MPC-based optimal scheduling of grid-connected low energy buildings with thermal energy storages

Accepted Manuscript Title: MPC-Based Optimal Scheduling of Grid-Connected Low Energy Buildings with Thermal Energy Storages Author: Yang Zhao Yuehong Lu Chengchu Yan Shengwei Wang PII: DOI: Reference:

S0378-7788(14)00864-0 http://dx.doi.org/doi:10.1016/j.enbuild.2014.10.019 ENB 5402

To appear in:

ENB

Received date: Revised date: Accepted date:

14-3-2014 8-10-2014 9-10-2014

Please cite this article as: Y. Zhao, Y. Lu, C. Yan, S. Wang, MPC-Based Optimal Scheduling of Grid-Connected Low Energy Buildings with Thermal Energy Storages, Energy and Buildings (2014), http://dx.doi.org/10.1016/j.enbuild.2014.10.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A model predictive control method using NLP algorithm is proposed It optimizes the scheduling of the energy systems in grid-connected low energy buildings.

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Evaluations are conducted on the Hong Kong Zero Carbon Building.

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It achieved significant reductions in CO2 emission, energy consumptions and operation cost

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MPC-Based Optimal Scheduling of Grid-Connected Low Energy Buildings with Thermal Energy Storages Yang Zhao, Yuehong Lu, Chengchu Yan and Shengwei Wang*

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Department of Building Services Engineering, The Hong Kong Polytechnic University Hong Kong

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Abstract: The mismatch between the energy demand and energy supply is one of the major

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problems in low or zero energy buildings with distributed power generations. The policy of timesensitive electricity pricing provides a possibility to improve the energy efficiency of the building energy systems. A model predictive control (MPC)-based strategy using nonlinear

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programming (NLP) algorithm is proposed to optimize the scheduling of the energy systems under day-ahead electricity pricing. Evaluations are conducted using a reference building based

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on the Hong Kong Zero Carbon Building. A stratified chilled water storage tank is introduced as the thermal energy storage, which makes possible to optimize the scheduling of the building energy systems. The distributed power generation in the building consists of a combined cooling

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and power system and a photovoltaic (PV) system. Two types of grid-connections (i.e., selling

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electricity to grid is allowed/forbidden) are considered. Results show that the proposed optimal scheduling strategy can achieve significant reductions in carbon dioxide emission, primary

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energy consumptions and operation cost. Sensitivity analysis shows uncertainties in the inputs do not affect the performance of the proposed method significantly. keywords: model predictive control, low energy building, thermal storage, uncertainty, realtime pricing.

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Corresponding author: Shengwei Wang, phone: 852-27665858, fax: 852-27657198, email: [email protected]

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1. Introduction

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Renewable and distributed power generations have been recognized as efficient, reliable and environment-friendly options towards sustainable development and low-carbon society [1]. The applications of renewable and distributed power generation systems in buildings have attracted

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increasing attentions in recent years, including combined cooling, heating and power (CCHP) systems [2], photovoltaic systems (PV) [3], small wind turbines [4], fuel cells [9] and other

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renewable energy resources. The optimal scheduling of the energy use, energy generation and the interaction with the power grid provides the possibility to achieve further pollution emission

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reductions, primary energy savings and operation cost savings.

The mismatch between the energy demand and supply is one of the major problems in the

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applications of renewable and distributed energy systems in buildings. Renewable energy systems, such as PV systems and wind turbines, generally provide the harvested energies that do

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not match with the demand load profiles [5],[6]. The CCHP systems also have mismatch problems in satisfying both the power demands and the heat/cold demands simultaneously.

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Energy storage systems have been recognized as effective means to reduce the mismatch

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between the demand side and the supply side by providing an additional degree of freedom to optimize the scheduling of the energy uses and generations. Martínez-Lera et al. demonstrated that the use of thermal energy storage (TES) in buildings with CHP (combined heating and power generation) systems could help alleviating the negative effects of the variability of electricity demands and thermal demands in buildings [7]. Similar conclusions can be found from the researches of Smith et al. [8] and Mago et al. [9], etc. On the other hand, the use of energy storage systems also increases the complexity of the energy systems in buildings since the periods of charge, discharge and standby of the energy storage systems need to be optimized. Almost all of the optimal scheduling methods follow the following basic idea. When the electricity price is low (i.e., during off-peak periods), the building stores as much energy as possible depending on the maximal storage capacity and the predicted energy demands in the coming n hours. When the electricity price is high (i.e., during

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peak periods), the building imports as less electricity as possible from the grid or exports as much electricity as possible to the grid. Model predictive control (MPC) methods are widely used in the optimal controls of HVAC

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systems of buildings, e.g. heating system [10], cooling systems [11], solar tank [12] and peak electricity demand control [13]. More details can be found in a literature review by Afram and Janabi-Sharifi [14]. MPC is also introduced for the optimal scheduling of the charge/discharge of

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energy storage systems and the distributed power generations. These methods transfer the scheduling problems to programming tasks which can be solved by powerful programming

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algorithms, such as linear programming algorithms, nonlinear programming (NLP) algorithms [15], mixed integer linear programming algorithms (MILP) [16] and even mixed integer

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nonlinear programming (MINLP) algorithms [17]. Ma et al. (2009) proposed a NLP-based method to optimize the operation of a chiller plant with a chilled water storage tank on a campus

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[15]. Results show that 24.5% of the operation cost can be saved. Kashima and Boyd proposed a MILP-based method to optimize the operation of a TES system for HVAC in terms of electricity cost [18]. Berkenkamp and Gwerder proposed a generic MPC algorithm to optimize the

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management of stratified thermal storage tanks [19]. Avci et al. proposed a practical cost and

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energy efficient MPC method for HVAC load under dynamic real-time electricity pricing [20]. Cigler et al. proposed a method to analyze performance of MPC controller in buildings. It

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enables uses to explore the controller behaviors, tune controllers, validate mathematical models in practical applications [21]. More details about HVAC scheduling techniques for buildings can be found in a review paper of Haniff et al.[22]. CCHP systems have been widely used in buildings in recent years concerning their significant benefits in carbon dioxide emission reduction, primary energy cost saving and operation cost saving [23]. There are already a few publications on optimal scheduling of CCHP/CHP/CCP (combined heating and power generation) systems. For instance, Chandan et al. proposed a NLP-based method for the optimal control of a CCHP plant with TES [24]. Mitra et al. proposed a MILP-based method for the optimal scheduling of the industrial CHP plants under time-sensitive electricity pricing [25] Ranjbar et al. concluded that the combination of cell power plants and wind energy in a hybrid structure for CHP systems causes lower operational cost than that of individual units [26]. However, only limited studies can be found on the optimal control of distributed energy systems involving both active energy resources (e.g. CCHP, CHP and CCP) and passive renewable energy resources (e.g.

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PVs, wind turbines). Smart grids adopting time-sensitive electricity pricings could also provide the possibility to improve the energy efficiency of the building energy systems. The scheduling control methods involving time-sensitive electricity price need to be investigated.

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This study therefore addresses the optimal scheduling of the energy systems (both active and passive energy systems) in buildings connected to a grid under the time-sensitive electricity pricing. A MPC-based strategy is developed using NLP algorithm to optimize the power

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generation/use and the TES charge/discharge. Evaluations are conducted using a reference building based on the Hong Kong Zero Carbon Building (the first zero energy building in Hong

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Kong). Quantitative sensitivity analysis is made to evaluate the effects of uncertainties in the performance of the proposed method. Comprehensive analysis is also made on the economic and

2.1 Description of the energy systems

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2. MPC-based Optimal Scheduling Strategy

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environmental benefits of the optimal scheduling strategy.

A building with typical energy systems is adopted as the reference building in this study, as

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shown in Figure 1, which is revised on the basis of the Hong Kong Zero Carbon Building. The

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building involves three main energy systems, i.e., a CCP system, a PV system and three electric chillers (EC). The CCP system consists of a power generation unit (PGU) and an adsorption

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chiller (AC). The exhaust gas from the PGU is utilized as the heat source of the adsorption chiller that generates a portion of the cold energy (i.e., the chilled water) for building airconditioning. In this study, a stratified chilled water storage tank (125 m3) is added into the building, which is not included in the Hong Kong Zero Carbon Building. In the building, the amount of supplied electricity should equal to the amount of consumed electricity at any time. The electricity suppliers are the photovoltaic system, the power generation unit of CCP and the power grid (when the system is buying electricity from grid). The electricity consumers are the electric chillers, the HVAC equipment excluding electric chillers, lighting, office appliances and the power grid (when the system is exporting electricity to grid). Meanwhile, there is a balance between the cold supply and the cold demand. The building is the main cold consumer. The adsorption chiller and the electric chillers are the cold suppliers. The TES is a supplier when it discharges and a consumer when it charges. As discussed in the

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introduction section, the TES could provide a degree of freedom to handle the mismatch problems of the CCP and PV systems. The TES also makes it possible to schedule the energy use for achieving maximum energy efficiency of the building.

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2.2 Model predictive control (MPC) using NLP algorithm MPC, also called receding horizon control, solves a discrete-time optimal control problem over a finite given horizon to minimize the objective function subject to some constraints. Figure 2

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shows the flow chart of the proposed MPC-based optimal scheduling strategy. The inputs are the predicted values of the following variables in the coming 24 hours with an interval of one hour,

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including the cooling load (Qtcl), PV power generation (PtPV), electricity consumption of the building except for the electric chillers ( Ptothers+PtHVAC’) and the electricity price (ctelec, provided

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by the grid day-ahead). The outputs are the schedule of the variables to be optimized in the coming 24 hours, including the tank (QtTES), gas consumption of the power generator (Vtgas),

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electricity import/export from/to the grid (Ptgrid), and cold provided by electric chillers (QtEC). In this study, the prediction horizon is 24 hours. It is divided into 24 intervals according to the interval of the day-ahead pricing. Thus, it determines 96 values (4x24) of the four output

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variables on the basis of the 96 values (4x24) of the four input variables in the coming 24 hours.

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The optimal scheduling problem of the MPC-based strategy is described mathematically as

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follows. Solving the problem is to minimize the objective function, Eq. (1a), subject to the constraints, i.e., Eq. (2)-(7). It can be solved by nonlinear programming (NLP) algorithm. An outline on NLP algorithm is given in Section 2.4. Objective function

(1a)

The simplified physical models described in the next section (2.3) are used to predict the energy system operation performance responding to the changes of the four input variables. In the simulation, Eq. (1a) is reformed to Eq. (1b) through correlating the four input variables and the four output variables by using Eq. (9)-(14). (1b) Constraint equations i. Electricity balance:

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(2) ii. Cooling load balance: (3)

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iii. Power generator of the CCP unit:

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iv. Electric chiller:

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v. Adsorption chiller:

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vi. Thermal storage tank:

(4)

(5)

(6)

(7)

It is worth noting that the PGU, electric chillers and adsorption chiller usually have their own

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minimum load ratio. The TES also should have the minimum water flow rate. Eq. (2)-(7) do not include those performance limits. In addition, the electric chiller cannot work when QtEC is lower

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than a certain load ratio, e.g. 30% of QEC,max. Eq. (8) is therefore more physically meaningful

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compared with Eq. (7)

, or

(8)

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However, equations in the form of Eq. (8) make the optimization problem to be a MINLP problem which is more complex to be solved mathematically. In reality, these components are set to have rather poor performance when part load ratios are lower than their lower limits. The optimization algorithm can therefore avoid the components to work under such low partial loads naturally most time. Therefore, using Eq. (4)-(7) is practically acceptable as it can be observed from the optimization outputs. 2.3 Energy system models

Models of the energy systems involved are the simplified physical models described as follows. They are very simple models developed for the use in the model predictive control strategy. Thermal storage tank Within the stratified chilled water storage tank, the warm water is at the upper part and the chilled water is at the lower part since the density of warm water is lower than that of chilled

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water. When the tank discharges, the chilled water is pumped from the bottom of the tank to the HVAC system as supply chilled water. Meanwhile, the same amount of return chilled water from the HVAC system is charged to the top of the tank. In this study, it is assumed that the warm water has the same temperature as the return chilled water, and the chilled water (TTES,cold) has temperature are assumed to be constants, e.g., 7oC and 12 oC respectively.

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the same temperature as the supply chilled water. The chilled water temperature and return water

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The amount of stored cold (QtTES,cold) at time t is calculated by Eq. (9). It is assumed that the cold

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loss of the tank is constant, i.e., a constant ratio (ηtTES) of the cooling storage capacity of the tank

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(QTES,cold,max), as represented in the second item on the right of Eq. (9). (9)

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where, mtTES,cold is the amount of chilled water in the tank. ηtTES is the cold loss coefficient. It is

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estimated to be 0.5% of the storage capacity per hour (12% per day) in this study. The delay effects of charging and discharging are ignored. Electric chiller

The power consumption of the electric chiller (PtEC) is a function of its cooling load (QtEC) and its COP (COPtEC), as Eq. (10).

(10)

where, COPtEC is a polynomial function of its part load ratio (PLRtEC), as Eq. (11). (11) where, a1, a2, a3 and a4 are coefficients which can be identified using operation data. Power generation unit

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The power generation of the PGU depends on the amount of the heat gas (Vtgas) consumed and its

(12)

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efficiency (ηtPG), as Eq. (12).

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where, ηtPGU is a polynomial function of its part load ratio (PLRtPG), as Eq. (13). b1, b2 and b3 are

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coefficients which can be identified using operation data.

Adsorption chiller

(13)

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The adsorption chiller generates cold using the exhaust hot gas from the power generation unit.

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The generated cold (QtAC) depends on the amount of heat from the exhaust hot gas, the heat

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recovery ratio of the adsorption chiller (ηhrs), and its efficiency (COPAC), as shown in Eq. (14).

ηhrs and COPAC are assumed as constants in this study.

(14)

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2.4 An outline of nonlinear programming (NLP) algorithm Nonlinear programming is a kind of mathematical programming as a branch of optimization theory. NLP problems are widespread in engineering, economics, physical sciences and

Minimize for i=1,…,m1

Subject to

(15)

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for j=1,…,m2

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mathematics, etc. The general NLP problem can be stated simply as follows [30]:

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where, f, gi and hj are functions defined on Rn. X is a subset of Rn. x = [x1,x2,…,xn]T is a vector of n decision variables. f is the objective function. The set X generally defines the lower and upper bounds for each variables. Each of the constrains

is called an equality function. Solving above problem is to find

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Each of the contraints

is called an inequality function.

the values of x that minmize the objective function f and the meanwhile statisfy the restrictions of

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constrains. It becomes a NLP problem if any of the constrains or the objective function is

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nonlinear. Otherwise, it is a linear programming problem. There are many methods for solving the NLP problems, e.g., gradient projection method [28],

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reduced gradient method [29] and penalty function method [30]. Many software tools are also available, such as Matlab optimization toolbox [34], Lingo [32] and Bonmin [33]. In this study, the Matlab optimization toolbox is introduced to solve such a NLP problem. 3. Evaluation of The Optimal Scheduling Strategy 3.1 Configuration of the building and the energy system The Hong Kong Zero Carbon Building [27] (with some minor revisions on energy systems) is introduced in this study as a reference building to evaluate the proposed strategy. It is a 3-storey building with net floor area of 1,520 m2. It adopts a few passive approaches (e.g., earth cooling tube, external shading and ultra-low thermal transfer) and a few active approaches (e.g., active skylight and high temperature cooling system). The building is used for multiple purposes including a visitor education center, offices, demonstration home and other ancillary functions.

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The design peak cooling load is 160kW. Space heating is not provided in this building. The office hour is between 9:00am and 19:00pm. A schematic of the energy system in the reference building is shown in Figure 1. A stratified chilled water storage tank with a volume of 125 m3 is added in the building. The main design parameters of the building energy systems are listed in

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Table 1. Three types of PV panels are used in the building, i.e., multi-crystalline on the inclined roof (1016 m2), BIPV (building integrated photovoltaics)-thin film covering the viewing

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platform (25 m2), and cylindrical CIGS (copper indium gallium selenide solar cells)-thin film integrated in the air-tree (15 m2). The peak capacities of PV panels are around 70 kW/m2 in

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winter, 95 kW/m2 in summer, and 125kW/m2 in spring and autumn. It is worth noticing that the adsorption chiller is resized from 100 kW to 130 kW since the desiccant wheel is not included in this study, which consumes a portion of the CCP exhaust heat in the Hong Kong Zero Carbon

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Building.

Table 2 shows the parameters of the models, including the coefficients of the electric chiller

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model and the PGU model, CDE factors, PEC factors and prices of electricity and natural gas in Hong Kong. The coefficients are -3.22, 3.60, 3.16 and 0.12 for a1, a2, a3 and a4 respectively in

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Eq.(11). The coefficients are 0.44, -1.02, 0.83 and 0.08 for b1, b2, b3 and b4 in Eq. (13). The actual data of the CDE factors and the PEC factors for Hong Kong are not available.

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Alternatively, the values from the previous publications are used in this study. The electricity cost of CCP, which considers the electricity saving by the recovered exhaust gas, is 0.2391

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USD/kWh in Hong Kong.

A dynamic simulator is developed on the TRNSYS [38] platform to predict the three input variables for the coming 24 hours while the MPC-based optimization strategy uses data with an interval of 1 hour. Evaluation tests are conducted in three days (i.e., a cloudy summer day, a cloudy spring day and a sunny spring day). Figure 3 shows the predicted load/generation profiles of the summer and the cloudy spring day. The building cooling load (Qttotal), is calculated using the building model (TYPE56) provided by TRNSYS using the Hong Kong weather data. The PV power generation (PtPV) is calculated on the basis of the weather data using the PV model (TYPE 94) of TRNSYS. The electricity consumption of the HVAC system except the electric chillers (PtHVAC’) is calculated using the HVAC system model developed on TRNSYS platform, which is calibrated using the actual HVAC system operation data monitored in the Hong Kong Zero Carbon Building. The electricity consumption profile of the lighting and office appliances

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(Ptothers) is formed on the basis of the data monitored in the same building. It is assumed that Ptothers is the same in every day in this study. The MPC-based optimization strategy is developed and tested on MATLAB platform. It is worth noticing that, in practical implementation, such

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prediction models or simulator should be integrated with the online MPC-based control. Two cases of grid-connections are considered in this study. In one case, selling electricity to the grid is allowed, which is also the most popular case worldwide. In the other case, selling

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electricity to grid is not allowed, which is the current practice in China. In the future, the latter is also likely to be adopted in Hong Kong since Chinese Mainland provides a large portion of the

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electricity to Hong Kong. The current electricity pricing policy for large consumers in Hong Kong is time-of-use (TOU) plus peak demand charge [36]. In this study, the electricity price is

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formed on the basis of the day-ahead pricing (DAP) in New York in 2013 [38] since nature of the consumers is similar. The average electricity price is 0.052 USD/kWh in New York in 2013

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[38]. The current electricity price is 0.1907 USD/kWh in Hong Kong Island. The DAP data of Hong Kong is therefore formed using Eq. (16).

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(16)

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New York electricity market uses a uniform clearing price auction to provide a common price at each location for all buyers and sellers [38]. In this study, the selling price is set to be the same as

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the buying price as Eq. (17):

(17)

In this study, if selling electricity to the grid is allowed, the real-time electricity price is assumed as Eq. (18). If selling electricity to the grid is forbidden, the real-time electricity price is assumed as Eq. (19).

(18) (19)

The carbon dioxide emission (CDE), primary energy consumption (PEC) and operational cost are calculated using Eq. (20), Eq. (21) and Eq. (22) respectively. Where, CDEe is the carbon dioxide emission factor for delivered electricity. CDEgas is the carbon dioxide emission factor for on-site natural gas combustion in PGU. Vtgas is the amount of the natural gas consumed at time t.

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PECe is the primary energy consumption factor for the delivered electricity. PECgas is the primary energy consumption factor for the delivered natural gas. The actual values used can be found in Table 2.

(21) (22)

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(20)

3.2 Case I - Selling electricity to grid is allowed

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In the summer day, the optimized schedule of the hourly electricity consumption/generation is shown in Figure 4. The PGU operates at full load when the grid electricity price is higher than

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the electricity cost of CCP (0.239 USD/kWh), i.e. between 12:00pm and 16:00pm. Meanwhile, the surplus electricity is sold to the grid. The TES is fully charged when the grid electricity price is low in the off-peak period (between 1:00am and 7:00am). There electric chillers operates at

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full load when the grid electricity price is low (0.037 USD/kWh) between 4:00am and 6:00am. The optimal scheduling of the hourly cold generation/consumption is shown in Figure 5. The

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adsorption chiller services a large portion of the cooling load of the building when the PGU

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operates at full load between 12:00pm and 16:00pm while the TES services the rest portion of the cooling load. Between 11:00am and 12:00pm, the cooling load is partially served by the TES

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while TES has high priority as the grid electricity price is high. In the rest of office hour (9:00am - 11:00am) building cooling is served by the electric chillers. It is worth noticing that the amount of chilled water in TES is initialized to mTES,min in all test cases. The CDE, PEC and the operation cost of the building in a summer day are calculated in four different situations according to the availabilities of PV, TES and CCP, as shown in Table 3. The first situation, which stands for the building with PV system, is used as the benchmark. The application of TES results in an increase of both CDE and PEC by 2% and reduction of operation cost by 18%. There is no surplus electricity from PV system in the cases. Therefore, there is no coupling between PV system and TES system. It is why the effects of adding TES to PV are the same as shown in Table 3 and Table 4, as well as Table 4 and Table 6. The application of CCP results in significantly reductions of CDE (27%) and PEC (15%) since the exhaust gas is well utilized. Compared with the third situation using CCP, the use of both CCP and TES (fourth

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situation) results in slight increases of CDE (2%) and PEC (1%). But the operation cost saving is significant (i.e. 29%). In

the

cloudy

spring

day,

the

optimized

schedule

of

the

hourly

electricity

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consumption/generation is as shown in Figure 6. The grid electricity price has two peaks. The PGU operates at full load once the grid electricity price is higher than the electricity cost of PGU (11:00am-14:00pm and 17:00pm-21:00pm). It is worth noting that the PGU still operates

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between 20:00pm and 21:00pm to sell electricity to grid since the electricity price is still high. The TES allows PGU to do so since it stores all of the cold from the adsorption chiller. The PGU

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does not work between 14:00pm and 17:00pm although the electricity price is slightly higher than the cost of the PGU. During this period, it could not save operation cost if the PGU works,

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since the surplus cold would be stored in TES and would not be used till the end of this day. The optimized schedule of the hourly cold generation/consumption is shown in Figure 7. The

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TES offers advantages in storing the surplus cold from the adsorption chiller. Benefited from the TES, the PGU can work longer to save the operation cost and CO2 emission.

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The CDE, PEC and operation cost of the building in the cloudy spring day in the four situations

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are presented in Table 4. The use of TES results the increases of CDE and PEC by 2% respectively, and reduction of the operation cost by 12%. The use of CCP results in significant

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saving of CDE (41%) and PEC (23%). Compared with the situation using CCP, the use of both CCP and TES results in more saving of CDE (48%) and similar saving of PEC (22%). The operation cost saving is also significant (28%). It is worth noting that a portion of cold in the TES can be used in the next day. The performance can be better if the cold left in the TES is considered in the calculation of CDE, PEC and operation cost. 3.3 Case II - Selling electricity to grid is forbidden In the summer day, the optimized schedule of the hourly electricity consumption/generation is shown in Figure 8. During the peak hours of the grid electricity price (12:00pm-17:00pm), the PGU works at partial load providing a portion of electricity (the other portion is provided by the PV system). The optimized schedule of the hourly cold generation/consumption is shown in Figure 9. The adsorption chiller and TES provide the cold during the peak hours. During the

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office hours, the electric chillers works longer time compared with the Case I since more cold from TES is consumed during the peak hours. The CDE, PEC and operation cost of the building in the summer day in the four situations are

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shown in Table 5. The use of CCP reduces CDE and PEC by 19% and 11% respectively. Compared with the situation using CCP, the use of both CCP and TES saves less CDE (12%)

In

the

cloudy

spring

day,

the

optimized

schedule

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and PEC (6%). But the operation cost saving is significant (i.e. 24%). of

the

hourly

electricity

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consumption/generation is shown in Figure 10. Compared with the Case I, the PGU does not work in the non-office hour (20:00pm-21:00pm) since it is forbidden to sell electricity to the grid.

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The optimized schedule of the hourly cold generation is shown in Figure 11. The surplus cold from the adsorption chiller is stored in the TES. It offers benefit to the PGU as the PGU can then work at full capacity during the peak hours. There is still cold left in the TES which can be used

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in the next day.The CDE, PEC and operation cost of the building in the cloudy spring day are shown in Table 6. Compared with the situation using CCP and PV, the use of both CCP and TES

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slightly (2%).

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results in less CDE and PEC savings (-3% and -3% respectively). The cost saving increases

In the case of using CCP and PV in the cloudy spring day, the savings of CDE, PEC and cost are

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the same as shown in Table 4 and Table 6. It is because the cooling load in the spring day is small. The cold from adsorption chiller (Qac) can satisfy all of the cooling load (Qcl). The PGU works in partial load to make Qac equal to Qcl. Therefore, the schedules of hourly electricity consumption/generation are the same in both spring cases. In the case of using CCP and PV in the sunny summer day, the savings of CDE, PEC and cost are the different as shown in Table 3 and Table 5. It is because the cooling load in the summer day is high. The cold from adsorption chiller (Qac) cannot satisfy all of the cooling load (Qcl). In Case I, the PGU works in full load to sell the surplus electricity since selling electricity to grid is allowed. In Case II, the PGU cannot work in full load since selling electricity to grid is forbidden. Therefore, the schedules of hourly electricity consumption/generation are different in both summer cases.It is of interest to evaluate how the system works when the PV system provides excess electricity. The optimized schedule of the hourly electricity consumption/generation is therefore evaluated in the sunny spring day, as shown in Figure 12. The electric chiller works to consume the surplus electricity. The surplus

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cold from the electric chiller is stored in the TES, as shown in Figure 13. The TES helps to avoid the waste of electricity. Such situation might also exist in Case I when the grid electricity price is low while the PV system generates surplus electricity.

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3.4 Sensitivity Analysis The MPC-based method determines 96 values (4x24) of the four output variables on the basis of

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the 96 values (4x24) of the four input variables for the coming 24 hours. Uncertainties in the 96 input values would affect the the output values. In this study, Monte Carlo simulation method

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[39] is used to assess the effects of uncertainties. The basic idea is to run simulations many times over with uncertainties in inputs in order to obtain the distributions of the unknown probabilistic all simulations are analyzed in a statistic way.

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results, i.e. CDE, PEC and cost. Such a simulation is repeated 1000 times. CDE, PEC and cost in

The simulations are on the basis of the following assumptions: The Qtcl, PtPV, Ptothers+PtHVAC’ and

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ctelec used in Case I and Case II are assumed to be the true values in the coming 24 hours; The errors in the predicted values are assumed to be normal distributed. The predicted values are

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simulated by adding normal distributed noises to the true values. The predicted values are used as inputs instead of the true values. Two uncertainty levels are considered according to a survey

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of prediction models, i.e. 5% and 10%. 5% means the error is 5% of the mean of true values.

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Noises are added for the first three variables during the office hours (9:00am-19:00pm). Noises are added into ctelec during 0:00am-19:00pm. The electricity prices in the next day during 0:00am-5:00am are revised to be smaller than the values during 20:00pm-24:00pm in the day concerned. It is because TES would be charged for the next day if ctelec is too small during 20:00pm-24:00pm.

The system is operated as follows: firstly, the energy usage is rescheduled once at the beginning of each hour for the coming 24 hours on the basis of the amount of chilled water left in TES and the new predictions for the coming 24 hours. It benefits to take the deviations caused by uncertainties in previous hours into consideration in the optimal schedule in the current hour; Then, in the current hour, the system works according to the schedules which are generated under uncertainties. The actual operating condition presents the true values of Qtcl, PtPV, Ptothers+PtHVAC’ and ctelec. For instance, the actual cooling load in hour t equals to the Qtcl in Case I

Page 16 of 35

or Case II. At the end of current hour, the amount of chilled water in TES is calculated which will be used as initial value for the MPC-based schedule and actual operation in the next hour. Due to uncertainties, the system cannot work exactly as the schedules. Some revisions are made for the actual operation strategy. In the case of selling to grid allowed, among the four output

ip t

variables, two of them are the same as the schedules, i.e. gas consumption of the power generator (Vtgas) and cold provided by electric chillers (QtEC). Sometimes, Vtgas and QtEC are adjusted to the

cr

limit values if their values are larger than the maximum limits. The left two output variables, i.e. Tank discharging/charging (QtTES) and electricity import/export from/to the grid (Ptgrid), are

us

calculated according to the balance of cooling and balance of electricity. In the case of selling to grid forbidden, if Ptgrid is scheduled to be zero, Vtgas is adjusted to maintain Ptgrid to be zero in

an

actual operation unless Vtgas achieves its maximum value. Tank discharging/charging (QtTES) is calculated according to the balance of cold.

M

Figure 14 illustrates histograms of CDE, PEC and cost of 1000 Monte Carlo simulations in the cloudy spring day with uncertainties (10%) in input variables, in the case of selling electricity to grid allowed. The CDE and PEC are almost normal distributed. The costs are not normal

d

distributed. Almost all costs under uncertainties are higher than the ideal value. Table 7 shows

te

the results of Monte Carlo simulations in the case of selling electricity to grid allowed. It is found that CDE, PEC and cost vary in small ranges. It is mainly because TES and grid have reduced

Ac ce p

the negative effects of uncertainties. Uncertainties in the predicted Qtcl are adjusted by TES. Uncertainties in the predicted PtPV and predicted Ptothers+PtHVAC’ are eliminated by grid. Uncertainties in prediced ctelec and QtEC affect CDE, PEC and cost significantly. For instance, if predicted ctelec is higher than electricity cost of CCP (0.239 USD/kWh) but the true ctelec is lower than that value, PGU will fully open which will lead to high cost and low CDE, PEC. Table 8 shows the results of Monte Carlo simulations in the case of selling electricity to grid forbidden. Uncertainties do not affect CDE, PEC and cost significantly. Results demonstrated that uncertainties can be partially handled by the actual operation strategy. The actual operation strategy contributes to maintain CDE, PEC and cost at near optimal levels. TES enhances robustness of this system which makes the adjustments of PGU operation to be possible. It reduces the negative effects of uncertainties.

Page 17 of 35

It is concluded that uncertainties in the four input variables do not affect the performance of the proposed method significantly. Uncertainties can be reduced by the actual operation strategy, TES and grid.

ip t

4. Conclusion A MPC-based optimal scheduling strategy using NLP algorithm is presented in this paper aiming

cr

at improving the energy efficiency of the energy systems in low/zero energy buildings. The strategy schedules the generation/use of electricity and cold as well as cold storage twenty-four

us

hours ahead on the basis of the predicted cooling load and electricity load of the building, the electricity generation of the PV energy system and day-ahead electricity price. It is found that the MPC-based control using NLP algorithm is a very effective method for optimizing the

an

scheduling of the energy systems in low/zero energy buildings.

Evaluation tests are conducted in a reference building. Results showed that the strategy could

M

solve the power generation/demand mismatch problem of a building involving PV system, combined cooling and power generation (CCP) and cold storage by scheduling their operation in

d

an optimal manner, and reduce building operation cost significantly. When selling electricity to

te

the grid is allowed, reductions of 25% and 48% in carbon dioxide emission (CDE), 14% and 22% in primary energy consumption (PEC), 29% and 28% in operation cost are achieved in a

Ac ce p

summer day and a cloudy spring day respectively, compared with situation without CCP and cold storage. When selling electricity to the grid is forbidden, reductions of 12% and 38% in CDE, 6% and 20% in PEC, 24% and 23% in operation cost are achieved in the same situation. Results also show that the use of cold storage together with distributed energy systems in low/zero energy buildings, which fully utilizes the CCP system, can reduce CDE, PEC and operation cost by storing the surplus cold from the adsorption chiller. Sensitivity analysis shows uncertainties in the inputs do not affect the performance of the proposed method significantly. Uncertainties can be reduced by the actual operation strategy, TES and grid. It is also worth noticing that this study focuses on the development and evaluation of the optimization method. For practical online applications, it is needed to further study the online predictions of the building loads and PV power generation as well as the integration of the optimization strategy with real-time energy management systems.

Page 18 of 35

Acknowledgement The research work presented in this paper is financially supported by a grant (5267/13E) of the

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cr

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ip t

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ip t

Madsen, Model Predictive Control for a Smart Solar Tank Based on Weather and [13] F. Oldewurtel, A. Ulbig, A. Parisio, G. Andersson, M. Morari, Reducing peak electricity

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demand in building climate control using real-time pricing and model predictive control, in: 2010 49th IEEE Conference on Decision and Control (CDC). Presented at the 2010 49th

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IEEE Conference on Decision and Control (2010) 1927-1932.

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an

[15] Y. Ma, F. Borrelli, B. Hencey, A. Packard, S. Bortoff, Model Predictive Control of thermal energy storage in building cooling systems, in: Proceedings of the 48th IEEE Conference

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[16] K.C. Sou, J. Weimer, H. Sandberg, K.H. Johansson, Scheduling smart home appliances using mixed integer linear programming, in: 2011 50th IEEE Conference on Decision and

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predictive controllers for buildings. Energy and Buildings 57 (2013) 34–41. [22] M.F. Haniff, H. Selamat, R. Yusof, S. Buyamin, F.S. Ismail, Review of HVAC scheduling techniques for buildings towards energy-efficient and cost-effective operations. Renewable and Sustainable Energy Reviews 27 (2013) 94-103.

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[23] P.J. Mago, A.K. Hueffed, Evaluation of a turbine driven CCHP system for large office buildings under different operating strategies. Energy and Buildings 42 (2010) 1628-1636.

cr

[24] V. Chandan, A.-T. Do, B. Jin, F. Jabbari, J. Brouwer, I. Akrotirianakis, A. Chakraborty, A. Alleyne, Modeling and optimization of a combined cooling, heating and power plant

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system. American Control Conference (ACC) (2012) 3069-3074.

[25] S. Mitra, L. Sun, I.E. Grossmann, Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices. Energy 54 (2013) 194-211.

an

[26] M.R. Ranjbar, M. Mohammadian, S. esmaili. Economic analysis of hybrid system consists and Buildings 68 (2014) 476–487.

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of fuel cell and wind based CHP system for supplying grid-parallel residential load. Energy [27] The Hong Kong Zero Carbon Building. http://zcb.hkcic.org.

d

[28] J.B. Rosen, The gradient projection method for nonlinear programming. Journal of the Society for Industrial and Applied Mathematics 8 (1) (1960) 181–217.

te

[29] P. Wolf, Methods of nonlinear programming. Recent advances in mathematical programming. McGrew-Hill, New York (1963).

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[30] M.S. Bazaraa, H.D. Sherali, L.M. Shetty, Nonlinear Programming: theory and algorithms.John Wiley and Sons, New York (2006). [31] M.A. Rajaeifar, B. Ghobadian, M. Safa, M.D Heidari, Energy life-cycle assessment and CO2 emissions analysis of soybean-based biodiesel: a case study. Journal of Cleaner Production (in press) (2013).

[32] LINDO Systems. www.lindo.com. [33] Bonmin - COIN-OR Project. https://projects.coin-or.org/Bonmin. [34] Matlab Optimization Toolbox. http://www.mathworks.com. [35] The Hong Kong and China Gas Company Limited. http://www.towngas.com. [36] CLP Power Hong Kong. https://www.clponline.com.hk. [37] TRNSYS 16, a Transient System simulation program, The Solar Energy Laboratory, University of Wisconsin-Madison; 2006.

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[38] The New York Independent System Operator. http://www.nyiso.com. [39] K. Binder, D.P. Landau. A guide to Monte Carlo simulations in statistical physics.

Ac ce p

te

d

M

an

us

cr

ip t

Cambridge University Press (2000).

Page 22 of 35

Nomenclature

te

d

M

an

us

cr

ip t

coefficients adsorption chiller coefficients specific heat capacity of water (kJ/m3) specific heat capacity of natural gas (kJ/m3) electricity price (USD) natural gas price (USD) combined cooling, heating and power system combined cooling and power generation system combined heating and power system carbon dioxide emission factor for delivered electricity carbon dioxide emission factor for on-site natural gas combustion in PGU coefficient of performance of electric chiller coefficient of performance of adsorption chiller total cost (USD) mixed integer nonlinear programming model predictive control flow rate of inlet water to TES (kg/s) flow rate of outlet water to TES (kg/s) amount of chilled water in TES (kg) nonlinear programming power generated by photovoltaic systems (kWh) power generated by power generation unit (kWh) electricity from grid (kWh) electricity consumed by electric chiller (kWh) electricity consumed by HVAC equipment except for electric chillers (kWh) electricity consumed by lighting and office appliances (kWh) photovoltaic systems primary energy consumption factor for delivered electricity primary energy consumption factor for delivered natural gas partial load ratio of electric chiller partial load ratio of PGU cold provided by electric chiller (kW) cold provided by adsorption chiller (kW) cooling load of building (kW) amount of stored cold in TES (kW) cold storage capacity of TES (kW) total cooling load (kW) thermal energy storage

Ac ce p

a1,a2,a3, a4 AC b1,b2, b3 cp,water cp,gas Ctelec Cgas CCHP CCP CHP CDEe CDEgas COPtEC COPAC J MINLP MPC mtTES,inlet mtTES,out mtTES,cold NLP PtPV PtPGU PtGrid PtEC PtHVAC’ Ptothers PV PECe PECgas PLRtEC PLRtPGU QtTES QtAC Qtcl QtTES,cold QTES,cold,max Qttotal TES

Page 23 of 35

temperature of cold water in TES (℃)

Vtgas ηtTES ηtPG

volume of on-site natural gas consumption at time t cold loss coefficient of TES efficiency of PGU

ip t

TTES,cold

cr

temperature of warm water in TES (℃)

Ac ce p

te

d

M

an

us

TTES,warm

Page 24 of 35

Table 1. Characteristics of the energy system of the office building Value 125 m3 100 kW 130 kW 70 kW 1015 m2

ip t

Amount 1 1 1 3 1

cr

Equipment Chilled water storage tank Power generation unit Adsorption chiller Electric chiller Photovoltaic system

us

Symbol TES PGU AC EC PV

Symbol

Variable

an

Table 2. Parameters of the models

Value

Cool loss coefficient of TES

ηhrs

Efficiency of the heat recovery system

0.8

COPAC

COP of adsorption chiller

0.8

CDEe

Carbon dioxide emission factor of electricity

0.608 kg/kWh [25]

CDEgas

Carbon dioxide emission factor of natural gas

0.60 kg/m3 [25]

M

ηTES

0.5% /h

Primary energy consumption factor of electricity

3.546 kWh/kWh [18]

PECgas

Primary energy consumption factor of natural gas

1.092 kWh/kWh [18]

Natural gas price in Hong Kong Island

0.0294 USD/MJ [29]

Electricity price in Hong Kong Island

0.1907 USD/kWh [30]

t

Ac ce p

C elec

te

cgas

d

PECe

Table 3. CDE, PEC and operation cost in the summer day-Selling electricity to grid allowed

PV

CDE (kg) 643

CDE saving -

PEC (kWh) 3747

PEC saving -

Cost (USD) 253

Cost saving -

PV+TES

654

-2%

3812

-2%

208

18%

PV+CCP

468

27%

3167

15%

215

15%

PV+TES+CCP

479

25%

3232

14%

180

29%

Situation

Page 25 of 35

Table 4. CDE, PEC and operation cost in the cloudy spring day-Selling electricity to grid allowed Saved CDE -

PEC (kWh) 2883

Saved PEC -

Cost (USD) 257

PV+TES

506

-2%

2948

-2%

227

PV+CCP

293

41%

2216

23%

203

PV+TES+CCP

255

48%

2243

22%

185

Saved Cost -

ip t

PV

CDE (kg) 494

12% 21% 28%

cr

Situation

PEC (kWh) 3747 3812 3350 3524

Saved PEC -2% 11% 6%

an

Saved CDE -2% 19% 12%

Cost (USD) 253 208 227 194

Saved Cost 18% 10% 24%

d

PV PV+TES PV+CCP PV+TES+CCP

CDE (kg) 642 654 523 567

M

Situation

us

Table 5. CDE, PEC and operation cost in the summer day - Selling electricity to grid forbidden

te

Table 6. CDE, PEC and operation cost in the cloudy spring day - Selling electricity to grid forbidden

CDE (kg) 494 506 293 304

Ac ce p

Situation

PV PV+TES PV+CCP PV+TES+CCP

Saved CDE -2% 41% 38%

PEC (kWh) 2883 2948 2216 2293

Saved PEC -2% 23% 20%

Cost (USD) 257 227 204 197

Saved Cost 12% 21% 23%

Page 26 of 35

Table 7. Results of Monte Carlo simulations with uncertainties in input variables -Selling electricity to grid allowed

10%

5% The summer day

Mean

CDE PEC cost CDE PEC cost CDE PEC cost CDE PEC cost

231 2218 185 195 2063 185 437 3100 180 375 2894 180

270 2290 191 338 2521 207 520 3377 187 570 3545 193

253 2243 187 253 2254 190 472 3217 181 467 3200 185

Ideal value 255 2243 185 255 2243 185 479 3232 180 479 3232 180

M

10%

Max

ip t

The spring day

Min

cr

5%

Item

us

Uncertainty level

an

Day

Table 8. Results of Monte Carlo simulations with uncertainties in input variables -Selling Uncertainty level

te

Day

d

electricity to grid forbiddden

Ac ce p

5%

The spring day

10%

5%

The summer day

10%

Item

Min

Max

Mean

CDE PEC cost CDE PEC cost CDE PEC cost CDE PEC cost

294 2265 197 283 2221 197 487 3246 194 488 3269 194

340 2416 203 370 2540 207 590 3611 198 614 3689 202

312 2326 199 324 2371 202 545 3458 196 548 3468 198

Ideal value 304 2293 197 304 2293 197 567 3524 194 567 3524 194

Page 27 of 35

Figure 1. Schematics of the energy systems of the reference building Figure 2. Flow chart of the MPC-based optimal scheduling strategy

ip t

Figure 3. (a) Outdoor air temperature and solar radiation of the summer day and cloud spring day; (b) Load/generation profiles predicted by the dynamic simulator for the two days

cr

Figure 4. Schedule of the hourly electricity consumption/generation in a summer day - Selling electricity to grid allowed

us

Figure 5. Schedule of the hourly cold consumption/generation in a summer day -Selling electricity to grid allowed.

Selling electricity to grid allowed

an

Figure 6. Schedule of the hourly electricity consumption/generation in a cloudy spring day -

electricity to grid allowed

M

Figure 7. Schedule of the hourly cooling consumption/generation in a cloudy spring day-Selling Figure 8. Schedule of the hourly electricity consumption/generation in a summer day - Selling

d

electricity to grid forbidden

te

Figure 9. Schedule of the hourly cooling consumption/generation in a summer day - Selling electricity to grid forbidden

Ac ce p

Figure 10. Schedule of the hourly electricity consumption/generation in a cloudy spring day Selling electricity to grid forbidden

Figure 11. Schedule of the hourly cold consumption/generation in a cloudy spring day - Selling electricity to grid forbidden

Figure 12. Schedule of the hourly electricity consumption/generation in a sunny spring day Selling electricity to grid forbidden

Figure 13. Schedule of the hourly cooling consumption/generation in a sunny spring day Selling electricity to grid forbidden Figure 14. Histograms of CDE, PEC and cost of 1000 Monte Carlo simulations in the cloudy spring day with uncertainties (10%) in input variables -Selling electricity to grid allowed

Page 28 of 35

Grid PV

ip t

Other HVAC equipment (HVAC')

cr

Power regulator

an

us

Electric chiller (EC)

Adsorption chiller (AC)

Power generation unit (PGU)

M

Stratified chilled water storage tank

d

Figure 1. Schematics of the energy systems of the reference building

Ac ce p

te

Inputs: Predicted loads/generation in the next 24 hours

+

Mathematic descriptions of optimization problem: Minimum: Eq.(1b) Input variables variables to be optimized (Inputs) (Outputs)

Subject to: Constrains in Eq. (11) to Eq. (16).

NLP solver

Outputs: Schedule of optimized variables in the next 24 hours

Figure 2. Flow chart of the MPC-based optimal scheduling strategy

Page 29 of 35

40

(a)

1000

25

600

20 400

15 10

200

0

Rsolar (Summer) Rsolar (Spring)

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)

(b)

us

180.0 160.0 140.0 120.0

an

100.0 80.0 60.0 40.0

Qcl(Summer) Phvac(Summer) Ppv(Summer) Pother Qcl(Spring) Phvac(Spring) Ppv(Spring)

M

Cooling load/electricity (kW)

Toa (Spring)

cr

5

Toa (Summer)

ip t

800

30

Solar radiation (W/m2)

Temperature (℃)

35

20.0 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)

d

Figure 3. (a) Outdoor air temperature and solar radiation of the summer day and cloud spring day;

200 200

Electricity (kW)

150 150 100 100

Positive value stands for generating or buying electricity

Buy electricity from grid

5050

0 0 -50-50

-100 -100 -150 -150 -200 -200

0.5 4 Grid electricity price (USD/kWh)

Ac ce p

te

(b) Load/generation profiles predicted by the dynamic simulator for the two days

0.4 3 0.3 2 0.2 0.1 1

0 0 1 1 2 2 3 3 4 45 56 67 78 89 910 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 21 20 22 21 23 22 24 23 24 -0.1 -1 -0.2 -2 -0.3 Sell electricity to grid -0.4 -3 Negative value stands for consuming or selling electricity -0.5 -4 Time (h)

Pec Pec Ppv Ppv Pgene Pgene Phvac Phvac Pother Pother Pgrid Pgrid Price Price

Figure 4. Schedule of the hourly electricity consumption/generation in a summer day - Selling electricity to grid allowed

Page 30 of 35

0.5 4

Discharge TES

Grid electricity price (USD/kWh)

200 200

0.4 3 0.3 2 0.2 0.1 1

150 150 100 100 5050

0 0 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 19 18 20 19 21 20 22 21 23 22 24 23 24 -50-50 1 1 2 23 34 45 56 67 78 89 910 10 -0.1 -1 -100 -100 -0.2 -2 -150 -150 -0.3 Charge TES -200 -200 -0.4 -3

Qec Qec Qac Qac Qtank Qtank

ip t

0 0

cr

Cooling capacity (kW)

250 250

-250 -250

Price Price

-0.5 -4

us

Time (h)

Figure 5. Schedule of the hourly cold consumption/generation in a summer day -Selling

d

0.5 4

Grid electricity price (USD/kWh)

0 0

te

150 100 Buy electricity from grid 100 50 50

Positive value stands for generating or buying electricity

0.4 3 0.3 2 0.2 0.1 1

0 0 1 1 2 2 3 3 4 45 56 67 78 89 910 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 21 20 22 21 23 22 24 23 24 -0.1 -1 -50 -50 -0.2 -100 -2 Sell electricity to grid -0.3 -100 -150 Non-working hour -0.4 -3 Negative value stands for consuming or selling electricity -150 -200 -0.5 -4 Time (h)

Ac ce p

Electricity (kW)

150 200

M

an

electricity to grid allowed.

Pec Pec Ppv Ppv Pgene Pgene Phvac Phvac Pother Pother Pgrid Pgrid Price Price

Figure 6. Schedule of the hourly electricity consumption/generation in a cloudy spring day Selling electricity to grid allowed

Page 31 of 35

0.4

150

Discharge TES

100

0.3 0.2

50

0.1

0

0

-50

2

3

4

5

6

7

8

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

Charge TES

-100

-0.2

Save the surplus cold from adsorption chiller to the TES

-150

-0.1

ip t

1

Grid electricity price (USD/kWh)

0.5

-0.3 -0.4

cr

Cooling capacity (kW)

200

-200

-0.5

us

Time (h)

Figure 7. Schedule of the hourly cooling consumption/generation in a cloudy spring day-Selling

Grid electricity price (USD/kWh)

M

0.5 4 0.4 3 0.3 2 0.2 0.1 1

0 0 1 1 2 2 3 3 4 45 56 67 78 89 910 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 21 20 22 21 23 22 24 23 24 -0.1 -1 -50 -50 -0.2 -100 -2 -0.3 -100 -150 -0.4 -3 Negative value stands for consuming or selling electricity -150 -200 -0.5 -4 Time (h)

te

0 0

Positive value stands for generating or buying electricity

d

150Import electricity from grid 100 100 50 50

Ac ce p

Electricity (kW)

150 200

an

electricity to grid allowed

Pec Pec Ppv Ppv Pgene Pgene Phvac Phvac Pother Pother Pgrid Pgrid Price Price

Figure 8. Schedule of the hourly electricity consumption/generation in a summer day - Selling electricity to grid forbidden

Page 32 of 35

Grid electricity price (USD/kWh)

0.5 4

Discharge TES

200 200

0.4 3 0.3 2 0.2 0.1 1

150 150 100 100 5050

0 0 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 20 19 21 20 22 21 23 22 24 23 24 -50-50 1 1 2 23 34 45 56 67 78 89 910 10 -0.1 -1 -100 -100 -0.2 -2 -150 -150 -0.3 Charge TES -200 -200 -0.4 -3

Qec Qec Qac Qac Qtank Qtank

ip t

0 0

cr

Cooling capacity (kW)

250 250

-250 -250

Price Price

-0.5 -4

us

Time (h)

Figure 9. Schedule of the hourly cooling consumption/generation in a summer day - Selling

80200

Positive value stands for generating or buying electricity

M

40100 20 50

-40-100 -60-150

Negative value stands for consuming or selling electricity

Ac ce p

-80-200

0.5 4 0.4 3 0.3 2 0.2 0.1 1

0 0 89 10 9 10 11 11 12 12 13 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 24 -0.1 -1

d

0 0 1 12 23 34 45 56 67 78 -20 -50

te

Electricity (kW)

60150Import electricity from grid

Grid electricity price (USD/kWh)

an

electricity to grid forbidden

-0.2 -0.3

-2

-0.4 -3

Pec Pec Ppv Ppv Pgene Pgene Phvac Phvac Pother Pother Pgrid Pgrid Price Price

-0.5 -4

Time (h)

Figure 10. Schedule of the hourly electricity consumption/generation in a cloudy spring day Selling electricity to grid forbidden

Page 33 of 35

Discharge TES

150

0.4 0.3

100

0.2

50

0.1

0

0

-50

2

3

4

5

6

7

8

-100

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

-0.1

Save the excess cold from adsorption chiller to the TES

-0.2

ip t

1

-0.3

Charge TES

-150

Grid electricity price (USD/kWh)

0.5

-0.4

cr

Cooling capacity (kW)

200

-200

-0.5

us

Time (h)

Figure 11. Schedule of the hourly cold consumption/generation in a cloudy spring day - Selling

Grid electricity price (USD/kWh)

0.5 4 0.4 3 0.3 2 0.2 0.1 1

0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 21 20 22 21 23 22 24 23 24 -20-50 -0.1 -1 -40 -0.2 -100 -2 -60 -0.3 -150 -80 -0.4 -3 Consume the excess electricity from PV by electric chiller -200 -100 -0.5 -4 Time (h)

d

0 0

Positive value stands for generating or buying electricity

M

80 150 60 100 40 2050

Pec Pec Ppv Ppv Pgene Pgene Phvac Phvac Pother Pother Pgrid Pgrid Price Price

Ac ce p

te

Electricity (kW)

200 100

an

electricity to grid forbidden

Figure 12. Schedule of the hourly electricity consumption/generation in a sunny spring day Selling electricity to grid forbidden

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Grid electricity price (USD/kWh)

0.5 4 Discharge TES

200 200

0.4 3 0.3 2 0.2 0.1 1

150 150 100 100 5050

0 0 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 20 19 21 20 22 21 23 22 24 23 24 -50-50 1 1 2 23 34 45 56 67 78 89 910 10 -0.1 -1 -100 -100 -0.2 -2 Save the excess PV electricity by means of cool to the TES -150 -150 -0.3 -200 -200 -0.4 -3

Qec Qec Qac Qac Qtank Qtank

ip t

0 0

cr

Cooling capacity (kW)

250 250

-250 -250

Price Price

-0.5 -4

us

Time (h)

Figure 13. Schedule of the hourly cooling consumption/generation in a sunny spring day -

100

d

150

te

Frequency

100

120

Frequency

200

M

250

150

Frequency

an

Selling electricity to grid forbidden

80

60

100

0 150

Ac ce p

50

200

250

300

CDE (kg)

350

40

50

0 2000

20

2200

2400

PEC (kWh)

2600

0 180

190

200

210

Cost (USD)

Figure 14. Histograms of CDE, PEC and cost of 1000 Monte Carlo simulations in the cloudy spring day with uncertainties (10%) in input variables -Selling electricity to grid allowed

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