Analysis of simplified CCHP users and energy-matching relations between system provision and user demands

Applied Thermal Engineering 152 (2019) 532–542

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Analysis of simplified CCHP users and energy-matching relations between system provision and user demands Lejun Fenga, Xiaoye Daib, Junrong Moa, Lin Shia,

T

⁎

a

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China b Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

H I GH L IG H T S

demands of users were simplified and its mathematical models were established. • Load load matching parameters and matching map were proposed. • Dimensionless types matching relations were established based on two capacity design modes. • 53 of the load and time-related parameters to matching relations were discussed. • Effect • Two capacity design modes for the three categories of CCHP users were compared.

A R T I C LE I N FO

A B S T R A C T

Keywords: Combined cooling, heating and power Energy-matching relations Load-matching map Capacity design methods Energy saving rate

Albeit numerous studies discussing manifold issues of combined cooling, heating and power (CCHP) systems, theoretical studies are still lack to indicate the energy-matching relations between system provision and user demands, and deficiency of research quantifying the influence of the key equipment capacities to energy saving rate (ESR) of systems. Therefore, in this research, theoretical discussions have been undertaken about the energy-matching relations. Comprehensive mathematical models of the load demands of users are established based on the simplified square wave demands, and three categories CCHP users are categorised based on the time-related parameters. Subsequently, according to the proposed dimensionless load-matching parameters, a load-matching map is drawn and 53 types load-matching relations for the three categories users are constructed based on two different capacity design methods. The research results indicate that “priority to providing electricity” method is a better choice to design the capacity of the CCHP systems for most load-matching relations and the users with smaller ratio of “mount load” to “valley load” and shorter synchronisation difference time between electricity and thermal energy will contribute higher ESR of CCHP systems.

1. Introduction As a kind of energy supply mode close to users, combined cooling, heating, and power systems (CCHP) have drawn increasing attention owing to its advantages of economy, environmental friendliness, and fuel consumption reduction by 10 – 20% when generating equivalent loads compared with traditional energy systems [1–3]. In practice, it is still debatable whether CCHP systems can replace all the traditional separated systems owing to their unsuccessful designs, failures in parameter settings, or deficiency in installation for user assess [4]. Therein, the fluctuation load demands of users, especially the unsynchronized demands of electricity and thermal energy, will often lead

⁎

to the energy mismatch between the supply from CCHP systems and the demand of CCHP users. A proper capacity design method [5,6], a suitable operating strategy [3,7–9] and the application of the energy storage system [10,11] will benefit the CCHP system performance. For example, Mago et al. [3,12,13] developed a CCHP operating model that follows the electrical or thermal load and compared the system performance for general offices in four different climate regions in US. Wang et al. [14] compared the performance of the CCHP systems with different operate strategies for four commercial building categories (hotels, offices, hospitals, and schools) in five climate zones in China. Zhai et al. [15] reviewed energy storage technologies for residents and also indicated that proper use of energy storage systems may greatly

Corresponding author. E-mail address: [email protected] (L. Shi).

https://doi.org/10.1016/j.applthermaleng.2019.02.098 Received 6 December 2018; Received in revised form 15 February 2019; Accepted 19 February 2019 Available online 22 February 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature C COP F f H k L l R P Q

E, EC

proportion of electricity ratio between EC system and CCHP systems H, EC proportion of thermal energy ratio between EC system and CCHP systems grid, buy electric load bought from the grid H heating HX heat exchanger nom nominal PGU power generation unit rec heat recovery system r actual reported energy consumption ab adjusted baseline energy use max average mount load min average valley load

cooling load coefficient of absorption chiller performance fuel part load factor heating load ratio of average “mount load” to average “valley load” dimensionless load operation line of CCHP systems thermal energy to electricity ratio electricity thermal energy

Abbreviations Superscripts AC CCHP ESR EC FEL HRS HX PGU PPE PPT

absorption chiller combined cooling, heating, and power energy saving rate electric chiller following the electric load heat recovery system heat exchanger power generation unit priority to providing electricity priority to providing thermal

user CCHP nom Variables

Cuser cooling demand of users Huser heating demand of users QCuser corresponding thermal demands for cooling of users QHuser corresponding thermal demands for heating of users Quser thermal demands of users hourly electricity demands Piuser Qiuser hourly thermal demands user daily electricity demands Pday user Qday daily thermal demands LE,max,i /LQ,max,i dimensionless load demands of “mount load” LE,min,i /LQ,min,i dimensionless load demands of “valley load” user Pmax average “mount load” of electricity user Qmax average “mount load” of thermal energy user Pmin average “valley load” of electricity user Qmin average “valley load” of thermal energy PCCHP electricity produced by CCHP systems QCCHP thermal energy produced by CCHP systems CCHP redundant electricity produced by CCHP systems Pexcess CCHP Qexcess redundant thermal energy produced by CCHP systems CCHP PEC redundant electricity that used to produced cooling by electric chiller CCHP QEC thermal energy that produced by electric chiller QCCCHP exhaust thermal energy that used by absorption chiller QHCCHP exhaust thermal energy that used by heat exchanger CCHP Pcap install capacity of PGU CCHP Qcap install capacity of HRS

Symbols ξ η λ μ φ τ

factor that accounts for PGU energy losses before the heat recovery system efficiency proportion of thermal demands for corresponding cooling demand of users relationship between load ratio of the users to the rated output of the systems synchronisation differences in electric and thermal demand time the mount load duration time

Subscripts AC Boiler C cap E excess EC

users CCHP systems nominal electrical generation efficiency of the PGU

absorption chiller supplementary boiler cooling capacity of the key components electricity excess electricity or thermal energy electric chiller

providing electricity” (PPE) and ‘‘priority to providing thermal” (PPT) are two practical capacity design modes [11,24,25]. Cardona et al. [24] used the maximum rectangle method to size the prime mover by considering a constraint on the primary energy saving as the primary criteria and using the following thermal load strategy. Ehyaei et al. [25] determined the size and number of micro gas turbines to follow the thermal load of a residential building in Tehran. Additionally, some optimisation methods were applied to obtain the optimum design capacity [26–28], e.g., genetic algorithm [27], self-adaptive learning charged system search algorithm [26], and heuristic and deterministic optimisation algorithm [26,28]. However, the case studies or the “black box” of the optimisation methods will limited to a certain loadmatching relation and will not suitable to another. Hence, a quantitative analysis in capacity design method is required for various load-

reduce the energy consumption and increase the energy savings. Jiang et al. [16] compared the energy saving rate (ESR) of CCHP systems when the energy storage units in different location. However, most of the literatures were focused on the case studies, especially the study of the load demands of users, such as hospitals [17], hotels [14,18], residential buildings [19,20], and office buildings [21–23], whose loads data are mostly based on simulation results from software, like DeST and Energyplus. Indeed, onsite data are far more complex than their simulation counterparts. Therefore, comprehensive models for CCHP users are still in pressing need and the quantitative analysis of the loadmatching relations for different categories CCHP users is urgent needed to fill the study void in CCHP systems. Meanwhile, the sizing of a prime mover is the most important parameter after selecting the type of prime mover [5,6]. “Priority to 533

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mount load: LE,i ⩾ 4.17%, LQ,i ⩾ 4.17% valley load: LE,i < 4.17%, LQ,i < 4.17%

matching relations to guide the system design. In this research, the load-related and time-related parameters are proposed to simplify the load variations in a typical day, and the comprehensive mathematical models of the load demands are established. Subsequently, the load-matching parameters and maps are proposed and drawn to express the load-matching performance quantitatively, and different types of matching-relations between the CCHP systems and users are discussed based the matching map. Finally, to select suitable users for CCHP systems, the effects of the load and timerelated parameters to different matching relations are discussed. Moreover, two capacity design modes for different categories CCHP users are compared to guide the system design for different matching situations.

As the office in Beijing as example, as shown in Fig. 1b, the dimensionless thermal and electric demands in 8:00–20:00 are greater than 4.17%, and the loads during this period are “mount load”, and the else time are the “valley load”. (iii) Simplification of “mount load” and “valley load” The “mount load” and “valley load” demands can be simplified as time-averaging values, as calculated in Eq. (6):

2. Methods for simplifying CCHP users and load demand model 2.1. Methods for simplifying CCHP users

A dimensionless parameter, L, which is defined as the ratio of hourly load to daily load. The hourly dimensionless electric and thermal energy are defined as LE,i and LQ,i, respectively, as shown in Eq. (2). The average ratio, Laver, in a typical day is a constant value of 4.17%, as calculated in Eq. (4). The dimensionless load demands of the office are shown in Fig. 1b.

∑ LE,i = ∑ LQ,i = 1(i = 0, 1, 2, ...23) i

Laver =

i

∑i LE,i 24

=

∑i LQ,i 24

= 4.17%(i = 0, 1, 2, ...23)

user Qmax =

∑ LQ,max,i

user valley load: Pmin =

∑ LE,min,i user ·Pday , 24 − τ E

user Qmin =

∑ LQ,min,i

τQ 24 − τQ

user ·Qday

user ·Qday

(6)

The users typically have “mount load” demands in the daytime and “valley load” demands at night or early in the morning. However, the “mount load” or “valley load” demands of electric and thermal load demands are unsynchronised; thus, the parameter φ is proposed to measure the synchronisation differences in the electric and thermal demands. The sign of φ is defined as follows: the mount load starting at an unsynchronised time is φ1, and the valley load disappearing at an unsynchronised time is φ2, as shown in Fig. 1c. To illustrate the numerical relationship between the mount and valley loads, another two load-related parameters are proposed: kE and kQ, as calculated in Eq. (7), representing the ratio of the average ‘‘mount load” to the ‘‘valley load” for electricity and thermal demands, respectively.

(1)

(i) Dimensionless load demands

Q user Piuser , LQ,i = iuser (i = 0, 1, 2, ...23) user Pday Qday

∑ LE,max,i user ·Pday , τE

2.2. Time-related and Load-related parameters of users in a typical day

Despite some fluctuations, the energy demands of CCHP users are relatively stable in certain periods of the day. Hence, in order to obtain the comprehensive mathematical models of CCHP users, the load demands in a typical day are simplified as square waves, and the process of simplification can be divided into three steps:

LE,i =

user mount load: Pmax =

where τE and τQ are proposed to quantify the “mount load” durations of electricity and thermal demands, respectively. The simplified load demands of the office are shown in Fig. 1c.

The load demands in a typical day show apparent “peak load” and “valley load,” e.g. the typical day load demands for an office in Beijing, as shown in Fig. 1a. The thermal demands of users are written as Eq. (1), which considered both the cooling and heating demands of users.

Quser = QCuser + QHuser = λQuser + (1 − λ ) Quser (QCuser = C user / COPAC, QHuser = H user / ηHX , λ = QCuser / Quser )

(5)

kE =

user Pmax Q user , kQ = max user user Pmin Qmin

(7)

2.3. Comprehensive mathematical models of users in a typical day

(2)

Based on the simplified square wave load demands and the time and load-related parameters, the comprehensive mathematical models of the hourly and daily electricity and thermal load demands are summarized in Eqs. (8) and (9), respectively.

(3)

(4)

{

1

( ) − tan ( ( ) − tan (

Piuser = (kE − 1)· π ·⎡tan−1 ⎣

(ii) Defining of the “mount load” and “valley load”

{

1

Qiuser = (kQ − 1)· π ·⎡tan−1 ⎣

i − i0 δ

i − i 0 − φ1 δ

−1 i − i 0 − τ E δ

) ⎤⎦ + 1} P ) ⎤⎦ + 1} Q

−1 i − i 0 + φ2 δ

user min user min

(8)

Fig. 1. Load demands of an office in Beijing in a typical day (a), dimensionless load demands (b), and simplified square wave load demands (c). 534

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The corrected pressure ratioπ̇c and efficiency characteristicsη̇c are defined as Eqs. (10) and (11), respectively.

(9)

where δ equals to 0.001 and i0 is the instantaneous time when the average “mount load” of the electricity starts to be demanded in a typical day.

2 π̇c = c1 (ṅc ) Gċ + c2 (ṅc ) Gċ + c3 (ṅc )

(10)

ηċ = [1 − c4 (1 − ṅc )2](ṅc / Gċ )(2 − ṅc / Gċ )

(11)

where:

3. Assumptions, system description, and energy-matching performance

π̇c = πc/ πc0, Gċ = G¯c/ G¯c0, G¯c =

Gc T1 p1

, ṅc =

n¯ c , n¯ c0

n¯ c =

nc T1

, ηċ = ηc / ηc0

c1 = ṅc /[p (1 − m / ṅc) + ṅc (ṅc − m)2]

3.1. Assumptions

c2 = (p − 2mnċ 2)/[p (1 − m / ṅc) + ṅc (ṅc − m)2] Assumption 1: If the thermal demand exceeds system’s provision, the exhaust thermal energy of the power generation unit (PGU) is prioritised to satisfy the heating demand; Assumption 2: The load-related parameters for electricity and thermal demands are equal (kE = kQ); Assumption 3: The proportions of thermal energy for the corresponding cooling demand for the average “mount load” and “valley load” are equal; Assumption 4: The system is operated in the FEL (following the electric load) operation strategy.

c3 = −(pmṅc − m2nċ 3)/[p (1 − m / ṅc) + ṅc (ṅc − m)2] (12) where c4 is undetermined constants, commonly c4 = 0.3, m and p are constants equal to 1.8, respectively. Gc, T1, p1 and nc are the mass flow rate, inlet temperature, inlet pressure, and rotating speed of the compressor, respectively. (ii) Performance of turbine The mass flow characteristics of turbine is defined as

3.2. System description

Gt / Gt0 = α T30/ T3 · (πt2 − 1)/(πt02 − 1)

Fig. 2 illustrates a typical type of CCHP systems with a hybrid chiller. The systems can be divided into two parts: (i) the co-generation part that is composed of a PGU, AC (absorption chiller) system, and heat exchanger (HX); (ii) the auxiliary part that comprises the grid and a supplementary boiler. Fuel (FPGU) is supplied to the PGU to generate electricity, and the exhaust gas from the PGU is recovered by the heat recovery system (HRS), thus driving the AC to provide cooling or the HX to provide heating. For some cases, the energy produced by the CCHP systems is insufficient to satisfy the user demand. In this case, the shortage in electricity or cooling, and the heating energy are compensated by the grid through an EC (electric chiller) or a supplementary boiler, respectively. For cases when the CCHP systems provides more electricity than required, we assume that the extra electricity cannot be returned to the grid.

(13)

where Gt, T3 and πt are refer to the mass flow, inlet temperature and the expansion ratio of the turbine; and α = 1.4 − 0.4n t / nt0 is adopted to consider the influence of rotating speed. nt refers to the rotating speed of the turbine and nt = nc. The efficiency characteristic of turbine is defined as

ηṫ = [1 − t4 (1 − ṅt )2](ṅt / Gṫ )(2 − ṅt / Gṫ )

(14)

where:

Gṫ = G¯t / G¯t0, G¯t =

Gt T3 n¯ nt , ηṫ = ηt / ηt0 , ṅt = t , n¯ t = p3 n¯ t0 T3

(15)

where t4 is constant equal to 0.3. (ii) Performance of recuperator

3.3. Thermodynamic models The recuperator effectiveness is defined as 3.3.1. Microturbine model The microturbine comprises compressor, combustor, turbine and recuperator. The analysis of the microturbine off-design performance is based on analytical solutions described in [29].

σ = σ0/[σ0 + (1 − σ0 )(G / G0 )0.2]

(16)

The electrical generation efficiency of the microturbine operating under part loads is shown in Eq. (17): nom ηPGU = (4.8f − 14.02f 2 + 23.88f 3 − 20.412f 4 + 6.752f 5 ) ηPGU

(i) Performance of compressor

Fig. 2. Schematic of the CCHP systems based on a hybrid chiller. 535

(17)

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f =

P CCHP CCHP Pcap

αH =

(18)

nom ηPGU is

Q CCHP Quser Q boiler Q , αboiler = CCHP , αH,excess = excess , αH,EC = EC CCHP CCHP Q Q Q QCCHP

(28)

where the nominal electrical generation efficiency of the microturbine, and can be calculated in Eq. (19) for different capacity.

According to Eqs. (27) and (28), the relationship between αE and αH is expressed as in Eq. (29):

nom CCHP ηPGU = 0.04049 ln(Pcap ) − 0.0687

αH Ruser = CCHP Ruser = αE R

(19)

(

(20)

αH,cap =

n

m ⎞ ΔTin − ΔTout κ = κD ⎛ , ΔTm = ΔT ln ΔT in ⎝ mD ⎠ out ⎜

RCCHP =

QCCHP P CCHP

)

(29)

The matching parameters αE,cap and αH,cap are now introduced to represent the ratios of thermal and electricity demands to the capacity of the PGU and HRS, respectively.

3.3.2. HRS model The heat transfer rate of the HRS can be calculated with the following equation

QCCHP = κF ΔTm

Quser , Puser

Quser P user , αE,cap = CCHP CCHP Qcap Pcap

(30)

⎟

Similarly, the relationship between αE,cap and αH,cap is expressed in Eq. (31):

(21)

where n represents a constant related to the structure of the heat exchanger, and its value is 0.4. ΔTin and ΔTout represent the inlet and outlet temperature differences between hot and cold streams, respectively. The inlet and outlet temperature of the HRS are 286–342 °C and 256–312 °C, respectively.

μuser =

αH,cap αE,cap

=

Ruser ⎛ nom RCCHP = nom RCCHP ⎝

CCHP Qcap CCHP Pcap

⎞ ⎠

(31)

Comprehensively, five dimensionless parameters αE, αH, αE,cap, αH,cap, and μuser can be used to express the matching relations. Therein, αE and αH measure the amount of bought or redundant electricity and thermal energy, respectively; αE,cap and αH,cap determine the off-design operation condition of the systems in different strategies; μuser is a crucial parameter used to reflect the load demand characteristic of users.

3.3.3. Absorption chiller model The detailed assumptions and analysis of energy conversion for the double-effect absorption chiller have been given in [30], and the COP of the double-effect absorption chiller is 1.2–1.4. 3.4. Energy balances

3.5.2. Load-matching map To obtain a direct insight into the energy-matching performance between CCHP systems and users, a dimensionless load-matching map is drawn based on the matching parameters proposed in Section 3.5.1, as shown in Fig. 3. The map is divided into nine different regions based on the magnitude of electric and thermal loads. The x-axis represents the non-dimensional electric load, which is denoted by the parameter αE,cap, while the y-axis represents the non-dimensional thermal load, which is denoted by the parameter αH,cap. The lower bounds of αE,cap and αH,cap are 0.2 and 0.415 for a micro gas turbine, respectively. The load demands are located in regions (1)–(9) and the curve lCCHP represents the provision relationship between the thermal and electric load, and the detailed load demands characteristics are summarized in Table 1. Moreover, the load demands can be expressed by the dimensionless parameter μuser, which is represented by the slope (tan θ) of the load points (tan θ = μuser). For example, the value of μuser is equal to 1 for the load point O2 (1, 1), whose electricity and thermal energy demand is equal to the system’s rated capacity. Hence, according to μuser = 1, these nine matching regions in the map can be divided into two zones: μuser > 1 zone (above lAB) and μuser < 1 zone (below lAB).

The energy balance for the systems is expressed as follows: user > P CCHP → P user = P CCHP + P grid,buy ⎧P CCHP CCHP ⎨ P user < P CCHP → P user = P CCHP − ω·PEC − Pexcess ⎩ Thermal energy balance

Electricity balance

CCHP user > QCCHP → Quser = QCCHP + Q boiler + ω · QEC ⎧Q CCHP user CCHP user CCHP ⎨Q
(22) where w = 1 when redundant electricity is produced, and w = 0 CCHP are summarised in Eqs. otherwise. The calculations of QCCHP and QEC (23) and (24):

QCCHP = P CCHP/ ηpgu ·(1 − ηpgu ) ξηrec = QCCCHP + QHCCHP

(23)

CCHP CCHP CCHP QEC = CEC / COPAC = PEC ·COPEC/ COPAC

(24)

where the values of COPEC [14], ηHX [3], and ξ [3,12,13] are 4, 0.8, and 0.9, respectively. 3.5. Dimensionless load-matching parameters and map 3.5.1. Dimensionless load-matching parameters Dividing PCCHP and QCCHP in Eq. (22) for the electricity and thermal energy balance, respectively, the energy balance can be rewritten as:

⎧ αE > 1 → αE = 1 + αgrid,buy ⎨ ⎩ αE < 1 → αE = 1 − ω·αE,EC − αE,excess

(25)

⎧ αH > 1 → αH = 1 + ω·αH,EC + αboiler ⎨ ⎩ αH < 1 → αH = 1 − αH,excess

(26)

These dimensionless load-matching parameters in Eqs. (25) and (26) can be calculated by Eqs. (27) and (28):

αE =

Pgrid,buy P CCHP P user P , αgrid,buy = CCHP , αE,excess = excess , αE,EC = EC P CCHP P P CCHP P CCHP

Fig. 3. Dimensionless load-matching map between CCHP systems and users.

(27) 536

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Table 1 Load-matching ranges and the corresponding operation strategies in different regions for the load-matching map. Zone

Region

Non-dimensional Loads demand

Operation strategy

>1

(1 ) (2) (3) (4) (5UB) (8UB) (9UB)

0 < αE,cap < 0.2, 0 < αH,cap < 0.415 0 < αE,cap < 0.2, 0.415 ≤ αH,cap ≤ 1 0 < αE,cap < 0.2, 1 < αH,cap 0.2 ≤ αE,cap ≤ 1, 1 < αH,cap 1 < αE,cap, 1 < αH,cap 0.2 ≤ αE,cap ≤ 1, 0 < αH,cap < 0.415 0.2 ≤ αE,cap ≤ 1, 0.415 ≤ αH,cap ≤ 1

stop j: FTL i: running at full load g: FEL or running at full load f: running at full load k: FEL a: FEL or FTL

μuser < 1

(5LB) (6) (7) (8LB) (9LB)

1 < αE,cap, 1 < αH,cap 1 < αE,cap, 0.415 ≤ αH,cap ≤ 1 1 < αE,cap, αH,cap < 0.415 0.2 ≤ αE,cap ≤ 1, 0 < αH,cap < 0.415 0.2 ≤ αE,cap ≤ 1, 0.415 ≤ αH,cap ≤ 1

c: running at full load b: FTL d: running at full load e: FEL a: FEL or FTL

μ

user

UB

Fig. 4. Three categories of simplified CCHP users. Table 2 Criteria for categorising CCHP users based on temporal relations. Line-users (L)

Triangle-users (T)

τE = τQ; φ1 = φ2 = 0

Quadrangle-users (Q)

T1-users

T2-users

Q1-users

Q2-users

τE = τQ + φ1 + φ2

τE = τQ − φ1 − φ2

τE = τQ + φ1 − φ2

τE = τQ + φ 2 − φ 1

4. Categories of CCHP users, load-matching relations, and evaluation criterion

Table 3 Numerical relations of thermal and electric loads in five subregions. Sub-region

➀

➁

➂

➃

➄

Numerical relations

user μmin

user μmin / kE

user μmax

user kQ·μmin

user μmin

4.1. Categories of CCHP users According to the simplified load demands in Section 2 and the dimensionless matching parameters in Section 3, the simplified CCHP users can be described by the dimensionless square waves, as illustrated in Fig. 4. The load-related parameters (i.e., k, αE,cap, and αH,cap) are determined by the ordinate, while the time-related parameters (i.e., τ and φ) depend on the abscissa. According to the time-related parameters, the load demands of users can be classified into three categories: in the first category, the electric and thermal load demand times are synchronised (τE = τQ, φ1 = φ2 = 0), and is named the L-users (Line-users). In the second category, two types of users are named T1-

Table 4 Capacity design modes of CCHP systems. Capacity design mode

Condition

Equipment capacities PGU

HRS

AC

CCHP Qmax

CCHP Qmax ·COPAC

CCHP Qmax ·ηHX

user Qmax

user Qmax ·COPAC

user Qmax ·ηHX

PPE

αE,cap = 1

user Pmax

PPT

αH,cap = 1

user CCHP Qmax / Rmax

HX

537

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PPE mode

PPT mode

Fig. 5. 53 types of matching relations based on PPE and PPT capacity design modes for the three categories users.

538

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(a) PPE mode

(b) PPT mode

Fig. 6. Effect of the load-related parameter kE to the 53 types of matching relations based on PPE (a) and PPT (b) capacity design modes.

users and T2-users (Triangle-users). To T1-users, the “mount thermal load” demand time is posterior to the electric load in the early morning, but disappears earlier at nightfall (τE = τQ + φ1 + φ2, τE > τQ); while to T2-users, the “mount thermal load” demand time occurs earlier in the early morning but disappear at nightfall compared to the “mount electric load” (τE = τQ − φ1 − φ2, τE < τQ). For the third users, the “mount thermal load” demand time lag or earlier than the electric both in the early morning and nightfall (τE = τQ + φ1 − φ2), and the corresponding users are named Q1-users and Q2-users (Quadrangle-users), respectively. The criteria for categorising the CCHP users based on temporal relations are summarised in Table 2. Meanwhile, the loadrelated and time-related parameters divide the hourly load diagrams into five different subregions (labelled ➀to ➄), and their numerical relations are summarised in Table 3. Further, the L-users, T1/T2-users, and Q1/Q2-users have three (➀➂➄), four (➀➁➂➄/➀➃➂➄), and five subregions (➀➁➂➃➄) in a typical day, respectively.

relations between the load demands for the three categories users and the system’s operation line lCCHP are constructed in the load-matching map, as shown in Fig. 5. The difference in the load-matching relations lies in the different load demand locations in the matching map. For example, L-user has four types of matching relations (I, II, III, IV) in PPE mode. And if both subregions ➀➄and ➂are located below the operation line lCCHP (type I), redundant thermal energy will be produced in a whole day (αH < 1); inversely, more thermal energy will be compensated (αH > 1) when both the load demands are located above the operation line lCCHP (type IV); additionally, the systems will buy thermal energy only in subregion ➂when the load demands in subregion ➂are located above the operation line lCCHP and subregion ➀➄are located below (type III); notably, the loads of the systems produced neither shortage nor surplus when the load demands in subregions ➀➄and ➂are located on the operation line lCCHP (type II), and the load demands and provision achieve the ideal matching (αH = 1, αE = 1). Hence, 53 types of load-matching relations between the load demands of these three categories users and system provision in PPE and PPT modes are established, as shown in Fig. 5. Therein, 4, 5, 5, 6, and 6 types of matching relations for L-user, T1-user, T2-user, Q1-user, and Q2user are constructed in PPE mode, respectively; and the corresponding matching relations for the PPT mode contain 4, 6, 5, 6, and 6 types, respectively.

4.2. Load-matching relations based on two different equipment capacity design modes user to first In PPE mode, the PGU is installed with a capacity of Pmax satisfy the users’ electricity demand (αE,cap = 1), inversely, the thermal demand is satisfied in priority with the HRS equipped with the capacity user of Qmax (αH,cap = 1) in PPT mode. The equipment capacities of the CCHP systems based on the two design models are summarised in Table 4. Based on these two capacity design modes, the load-matching

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(a) PPE mode

(b) PPT mode

Fig. 7. Effect of the time-related parameters φ and τE to the 53 types of matching relations based on PPE (a) and PPT (b) capacity design modes.

conversion coefficient from kWh to kgce; therefore, its units are kgce/ kWh. If the energy resource of a CCHP system is natural gas, a can be assigned to 0.1229 kgce/kWh [11]. The energy supplemented in a typical day for each subregion can be calculated in Eqs. (35)–(38):

4.3. Evaluation criterion To correct the effect of climate on the evaluation criterion of CCHP systems, the ESR is selected to quantify the benefits achieved using CCHP systems over the separated reference system [1,11,16,17]. The ESR is defined as the ratio of energy savings to the adjusted baseline energy use, as shown in Eq. (32):

ESR = 1 −

Er + E sup Eab

subregions 1 and 5: EQsup (1, 5) = {ω1·(1 − 1/ αH ) COPAC Eref,c + ω2 ·[(1 − λ min − 1/αH ) a + λ min COPAC Eref,c]}·

(32)

user (24 − τQ ) Qmin user EPsup (1, 5) = ω3 ·(1 − 1/ αE)·Eref,p·(24 − τQ ) Pmin

where Er represents the total actual reported energy consumption for the CCHP system, and Eab is the adjusted baseline energy use for the separate system, as calculated in Eq. (33). Esup is the supplementary energy in the typical day, and comprises electricity (EPsup ) and thermal energy (FQsup ), as calculated by Eq. (34). CCHP Er = [(24 − τE)/ ηmin + kE τE/ηmax ] Pmin ·a user user user Eab = Pday × Eref,p + Hday × Eref,h + Cday × Eref,c 5

E sup =

∑ EPsup (j) j=1

subregion 2: EQsup (2)

user EPsup (2) = ω3 ·(1 − 1/ αE ) Eref,p·φPmin

(33)

(36)

subregion 3:

∑ EQsup (j) j=1

= {ω1·(1 − 1/ αH ) COPAC Eref,c user + ω2 ·[(1 − λ min − 1/αH ) a + λ min COPAC Eref,c]}·φQmin

5

+

(35)

EQsup (3) = {ω1·(1 − 1/ αH ) COPAC Eref,c

(34)

user + ω2 ·[(1 − λ max − 1/αH ) a + λ max COPAC Eref,c]}·τQ kQ Qmin

In Eq. (33), Eref,p, Eref,c, and Eref,h are the reference values used to quantify the energy consumption per unit energy supply in separated energy systems. These values depend on the climate zone, and the specific values for China can be found in Refs [1,11,16,17]. a is the unit

user EPsup (3) = ω3 ·(1 − 1/ αE ) Eref,p·τQ kE Pmin

(37) 540

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(a) Two scenarios according to the “mount load” demand location in the matching map

(b) #1:“mount load” demands are located above the operation line lCCHP (μ user=1.2)

(c) #2:“mount load” demands are located below the operation line lCCHP (μ user=0.7)

Fig. 8. Comparison of the PPE and PPT capacity design modes for different category users (a) two scenarios according to the “mount load” demand location in the matching map; (b) “mount load” demands are located above the operation line lCCHP (μuser = 1.2); (c) below the operation line lCCHP (μuser = 0.7).

subregion 4: EQsup (4)

kE will benefit the energy saving of the CCHP system when the system is designed in the PPE mode or when the load demands are below the operation line lCCHP in the PPT mode; meanwhile, the larger value of kE will contribute to more energy saving when the load demands are located above the operation line lCCHP in the PPT mode. Moreover, the influence of the time-related parameters τE and φ to the 53 types of matching relations is also illustrated in Fig. 7. When the system is designed in the PPE mode, as shown in Fig. 7a, the longer duration time of the “mount load” demand time (τE) in a typical day will save more energy for L-user; however, in the PPT mode, as shown in Fig. 7b, the longer duration time will deteriorate energy saving for the matching relations I and III of the L-user. Meanwhile, the system will save more energy if the synchronisation differences in the electric and thermal demand times (φ) are smaller whether the system is designed in the PPE or PPT mode. However, to the matching relations I and III of the T2-user in the PPE mode and the load demands above the operation line lCCHP in the PPT mode, inversely, the longer synchronisation difference time (φ) will benefit the system’s energy saving. Therefore, the smaller value of the kE (load-related parameter) and φ (time-related parameter) of the user will benefit the system’s energy saving for most matching relations. Further, a longer duration time of the “mount load” demand time (τE) in a typical day will save more energy to the CCHP systems. However, the variation tendency shows the opposite results for some special matching relations, especially for the load demands located above the operation line lCCHP. Moreover, the system will save more energy in winter than in summer.

= {ω1·(1 − 1/ αH ) COPAC Eref,c user + ω2 ·[(1 − λ max − 1/αH ) a + λ max COPAC Eref,c]}·φkQ Qmin user EPsup (4) = ω3 ·(1 − 1/ αE ) Eref,p·φkE Pmin

(38) where the values of w1, w2, and w3 can be obtained by Eq. (39):

1 ⩽ αH ⩽ (1 − λ )−1 ⎧ ω1 = 1, ω2 = 0 ω = 0, ω2 = 1 αH > (1 − λ )−1 ⎨ 1 = > ω 1 when α 1; ω E 3 = 0 when αE⩽1 ⎩ 3

(39)

5. Results and discussion 5.1. Influence of the load and time-related parameters to the 53 types of matching relations Based on the assumptions in Section 3.1, the influence of the loadrelated parameters kE to the 53 types of matching relations in summer and winter are illustrated in Fig. 6, respectively. When the system is designed in the PPE mode, as shown in Fig. 6a, the ESR of the systems decreased along with increasing kE for the 19 types of matching relations of the three category users; inversely, the ESR increased for the matching relations V of the T1-user. Similarly, when the system is designed in the PPT mode, as shown in Fig. 6b, the ESR of the systems decreased along with the increasing kE for the 15 types of matching relations of the three category users; meanwhile, for the six types matching relations: IV of L-user, V and VI of T1-user, V of T2-user, V and VI of Q-user, whose load demands are located above the operation line lCCHP, the ESR increased along with increasing kE. Hence, for most of the matching relations, the smaller value of the load-related parameter

5.2. Comparison of the PPE and PPT modes for different category users To select a preferable capacity design mode of the CCHP system, the energy saving performance of the PPE and PPT design modes for different category users are compared, as shown in Fig. 8. The comparison 541

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can be divided into two scenarios according to the “mount load” demand location in the matching map, as shown in Fig. 8a. Scenario #1: the “mount load” demands are located above the operation line lCCHP, e.g., μuser = 1.2. The capacity of the PGU is equal to the “mount load” demands in the PPE mode (αE,cap = 1, αH,cap > 1), which is represented by the load point “a” in the load-matching map; meanwhile, the capacity of the PGU is smaller than the “mount load” demands in the PPT mode (αE,cap < 1, αH,cap = 1), which is represented by the load point “b.” The corresponding load points of “valley load” in the PPE and PPT modes can be represented by the points “a′” and “b′” respectively. Scenario #2: the “mount load” demands are located below the operation line lCCHP, e.g., μuser = 0.7. The capacity of the PGU is equal to the “mount load” demands in the PPE mode (αE,cap = 1, αH,cap < 1), which is represented by the load point “d” in the load-matching map; meanwhile, the capacity of the PGU larger than the “mount load” demands in the PPT mode (αE,cap > 1, αH,cap = 1), which is represented by the load point “c.” The corresponding load points of the “valley load” in the PPE and PPT modes can be represented by the points “d′ ”and “c′” respectively. To the L-user, the energy saving performance for the PPT mode is better than that for the PPE mode whether in winter or summer when the value of kE is smaller for scenario #1 (Fig. 8a). Inversely, the PPE mode demonstrates better energy saving along with increasing kE. For scenario #2, as shown in Fig. 8b, the PPE mode is better than the PPT mode for both summer and winter. To the T1-user and T2-user, the PPE mode is the better choice to design the capacity of the system whether for scenario #1(Fig. 8a) or scenario #2 (Fig. 8b). Similarly, the PPE mode demonstrates better energy saving performance for the Q-user with a smaller value of kE in scenario #2 and scenario #1; however, these two design modes demonstrate an equivalent energy saving performance for larger kE in scenario #1. Meanwhile, for scenario #2, as shown in Fig. 8b, the systems will achieve the maximum values of ESR in PPT mode when the valley load is located in the operation line of CCHP systems, and kE = 1/μuser. Comprehensively, the PPE mode is a better choice to design the capacity of the CCHP system for the three category users with smaller kE.

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6. Conclusion This research focused on the load-matching relations between system provision and user demands, which is inherently influenced by CCHP users and capacities of systems’ key components. Instead of the case studies, comprehensive mathematical models of user demands are established based on the parameters regarding time (τ and φ) and load characters (k). Based on the time-based categorizing method, CCHP users are simplified as square wave and categorised into three categories (L-user, T-user and Q-user). Then, five dimensionless loadmatching parameters, αE, αH, αE,cap, αH,cap, and μuser, are proposed to measure the energy-matching and off-design operating conditions of system, respectively. And 53 types load-matching relations are constructed and discussed based on the dimensionless load-matching map. Theoretical analysis indicates that users in cold climate zones with smaller values of k and φ, and greater values of τ are more suitable for CCHP systems, and the PPE mode is a better capacity design methods for most load-matching relations. Although assumptions are established, the methodology, results and conclusions can also be extended to CCHP system studies without constraints in this paper. Acknowledgements This work was supported by the National Key Research and Development Program of China (Grant No. 2016YFB0901405); the

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