Qch (t)). Qex,ab (t) is not included since it is represented in the energy balance of absorption chiller. Qex,ch (t) means part of low-grade condensation heat(Qch (t)) is abandoned. )()()()()( ,, tQtQtQtQtQ chexhwloadchhwuhwe +=++ (14) First, the heat recovered from a power generator to produce hot water (Qhwe (t)) can be presented as: hwehrehwe tQttQ ηα ⋅⋅−= )())(1()( (15) where (1-α(t))·Qhre (t) means the heat from the power generator which is sent to the hot water heat exchanger, and ŋhwe is the efficiency of the hot water heat exchanger. Second, the heat recovered from the condensation heat recovery unit (Qch (t)) is from the condensation heat from heat pump (Qhp,ch (t)) and the condensation heat from absorption chiller (Qab,ch (t)). ŋchr is the efficiency of the condensation heat recovery unit. ))()(()( ,, tQtQtQ chabchhpchrch +⋅=η (16) Since the energy produced by refrigerant condensation and evaporation are similar, the cooling produced by heat pump (Qch (t)) is equal to the heat it generates (Qhp,ch(t)), as shown in Eq(17). )()(, tQtQ hpchhp = (17) The condensation heat from the absorption chiller (Qab,ch (t)) is calculated in Eq(18), where Qab (t) is the cooling from the absorption chiller, Qhre,ab (t) is the heat recovered from the power generator to drive the absorption chiller, and Qex,ab (t) is the waste heat disposed of by the absorption chiller. Qab (t) and Qhre,ab (t) represent the external heat supply while Qab,ch (t) and Qex,ab (t) represent where the heat going. )()()()( ,,, tQtQtQtQ abexabhreabchab −+= (18) In the condensation heat recovery unit, cool water is preheated by the low grade heat recovered from the absorption chiller (Qab,ch (t) ·ŋchr) in the first condensation heat exchanger, and then enters the second condensation heat exchanger to exchange energy with the high grade energy recovered from the PGU (Qhwe (t)) and heat pump (Qhp,ch (t) ·ŋchr). Since the heat exchanged capacity of high-grade energy is stronger than that of the low grade, Eq(19) is given: chabhw hwechrchhp wchab chrchab TT tQtQ TT tQ , , , , )()()( − +⋅ ≤ − ⋅ ηη (19) where Tab,ch is the temperature of condensation water from absorption chiller, Tw is the environmental water temperature, and Thw is the hot water temperature in the building. 3.4 Objective function The objective of the optimal operation of CCHP-CHR systems is to minimise the total energy consumption, as shown in Eq(20). )()( tFtFMin gridpgu + (20) The deterministic model for optimising CCHP-CHR operation consists of the objective function given in Eq(20) and the constraints given from Eqs(1) - (19). It can be noted that the CCHP-CHR operation addressed is featured by many nonlinearities, such as Eqs(2) - (4), Eq(6), Eqs(10) - (13), Eq(15) and Eq(19). 4. Case study In case studies, the stochastic method (GA) and the deterministic method are used to find the optimal operational solutions of the CCHP-CHR. GA is based on biological evolution and uses three basic operators (selection, crossover, and mutation) to search for the global optimal solution. GA will search the optimal set- 184 point of the PGU and cooling ratio, while the other variables are calculated through energy balance until the convergent condition is reached or the maximum number of iteration is achieved. GA usually uses penalty function to solve the problem with constraints. Even the value of the penalty function is small, and the error could be intolerable in this case since the errors are enlarged after calculation. The number of evolutionary generations here was 500, and the population size was 50. Our method employs branch-and-cut methods to break an NLP model down into a list of subproblems. Each subproblem is analysed and either a) is shown to not have a feasible or optimal solution, or b) an optimal solution to the subproblem is found, e.g., because the subproblem is shown to be convex, or c) the subproblem is further split into two or more subproblems which are then placed on the list. Given appropriate tolerances, after a finite, though a possibly large number of steps a solution provably global optimal to tolerances is returned. The CCHP-CHR parameters are shown in Table 1. Table 1: The CCHP-CHR parameters Parameters Symbol Value Parameters Symbol Value Coefficients of electrical efficiency a0 0.03998 Cool water temperature Tw 15 oC a1 0.7597 The temperature of condensation water from the absorption chiller Tab,ch 31 oC a2 -0.5147 Hot water temperature Thw 45 oC Coefficients of thermal efficiency b0 0.7361 The efficiency of power generation ŋpg,grid 0.35 b1 0.3016 The efficiency of power transmission ŋpt,grid 0.92 b2 -0.1193 Peak value Electricity price /¥/(kWh) (8:00 - 10:00, 18:00 - 23:00) 1.346 Coefficients of absorption chiller c0 0.425 Flat value Electricity price /¥/(kWh) (7:00 - 8:00, 11:00 - 17:00) 0.9 c1 1.683 Valley value Electricity price /¥/(kWh) (1:00 - 6:00, 23:00 - 24:00) 0.475 c2 -2.419 Gas price /¥/(kWh) 0.315 c3 1.108 Rate capacity of the grid (kW) Egrid,rc 50 COP of heat pump COPhwu 4.43 Rate capacity of PGU (kW) Epgu,rc 100 Waste heat recovery unit efficiency ŋhre 0.8 Rate capacity of absorption chiller (kW) Qab,rc 104 Condensation heat recovery efficiency ŋchr 0.96 Rate capacity of a heat pump (kW) Qhp,rc 115 Heat exchanger efficiency ŋhex 0.96 Rate capacity of hot water unit (kW) Qhwu,rc 92 Figure 2: Optimal results of CCHP-CHR obtained by our method Table 2 presents a comparison of the optimal solutions obtained by GA and our method. It can be found that GA gives a solution with minor errors, as Qhre,hwe(t)+Qhre,ab(t) is larger than Qhre(t) in the time intervals 9, 15, 17 - 21, which does not satisfy the constraint that the waste heat recovered from the PGU is the only heat source providing to the absorption chiller and hot water heat exchanger (Figure 1). The solution obtained by the proposed method is under all operational constraints in the CCHP-CHR system, and achieves the same objective values as the GA. Worth to be mentioned, the solve time of the proposed method is no more than 3 seconds while GA spends much more time than it. Figure 2 expresses our optimal results of the energy balances between the suppliers and consumers in electricity dispatching, cooling dispatching, and hot water dispatching. In electricity dispatching, electricity from grid and PGU is supplied to a heat pump, hot water unit and the electricity load of the building. The cooling load of the building is supported by the absorption chiller and heat pump in cooling balance. The energy balance in a heating system is that the recovered heat from 185 PGU, heat produced by hot water unit, the condensation heat from absorption chiller and heat pump is equal to the heat load of the building and excrescent heat. The CCHP-CHR uses the condensation heat from the heat pump and absorption chiller to provide building hot water in most of the time intervals (Figure 1), and reduces the overall energy saving and cost-efficiently. Table 2: Comparison of GA and our method Genetic Algorithm (GA) method Our method Energy- saving (%) 21.44 21.40 Time t (hour) Qhre,hwe(t) Qhre,ab(t) Qhre,hwe(t)+Qhre,ab(t) Qhre(t) Qhre,hwe(t) Qhre,ab(t) Qhre,hwe(t)+ Qhre,ab(t) Qhre(t) 9 83.47 47.14 130.61 122.57 75.43 47.14 122.57 122.57 15 18.73 130.49 149.22 146.03 9.57 130.49 140.06 140.06 17 35.16 108.19 163.61 155.77 31.83 127.41 159.24 159.24 18 25.15 95.99 155.64 151.91 21.73 130.30 152.03 152.03 19 11.68 57.84 133.63 126.73 7.82 119.57 127.39 127.39 20 9.51 57.46 125.82 119.28 5.87 113.89 119.75 119.75 21 9.23 58.26 110.32 104.89 6.11 98.97 105.08 105.08 5. Conclusions Due to the strongly nonlinear nature of the combined cooling, heating, and power (CCHP) operations, their optimisation problems are usually formulated as a nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP). Many stochastic methods based on Genetic Algorithm (GA) have been reported for optimising the CCHP operations. However, the stochastic methods use stochastic search operators and may fail to find feasible solutions for large scale problems as the searching space of the stochastic algorithm increases significantly. Taking advantage of the recent development of the deterministic method, this paper presents a rigours nonlinear programming model for CCHP-CHR. A detailed comparison of GA and our deterministic method has been carried out in an industrial case, where GA solutions showed some deviations from the system operations, while our solutions can obey all operational constraints completely. The two methods can achieve the same level of energy-saving ratio, which are 21.44 % and 21.40 %, while our method can find the optimal solution in a relatively computing time (no more than 3 s). 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