Self-Learning Fuzzy Controller-Based Energy ... - IEEE Xplore

2016 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData)

Self-Learning Fuzzy Controller-Based Energy Management for Smart Home Leehter Yao, Wei Hong Lim, Chien-Chi Lai Department of Electrical Engineering National Taipei University of Technology Taipei 10608, Taiwan Therefore, more sophisticated HEMS are required to optimize the energy sustainability and energy utilization.

Abstract—The advances of smart grid technology have drawn wide research interests of home energy management system (HEMS). In this paper, the hardware demonstration of a smart home consisting of main grid, renewable energy source (RES), and energy storage system (ESS) is deployed. A self-learning fuzzy controller (SLFC) is proposed in HEMS to control the amount of electricity purchased from main grid by considering the load demands, energy stored in ESS, and electricity prices. A self-learning scheme using genetic algorithm (GA) is used for automatic parameter tuning of SLFC, aiming to enhance the robustness of controller under different household environments. An efficient parameterization schemes used to represent the antecedent and consequent part of fuzzy rule base with fewer parameters are also introduced to improve the parameter learning efficiency of SLFC further. Extensive studies show that the proposed SLFC is able to achieve the energy cost saving up to 37.70% by exploiting the energy storage capability of ESS.

Computational intelligence approach is widely used to solve the energy management problem of smart home equipped with RES and ESS. In [4], a fuzzy logic control (FLC) was deployed to determine the load shifting of appliances so that both energy cost and comfort level violation of user were minimized. The control rules of FLC in [5] optimized the energy distribution of microgrid and improved the battery’s life cycle. The cost minimization of a mircogrid with RES as the main power source and ESS as a buffer against the predicted large load was achieved in [6]. A fuzzy logic was used to determine the energy drawn from ESS during the power deficiency periods without compromising the voltage stability of system. A low complexity FLC with optimized rule-based was designed in [7] to minimize the grid power profile fluctuations while keeping the state-of-charge (SOC) of ESS within secure limits. In [8], a multiagent system was utilized to manage the energy flow of a hybrid energy system, where the power exchange between ESS and DC bus was computed using both fuzzy and crisp logics. A distributed controller consisting both scheduler and coordinator modules was implemented in [9] using artificial neural network for load scheduling, aiming to maximize the use of local generation.

Keywords—Genetic algorithm (GA); home energy management system (HEMS); Internet of Things (IoT); modulated membership function (MMF); self-learning fuzzy controller (SLFC).

I. INTRODUCTION The advances of Internet of Things (IoT), smart metering and home energy management system (HEMS) infrastructures in recent year envision the potentials of smart home concept to achieve demand side management (DSM) in residential household [1]. IoT and smart metering enables the two-way communication capability between smart home users and utility via computer networking. By periodically monitoring household power consumptions and receiving dynamic electricity pricing signal from utility, HEMS can perform DSM to achieve the most economic operations of smart homes.

Numerous challenges were identified for these state-of-thearts. First, the control strategies of most HEMS designed using FLC approach relied on the fuzzy parameters that were finely tuned with respect to a given smart home environment, hence their applicability in other household conditions is limited. Second, majority of the computational intelligence based HEMS strategies neglected the dynamic electricity price factor, therefore their electricity cost minimization capability were not guaranteed. Finally, most HEMS proposals were not deployed with hardware demonstrations, leading to their questionable performances in real environments.

Another DSM solution involves the integration of renewable energy source (RES) such as photovoltaic (PV) power or wind power in smart home [2]. Nevertheless, these generated power tends not be fully utilized by the smart home user due to the intermittent nature of RES. A promising solution to address this challenge is to incorporate a set of batteries as energy storage system (ESS) into smart home [3]. ESS is able to achieve peak shaving and energy cost reduction by storing the electricity from main grids during the off-peak price periods or when there is excessive RES generation, and supplying energy to end user during peak price periods or when there is insufficient local generation. The integration of RES and ESS into smart home introduces further challenges of power management issue between the smart home elements. 978-1-5090-5880-8/16 $31.00 © 2016 IEEE DOI 10.1109/iThings-GreenCom-CPSCom-SmartData.2016.41

In this paper, the hardware demonstration of a smart home considering day-ahead electricity tariff and equipped with a PV module and an ESS is deployed. A HEMS structure is then developed using a fuzzy controller to obtain the power drawn from main grid by considering the solar power generated, energy stored in ESS, household load demands, and electricity prices. By leveraging the local generation of PV module and energy storage capability of ESS, the proposed HEMS aims to minimize the electricity drawn from grid required for satisfying the load demands. Note that the optimal parameter settings of

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fuzzy controller in HEMS might vary in different household. Manually tuning these fuzzy parameters by trial and error is tedious and inefficient. A number of delicate mechanisms are therefore introduced in this paper to facilitate the self-learning capability of fuzzy controller based on historical data and to improve the efficiency of parameter learning. The technical novelty and main contributions of the proposed work in this paper are summarized as follows: 1) A self-learning fuzzy controller (SLFC) is proposed in HEMS, aiming to minimize the electricity cost required for satisfying household load demands by prioritizing the use of local generated PV power and stored energy in ESS. 2) A self-learning scheme using genetic algorithm (GA) is proposed to enable the automatic parameter tuning of SLFC based on historical data, aiming to enhance the robustness of SLFC under different household environments.

Fig. 1. The power architecture of smart home considered in this study.

are monitored by HEMS and stored in a database. Given these information, HEMS can adjust the electricity drawn from grid, aiming to minimize the cost for satisfying load demand. The two-way communication between HEMS, PV module, ESS, main grid, and database are established via a local area network with communication media such as Wi-Fi, RS-485, or Ethernet.

3) An efficient parameterization scheme is used to represent each membership function in the antecedent and consequent parts for the entire fuzzy rule base for SLFC with fewer parameters. GA is then applied to learn as few as nine parameters and yet successfully learns the entire fuzzy rule base of SLFC within shorter learning time.

Denote Pjload as the household load demand, PjPV as the solar power generated, PjESS as the charging or discharging rate of ESS, and Pjgrid as the electricity drawn from main grid at every j-th time step, j = 1,…,J. Both PjPV and Pjgrid are positive because neither of these power can be injected to main grid. PjESS can have both positive and negative values as ESS can be discharged to supply power to loads and charged by the PV module or grid, respectively. Given this sign convention, the power balance equation at any j-th time step is given as:

This paper is organized as follows. In Section II, the system architecture of smart home is described. The proposed SLFC is described in Section III. Section IV investigates the modulated orthogonal parameterization scheme employed by SLFC. The automatic parameter learning of SLFC using GA is described in Section V. Experimental results are discussed in Section VI and finally the conclusions are drawn in Section VII.

j Pload

II. SYSTEM ARCHITECTURE OF SMART HOME

j j PPVj  PESS  Pgrid .

(1)

In this study, all PjPV generated are first used to meet Pjload. Define Pjnet as the net load demands of smart home after being satisfied by solar power generated, then

The power architecture of smart home deployed in this study is depicted in Fig. 1. Three energy sources used to satisfy the household load demands are main grid, PV module, and ESS. There are no power exchanges between the PV module and main grid because all solar power is used to satisfy household load demands and the excess local generation are used for ESS charging. In contrary, power exchanges are allowed between ESS and main grid because the electricity drawn from grid can also be used for ESS charging. While the electricity drawn from main grid can be adjusted, remaining elements such as PV module, ESS, and load demands are uncontrollable in this study. An energy management is hence required to determine the electricity drawn from grid to ensure the household load demands can be met with minimum cost without violating the operating constraints of smart home.

Pnetj

j Pload  PPVj .

(2)

Two operating modes are identified based on Pjnet obtained. For first mode, Pjload d PjPV or Pjnet d 0, therefore no electricity needs to be drawn from grid. For second mode, Pjload t PjPV or Pjnet t 0, and the power deficiency is compensated by either drawing electricity from grid, discharging ESS, or both. As shown in next section, a SLFC is designed in HEMS to determine Pjgrid required to satisfy Pjload with minimum cost. Define ] j as the electricity price and J j as the SOC of ESS at every j-th time step. Let F( ˜ ) be the fuzzy inference of SLFC used to determine Pjgrid based on Pjnet, ] j and J j , then

A HEMS is designed in smart home to satisfy load demands by prioritizing the use of locally generated solar power, energy stored in ESS, and the electricity drawn from grid during off-peak price periods. The energy management problem is approximated using the slotted time modelling approach, i.e., the total available time period H for optimizing electricity drawn from grid during a day is evenly divided by the sampling interval Ts into J intervals, where J = H/Ts. Utility company announces the dynamic tariffs to HEMS periodically via internet throughout the control interval. The solar power generated, the SOC of ESS, and the household load demands

j Pgrid

F  Pnetj ,J j ,]

j

.

(3)

Since the ESS is not controllable, PjESS can only be computed based on the difference of Pjnet and Pjgrid as follow: j PESS

j Pnetj  Pgrid .

(4)

Let Ecap and f (n) be the battery capacity and efficiency of ESS, respectively. Define nc and nd as the charging and discharging efficiencies of ESS, then f (n) = nc for charging mode and f (n)

88

m1 m2

= 1/ nd for discharging mode. Based on PjESS obtained from (5), the SOC of ESS at any j-th time step is updated as:

J

J

j

j 1

Pj T  f  n ESScap s . E

j Pgrid

j Pgrid

P

v

c c

c

iv 1 v

c

iv v

, ,

if c

(6)

if c d xv d c

(7)



P

mv 1 v

 xv

­ xv  cvmv 2 ° ° ®1, °0 , °¯

c

mv 1 v

m1 m2 m3

IV.

Meanwhile, the membership functions for the first and last fuzzy sets, i.e., iv = 0 and iv = mv -1 are defined as:

Pv0  xv

iv ' v

v

iv ' v

v

i1 ,i2 ,i3

3

–P x iv v

v

(12)

v 1

MODULATED MEMBERSHIP FUNCTIONS

An efficient scheme called modulated membership function (MMF) is used to represent the proposed SLFC consisting a set of m1 u m2 u m3 fuzzy rules and the fuzzy sets with orthogonal

(8)



 cvmv 2 , if cvmv 2 d xv d cvmv 1 if cvmv 1 d xv

1. (11)

v 1

output fuzzy singletons z i1 ,i2 ,i3 in Fig. 2 are constrained between a lower limit Zmin and an upper limit Zmax to ensure the electricity drawn from grid are within the secure limits.

otherwise.

1 1 0 0 1 ­ ° cv  xv  cv  cv , if cv d xv d cv ® otherwise. ° ¯0 ,

3

v

increases with Pjnet and decreases with both J j and ] j . All

d xv d c

iv 1 v

v

decrement for J j or ] j increase from A2i2 or A3i3 to A2i2 1 or A3i3 1 are D 2 and D 3 , respectively. Fig. 2 shows that the power output

iv v

iv v

v

The fuzzy rule base in (8) is mapped as in Fig. 2. Let the output fuzzy singleton z i1 ,i2 ,i3 of SLFC corresponds to the fuzzy sets with minimum inputs of Pjnet and J j be a baseline value denoted as Z . Let the power output increment for Pjnet increases from A1i1 to A1i1 1 be D1 , while the power output

The simplified symmetrical triangular functions used to define the membership functions of the fuzzy set Aviv for v-th input where 1 d iv d (mv - 2), v =1,..,3 are then given as:

 x 

iv v

¦¦¦ z i1 1 i2 1 i3 1

j If Pnetj is A1i1 and J j is A2i2 and ] j is A3i3 , then Pgrid is z i1 ,i2 ,i3 .

iv v

(10)

The output of SLFC in (10) can be further simplified as:

Pjnet, J j , and ] j , respectively. Notably, m1, m2, and m3 are odd numbers and t 3. Then, the fuzzy rules of SLFC is given as:

iv 1 v

3

i1 i1 ' i2 i2 ' i3 i3 ' v 1

A . Assume that there are m1, m2, and m3 fuzzy sets for inputs

iv 1 v

iv v

¦ ¦ ¦ – P  x –  P  x  1  P  x

i3 3

iv v

.

¦¦¦– P  x

i1 ' 1 i2 ' 1 i3 ' 1

of J j , A3i3 be the i3-th fuzzy set of ] j , z i1 ,i2 ,i3 be the output fuzzy singleton of Pjgrid corresponds to input fuzzy sets A1i1 , A2i2 , and

v 1,..,3

v

v

i2 2

0,..., mv  1 ,

3

margins of Pviv  ˜ are cviv 1 and cviv 1 , respectively. For any v-th input, the membership values of both adjacent functions add to one, i.e., Pviv 1  xv 1  Pviv  xv . The fuzzy sets given in (7)-(9) are called orthogonal fuzzy sets because there are always two adjacent membership functions to be activated for each input. For the v-th input with magnitude xv and cvi ' d xv d cvi ' 1 , assume that the iv’-th input and (iv’+1)-th membership functions get activated. The denominator of (10) can then be simplified as:

Let A be the i1-th fuzzy set of P net, A be the i2-th fuzzy set

iv

iv v

v 1

From (7), the center of Pviv  ˜ is cviv , while the left and right

Heuristics used to design the SLFC in HEMS are explained herein. When the SOC level of ESS is high and Pjnet is low, smaller amount of Pjgrid are drawn as most load demands can be met by discharging ESS. Given the similar SOC level and as Pjnet becomes greater, Pjgrid increases correspondingly to avoid deep discharging of ESS. For ESS with low SOC, more Pjgrid are drawn from grid regardless the amount of Pjnet needs to be fulfill. For lower tariff, more Pjgrid can be drawn to meet load demand and charge the ESS for future use. Higher tariffs discourage purchasing power from main grid unless Pjnet is too high or the SOC level of ESS is too low for discharging.

­ xv  cviv 1 ° ° iv 1 ® cv  xv ° 0, ° ¯

i1 1 i2 1 i3 1 m1 m2 m3

i1 1 i2 1 i3 1 v 1

III. SELF-LEARNING FUZZY CONTROLLER

j

3

i1 ,i2 ,i3

(5)

i1 1

m3

¦¦¦ z – P  x

(9)

otherwise.

Since the inputs for SLFC in (8) are all positive values, the universe of discourse for each input in SLFC is normalized in the between 0 and 1, i.e., cviv  >0,1@ , v 1,...,3 . Then, the output of SLFC is computed using the product inference and center average defuzzification as shown: Fig. 2. The fuzzy rule base employed by the proposed SLFC.

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The constraint of U v is obtained by calculating the least upper

membership functions using fewer parameters. Let cviv be the centers of MMF for the v-th input of fuzzy controller, it is first set to be uniformly distributed in universe of discourse [0,1] as:

iv , iv mv  1

cviv

0,..., mv  1 .

bound in (20), i.e., h = 1 for h  ª¬1, mv  1 2º¼ . Therefore,

Uv d

(13)

2 . mv  2

(21)

Let U v and I  iv be the modulation factor and modulation

Theorem 1 shows that cviv d 1 if 1  Uv d 2  mv  2 . Then,

exponent associated with cviv , respectively. The centers of membership functions in (13) can be further modulated as:

cviv d 1 is satisfied if cviv d 1 is guaranteed with the constraint

I  iv

c 1  Uv

iv v

iv v

c

of N v defined in the next theorem and the constraint of U v .

(14)

Theorem 2: Given that cviv d 1 , if N v d 1 then cviv d 1 .

where Uv d 1 and the modulation exponent is defined as: mv  1 m 1 , iv  iv  v 2 2

I  iv

Proof: Note that cviv d 1 implies for two separate conditions of

0,..., mv  1 .

0 d cviv d 1 and 1 d cviv  0 . For 0 d cviv d 1 ,

(15)

cviv

The set of membership functions for every v-th fuzzy input needs not to be centered at the origin. Therefore, an offset factor N v is added to fine tune the distribution of the sequence of membership centers as follow: iv v

c

1  c N c iv v

v

 N v , iv

iv v

0,..., mv  1 .



cviv d cviv  1  cviv

(16)

cviv

I  iv

.

§ mv  1 · ¸ 1 . © mv  1  h ¹



(24)



1.

(25)

Genetic algorithm (GA) is used to automatically learn the nine parameters of SLFC online based on the historical data of smart home. Assume that there are G chromosomes to converge, the k-th chromosome for every i-th generation is represented as uik  U1ik , U2ik , U3ik ,N1ik ,N 2ik ,N3ik ,D1ik ,D 2ik ,D3ik , k =

and let h be an integer value, then

Uv d ¨



V. AUTOMATIC PARAMETER TUNING OF SLFC

d1

needs to be met based on (14). Given I  iv h  ¬ª1, mv  1 2¼º

1



and D 3 with respect to the inputs Pjnet, J j , and ] j , respectively, for the output fuzzy singletons in the consequent part. The performance of SLFC relies on the optimality of its parameter settings, which in turn change under different smart home environments. Manually tuning these parameters for a specific household is tedious and inefficient. A self-learning scheme is proposed in next section to enable automatic parameter tuning of SLFC under different household environments.

(18) I  iv

mv  1 . mv  1  h



antecedent part Aviv , v =1,..,3, as well as the variations of D1 , D 2 ,

(17)

To satisfy cviv d 1 , the condition of cviv 1  Uv

d

(23)

Nine parameters need to be tuned for SLFC, including the modulation factors U v and offset factors N v for three inputs of

! 0 , then

mv  1  h ª m  1º ,h  «0, v » mv  1 2 ¼ ¬

h

(22)

Theorem 2 can thus be shown from both (23) and (25).

for iv = 1,…,( mv–2). It is also shown in (13) that

1  Uv

1.

cviv  1  cviv N v d cviv  1  cviv N v .



The condition of I  iv 0 is omitted as U v is arbitrary value from (17). Both conditions of iv = 0 and iv = mv–1 are discarded for producing I  iv 0 from (15). Hence, I  iv  ª¬1, mv  1 2 º¼

cviv



cviv d cviv  1  cviv

Theorem 1: With mv ! 3 , if Uv d 2  mv  2 , then cviv d 1 .

cviv 1  Uv



Then, if N v d 1 ,

fulfilled according to (16) using the constraint of U v defined in the following theorems.

cviv



Similarly, for 1 d cviv  0 ,

be satisfied. To have cviv d 1 , the condition cviv d 1 needs to be

I  iv



Then, if N v d 1 ,

Since the universe of discourse for every v-th fuzzy input is normalized in the range of [0,1], the condition cviv d 1 needs to

Proof: Since Uv  1 and 1  Uv



cviv  1  cviv N v d cviv  1  cviv N v .

(19)

1,…,G, i = 1,…, L. The search ranges of U v and N v for v = 1,..,3 are set as Uv d 2  mv  2 and N v d 1 using Theorems 1 and 2,

h

(20)

respectively. Meanwhile, the search range of D v is constrained between >D min ,D max @ .

90

GA is applied to search for the optimal parameterizations of

values from small to large. The first chromosome consists of the best searched parameters leading to the least fitness value. Elitism scheme is employed where the best chromosome corresponding to the least fitness value in every generation is passed onto the next generation. The searching process of GA is repeated until the maximum generation L is reached.

U v , N v , and D v ,v = 1, 2, 3, for SLFC to minimize the total

electricity cost incurred throughout the J control intervals with a sampling length of Ts for each j-th time step. To prevent the deep discharging of ESS, the fitness function is also designed to penalize the searched chromosomes in case the ESS of associated chromosomes fails to produce a SOC level higher than that of a threshold denoted as : at the end of control interval. Define 4  ˜ as a penalty function and E as a penalty coefficient, then

if J J >:

­0,

4 J J ®

VI.

A. Experiment Settings A smart home with the day-ahead tariff as provided in [10] is deployed in this study for performance evaluation. The total available time period H for controlling is 24 hours and the sampling interval Ts to for calculating the power to be drawn from grid is set to 5 minutes. Thus, the number of time steps J = H/Ts = 288. The smart home is provided with the PV modules with maximum output power of 4kW, the main grid from utility with nominal voltage of 110V, and an ESS with the nominal voltage and capacity of 48V and 300Ah, respectively. A SLFC with three inputs and nine modulated triangular membership functions for each input is designed. Given mv = 9 for v = 1,..,3, the search space of modulation factor is computed as Uv d 0.285 . Related GA parameters are summarized as: G = 50, L = 100, c1 = c2 = 0.5, pt = 0.02, E = 10,000, and : = 60%. All experiments are implemented in an embedded system with Linux environment with C language.

(26)

¯ E !! 0, otherwise

Define Tdiv as the number of available time slot in each hour given the sampling interval Ts, i.e, Tdiv = 60/ Ts. Then, the fitness function corresponding to uik is then defined as: E  uik

J

¦

j Pgrid ]

Tdiv

j 1

Denote uˆ ik

j

 Uˆ

ik 1

 4 J J

(27)

, Uˆ 2ik , Uˆ 3ik ,Nˆ1ik ,Nˆ 2ik ,Nˆ 3ik ,Dˆ 1ik ,Dˆ 2ik ,Dˆ 3ik as the best

solution for the g-th generation. GA is applied to minimizing the fitness function in (27), i.e.,

uˆ ik

 Uˆ

Arg min ik v



,Nˆ vik ,Dˆ vik ,i 1,..,L,k 1,...G,v 1,2 ,3

E  uik

(28)

B. Experiment Results Two test cases of cloudy and sunny days are considered for performance evaluations of SLFC. The experimental results including the net load demand, solar power generated, grid power purchased (denoted as rectifier setting), variation SOC for ESS, and electricity prices for these two cases are depicted in Fig. 3(a) and 3(b), respectively.

Crossover is performed parameter by parameter on Uvik , N vik , and D vik using the localizing and dispersing operators with the probabilities of c1 and c2, respectively, where k = 1,…,G, i = 1,…,L, v=1,2.,3, and c1 + c2 = 1. Without loss of generality, consider Uvik as an example, then

­ Uvl1 k 1 ° Localizing ® l k 1 2 ° ¯ Uv

Uvl k  9  Uvl k  Uvl k

­ Uvl1 k 1 ° Despersing ® l k 1 2 ° ¯ Uv

Uvl k  9  Uvl k  Uvl k

1

U

1

l2 k v

1

2

9 U  U l1k v

2

l2 k v



2

2

As shown in Figs. 3(a) and 3(b), the electricity drawn from grid, as determined by SLFC, are relatively low during the day time (i.e., from 7:00AM to 12:00PM). The solar power gained at these periods are sufficient to meet all load demands and the excess generation are used to charge ESS, as implied by its increment of SOC level in these periods.

(29)

1

Uvl k  9  Uvl k  Uvl k

(30)

1

The economic benefits of ESS are demonstrated from 12:00PM to 7:55PM. During these periods, the load demands gradually increase, while the electricity price are higher. Since the SOC of ESS is relatively high, it is more economic feasible to discharged the stored energy to cover most load demands. The role of ESS as main energy provider at these periods are verified by its decreasing SOC. An increment of grid electricity usage is observed from 3:55PM to 5:55PM and 5:55PM from 7:55PM. The former case is due to lower electricity price, while the latter case aims to preserve battery lifetime by avoiding the deep discharging of ESS.

where 9   0,1 is a random number, l1 and l2 are the indices of two chromosomes selected for crossover. The same crossover in (29)-(30) are also applied to N vik and D vik . Mutation is performed along the crossover operations with probability of pt for every parameter encoded in chromosome uik. Without loss of generality, consider Uvik as an example and M as the perturbation signal added, then

Uvi k 1

EXPERIMENTS

Uvik  M

(31)

The electricity drawn from grid are relatively high from 7:55PM to 5:55AM of next day because no solar powers are generated and the remaining energy stored in ESS is low. While purchasing of power from gird is inevitable at these periods, no significantly high electricity bills are incurred due to the lower electricity prices. The SOC level of ESS is also

The same mutation in (31) is also applied to N vik and D vik . For every generation of GA, all chromosomes are rearranged in the gene pool by sorting corresponding fitness

91

(a)

(b) Fig. 3. The experimental results for the (a) cloudy and (b) sunny days.

gradually increasing at these periods, indicating that a portion of electricity drawn from grid are used for ESS charging. Both test cases also reveal that the SOC of ESS at the end of control interval is approaching towards the threshold : .

TABLE I.

Case 1 (Cloudy) Case 2 (Sunny)

The cost minimization capability of SLFC is further investigated. Let K d be the total electricity bill incurred for satisfying the net load demand without considering ESS, then

Kd

Pnetj ] ¦ j 1 Tdiv J

J

¦ j 1

j Pgrid ]

Tdiv

K d (NTD) 52.92 58.42

K a (NTD) 35.41 36.39

Cost Saving (%) 33.08 37.70

electricity drawn from grid required in order to satisfy the net

j

load demands. Table I reports that the values of K a in both

(32)

cases are smaller than those of K d , and the proposed SLFC is proven to be able to achieve the cost saving up to 37.7%.

Meanwhile, the total electricity bill incurred for satisfying the net load demand by considering ESS is denoted as K a , where

Ka

EVALUATION OF COST SAVING CAPABILITIES OF THE PROPOSED WORK

Finally, the computation time required by GA to learn the parameters of antecedent and consequent parts for each membership function as well as the fuzzy rule base of SLFC is measured in computational complexity analysis. Extensive analysis shows that the proposed automatic parameter tuning scheme takes not more than 1 seconds to learn the optimal values of all nine parameters required to model the entire membership functions and fuzzy rule base of SLFC. The efficient computation speed demonstrated by the GA-based automatic parameter tuning scheme suggests the feasibility of

j

(33)

The first component of fitness function in (29) aims to minimize total electricity bill. Therefore, K a is expected to be smaller than K d because the proposed SLFC tends to leverage the energy storage capability of ESS in minimizing the

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SLFC to be deployed in real-time smart grid applications.

[2]

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VII. CONCLUSION A SLFS is proposed to satisfy the household load demand of a smart home equipped with RES and ESS in real time. Delicate mechanisms are introduced to improve the efficiency of parameter learning and the robustness of SLFC in different smart home environments. Extensive experiments shows that different energy sources become dominant in supplying powers to the household appliances for different time periods. By exploiting the energy storage capability of ESS, SLFS is able to satisfy the load demands with minimum electricity bill without significantly compromising the battery lifetime. Some future works can be suggested based on the current proposal. First, the load scheduling problem of interruptible and noninterruptible household appliances can be considered to extend the smart home concept. Second, a more comprehensive selflearning mechanisms of fuzzy controller can be developed by considering parameter learning as a multi-objective optimization problem by considering the benefits of different parties such as the smart home owner, load service provider, aggregator, retailer, and etc. REFERENCES [1]

T. Perumal, A.R.Ramli, and C. Y. Leong, "Design and implementation of SOAP-based residential management for smart home systems " IEEE Trans. Consum. Electron., vol. 54, no. 2, pp. 453-459, May 2008.

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