Optimal scheduling of buildings with energy generation and thermal energy storage under dynamic electricity pricing using mixed-integer nonlinear programming

Applied Energy 147 (2015) 49–58

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Optimal scheduling of buildings with energy generation and thermal energy storage under dynamic electricity pricing using mixed-integer nonlinear programming Yuehong Lu a, Shengwei Wang a,⇑, Yongjun Sun b, Chengchu Yan a a b

Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Division of Building Science and Technology, City University of Hong Kong, Kowloon, Hong Kong

h i g h l i g h t s  Optimal scheduling strategy for building energy systems is developed.  Mixed-integer nonlinear programming approach is used for the optimal scheduling.  Four scenarios are investigated to evaluate the optimal scheduling strategy.  Case studies are conducted on the Hong Kong Zero Carbon Building.

a r t i c l e

i n f o

Article history: Received 2 January 2015 Received in revised form 13 February 2015 Accepted 14 February 2015

Keywords: Optimal scheduling Mixed-integer nonlinear programming Zero energy building Renewable energy systems Thermal energy storage

a b s t r a c t The increasing complexity of building energy systems integrated with renewable energy systems requires essentially more intelligent scheduling strategy. The energy systems often have strong nonlinear characteristics and have discrete working ranges. The mixed-integer nonlinear programming approach is used to solve their optimal scheduling problems of energy systems in building integrated with energy generation and thermal energy storage in this study. The optimal scheduling strategy minimizes the overall operation cost day-ahead, including operation energy cost and cost concerning the plant on/off penalty. A case study is conducted to validate the proposed strategy based on the Hong Kong Zero Carbon Building. Four scenarios are investigated and compared to exam the performance of the optimal scheduling. Results show that the strategy can reduce operation energy cost greatly (about 25%) compared with a rule-based strategy and the reduction is even increased to about 47% when a thermal energy storage system is used. The strategy can also reduce the on/off frequency of chillers significantly. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The use of renewable energy resources has been recognized as a solution to the energy problems in future for low carbon society construction and sustainable development [1,2]. A wide range of technologies including photovoltaic system (PV) [3], wind turbine (WT) [4], combined cooling, heating and power system (CCHP) [5], thermal energy storage (TES) [6] and other renewable energy systems [7] have been employed in various types of buildings. These energy systems integrated in buildings can be considered as a kind of small distributed energy systems. Such distributed energy systems should be more intelligent so as to respond to

⇑ Corresponding author. E-mail address: [email protected] (S. Wang). http://dx.doi.org/10.1016/j.apenergy.2015.02.060 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

the dynamic or time-sensitive electricity price under micro/smart grids. Facing these challenges, optimal scheduling of building energy systems is important to achieve operation cost saving and to contribute to improving the reliability of grids. However, the integration of renewable energy systems and energy storage systems in buildings results in more complex energy systems, which poses the complexity and great challenge for the optimal control of these integrated energy systems. Energy generations of some renewable energy systems (e.g. PV system and wind turbines) are depending on passive renewable energy resources, which are difficult to be controlled according to the demanded load during operation. Other energy systems (e.g. CCHP, CHP, CCP and TES) could be controlled effectively to alleviate the peak load on power grid and improve the efficiency of energy conversion [8,9]. In CCHP systems, ‘‘following the thermal load’’ (FTL) and ‘‘following the electric load’’ (FEL) are

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

the two basic control strategies in applications [10,11]. However the mismatch problems of the thermal and electric loads are still difficult to be solved by both two strategies. Thermal energy storage (TES) systems can be installed in buildings to shift energy demands from peak periods to off-peak periods, and an optimal control strategy for thermal energy system could contribute significant peak electricity load reduction [12]. Nearly all the energy systems have the scheduling problem [13,14]. There have been already considerable studies conducted on scheduling problems of cogeneration/thermal energy storage systems [15–25]. Mathematic programming techniques, such as linear programming algorithms [15,16], mixed-integer linear programming algorithms (MILP) [17–19], nonlinear programming (NLP) algorithms [8,22,26], and even mixed-integer nonlinear programming (MINLP) algorithm [23,25], were widely used to address the scheduling problems. Ren and Gao [18] formulated the optimal control scheduling of industrial CHP plants under time-sensitive electricity prices as a mixed-integer programming problem which considering different operating modes for each plant. Chandan et al. [8] employed the NLP solver in MATLAB to address a model-based, look-ahead optimization strategy for a campus CCHP plant with TES. Ozoe et al. [17] formulated the problem of the power scheduling for a smart house as a mixed-integer programming problem to seek the optimal power schedule at the least operation cost. They formulated the uncertainty problem of electricity demand, heat demand and PV generation as a stochastic programming problem. Ma et al. [22] presented a study on the application of model-based predictive control on the operation of thermal energy storage in building cooling systems. As the problem of MINLP is complex for real time application, they then simplified it to a nonlinear program (NLP) problem by fixing the tank operation mode. Kitagawa et al. [23] proposed ‘‘particle swarm optimization’’ for optimal operational planning of a cogeneration system which was formulated as a mixed integer nonlinear optimization problem. They mainly focused on the analysis of optimization method. Wu et al. [24] presented an optimal operation strategy for micro-CCHP system based on MINLP model. Two objective functions including energy saving ratio and cost saving ratio were considered hierarchically. However, very limited studies have been conducted on the optimal scheduling of the building energy systems using passive renewable energy resources (e.g. solar irradiation and wind), active energy resources (e.g. bio-diesel, the grid electricity) and thermal storage under dynamic/time-sensitive electricity pricing. Our previous study proposed a model predictive control method using NLP algorithm to optimize the scheduling of the building energy systems [26]. But, the NLP algorithm cannot handle the discrete working ranges of the energy system which often occur in actual operation. Furthermore, the on/off frequencies of the active energy devices (i.e. CCP and chillers) have a negative influence on the lifetime of the devices, but it is not considered properly in existing studies on the scheduling problems. This paper therefore presents a new optimal scheduling strategy, which is based on MINLP considering both the nonlinear input–output characteristics and the discrete working ranges of the active energy systems, for buildings with active/passive generations and thermal energy storage to minimize the daily operation cost. A cost penalty is introduced to consider the on/off number of the active energy systems and therefore reduce their on/off switching frequencies. Section 2 gives an outline on the optimization approach. Section 3 describes the MINLP approach used in the optimal scheduling strategy. The simplified physical models are built for the energy systems and presented in Section 4. In Section 5, a case study is presented and the system performance under different scenarios are analyzed and compared. Conclusion is given in Section 6.

2. Outline of optimization approach Fig. 1 illustrates the general approach of scheduling the building energy systems based on forecasted weather (e.g. outside air temperature, solar radiation) and electricity price given by the grid. The optimization objective is to serve the building electric load and cooling load in the control trajectories with least electricity   cost. The values of day-ahead building cooling load Q tcl , electricity  t  consumption of the building Pothers þ PtHVAC 0 and PV power gen  eration P tPV in the interval of one hour are the input variables for the proposed scheduling strategy. The strategy minimizes daily operation cost comprising of the electricity bills from grid     ctelec  Ptgrid , the oil consumed by CCP C toil  V toil and cost penalty   C tseq  N tseq considering the on/off number of the electric chillers   and CCP. The oil usage by the CCP V toil and the cooling provided  t  by the electric chillers Q EC are the two input control variables. The prediction horizon considered in this study is 24 h. Therefore, there are 48 values ð2  24Þ of the two input control variables. Finally, 96 values (4  24) of four control variables (cool    ing charged/discharged by TES Q tTES , the oil usage by CCP V toil ,  t  the cooling provided by electric chillers Q EC , and electricity   received/delivered from/to the grid P tgrid Þ in the next 24 h are determined by the strategy. In this study, the electricity price is formed based on the day-ahead pricing profile in New York in 2013, which has the average converted to the average electricity price in Hong Kong [26]. It is also assumed that the selling electricity price is the same as the buying price. The proposed optimal scheduling strategy is based on predictive models. The main steps are as follows. At the current time k, the optimal control variables are obtained on a fixed horizon for the next term, say [k; k þ N]. Among the optimal controls on the fixed horizon [k; k þ N], only the first one k + 1 is

Inputs: Electricity price and weather data in next 24 hours Power grid

Weather )

Temperature, solar radiation, etc.

Prediction of power/energy generations/consumptions in next 24 hours Cooling Models of Load profile of Model of demand model HVAC System Lighting, etc. Photovoltaic

MINLP-based Optimization MINLP solver Objective Function Variables to be optimized

Subject to: Constrains in Eq. (3) to Eq. (7).

Outputs: Control schedule in next 24 hours Thermal storage tank

Combined cooling and power unit

Electric chillers

Power grid

Fig. 1. Optimal scheduling based on predicted loads/generations of building energy systems and electricity price.

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

First 24h planning

At 00:00 am on day 1 0

1

2

3

4

5

6

7

8

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23

Second 24h planning At 00:00 am on day 2 0

1

2

3

4

5

6

7

8

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23

Third 24h planning

At 00:00 am on day 3 0

1

2

3

4

5

6

7

8

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23

Fig. 2. Illustration of one day-ahead (24 h) scheduling.

adopted as the current control law. The procedure is then repeated at the next time, say [k + 1, k + 1+N]. This procedure is called ‘receding horizon’ since the horizon recedes as time proceeds [27]. The scheduling strategy adopted in this study is considered as ‘‘intervalwise receding horizon control’’ since the horizon recedes intervalwise or periodically as time proceeds. This procedure is shown as Fig. 2. At the beginning of a day, say at 00:00 am on day 1, the optimal strategy is activated and the schedules of the energy systems are obtained on a finite fixed horizon of 24 h. The schedule trajectories of control variables obtained are adopted as the control law in the next 24 h – day 2. The procedure is then repeated at beginning of the next day – day 3.

which is given 24 h in advance. The weather forecast can provide 24 h data of solar radiation, ambient temperature and relative humidity, etc. The optimal scheduling problem is solved by the mixed-integer nonlinear programming (MINLP) algorithm. The objective function is shown in Eq. (2a). By correlating the predicted values and two input variables, it can be reformed as Eq. (2b).

min J ¼

C telec Ptgrid þ C oil V toil

i

ð2aÞ

t¼1

min J ¼

24 X   f ðC tGrid ; Q tCL ; PtHVAC 0 þ Ptothers ; PtPV ; V toil ; Q tEC Þ

ð2bÞ

t¼1

3. MINLP-based optimal scheduling strategy 3.1. An outline of mixed-integer nonlinear programming (MINLP) algorithm Many optimization problems in engineering, scientific and industry applications are related to discrete decisions and nonlinear system characteristics that have great influence on the quality of the decisions. Mixed-integer nonlinear programming (MINLP) is one of the most general optimization methods, which includes both mixed-integer linear programming (MILP) and nonlinear programming (NLP). The general form of an MINLP can be conveniently expressed as Eq. (1) [28]:

Minimize f ðx; yÞ subject to : gðx; yÞ 6 0; x 2 X; y 2 Y

n h X

ð1Þ

ðY is an integerÞ where the function f : Rnþs ! R and g : Rnþs ! Rm are possibly nonlinear objective function and constraint function respectively. The variables x and y are the decision variables and y is required to be integer valued. The sets X # Rn and Y # Rs are boundingbox-type restrictions on the variables. 3.2. Objective function and constraints The optimal scheduling problems of MINLP-based strategy in this study is to minimize the operation energy cost in the coming 24 h, as shown in Eq. (2a), subject to all the operation technical constraints (i.e., Eqs. (3)–(7)). The operation energy cost includes the electricity cost of the power from the grid and the cost of the waste oil from market. The strategy provides the day-ahead optimal scheduling of the energy systems. A few assumptions are made as follows when developing the strategy. Equipment capacity selection is not considered and equipment capacities are given. The electricity price from the grid varies as a time-based profile,

To consider the sequence control of chillers and CCP, which is more realistic and feasible from an operation point of view, a cost penalty ðC seq Nseq Þ is added into the objective function. The overall operation cost, including operation energy cost and cost penalty concerning the plant start/stop is shown in Eq. (2c).

min J 0 ¼

n h X

C telec Ptgrid þ C oil V toil þ C seq Ntseq

i

ð2cÞ

t¼1

The operation of the sub-system is subject to constraints as listed in Eqs. (3)–(7). The outputs of sub-systems (CCP unit, electric chillers and TES) should not be over their design capacities and should not be less than their minimum load ratios (i.e. Eqs. (3)–(5)). The electricity consumed by the sub-systems (electric chillers, other HVAC systems, other devices) during control interval is equal to the power provided by the PV, CCP and grid, as shown by Eq. (6). The cooling consumed during each control interval is equal to that provided by the electric chillers, absorption chiller (driven by the CCP) and the thermal energy storage, as shown in Eq. (7). Operation range of CCP unit:

0:3  F oil;max 6 F toil 6 F oil;max ; or F toil ¼ 0

ð3Þ

Operation range of electric chillers:

0:3  Q EC;max 6 Q tEC 6 Q EC;max ; or Q tEC ¼ 0

ð4Þ

Operation range of thermal energy storage:

0 6 mtTES 6 mTES;max

ð5Þ

Electricity balance of building energy system:

PtPV

þ PtCCP þ Ptgrid ¼ PtEC þ PtHVAC þ Ptothers

ð6Þ

Cold energy balance of building:

Q tCL ¼ Q tEC þ Q tAC þ Q tTES

ð7Þ

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

Grid

PPV

Pgrid

PV PHAVC

PEC

HVAC

PCCP Electric chillers

QEC Q

Fg

Combined cooling and power unit (CCP)

Heat recovery system

Qr

Absorption chiller

Others (Lighting, computers etc.)

QAC QTES Thermal storage tank (TES)

Building

Fig. 3. Energy flows among the energy systems in the building studied.

4. Energy system models To ensure the computation efficiency of the optimization, the energy sub-system models used by the optimal control strategy are simplified models described as follows. Photovoltaic: The PV power generation is computed by Eq. (8) [29,30]. Where Ades is the total area of PV (m2). gm is the PV module efficiency. pf is the packing factor. gPC is the power conditioning efficiency. Itirra is the hourly irradiance (kWh/m2).

PtEC ¼

PtPV ¼ Ades  gm  pf  gPC  Itirra

ð8Þ

Combined cooling and power system: The power generation of the CCP is computed as Eq. (9). Where, gtCCP is a polynomial func  tion of its part load ratio PLRtCCP , as Eq. (10). In this study, the coefficients (b1 ¼ 0:2861; b2 ¼ 0:7651; b3 ¼ 0:7223 and b4 ¼ 0:0872) are identified by fitting operation data with a fitting coefficient of 0.96, and the rated efficiency, gCCP , is 0.33.

PtCCP ¼ cp;oil  F toil  gtCCP t CCP

g

¼

3 b1 PLRtCCP

þ

2 b2 PLRtCCP

ð9Þ þ

b3 PLRtCCP

Eq. (13) [31]. Where a = 1.6757, b = 0.3083, c = 3.5093, d = 0.853. These parameters (a; b; c and dÞ are obtained by fitting the models with the site data of chillers with R2 = 0.9. COP N is the nominal COP of chillers and the value used in this study is 4.2. The outlet water temperature of the evaporator ðT ev a;out Þ is assumed to be 7 °C, and the inlet water temperature of condenser ðT con;in Þ is assumed to be 5 K above the wet-bulb temperature of the cooling tower inlet air.

Q tEC COP tEC

ð12Þ

COPtEC ¼ COP N 

  3 2  a  PLRtEC þ b  PLRtEC þ c  PLRtEC þ d

þ b4

ð10Þ

Q tAC ¼ ghrs  ð1  gtCCP Þ  cp;oil  F toil  COP AC

ð11Þ

Electric chiller: The electricity consumption of the electric chil  lers is calculated based on the cooling load Q tEC and coefficient   of performance COPtEC , as shown by Eq. (12). An empirical model

HVAC system: The energy consumed by the HVAC system except chillers (i.e. Eq. (17)) includes the energy consumption of the air handling units ðPtfan Þ, i.e. Eq. (14), cooling towers ðP tct Þ, i.e. Eq. is built based on its actual load and design capacity. Where, tta is the air flow rate, mtw is the water flow rate, k is a constant parameter depending on the tower size with the assumed value is the cooling tower cooling capacity, of 1.5, Q tct Q tct;design ; Ptct;design ; mtw;design and

Ptfan ¼ afan 

Table 1 Specifications of the energy systems in the building studied.

TES

Ptp ¼ acwp 

Specification

1

Volume = 125 m

1

AC EC

Electric chiller

3

PV

Photovoltaic system

1

Rated power = 100 kW, Rated efficiency = 0.33 Rated capacity = 130 kW, COPN = 0.8 Rated capacity = 70 kW, Nominal COPN = 4.2 Area = 1015 m2

1

are the rated cooling capacity

v a;design 

þ bfan 

Q tct

v ta

3 ð14Þ

v a;design

k ð15Þ

Q ct;design

mtw mw;design

 þ bcwp 

mtw

mw;design

2 ð16Þ

3

Chilled water storage tank Combined cooling and power unit Absorption chiller

CCP



v ta

Ptct ¼ Pct;design 

Amount

v ta;design

of cooling tower, rated fan power of cooling tower, design water flow rate and design air flow rate of the building respectively. acwp ¼ 10; bcwp ¼ 1; afan ¼ 8; bfan ¼ 12.

is adopted to calculate the COPtEC of electric chiller, as shown in

Equipment

ð13Þ

(15), and pumps ðP tp Þ, i.e. Eq. (16). The model of each sub-system

Absorption chiller: The absorption chiller is driven by the recovered heat from the CCP. The cooling generated by the absorption chiller depends on the exhaust heat from the CCP, as shown in Eq. (11). Where, ghrs is the heat recovery system efficiency, COPAC is coefficient of performance of the absorption chiller.

Symbol

T ev a;out T tcon;in  T ev a;out

PtHVAC ¼ P tfan þ Ptct þ Ptp

ð17Þ

Thermal storage tank The chilled water in the thermal energy storage tank is stratified with warm water at the upper part and the cool water at the lower part. The cool water ðT TES;cold Þ charged to the tank is assumed to have the same temperature as the supply chilled water. When

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

1200 Solar radiation

40

800 35 600 30 400 25

200

20

2

1000

Solar radiation (W/m )

Outdoor temperature (℃)

45

Power generation/consumption (kW)

120 Outdoor temperature

2

4

6

8

Other PV

80

CCP

60 40 20 0

0 0

HVAC

100

0

10 12 14 16 18 20 22 24

2

4

6

8

10

12

14

Time (h)

Time (h)

(a)

(b)

16

18

20

22

24

Fig. 4. Ambient conditions and power generation/consumptions in a typical day in August.

the tank discharges, the cool water stored in the bottom of the tank will be supplied to the HVAC system as supply chilled water. Meanwhile, the same amount of chilled water from the HVAC system will also be returned to the tank on the top as warm water.

  Q tTES;cold ¼ mtTES;cold cp;w T TES;warm  T TES;cold  gtTES Q TES;cold;max

ð18Þ

  The amount of cold energy Q tTES;cold stored in the thermal storage tank at time t is estimated by Eq. (18). Where mtTES;cold is the amount of cold water stored in the tank. gtTES is the cold loss coefficient and assumed to be 0.5% of the storage capacity per hour. The delay effects of charging and discharging are ignored in this study. 5. Case study 5.1. Description of the energy systems in the building The Hong Kong Zero Carbon Building (ZCB) is introduced as an illustrative example for evaluating the economic performance of the energy systems using the proposed scheduling control strategy. The Hong Kong ZCB covers a total land area of 14,700 m2 with a three-stories building (total net floor area of 1520 m2). The stateof-the art eco-building design and technologies are applied in the building, wind catcher, earth cooling tube, high performance glazing and ultra-low thermal transfer, etc., are adopted as passive energy systems. High volume low speed fans, active skylight and high temperature cooling system, etc., are adopted as active energy systems. PV and a bio-diesel generator/CCP are applied as on-site energy generation systems. In this study, several assumptions are made on the energy systems in the building as follows. (1) The fire pool with a volume of 125 m3 is assumed as the stratified chilled water storage tank in this building. (2) The absorption chiller driven by waste heat from bio-diesel generator/CCP is used instead of adsorption chiller in ZCB. (3) Different from the actual arrangement in ZCB where the waste heat from electricity generation process in CCP is used for both cooling and dehumidification, it is assumed in this study that all the waste heat is used by the absorption chiller for generating cooling. (4) If more electricity is generated than building electricity demand, surplus electricity will be sent back to the grid the same as the arrangement in ZCB. Fig. 3 illustrates the energy flows among energy systems in the building studied. The building electricity demand, including electricity consumed by the electric chillers, HVAC, and other devices (lighting, computers, etc.), is supplied by the on-site generation systems, i.e. PV and combined cooling and power unit. The grid power can be considered as an electricity storage, which provides

electricity when on-site generation is not sufficient and receives electricity when surplus electricity is generated on site. The building cooling demand is satisfied mainly by the electric and absorption chillers. Thermal energy storage system stores cooling when surplus cooling is provided by chillers and discharges cold when the electricity price is high. The specifications and parameters of the energy systems are listed in Table 1. Fig. 4 shows the solar radiation, outdoor air temperature, power generations of PV and CCP, power consumptions of HVAC and other devices in a typical day in August, which is retrieved from the BMS installed in Hong Kong ZCB. The outdoor temperature varied from 27 to 35 °C and peak solar radiation was about 900 W/m2 in that day. Corresponding to the weather conditions, the CCP was running at rated capacity with electricity generation of 100 kW and the daily peak generation by PV was approximately 90 kW. The electricity consumptions of HVAC system and other devices (lighting, computers, etc.) were about 60 kW and 30 kW respectively during office hours. 5.2. Comparison of optimal scheduling control strategy with rulebased control strategy Table 2 lists the combinations of the systems and strategies in the four scenarios studied. The performances of the energy systems using the proposed optimal scheduling control strategy (Scenario S1, S3) are evaluated and compared with that using the rule-based control strategy (Scenario S0, S2). The optimal control strategy based on MINLP used under Scenario S1 and S3 has been introduced earlier in Section 3, which provides a long-term operation planning for 24 h in advance. Under scenario S0, the CCP is controlled according to the building cooling load. The absorption chiller is driven by the CCP and thus its cooling ability depends on the operation of CCP. When the building cooling demand excesses the maximum capacity of the absorption chiller, the extra cooling load is provided by the electric chillers. This control strategy is also named as ‘‘following thermal load’’ control strategy which is independent from the electricity price. Under scenario S2,

Table 2 System and control strategy of four scenarios studied. Scenarios

System

Strategy

S0 S1 S2 S3

PV + CCP PV + CCP PV + CCP + Tank PV + CCP + Tank

Rule-based MINLP Rule-based MINLP

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

(a) – S0 Qac

120

Cooling (kW)

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Qec

140

Price

100 80 60 40 20 0 1

2

3

4

5

6

7

8

9

Dynamic price (USD/kWh)

160

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

(b) – S1 0.50

140

Cooling (kW)

120

Qec

0.45

Qac

0.40

Price

0.35

100

0.30

80

0.25

60

0.20 0.15

40

0.10

20

Dynamic price (USD/kWh)

160

0.05

0

0.00 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

(c) – S2 Qec Qtank

150

Cooling (kW)

100

0.5 0.4

Qac

0.3

Price

0.2 0.1

50

0.0 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-0.1 -0.2

-50

-0.3 -100

Dynamic price (USD/kWh)

200

-0.4 -0.5

-150

Time (h)

Qec Qtank Qac Price

150

Cooling (kW)

100 50

0.5 0.4 0.3 0.2 0.1 0.0

0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-50

-0.1 -0.2

-100

-0.3

-150

Dynamic price (USD/kWh)

(d) – S3

200

-0.4 -0.5

-200

Time (h) Fig. 5. Schedule of the hourly cooling generations in a day under different scenarios.

the chillers are operated in early morning, when the electricity price is low, to charge the storage tank in order to meet the buildings demand in the following day. Electric chillers will operate when the absorption chiller cannot satisfy the cooling demand. In order to validate the proposed optimal scheduling strategy in realistic working condition, the real cooling load of Hong Kong ZCB

recorded by the BMS on-site was used in the validation tests. The schedules of hourly cooling generations determined by the strategies under different scenarios are shown in Fig. 5. Under scenario S0 (Fig. 5a), the absorption chiller served a large portion of the building cooling load and only a small portion was served by the electric chillers (i.e. at 9:00 am, 16:00 am 18:00 am).

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Y. Lu et al. / Applied Energy 147 (2015) 49–58

0.5

150

0.4 0.3

Electricity (kW)

100

0.2

50

0.1

0

0.0 1

-50

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-0.1 -0.2

-100

-0.3

-150

Dynamic price (USD/kWh)

(a)-S0 200

-0.4

-200

-0.5

Time (h)

(b)-S1 150

0.4

Electricity (kW)

100

0.3 0.2

50

0.1 0

0.0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-50

-0.1 -0.2 -0.3

-100

Dynamic price (USD/kWh)

0.5

-0.4 -150

-0.5

Time (h)

(c)-S2

150

0.5

Electricity (kW)

0.3 0.2

50

0.1 0

0.0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-50

-0.1 -0.2 -0.3

-100

Dynamic price (USD/kWh)

0.4 100

-0.4 -150

-0.5

Time (h)

(d)-S3 0.50

150

Electricity (kW)

0.30 0.20

50

0.10 0

0.00 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-50

-0.10 -0.20 -0.30

-100

Dynamic price (USD/kWh)

0.40 100

-0.40 -150

-0.50

Time (h) Fig. 6. Schedule of the hourly electricity generation/consumption in a day.

Under scenario S1 controlled by the MINLP-based strategy (Fig. 5b), the electric chillers undertook a large portion of cooling load when the grid electricity price was not very high (8:00–11:00 am and 16:00–18:00 pm). The absorption chiller served the cooling load only at the peak period (12:00 am–16:00 pm). Under scenario S2 (Fig. 5c), using the rule-based control strategy, the TES was fully charged by the electric chillers in the off-peak period (1:00–7:00 am) and it was completely discharged

first to provide cooling before switching on the absorption/electric chillers. When the capacity of absorption chiller was not sufficient, the electric chillers will be switched on as the supplementary (16:00–18:00 pm). Under scenario S3 (Fig. 5d), using MINLP-based control strategy, the electric chillers continued to operate providing a small portion of cooling (8:00–10:00 am) after the TES was fully charged. The absorption chiller provided the cooling when the electricity price was high (12:00 am–17:00 pm), and the

Y. Lu et al. / Applied Energy 147 (2015) 49–58 SOS (S2) SOS (S3) Price

(a) 1.2

0.5

1.0

0.4

SOS

0.8

0.3

0.6 0.2

0.4

0.1

0.2 0.0

0.0 0

2

4

6

8

Dynamic price (USD/kWh)

56

10 12 14 16 18 20 22 24

Time (h)

(b)

SOS (S2) 1.2

SOS (S3)

1.0

SOS

0.8 0.6 0.4 0.2 0.0 0

24

48

72

96

120

144

168

Time (h) Fig. 7. TES charge/discharge schedule in a day (a) and in a week (b).

TES was discharged to provide the cooling at the rest of the time. Note, there was a very small amount of TES discharge in the figures when TES was not used, which was actually the cold loss. The schedules of the hourly electricity consumptions/ generations determined by the control strategies under different scenarios in the same test day are shown in Fig. 6. Under scenario S0 (Fig. 6a), the CCP operated to provide electricity in the entire office hours between 8:00am and 18:00 pm. Surplus electricity generated by the CCP was sent to the grid during this period and a large amount of surplus electricity (433.5 kWh, see Table 5) was sent to the grid in that day. Under scenario S1 using the optimal strategy (Fig. 6b), the CCP operated to provide electricity (and heat for the absorption chiller) only when the grid electricity price was high (12:00–15:00 pm) and thus electric chillers consumed much more electricity in the test day. Surplus electricity generated by the CCP was sent to the grid only in this short period and a large amount of electricity (121.5 kWh) was taken from the grid in that day. Under scenario S2 (Fig. 6c), the electric chillers consumed about 40 kW electricity per hour to charge the TES during off-peak period (1:00–7:00 am). The CCP kept running to provide electricity for six hours (13:00–19:00 pm) after cold stored in the TES was

completely discharged. Under scenario S3 (Fig. 6d), using the optimal control strategy, electricity consumed (and cold generated) by the electric chillers not scheduled as constant (1:00–9:00 am). The CCP was scheduled to operate at its rated power for five hours (12:00–17:00 pm) when the electricity price was high. The schedule of the TES charge/discharge in a day and in a week is shown in Fig. 7. The TES was charged at the beginning of the day under both scenario S2 and scenario S3 when electricity price was low. Under scenario S2, the TES discharged to provide cooling until the cooling stored in the TES reached its minimum level based on rule-based strategy, while, under scenario S3, the TES discharged to provide cooling during non-peak periods (i.e. 8:00–11:00 am, 16:00–18:00 pm). Table 3 lists the daily operation costs and cost savings under different scenarios. Under scenario S0, the daily operation cost in that week was between 111.4 USD and 185.3 USD, and the total operation cost in the week was 1011.5 USD. Compared with scenario S0, the daily cost savings of the range between 10.1% and 22.7% were obtained when the MINLP-based strategy was applied in the PV + CCP system under scenario S1. Under scenario S2, daily operation costs and total operation cost in the week were reduced significantly when the TES was used in the building. The daily cost savings achieved were around 29.5% (between 26.2% and 33.4%) compared with that under scenario S0. Under scenario S3, when the TES and the MINLP-based optimal strategy were used, both daily operation costs and total operation cost in the week were reduced dramatically compared with that under scenario S0 (i.e. the total operation cost in the week reduced from 1011.5 USD to 536.15 USD). The total operation cost savings in the week under scenario S3 were 36.2% compared with that under scenario S1 when TES was not used in the building, and 24.8% compared with that under scenario S2 when rule-based control strategy and TES were used. Table 4 summaries the effects of the proposed MINLP-based optimal scheduling strategy and the TES on the cost saving. The use of MINLP-based control achieved a saving of 16.9% on the energy system without TES and a saving of 24.8% on the energy system with TES. The use of TES achieved a saving of 29.5% under rule-based control and a saving of 36.2% under MINLP-based control. When using both MINLP-based control and TES, the saving achieved in the week was as high as 47%. The oil consumption and net electricity input from the grid (electricity received from grid minus electricity delivered to grid) under the four scenarios are shown in Table 5. Under the scenario S0, the oil consumption was about two times of that under the scenario S1, S2 and S3. This may be positive to the grid since the grid could receive surplus electricity generated from the building when the load of the grid is high. Under the scenario S1 and S2, the oil consumptions were reduced significantly since the TES or

Table 3 Daily and weekly operation costs and saving under different scenarios. S0

S1

Days

Cost (USD)

Cost (USD)

Saving (S1 vs S0) (%)

S2 Cost (USD)

Saving (S2 vs S0) (%)

S3 Cost (USD)

Saving (S3 vs S2) (%)

Saving (S3 vs S1) (%)

Saving (S3 vs S0) (%)

1 2 3 4 5 6 7 Average Total

158.8 175.9 125.7 132.7 121.7 185.3 111.4 144.5 1011.5

132.7 149.5 98.4 102.5 97.0 166.6 94.0 120.1 840.6

16.5 15.0 21.8 22.7 20.3 10.1 15.6 17.4 16.9

116.6 117.7 87.2 88.3 86.7 134.0 82.3 101.8 712.8

26.6 33.1 30.6 33.4 28.8 27.7 26.2 29.5 29.5

92.5 90.5 61.6 67.2 60.6 109.9 54.0 76.6 536.2

20.7 23.1 29.5 24.0 30.1 18.0 34.3 25.7 24.8

30.3 39.5 37.4 34.5 37.5 34.0 42.6 36.5 36.2

41.8 48.5 51.0 49.4 50.2 40.7 51.5 47.6 47.0

(S0: PV + CCP (Rule-based), S1: PV + CCP (MINLP), S2: PV + CCP + Tank (Rule-based), S3: PV + CCP + Tank (MINLP)).

57

Y. Lu et al. / Applied Energy 147 (2015) 49–58 Table 4 Effects of the TES and the proposed optimal scheduling strategy. Strategy

Table 6 Comparison between the energy costs obtained by MINLP and NLP.

System

Rule-based MINLP-based Cost saving

Days

PV + CCP

PV + CCP + TES

Cost saving (%)

1011.5 (USD) 840.6 (USD) 16.9%

712.8 (USD) 536.2 (USD) 24.8%

29.5 36.2 47.0

1 2 3 4 5 6 7 Total

MINLP-based scheduling strategy was used. The grid provided about 2000 kWh of electricity in the week. Under the scenario S3, The oil consumption was the lowest, which was benefited from the effects of both TES and MINLP-based strategy.

5.3. Comparison between MINLP and NLP optimization approaches and effect of plant start/stop penalty Compared with the NLP method, the MINLP approach requires additional computational effort since it combines algorithms from linear programming, nonlinear programming and integer programming. However, it should be noted that the results obtained using MINLP approach are more feasible and realistic, since the devices (i.e. electric chillers, CCP) usually have their own minimum load ratios while the devices may also have off-status in practice (i.e. discrete working ranges). It can be observed from Fig. 8 that the load of the electric chillers assigned by NLP was less than the 21 kW (i.e. less than the minimum load (30%) of a chiller) between 16:00 pm and 17:00 pm, which is unacceptable from an operational point of view. The effects of the MINLP and NLP approaches on outputs of optimization are investigated by comparing the operation energy costs of the building when using the two optimization approaches. The differences between the operation energy costs of the system scheduled by two optimization

Cost (USD)

Cost (USD)

NLP

MINLP(S1)

Saving (%)

NLP

MINLP(S3)

Saving (%)

137.9 146.4 98.4 102.5 97.0 162.5 93.0 837.7

132.7 149.5 98.4 102.5 97.0 166.6 94.0 840.6

3.77 2.12 0.00 0.00 0.00 2.52 1.08 0.35

92.4 90.7 61.6 67.1 62.6 110.2 53.5 538.0

92.5 90.5 61.5 67.1 60.6 109.9 54.0 536.1

0.11 0.22 0.16 0.00 3.19 0.27 0.93 0.35

approaches were very small in most of the test days (less than 4.00%) and could be negligible (Table 6). However, the load of the electric chillers scheduled by NLP was sometimes lower than its minimum load resulting that the schedules determined by the NLP optimization approach cannot be practically implemented. The MINLP approach can well address these problems since the integer variables, which handle capacity ranges of devices as discrete variables, are available. This allows that the schedules determined by the MINLP optimization approach can be practically implemented in practical operation. Considering the start/stop frequency of the electric chillers and CCP, a plant start/stop cost penalty is included in the objective function to prohibit frequent on/off switching of the electric chillers and CCP. The effects of including the cost penalty on the operation energy cost and start/stop number of chillers and CCP are shown in Table 7. The daily start/stop number of the electric chillers was reduced significantly (16.7–60%) when the start/stop cost penalty was included. The effect of including the start/stop cost penalty on the operation energy cost is not significant since the energy cost saving is sometimes positive and sometimes

Table 5 Oil consumption and net electricity input from grid. Day

1 2 3 4 5 6 7 Average Total

S0

S1

S2

S3

Oil (kg)

Electricity (kWh)

Oil (kg)

Electricity (kWh)

Oil (kg)

Electricity (kWh)

Oil (kg)

Electricity (kWh)

229.5 252.9 155.5 196.2 178.5 239.3 171.0 203.3 1423.0

433.5 483.9 192.3 355.5 275.5 325.7 271.6 334.0 2337.9

125.5 121.8 60.3 72.9 70.3 65.7 91.0 86.8 607.4

121.5 222.6 288.1 300.0 286.8 607.7 142.9 281.4 1969.6

117.4 166.5 44.9 81.1 65.9 162.1 59.1 99.6 697.0

227.9 29.3 440.5 318.2 377.0 135.1 381.0 272.7 1909.0

97.6 119.6 48.8 68.3 68.4 122.0 67.0 84.5 591.7

321.5 253.0 395.6 377.8 347.7 327.5 322.6 335.1 2345.8

(S0: PV + CCP (Rule-based), S1: PV + CCP (MINLP), S2: PV + CCP + TES(Rule-based), S3: PV + CCP + TES(MINLP)).

0.5

160 Qec(MINLP)

Cooling (kW)

120

0.4

Price

0.3 80 0.2 40

Less than 21 kW

0.1

0.0

0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h) Fig. 8. Comparison of the cooling distribution for electric chillers using MINLP and NLP.

Dynamic price (USD/kWh)

Qec(NLP)

58

Y. Lu et al. / Applied Energy 147 (2015) 49–58

Table 7 Effects of plant start/stop cost penalty under scenario S3. Day

1 2 3 4 5 6 7

Cost penalty not concerned

Cost penalty concerned

Energy cost (USD)

Start/ stop number

Energy cost (USD)

Start/ stop number

94.97 90.68 61.33 66.39 61.24 112.72 53.85

14 30 12 14 12 22 14

97.47 90.51 61.55 67.15 60.59 109.87 54.01

8 12 10 6 6 12 8

Cost Saving (%)

Reduction of start/stop number (%)

2.64 0.19 0.35 1.15 1.06 2.53 0.29

42.9 60.0 16.7 57.1 50.0 45.5 42.9

negative (varying between 2.64% and 2.53%). Therefore, the introduction of the cost penalty had a significant contribution to reducing the start/stop frequency of electric chillers, which could help to avoid irregular operating patterns and hence benefit to the service life of the devices. It is worth noticing that the effect of the start/stop cost penalty of the CCP can be ignored in the case studied since the optimal schedule of CCP had always only two on/off switches in each of the test days due to the electricity price profile used. 6. Conclusion In this paper, a strategy based on the mixed-integer nonlinear programming is presented to optimize the operation schedule of building energy systems. A case study was conducted to evaluate the proposed strategy based on the Zero Carbon Building in Hong Kong. Results show that the MINLP-based strategy could achieve an operation energy cost saving of 16.9% and a cost saving of 24.8% when applied on the energy systems without and with thermal energy storage respectively. The use of thermal energy storage in the building energy system studied could achieve a cost saving of 29.5% under rule-based scheduling control and a saving of 36.2% under MINLP-based scheduling control. The proposed scheduling strategy together with the thermal energy storage could eventually achieve a cost saving of up to 47%. The performances of the energy systems scheduled by the MINLP-based optimization approach and by another optimization approach, namely nonlinear programming (NLP) approach, are compared. The NLP-based approach can consider the nonlinear input–output characteristic of energy systems but the forbidden working ranges of the energy systems are ignored. Thus the load of electric chillers scheduled by the NLP optimization approach is sometimes lower than their minimum load, resulting in that the optimal schedule determined cannot be implemented in practical operation. The MINLP-based approach has well addressed these problems as observed in the tests since the capacity ranges of the energy systems are handled as discrete variables, which truly reflects the actual operation. Acknowledgement The research work presented in this paper is financially supported by a Grant (5267/13E) of the Research Grants Council (RGC) of the Hong Kong SAR. References [1] Alanne K, Saari A. Distributed energy generation and sustainable development. Renew Sustain Energy Rev 2006;10:539–58.

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