multi-objective optimization model of source-load-storage...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2017.2781639, IEEETransactions on Industry Applications

Multi-objective Optimization Model of Source-Load-Storage Synergetic Dispatch for Building Energy System Based on TOU Price Demand Response

Fei Wang, Lidong Zhou, Hui Ren

North China Electric Power University, Baoding 071003, China, also with University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

[email protected], [email protected]

Xiaoli Liu

Shuozhou Power Company of State Grid Shanxi Electric Power Company, Shuozhou 036000, China

[email protected]

Saber Talari, Miadreza Shafie-khah

C-MAST, Univ. Beira Interior, Covilhã, Portugal [email protected]

[email protected]

João P. S. Catalão

INESC TEC and the Faculty of Eng. of the Univ. Porto, Porto, also with C-MAST, Univ. Beira Interior, Covilhã, and also with INESC-ID, IST, Univ. Lisbon, Portugal

[email protected]

Abstract–The optimized operation of building energy management system (BEMS) is of great significance to its operation security, economy and efficiency. This paper proposed a day-ahead multi-objective optimization model for a BEMS under time-of-use (TOU) price based demand response (DR), which integrates building integrated photovoltaic (BIPV) with other generations to optimize the economy and occupants’ comfort by the synergetic dispatch of source-load-storage. The occupants' comfort contains three aspects of the indoor environment: visual comfort, thermal comfort, and indoor air quality comfort. With the consideration of controllable load that could participate in DR programs, the balances among different energy styles, electric, thermal and cooling loads are guaranteed during the optimized operation. YALMIP toolbox in MATLAB was applied to solve the optimization problem. Finally, a case study was conducted to validate the effectiveness and adaptability of the proposed model.

Index Terms--Building energy management system; demand response; indoor environmental modelling; multi-objective optimization; synergetic dispatch

I. NOMENCLATURE

t Time interval n The number of lights φ Each light source flux (lm) U Utilization factor of the light source M Maintenance factor of the light source A Illuminated room area (m2)

SETE Standard illuminance (lux)

eqR Room equivalent thermal (℃/W)

airM Indoor air quality (kg)

pC Air specific heat capacity(J/(kg·℃))

SETT Standard temperature (℃) L Amount of fresh air (m3)

wN Outdoor 2CO concentration (ppm) V Volume of the room (m3)

2cov Indoor CO2 generation at time t (m3)

FACL Fresh air cooling load (kW) ρ Air density (kg/m3)

wh Outdoor air enthalpy (kJ/kg)

nh Indoor air enthalpy (kJ/kg) d Moisture content in the air (g/kg)

SETN Standard CO2 concentration (ppm)

CHPη Efficiency of MT (%)

lη Heat loss rate of CHP (%)

NGLHV Low calorific value of natural gas (kWh/m3)

NGP Unit price of natural gas (¥)

GBR Rated heat of boiler (kW)

GBη Thermal Efficiency of GB (%)

chη Charge efficiency (%)

disη Discharge efficiency (%)

miC Unit operation costs (¥) USCC Start-up costs of CHP (¥) )(tCb Electricity sale price at time t (¥/kW) )(tCs Electricity purchase price at time t (¥/kW)

jα Conversion factor of pollutant j (¥/kg)

ji,β Emission factor of generation i for pollutant j (kg/kW)

dt Starting time of deferrable loads (h)

'ttx → Amount of deferrable load shift from time t

to t’ (kW)

tx Amount of deferrable load at time t before optimization (kW)

)(tE Indoor illumination at time t (lux) )(tTroom Indoor temperature at time t (℃) )(tTout Outdoor temperature at time t (℃) )(tQ Heat transferred from indoor at time t (J) )(tN Indoor CO2 concentration at time t (ppm) )(tPE Lighting power at time t (kW) )(tPL Total electrical load power at time t (kW) )(tPCHP Electric power output of CHP at time t (kW) )(tPPV BIPV power output at time t (kW) )(tPEX Interactive power with grid at time t (kW) )(tPEES Electric power output of EES at time t (kW) )(tEEES State of charge (SOC) for EES at time t (kW) ( )EESC t Cost of EES at time t (¥)

EESζ Cost coefficient of investment and loss for EES at time t (¥/kWh)



)(tQL Total heat load power at time t (kW) )(tQCHP Heat power output of CHP at time t (kW) )(tQGB Heat power output of GB at time t (kW) )(tQTES Heat power output of TES at time t (kW) )(tHTES Capacity of TES at time t (kW)

( )TESC t Cost of TES at time t (¥)

TESζ Cost coefficient of investment and loss for TES at time t (¥/kWh)

)(tRL Total cooling load power at time t (kW) )(tRAR AR cooling load power at time t (kW) )(tRECR ECR cooling load power at time t (kW)

)(tVCHP Natural gas consumption of CHP at time t (m3)

)(tVGB Natural gas consumption of GB at time t (m3)

II. INTRODUCTION

With the increasing urbanization in recent years, a great deal of buildings emerged, resulting in the increase of energy consumption of buildings [1]. Consequently, building energy saving and efficiency improvement are imminent, especially in the situations of energy crisis and environmental pollution [2]. The main function of building energy management system (BEMS) is to manage and control the energy flow in the building through different kinds of information so as to ensure the operation safety, reliability and economy [3]. The building energy system (BES) is complicated because that the structure, service and management are closely connected and have to be considered as a whole and optimized simultaneously [4]. With the application of renewable energy sources [5], it is even more complicated due to the widely adoption of building integrated photovoltaic (BIPV) in modern buildings for its eco-friendly and economic characteristics [6].

In order to improve the efficiency of BES, the optimal dispatch of generation from different technologies or loads is necessary and very important during the operation. The optimal operation of buildings is influenced by many factors. The output of photovoltaic (PV) is random because of the variation of weather conditions [7], which affect the dispatch accuracy greatly. As a result, improving the forecasting precision of PV output is an important premise for the follow-up work [8]. And as the development of demand response (DR), the demand side has to be considered to improve the system reliability [9]-[10]. In addition, energy storage also plays a significant role in smart building’s operation optimization [11]. The dual-role (load and source) of storage could realize peak-load shifting. That’s to say, energy storage devices are able to store energy during valley-load period or when the energy price is low, and export the stored energy during peak-load period or when the energy price is high. But the investment and loss of storage devices should be concentrated in the process of realizing the optimal operation for BEMS.

Researchers around the world have devoted much effort to study the optimized operation of BES and gained a lot of achievements [12]-[14]. A distributed management method

for BES was proposed using multi-agent system to improve the energy efficiency and reducing energy costs [15]. Andrea Staino etc. presented a cooperative optimization approach for a group of buildings to realize economic operation and load reduction [16]. A model of BEMS considered the occupants’ comfort and the energy consumption was raised in [17]. Reference [18] integrated the plug-in hybrid electric vehicle (PHEV) into energy and comfort management in a smart building environment. All the studies achieved good results in setting BESs and operational situations, but limitations about the system economy are also existed especially with the penetration increase of renewable energy and the development of DR.

The overall optimization objective of BEMS is to meet occupants’ comfort while reduce energy consumption and improve economy for the whole system [19]. However, BES is a highly complex system and the uncertainties of BIPV’s output and load fluctuation directly affect the economic operation of BES. The problem is that the existing researches usually focus on the single optimization of sources (power supplies) or simple coordination between sources and energy storages. That means the advantages of synergetic dispatch of source-load-storage are not spared, which is important to the optimal operation of BEMS exactly. For example, when the output of BIPV is low in rainy days, other power supplies should export more energy if the storages and loads are not considered into the optimization. This is not economic or even infeasible when the cost of other power supplies is high or the output has reached the upper limit. At this time, the storages and loads are both effective means to maintain power balance if the synergetic dispatch of source-load-storage is adopted. In addition, the type of units integrated into BES is not enough compared with actual situation and the models of each unit are relatively simple, resulting in discrepancies between actual operation and mathematic model. Consequently, the optimized operation of BEMS could not be realized. On the other hand, controllable loads are usually considered as the participants for DR in existed studies, while the deferrable loads are ignored sometimes. However, deferrable loads also play an important role in DR programs and have become an effective means to improve the system economy [20], especially with the large-scale applications of different domestic appliances. So the function of deferrable loads should also be included in BEMS. Furthermore, as one of the development tendencies, time-of-use (TOU) is necessary to be considered as the operational environment for BES.

In this paper, the operation economy and occupants’ comfort level are considered at the same time for a residential building. Based on the prediction of BIPV’s output, non-controllable loads and outdoor temperature, this paper established a multi-objective optimization model with relevant constrains to improve the system economy and guarantee the occupants’ comfort simultaneously through the synergetic optimized dispatch of sources, loads and storage devices.



On the basis of the loads classification in the building, DR was carried out effectively in the conditions of TOU price. The occupants’ comfort level is described by the indoor environment, which was established by the construction of three most important factors for building indoor environment: visual comfort, thermal comfort and indoor air quality comfort. YALMIP toolbox in MATLAB was chosen to solve the model for its convenience and quickness. The main contributions of this paper can be summarized as follows:

(1) We propose a multi-objective optimization model for BEMS to optimize the system economy and occupants’ comfort by a synergetic dispatch of source-load-storage. BIPV is integrated into the building.

(2) We consider the function of controllable loads and deferrable loads in economic operation and power balance under TOU price. Then the consumption behavior variation of users is analyzed.

(3) We validate the proposed model by simulation from two aspects: one is the comparison between synergetic and non-synergetic dispatch of source-load-storage; another is the comparison between TOU and non-TOU price. The results demonstrate the effectiveness of the presented model.

The remainder of this paper is organized as follows. In Section III, the studied BES was described in detail. In Section IV, the models of indoor environment and comfort level parameters were presented. Then Section V proposed BES’s optimization model, including the optimization objectives and constraints. Section VI provided a simulation analysis and a conclusion was given in Section VII.

III. THE BUILDING ENERGY SYSTEM The BES considered in this paper is a hybrid energy

system which consists of different sources, loads and storages. Specifically, the sources include BIPV, utility grid, controllable generations such as combined heat and power (CHP) system and gas boiler (GB). Storage devices are composed of electricity energy storage (EES) and thermal energy storage (TES).Loads are consisted of electrical load (EL), thermal load (TL) and cooling load (CL). And the system CL is composed by indoor cooling load (ICL) and fresh air cooling load (FACL) which are supplied by electric compression refrigeration (ECR) combined with absorption refrigeration (AR). The structure of the BES in this paper is shown in Fig. 1. A. Building Integrated Photovoltaic (BIPV)

BIPV is a new concept for solar power application and an advanced form of photovoltaic power generation integrated in buildings [21]. It has higher requirements for PV modules which not only need to meet the functional requirements of photovoltaic power generation but also need to take the basic functional requirements of the buildings into account. The power output of photovoltaic system changes with the seasons, weather, solar radiation, temperature and other factors, which is very unstable and difficult to adjust according to actual demands [22].

Grid

EES

Electrical MeterCHPHeat

integrator

GB

BIPV

TES

TL

EL

ECR

AR

ICLFACL

CL

Power flowHeat flow

Fig. 1. The structure of the BES Thus, forecasting the output power of photovoltaic

generation system is one of the foundations for the optimization of BES. B. The Model of Controllable Generations and Storage Devices

CHP system, which uses micro turbine (MT) as the motive device, could provide electrical power and utilize waste heat to meet the heating or cooling load demand of buildings at the same time [23].

The model of CHP system can be expressed as:

( )(1 )( ) CHP CHP l

CHPCHP

P tQ t

η ηη− −

= (1)

NGCHP

CHPCHP LHV

ttPtV×

Δ=η

)()( (2)

24

1

( )CHP NG CHPt

C P V t=

= ×∑ (3)

In (1), heat power output of CHP at each time is obtained through efficiency of MT and the electricity power output of CHP at the time. Natural gas consumption at each time by CHP is calculated in (2) via calorific volume of natural gas, efficiency of MT and electricity power output at the time. The results of (2) along with natural gas price are used to achieve the CHP fuel cost ( CHPC ) for a day in (3).

GB coordinates the CHP system to meet the TL demand of the building and the mathematical model can be expressed as:

GBGBGB RtQ η×=)( (4)

NGGB

GBGB LHV

ttQtV×

Δ=η

)()( (5)

24

1

( )GB NG GBt

C P V t=

= ×∑ (6)

The equations of (4) – (6) are applied to calculate the daily GB operation cost. In (4), heat power output of GB is obtained by using the heat efficiency of GB and rated heat of boiler. Finally, by results of (5) as well as gas price, the daily fuel cost of GB is calculated in (6).



Energy storage devices including EES and TES play a dual role as source and load. They could coordinate the imbalance between power supply and load demand within the system, improve system reliability and economy [24].

It should be noted that the impact of capacity loss (such as battery degradation) to investment recovery period must be considered in capacity configuration. That’s to say, a dynamic available capacity that decreases over time instead of a fixed capacity should be included in the mathematic model calculating the return of investment. And this feature could refer to the test data of battery making corresponding estimations. On the other hand, the influence of battery’s capacity degradation on operation is a relatively slow in terms of short-term time scale for operation. However, the battery's actual available capacity needs to be measured, estimated and modified regularly so as to update the model parameters to prevent the impacts on BES’s operation.The investment and loss of storage devices should be considered as part of the cost of BES in related mathematical models.

The equations (7)–(8) present the EES model and equations (9)–(10) express the TES model. In (7), the SOC for EES is calculated and the hourly cost of EES operation is presented in (8). The SOC at each hour for TES is expressed in (9) and the hourly cost of TES is given in (10):

__

( )( ) ( 1) ( )EES dis

EES EES EES ch chdis

P t tE t E t P t tη

η

Δ= − − + Δ (7)

( )_ _( ) ( ) + ( )EES EES EES dis EES chC t P t P t tζ= ⋅ Δ (8)

__

( )( ) ( 1) ( )TES dis

TES TES TES ch chdis

Q t tH t H t Q t tη

η

Δ= − − + Δ (9)

( )_ _( ) ( ) + ( )TES TES TES dis TES chC t Q t Q t tζ= ⋅ Δ (10)

C. Load Classification According to the characteristics, the loads in the

buildings can be divided into non-controllable loads and loads that could participate in DR. The latter can be further split into controllable loads and deferrable loads, which are both important variables to optimized operation. And these two types of loads are also the concentration of this paper.

The energy consumption of controllable loads, such as lights and air conditioning, accounts for about 70% of building’s total consumption [25]. Deferrable loads mainly refer to the loads whose operation time could be adjusted, such as washing machines, disinfection cabinets and dishwashers etc. By altering the starting time of deferrable loads in appropriate period, the overall economy could be improved without changing their basic electric characteristics.

IV. INDOOR ENVIRONMENT MODELLING

In order to understand the optimization procedure preferably, a room model is shown in Fig. 2 and assuming that all the rooms were the same.

The room is an environment with a rectangular plan whose length is 20m, the depth is 10m, and the height is 3m. There are four windows in the room whose length is 1.2m and height is 1.5m.

20m

10m

3m

1.2m

1.5m

Fig. 2. Schematic view of room in BES

Visual comfort, thermal comfort and indoor air quality comfort are the three basic factors that determine the environmental conditions in a building. In detail, indoor illumination level can be taken as the index for visual comfort [26]. The thermal comfort in a room is determined by the indoor temperature. CO2 concentration is an index for evaluating the indoor air quality that can be improved by the ventilation system generally. A. Visual Comfort

For the lighting equipment whose luminance could be adjusted, its power can be continuously changed within a certain range. That is to say, the indoor illumination will vary with the power change of lighting devices. The indoor illumination index can be expressed as:

( )( ) En P t U ME tAϕ⋅ ⋅ ⋅ ⋅

= (11)

Visual comfort index is represented by indoor illumination that changes within an acceptable range that was set by users:

2

1)(-1)( ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

SET

SET

EEtEtD (12)

where D1(t) represents the visual comfort at time t. B. Indoor Air Quality Comfort

To maintain a good indoor air quality, the indoor CO2 concentration must be remained stable and the ventilation system must provide a certain amount of fresh air into the room. The mathematical relationship between indoor CO2 concentration and the amount of fresh air can be expressed as (13):

V

vtNNLtNtN cow 2

))1-(()1-()(

+−×+= (13)

And the model of fresh air cooling load is in (14): ( )FAC w nL L h hρ= × × − (14)where hw and hn are outdoor and indoor air enthalpy, respectively and both can be calculated by (15):

))(84.12500(1000)()(01.1)( tTtdtTth ×+×+×= (15)

Indoor air quality comfort index is represented by indoor CO2 concentration and it changes within an acceptable range that was set by users shown in (16):

2

2( )

( ) 1- SET

SET

N t ND t

N⎛ ⎞−

= ⎜ ⎟⎝ ⎠

(16)

where D2(t) represents the indoor air quality comfort at time t.



C. Thermal Comfort Air conditioning is regarded as a “black box” whose

internal structure is unknown when considering the energy consumption. The mathematical relationship among energy consumption of air conditioning, indoor temperature, and outdoor temperature is shown in (17):

pair

eq

roomout

roomroom CM

tQR

tTtT

tTtT)()1()(

)1()(−

−−

+−= (17)

And room equivalent thermal Req is calculated by (18) via wall thermal and window thermal of the room:

windowwall

windowwalleq RR

RRR+

= (18)

The thermal comfort index is represented by indoor temperature and it changes within an acceptable range that was set by users which is presented in (19):

2

3( )

( ) 1- room SET

SET

T t TD t

T⎛ ⎞−

= ⎜ ⎟⎝ ⎠

(19)

where D3(t) represents the thermal comfort at time t.

V. OPTIMIZATION MODEL The operation objective of BEMS is to maximize the

energy economy meanwhile guarantee the occupants’ comfort. Based on the prediction of BIPV’s output, non-controllable loads and outdoor temperature, BEMS optimizes the operation of all components of the system and proposes a synergetic dispatch scheme of source-load-storage in the presence of different physical constraints and TOU price. In this paper, the optimized results contained the power output of controllable generations, the power exchanged with utility grid, storage charge/discharge energy, the power of controllable load, the power of deferrable load and three indoor environment parameters. The whole optimization is shown in Fig. 3.

BEMS

Inputs Outputs

Sour

ces

and

EE

SL

oads

Indo

or

envi

ronm

ent v

aria

bles

Multi-Objective Optimization

BIPV prediction

Load prediction

Output temperature prediction

TOU price

Constraints

Controllable power generation

Power exchange with grid

Charge/discharge power

Controllable load Deferrable load

IlluminationTemprature

CO2

Minimization total daily operation cost

Maximization total comfort level

Fig. 3. Optimization overview of BEMS

A. Economic Optimization Objective The economic objective is to minimize the total daily

operational cost [27]. It includes: the fuel cost of CHP and GB; the operation and maintenance cost of BIPV, CHP and GB; the start-up cost of CHP and GB; the cost of electricity purchased from the grid and the revenue from electricity sold to the grid; the environmental conversion cost of utility grid, CHP and GB; the investment and loss cost of EES and TES. The total cost can be calculated in (20):

24

1[ ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )]

CHP GB OM SC EXt

EN EES TES

C C t C t C t C t C t

C t C t C t=

= + + + +

+ + +

∑ (20)

where C represents the total cost in an optimization cycle, it is 24 hours. CCHP(t), CGB(t), COM(t), CSC(t), CEX(t), CEN(t), CEES(t) andCTES(t) are fuel cost of CHP and GB, operation and maintenance cost, start-up cost, grid interactive power cost (income), environmental conversion cost, investment and loss cost for EES, TES at time t, respectively. 1) Fuel cost of CHP and GB can be expressed in (21) and (22):

NGCHP

CHPNGCHP LHV

ttPPtC×

Δ×=η

)()(

(21)

NGGB

GBNGGB LHV

ttQPtCη

Δ×=

)()( (22)

2) Operation and maintenance cost includes the operating and management cost of BIPV, CHP and GB which shown in (23):

∑=

=3

1)()(

imiiOM CtPtC (23)

3) The start-up cost of controllable generations can be expressed in (24):

{ } USCSC CtUtUtC )1()(,0max)( −−= (24)

where U(t)=1 when CHP or GB is under working condition, otherwise U(t)=0. 4) Grid interactive power cost can be expressed by electricity sale income and purchase cost in (25): ( ) ( ) ( ) (1 ) ( ) ( )EX s EX b EXC t sC t P t s C t P t= − − (25) where s is the buy/sell state, if BES buy electricity from utility grid, s=0; otherwise, s=1. 5) Environmental conversion cost includes the cost of utility grid, CHP, GB and the pollutants that require conversion are CO2, SO2 and NOX. The conversion factors and emission factors are shown in Table I. CEN(t) is expressed in (26):

3 3

,1 1

( ) ( )EN j i j ii j

C t P tα β= =

=∑∑ (26)

B. Comfort Optimization Objective The occupants’ comfort is determined by three basic

comfort factors as shown in Section IV. The general dispatch objective is to maintain the

comfort value within a reasonable range in different conditions and the total comfort level can be expressed in (27):

)]()()([ 321

24

1tDtDtDD

tγβα ++=∑

=

(27)

where D represents the total comfort objective in an optimization cycle, among which α, β, γ are set by users [28] according to their own preferences and satisfy α+β+γ=1.



TABLE I CONVERSION AND EMISSION FACTORS FOR POLLUTANTS

Type

Conversion

Factors

/(¥/kg)

Emission Factors

CHP

/(kg/kWh)

GRID

/(kg/kWh)

GB

/(kg/kWh)

CO2 6.65 0.1995*10-3 0.2469*10-3 0.0997*10-3

SO2 2.375 1*10-9 0.5*10-6 0.556*10-9

NOX 2.12 0.55*10-9 0.444*10-6 0.278*10-9

C. The Overall Optimization Objective In multi-objective optimization problems, the objectives

to be optimized are usually in conflict with each other. In this paper, the weighted aggregation method is utilized to transfer a multi-objective optimization into a single objective optimization. The overall optimization objective is expressed as:

1min (1 )F CD

µ µ= + − (28)

where µ is the weight between economy and comfort level which is set by the users according to their actual demand. D. Operation Constraints

1) Power Balance In each dispatch interval, the total energy consumption

including electrical, heating, and cooling load should be equal to the energy supplied by the power sources which are presented in (29), (30), and (31), respectively: )()()()()( tPtPtPtPtP EXEESCHPPVL +++= (29) )()()()( tQtQtQtQ TESGBCHPL ++= (30) )()()( tRtRtR ECRARL += (31)

2) Power Output Constraints The output of each equipment should not exceed the

power or capacity range. Equation (32) is the limitation of CHP power production, limitation of power exchange with grid is in (33). Minimum and maximum electric output power of EES, heat output of TES and GB are in (34) – (36), respectively. maxmin )( CHPCHPCHP PtPP ≤≤ (32) maxmin )( EXEXEX PtPP ≤≤ (33) maxmin )( EESEESEES PtPP ≤≤ (34) maxmin )( TESTESTES QtQQ ≤≤ (35) maxmin )( GBGBGB QtQQ ≤≤ (36)

3) Capacity Constraints Energy stored in the storage devices at time t is equal to

the amount stored at time t-1 minus the energy discharged or plus the energy charged. The stored energy in EES and TES cannot exceed the designed range which are presented in (37) and (38), respectively: maxmin )( EESEESEES EtEE ≤≤ (37) maxmin )( TESTESTES HtHH ≤≤ (38)

4) Starting Time and Deferrable Amount Constraints The starting time of deferrable loads must change within

the time interval that the users defined according to (39) – (41) [29]: maxmin ddd ttt ≤≤ (39)

0' ≥→ttx (40)

t

T

ttt xx =∑

=→

1'' (41)

5) Indoor Environment Parameters Constraints Indoor environment parameters including indoor

illumination, temperature, and CO2 cannot exceed the defined range set by the users during the optimization process according to (42) – (44), respectively: maxmin )( EtEE ≤≤ (42)

maxmin )( roomroomroom TtTT ≤≤ (43)

maxmin )( NtNN ≤≤ (44)

VI. SIMULATION ANALYSIS

A. Simulation Environment 1) Hardware Environment All the simulations are carried out by MATLAB and

run on an Intel Core i3-2310M CPU @ 2.10 GHz computer with a 4 GB RAM.

2) Software Environment: YALMIP Toolbox According to the established model above, it’s obvious

that the optimized operation of BEMS is a multi-constraint nonlinear optimization problem. For the past few years, intelligent algorithms instead of traditional optimization algorithms are generally adopted [30]. But the model in this paper contains many variables and constraints. As a result, it is very difficult to design an intelligent algorithm program code that is able to deal with all these variables and constraints effectively. A little negligence or error may lead to a terrible convergence and search performance, which is fatal to an optimization problem. YALMIP is a toolbox that integrates different optimization algorithms in MATLAB with the following advantages: - YALMIP is convenient for users to describe variables and constraints with easy program statements, which save the time for programming and ensure a high accuracy; -YALMIP could detect what kind of optimization problem the user has defined automatically, and select a suitable solver based on this analysis. If no suitable solver is available, YALMIP tries to convert the problem to be able to solve it. This characteristic avoids the drawback of artificial algorithm selection.

Based on these advantages, YALMIP is selected to solve the model in this paper. More details can be found in [31]. B. Results Analysis

The controllable loads in the simulation include lightings and air conditionings, while the deferrable loads contain washing machines, disinfection cabinets and dishwashers [32].



TOU price has been considered as the operation environment of BES. The system operating parameters are shown in Table II and parameters of deferrable loads are shown in Table III.

Assuming that the house wall is equivalent to building brick whose thickness is 240 mm and the windows are equivalent to glass whose thickness is 10 mm. The thermal conductivity of house wall and windows are 0.69 W/(m·K) and 1.09 W/(m·K), respectively.

Other parameters of the optimization model are listed in Table IV.

TABLE II SYSTEM OPERATING PARAMETERS

Power Supply

Output Power Limit/kW

Fuel Cost /(¥/kWh)

Operation and Management Cost/(¥/kWh)

Start-up

Cost/¥ Lower Upper

BIPV 0 70 — 0.0096 —

CHP 0 65 0.75 0.0401 3

GB 0 100 0.25 0.0102 1

EES -3 3 — — —

TES -5 5 — — —

TABLE III

DEFERRABLE LOADS PARAMETERS

Type Power(kW) Earliest starting time(h)

Latest starting time(h)

Duration (h)

Washing

machine 0.4 0.25 8:00 16:00 2

Disinfection

cabinet 0.7 1:00 24:00 1

Dishwasher 2 1.5 1.2 7:00 19:00 3

TABLE IV OTHER PARAMETERS OF THE OPTIMIZATION

Parameter Value Parameter Value n 20 Mair 723 ϕ 5000 Cp 1005.4 U 0.8 LHVNG 9.78 M 0.8 PNG 2.2

vCO2 0.000056 α, β, γ 1/3 Ρ 1.2 µ 1/2 A 200 V 600

TABLE IV

INDOOR ENVIRONMENTAL PARAMETERS

Parameters Initial Set Maximum Minimum

Illuminance/lux 320 320 320 290

Temperature/℃ 25 25 26 20

CO2/ppm 800 800 900 750

The initial values of indoor environment parameters, standard setting values and user’s allowable variation range

are shown in Table V, including illuminance, temperature and CO2 concentration indexes. In order to validate the model, three different scenarios were designed according to weather conditions: sunny, cloudy and rainy. The TOU price adopted in this paper is shown in Fig. 4 and basic prediction values for the optimization are shown in Fig. 5.

In terms of the optimization model established in this paper, the objective function can be expressed by the decision variables as:

min ( , , , , , , , , )CHP GB PV EX EES TES roomF g P P P P P Q E T N= (45)

4:00 8:00 12:00 16:00 20:00 24:000

0.5

1

1.5

Time (h)Pr

ice

(￥/k

Wh)

Fig. 4. The TOU price

4:00 8:00 12:00 16:00 20:00 24:000

10

20

30

40

50

60

Time (h)

Pow

er (k

W)

SunnyCloudyRainy

(a) The prediction of BIPV’s output

4:00 8:00 12:00 16:00 20:00 24:0020

25

30

35

40

Time (h)

Tem

pera

ture

(℃)

SunnyCloudyRainy

(b) The outdoor temperature prediction

Fig. 5. The basic prediction values for simulation The optimization model was solved by the YALMIP

toolbox in MTALAB. The whole optimization process can be represented as:

(1) Get the predicted values including BIPV’s output, uncontrollable EL and outdoor temperature.

(2) Run the YALMIP toolbox according to the objective function and corresponding constraints.

(3) Obtain the optimization results such as the power outputs of controllable generations, power exchanged with utility grid, storage charge/discharge, controllable load power, deferrable load power and indoor environment parameters.



The optimization results in different scenarios for EL, TL, CL and storage devices are shown in Fig. 6~9, respectively. As we can see in Fig. 6, EL was mainly supplied by the utility grid when the TOU price was low, and the CHP system ran on full power state when the TOU price was expensive. The optimization results are consistent to the objective that aims to maximize the system economy. In Fig. 8, the CL was mainly satisfied by AR and the shortfall of CL was met by ECR. AR could make use of the waste heat produced by CHP and has a series of advantages such as low cost and high energy efficiency, which is in line with the economic optimization goal. Thus, AR was prior in the operation process.

The optimization results for indoor environmental parameters and deferrable loads are shown in Fig. 10~12, and Fig. 13, respectively.

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:00-20

0

20

40

60

80

Time (h)

Pow

er (k

W)

BIPV GRID CHP EL EES

Sunny Cloudy Rainy

Fig.6. The optimization results for EL balance

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:00

0

50

100

150

Time (h)

Pow

er (k

W)

GB CHP AR TL TES

Sunny Cloudy Rainy

Fig. 7. The optimization results for TL balance

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:00-50

0

50

100

150

200

250

300

Time (h)

Pow

er (k

W)

ECR AR ICL FACL

Sunny Cloudy Rainy

Fig. 8. The optimization results for CL balance

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:000

0.2

0.4

0.6

0.8

1

Time (h)

SOC

Val

ue

EES TES

RainyCloudySunny

Fig. 9. The optimization results for storage devices’ states

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:0020

21

22

23

24

25

26

Time (h)

Tem

pera

ture

(℃)

Sunny Cloudy Rainy

Fig. 10. The optimization results for indoor temperature parameters

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:00317

317.5

318

318.5

319

319.5

320

Time (h)

Illum

inin

ce (l

ux)

Sunny Cloudy Rainy

Fig. 11. The optimization results for indoor visual parameters

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:00750

760

770

780

790

800

810

Time (h)

CO

2 co

ncen

tratio

n (p

pm)

Sunny Cloudy Rainy

Fig. 12. The optimization results for indoor air quality parameters

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:000

0.5

1

1.5

2

Time (h)

Pow

er (k

W)

BeforeAfter

(a)

8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:000

5

10

15

Time (h)

Pow

er (k

W)

BeforeAfter

(b)



8:00 16:00 24:00 8:00 16:00 24:00 8:00 16:00 24:000

2

4

6

8

10

Time (h)

Pow

er (k

W)

BeforeAfter

(c)

Fig. 13. The optimization results for deferrable loads

From the results, it could be found that all the indoor environment indexes are limited in setting range, guaranteeing the comfort feel for occupants.

But in rainy days, the indoor environment indexes behaved greater fluctuations than those of sunny and cloudy days. That’s due to the low power generation of BIPV. Other controllable generations must be started to satisfy load demand and the cost would rise therefore. By the guidance of objective function, the cost and comfort level may perform more variations.

TABLE VI THE RESULTS WITH AND WITHOUT SYNERGETIC DISPATCH OF SOURCE-LOAD-STORAGE

Scenarios Sunny Scenario Cloudy Scenario Rainy Scenario

Before After Change/% Before After Change/% Before After Change/%

Total Cost/¥ 967.79 927.58 -4.15 1039.13 918.69 -11.59 1095.97 620.06 -43.42

Comfort level 1 0.998 -0.2 1 0.996 -0.4 1 0.963 -3.7

TABLE VII

THE RESULTS WITH AND WITHOUT TOU PRICE

Scenarios Sunny Scenario Cloudy Scenario Rainy Scenario

With Without Change/% With Without Change/% With Without Change/%

Total Cost/¥ 927.58 991.46 -6.44 918.69 983.95 -6.63 620.06 998.69 -37.91

Comfort level 0.998 0.998 0 0.996 0.996 0 0.963 0.983 -2.03

When the TOU price was low, indoor illuminance raised, temperature and CO2 concentration values were relatively low. As a result, a relatively good indoor environmental comfort could be maintained. The reduction of controllable loads plays an important role in load shifting and improving the system economy, which has great significance for the security and stability of the energy system [33].

Changing the starting time of deferrable loads within the range set by the users could avoid the power growth on peak period and improve the economy of the system without changing its basic electrical properties [34].

From the results, it can be found that the deferrable loads have realized the time translation according to the dispatch scheme, aiming to achieve higher economic benefits without affecting people’s life quality. In order to ensure the system economy during peak price periods, the optimization results of controllable load reduced significantly resulted in a change of indoor environment parameters and the comfort level reduced slightly within an acceptable range. The results for deferrable loads are the same because TOU price are fixed in a period.

The occupants could determine the weight between economy and comfort based on the actual needs to improve overall system economy and ensure the indoor environment within an acceptable range. The optimization results reflect the balance between system economy and comfort.

Table VI exhibits the comparison with and without synergetic dispatch of source-load-storage while

Table VII displays the comparison with and without

TOU price. It’s obvious that the simulation with consideration of synergetic dispatch of source-load-storage under TOU price obtained better performance.

Specially, the total cost reduced greatly at the expense of little comfort decrease. C. Discussion

This paper concentrated on the optimized operation of BES and proposed a multi-objective optimization model under TOU price environment. Through the optimization, the proposed method achieved the synergetic optimized dispatch of source-load-storage, maintaining the occupants’ comfort and enhancing the economy of the system at the same time. The following simulation validated the advantages of synergetic dispatch of source-load-storage and TOU based DR.

It should be noted that only the price based DR, TOU price, was considered in the optimization model. In the future, other types of DR technologies, such as incentive based, direct control and autonomous, would be deployed for the same region. Consequently, loads will show different response characteristics and the model proposed in this paper should make corresponding changes. That to say, effective DR control and coordination schemes [35], which could deal with the simultaneous existence of multiple DR techniques, are required to be contained in the optimization model. And this is also the future research of this paper.



VII. CONCLUSION This paper presented a multi-objective optimization

model for intelligent BEMS based on the prediction of BIPV’s output, non-controllable load and outdoor temperature. The overall economy of BES and occupants’ indoor environmental comforts were optimized through the synergetic dispatch of source-load-storage in the situation of TOU price. Indoor environment modelling quantized occupant’s comfort feel and load classification spared the functions of controllable and deferrable loads in economic operation. The simulation results showed that the model could improve the system economy without affecting occupants’ comfort feel by the synergetic optimized dispatch.

ACKNOWLEDGMENT This work was supported in part by the National Natural

Science Foundation of China (grant No. 51577067), the Beijing Natural Science Foundation of China (grant No. 3162033), the Hebei Natural Science Foundation of China (grant No. E2015502060), the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (grant Nos. LAPS16007, LAPS16015), the Science & Technology Project of State Grid Corporation of China (SGCC), the Open Fund of State Key Laboratory of Operation and Control of Renewable Energy & Storage Systems (China Electric Power Research Institute) (No. 5242001600FB), the China Scholarship Council. M. Shafie-khah and J. P. S. Catalão acknowledge the support by FEDER funds through COMPETE 2020 and by Portuguese funds through FCT, under Projects SAICT-PAC/0004/2015 - POCI-01-0145-FEDER-016434, POCI-01-0145-FEDER-006961, UID/EEA/50014/2013, UID/CEC/50021/2013, and UID/EMS/00151/2013, and also funding from the EU 7th Framework Programme FP7/2007–2013 under GA No. 309048. Moreover, the authors appreciate the suggestions of Prof. Wei-Jen Lee, the director of the Energy Systems Research Center, the University of Texas at Arlington.

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