Impacts of water storage on robust optimal design of cooling system considering uncertainty

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Energy (2019) 000–000 430–435 EnergyProcedia Procedia159 00 (2017) www.elsevier.com/locate/procedia

Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018, 29–30 September 2018, Rhodes, Greece

Impacts of water onSymposium robust optimal of cooling The 15thstorage International on Districtdesign Heating and Cooling system considering uncertainty Assessing the feasibility of using the heat demand-outdoor b, QIN Kaimingc, NIU Jideb*, HONG Haifenga, LIU Hongd, ZHAO LItemperature Yanga , TIAN Zhe function for a long-termb district heat demand forecast a

Hongfang a b Andrić *, A.Research Pina ,Institute P. Ferrão J. Fournier B. Lacarrièrec, O. Le Correc Co., Ltd,,Guangzhou 510080,., China GuangdongI.Power Grid Development a,b,c

a

b School of Environmental Science and Engineering, Tianjin University, Tianjin 300072, China a c Innovation, and Policy Research - Instituto Superior Técnico, StateIN+ GridCenter Henanfor Electric PowerTechnology Company, Zhengzhou, 450018, China. b d

Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Veolia Innovation, 291 Avenue Daniel, 78520 Limay, France Laboratory of Smart Grid, Ministry of Recherche Education, & Tianjin University, TianjinDreyfous 300072, China c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Abstract Abstract Uncertainties of cooling load may make cooling system oversized. Most of previous studies implement

probabilistic-based uncertainty analysis, intending to achieve optimization and reliability simultaneously. However, District heatingthe networks are commonly addressedlittle in the literatureThis as one of investigates the most effective solutions for decreasing the how to reduce load uncertainty has received attention. paper the impact of water storage on greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat the design of cooling system considering load uncertainty. Information entropy is used as a convergence index of load sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, uncertainty and used to determine how many random simulations should to be performed. A cooling system prolonging the investment return period. configured with water storage (system B) and another system without water storage (system A as a comparation The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand system) are investigated in this paper. In this paper, the configure of system A and system B are optimized respectively. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 The result shows the capacity distribution of typology. system AThree is consistent with the distribution of high) extreme But, buildings that varythat in both construction period and weather scenarios (low, medium, and loads. three district the capacity distribution of system B is more concentrated as the water storage can reshape the load curve. Water renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were storage improves the flexibility of system B. Therefore, system Bdeveloped is more reliable and economical than system A. compared with results from a dynamic heat demand model, previously and validated by the authors.

results showed that when only weatherLtd. change is considered, the margin of error could be acceptable for some applications ©The 2019 The Authors. Published by Elsevier Copyright ©in2018 Elsevier Ltd.was All rights than reserved. (the iserror annual 20% for alllicense weather scenarios considered). However, after introducing renovation This an open accessdemand article underlower the CC-BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of(depending the scientific committee of the Applied Energy Symposium Forum, scenarios, the error value increased up to 59.5% on the weather and renovation combinationand considered). Selection and peer-review under responsibility of the scientific committee of the Applied scenarios Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. The value Energy of slopeIntegration coefficientwith increased on average REM within2018. the range of 3.8% up to 8% per decade, that corresponds to the Renewable Mini/Microgrids, decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Keywords: robust optimization; information water storage; load uncertainty; renovation scenarios considered). On entropy; the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. * Corresponding author. Tel.: +86 13672086760; fax: 022-27407800.

© 2017 The Authors. Published by Elsevier Ltd. E-mail address: [email protected] Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. Keywords: Heat demand; Forecast; Climate change

1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Renewable Energy Integration with Mini/Microgrids, REM 2018. 10.1016/j.egypro.2018.12.064



LI Yang et al. / Energy Procedia 159 (2019) 430–435 Author name / Energy Procedia 00 (2018) 000–000

431 2

Introduction The design of the cooling system not only affects the initial investment of the system, but also affects the system efficiency. Uncertainties such as load, renewable energy and so on make cooling system design complicated. The traditional cooling design method cannot balance optimization and reliability well as these uncertainties[1]. Many uncertainty analysis methods have performed to investigate the uncertainty in the energy system design process. Lu et al. used sensitivity analysis to explore the factors that affect the system efficiency [2]. Furtherly, Lu et al. proposed a robust design method for sizing renewable energy systems in near zero building concerning uncertainties in renewable resources and demand load. The failure rate, annual zero energy consumption balance rate and system comprehensive evaluation index was analysed [3]. Even Monte Carlo simulation method can achieve random simulation of uncertain factors, Tian et al. pointed out that it is difficult to obtain accurate building information and probability distribution of building information during the architectural planning stage. Therefore, the author used Dempster-Shafer theory to describe the uncertain construction information [4]. The Prediction Intervals such as delta technique、Bayesian technique、Bootstrap and mean-variance estimation have been studied and adopted by a large number of scholars. Khosravi et al. proposed the SA+NN (simulated annealing + neural network) method for interval prediction and proposed the target value coverage probability and the normalized target scale interval prediction evaluation index [5,6]. Hussain et al. used the method in [5] to predict the interval of cold, hot and electric load. The author further used a two-stage planning approach to optimize the site and size of integrated energy systems. In the sizing process, the author adopted the worst-case method to select the upper bound of load and the lower bound of renewable energy output as the boundary conditions, considering that if the integrated community energy system can meet the demand in the most adverse conditions, it can meet any other situation [7]. Obviously, this method is too conservative. For quantification of uncertainty parameters in integrated energy system (IES) system，Fu et al. quantified the uncertainty of integrated energy systems using information entropy and used the principle of maximum entropy to select the optimal uncertainty parameter description model [8]. In addition to studying uncertainty from various methods, Cheng et al. explored the overall system efficiency by combining different type of chiller. Through scenario analysis method, the optimal sequence is obtained. Reliability and economical optimization are achieved through the improvement of the structure [9]. Cheng et al. also investigated the design method of chilled water systems considering uncertainty of design cooling load and pump design flow. The author further discussed the reliability of pump systems with different configurations using Markov method and obtained the optimal water pump configuration scheme considering reliability [10]。Probability constraint problem is the key point for solving uncertain optimization problems ， Hu et al. established a probabilistic constraint condition and converted probability constraints to deterministic constraints [11]. As we all know, load demand and renewable energy can be represented by probability distribution function. However, their temporal characteristics as time series are usually ignored. How to consider load temporal characteristics and probability distribution characteristics simultaneously in the optimal design of cooling system is the key to realize the system optimal design. When energy storage device is considered in the cooling system, the temporal characteristics of the chiller power will be changed and probability distribution characteristics will be changed accordingly. This paper investigates the effect of water storage on design of cooling system considering load uncertainty. A robust optimization design method is proposed and applied in a hospital building in Tianjin. 1. Methodology This paper presents a two-step optimization method for robust optimization of cooling systems with water storage. Fig.1 shows the step of the robust optimal design. In the first step, M trials of cooling load simulations are performed firstly considering internal load and building uncertainties, as shown in Tab. 1. Next, we obtain M optimized configuration schemes considering load uncertainty. In the second step, system reliability is evaluated without considering the operation cost. A robust optimal system configuration is obtained considering the reliability and the life cycle economy of the system simultaneously.

LI Yang et al. / Energy Procedia 159 (2019) 430–435 Author name / Energy Procedia 00 (2018) 000–000

432

3

M=1 (used to count the number of simualtion) j=1

Stochastic simulation of cooling load System j without strorage

Yes

reevaluate the max capacity of system j

max F(i)=f(Q,load)

Optimal design system j

j=j+1

min F(j)=f(x(j),y(j))

Calculate the Information Entropy of cooling loads

H (load )

M=M+1

p (load )

N n 1

j>=M

p (load n )

Yes

If the H(load) coverage?

No

Robust cooling system

Fig. 1 A flow chart of the robust optimal design

1.1. Quantify cooling load uncertainty In general, stochastic input parameters can be depicted by a probability distribution function, however, it is difficult to find an accurate distribution function to depict load distribution characteristics [4]. Therefore, other indicators need to be proposed to quantify the uncertainty of the cooling load. In 1948, Shannon proposed the theory of information entropy. Information entropy represents the average amount of information of a random variable, so this value can be used as a measure of data uncertainty [12]。This paper uses information entropy as an index of the uncertainty of the cold load，Information entropy can be expressed as: q

H (X )

a 1

p ( xa ) log 2 p ( xa )

（1）

H ( X ) presents the information entropy of the random variable X, p( xa ) presents the probability of occurrence of the event xa . In Eq. (1),

1.2. Cooling system robust optimization method Setp01：Economic optimization (minimizing) Firstly, the optimal cooling system configuration is obtained by minimizing system life cycle cost. Initial investment cost and operation and maintenance costs of the system is presented in Eq. (2). Eq. (3) and Eq. (4) presents cooling and power balance constraints. Eq. (5)-Eq. (9) are equipment constraints。

N i RC i UP i θ i + RF S V S UP S θ S +

min F = RF C i

T

E(d,τ) UP E (d , )

（2）

τ=1

i

QDi (d,τ) Q SO (d,τ)

SO

Cload j (d , )

QDi (d,τ) QSi (d,τ) COPi

E(d,τ) i

QDi (d,τ)+ QSi (d,τ)

N i RC i

（3）

i

（4）

i

（5）

Q S ('d1','τ1') = 0 Q S (d,'τ1')

Q S (d - d1,'τ24') (1

S

) i

QSi (d,τ)

（6） SI

Q SO (d,'τ1')

( for d

d1) （7）



LI Yang et al. / Energy Procedia 159 (2019) 430–435 Author name / Energy Procedia 00 (2018) 000–000

Q S (d,τ) = Q S (d,τ - τ1) (1

S

) i

QSi (d,τ)

Q SO (d,τ)

SI

433 4

( for

1)

Q S (d,τ) V S R S

（8） （9）

These variables are: N is the number of chiller, V S is water storage tank volume m3, E(d,τ) is electric power of chiller (kW), QDi (d,τ) is cooling power of chiller for meeting load (kW), QSi (d,τ) is cooling power of chiller for storage (kW), Q SO (d,τ) is discharged rate of water storage (kW)， Q S (d,τ) is quantity cold energy stored in tank kWh。 These parameters are： RF is investment recovery coefficient, RC is rated capacity of chiller (kW), UP is SI

SO

unit price of equipment (yuan/kW), θ is a coefficient of auxiliary equipment investment, / is energy charge/discharge efficiency of water storage tanks, Cload j (d , ) is cooling load in scene j (kW), COPi is chiller i

coefficient of performance, is a coefficient of auxiliary equipment energy consumption, d day (1-107), is during time (1 hour). (1-24),

hour

Step02： capacity optimization (maximizing) When encounter extreme load condition, the energy supply reliability should be guaranteed at the expense of economy. The reliability of M system schemes obtained in the first step is evaluated separately in this section. Maximum energy supply capacity is defined as the objective function. Eq. (10) and Eq. (11) can guarantee the maximum energy supply capacity. bin(d,τ) is a binary variable (0 means cooling system is unable to meet cooling demand, 1 means cooling system can meet cooling demand, M is a constant.

max F =

bin(d,τ)M d

i

（10）

τ

QDi (d,τ) Q SO (d,τ)

SO

Cload j (d , )bin(d,τ)

（11）

2. Case study A hospital building in Tianjin is illustrated in this paper. The uncertainties of parameters such as building envelope, room temperature setting, fresh air volume and infiltration are considered in the random cooling load simulation, as shown in Tab. 1. Information entropy of cooling load is used as a convergence index of Monte Carlo (MC) simulations. It is believed that with the increase of the number of random simulations, the information entropy of the uncertainty load will gradually converge. Therefore, when the load information entropy converges, the cooling loads will have a determined boundary. Table 1 Information of input used in cooling load uncertainty study Items Parameters Building construction Wall conductivity W/m2.K Window conductivity W/m2.K Roof conductivity W/m2.K Indoor condition Occupancy density W/m2 Power density W/m2 Lighting density W/m2 Ventilation rate 1/hr Indoor set temperature ℃

Reference value

Distribution

0.45 2.85 0.25

T (0.36, 0.60, 0.45) T (2.50, 3.24, 2.85) T (0.20,0.30,0.25)

6 9.6 6.4 0.7 24

T (3, 9, 6) T (3.6, 14.4, 9.6) T (2.4, 9.6, 6.4) U (0.4, 0.9) N (24, 0.1)

LI Yang et al. / Energy Procedia 159 (2019) 430–435 Author name / Energy Procedia 00 (2018) 000–000

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5

2.1. MC simulation of building cooling load

3.0%

5.10

2.5%

5.00

2.0%

4.90 4.80

4.70

80%

frequency cumulative frequency

1.5%

20%

0.5%

Fig. 2 Information entropy of cooling load

2291

2177

2062

1948

1833

1718

1604

1489

0% 1375

0.0% 1260

100

1146

90

917

80

802

70

1031

60

687

50

Simulation times

573

40

458

30

344

20

0

10

229

0

60% 40%

1.0%

115

4.60

100%

cumulative frequency %

5.20

frequency %

Information Entropy

As shown in Fig. 2, it can be found that the information entropy of cooling load has converged after 100 random simulations. It means that performing more simulations will not change the uncertainty of the load. Therefore, cooling system can be optimized based on the 100 simulation cooling loads. As shown in Fig. 3, the cooling loads complied with a bimodal Gaussian distribution, and the maximum load is 2291 kW.

Coolingload kW

Fig. 3 Building cooling load distribution of 100 simulations

2.2. Cooling system analysis The cooling load shown in Figure 3 is used as the boundary condition for optimal design of the cooling system. By using GAMS-Cplex[12], optimization calculation for system A (without storage) and system B (with storage) is performed separately. As shown in Fig. 4, the distribution of the capacity of cooling system A is close to the peak load distribution. Whereas, the chiller capacity is far smaller than the peak load value when the water storage tank is configured in the system (system B). Furthermore, chiller capacity distribution is more concentrated. It means that water storage reduces load uncertainty. Due to the water storage can change the uncertainty of chiller cooling power, the economy of system B is significantly improved under any load scenario (M=100 trials of load simulations), as shown in Fig. 5.

Investment ￥（with storage）

3100000

2600000

y = 0.7329x + 41034 R² = 0.9814 2100000

1600000 1600000

2100000

2600000

3100000

Investment ￥（without storage）

Fig. 4 Capacity distribution of system A/B and extreme Fig. 5 Investment of system A and B load distribution To further investigate the reliability of system B, 100 system configuration schemes (system B) are optimized again. In this section, the maximum load at any time is used as cooling load boundary condition (the blue line in Fig. 6) and the maximum energy supply capacity (as defined in Eq. 10) as the objective function. As shown in Fig. 7, it was found that the max failure hours are 169h when cooling system configured water storage (system B). However,



LI Yang et al. / Energy Procedia 159 (2019) 430–435 Author name / Energy Procedia 00 (2018) 000–000

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max failure hours can reach 1200h when cooling system without considering water storage (system A). This reveals that water storage can reshape the energy supply curve by adjusting the charge and discharge strategy. Therefore, the water storage system can flexibility adapt to the random variation of cooling load.

Fig.6 100 trials of cooling load simulations and hourly maximum cooling load

Fig. 7 Hours of failure of system A (without water storage) and B (with water storage)

3. Conclusions This paper investigates the impact of water storage on robust optimal design of cooling system. Through random simulation of cooling load, it can be found that information entropy can be used as a convergence index of MC simulation. By performing optimization calculation for system A (without water storage) and system B (with water storage) separately in 100 uncertain load scenarios, the results indicate that water storage can not only improve the economy of cooling system, but also can achieve random load by adjusting storage strategies. Therefore, Water storage can improve system reliability to some extent. Acknowledgements This paper is supported by Guangdong Grid Company Limited of China, project number: GDKJQQ20161202. References Gang W, Wang S, Xiao F, et al. Robust optimal design of building cooling systems considering cooling load uncertainty and equipment reliability[J]. Applied Energy, 2015, 159:265-275. [2] Lu Y H, Wang S W, Yan C C, et al. Impacts of renewable energy system design inputs on the performance robustness of net zero energy buildings.[J]. Energy, 2015, 93:1595-1606. [3] Lu Y, Wang S, Yan C, et al. Robust optimal design of renewable energy system in nearly/net zero energy buildings under uncertainties[J]. Applied Energy, 2017, 187(2):62-71. [4] Tian W, Meng X, Yin B, et al. Design of Robust Green Buildings Using a Non-probabilistic Uncertainty Analysis Method[J]. Procedia Engineering, 2017, 205:1049-1055. [5] Khosravi A, Nahavandi S, Creighton D. Construction of Optimal Prediction Intervals for Load Forecasting Problems[J]. IEEE Transactions on Power Systems, 2010, 25(3):1496-1503. [6] Khosravi A, Nahavandi S, Creighton D, et al. Lower Upper Bound Estimation Method for Construction of Neural Network-Based Prediction Intervals[J]. IEEE Transactions on Neural Networks, 2011, 22(3):337-346. [7] Hussain A, Arif S M, Aslam M, et al. Optimal siting and sizing of tri-generation equipment for developing an autonomous community microgrid considering uncertainties[J]. Sustainable Cities & Society, 2017, 32:318-330. [8] Fu X, Sun H, Guo Q, et al. Uncertainty analysis of an integrated energy system based on information theory[J]. Energy, 2017, 122:649-662. [9] Cheng Q, Yan C, Wang S. Robust Optimal Design of Chiller Plants Based on Cooling Load Distribution ☆[J]. Energy Procedia, 2015, 75:1354-1359. [10] Cheng Q, Wang S, Yan C. Robust optimal design of chilled water systems in buildings with quantified uncertainty and reliability for minimized life-cycle cost[J]. Energy & Buildings, 2016, 126:159-169. [11] Hu M, Cho H. A probability constrained multi-objective optimization model for CCHP system operation decision support[J]. Applied Energy, 2014, 116(116):230-242. [12] https://www.gams.com/ [1]