2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

Real Time Multi-Objective Energy Management of

a Smart Home
Arunava Chatterjee, MIEEE Subho Paul, MIEEE Biswarup Ganguly, MIEEE
Electrical Engineering Department Electrical Engineering Department Electrical Engineering Department
Raghunathpur Govt. Polytechnic Indian Institute of Technology Roorkee Meghnad Saha Institute of Technology
Purulia, West Bengal, India Roorkee-247667, Uttarakhand, India Kolkata- 700150, West Bengal, India
arunava7.ju@gmail.com spaul@ee.iitr.ac.in bganguly@msit.edu.in

Abstract—Home energy management comes under the Tt in,i Temperature inside the room in oC
umbrella of decentralized demand response techniques, where
Outdoor ambient temperature in oC
2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES) | 978-1-7281-5672-9/20/$31.00 ©2020 IEEE | DOI: 10.1109/PEDES49360.2020.9379539

home occupants schedule their appliances for achieving lowest Tt amb

energy cost at minimum discomfort level. However, smart Pt ,AC Power absorbed by air-conditioner in kW
i
home energy management becomes challenging due to
penetration of intermittent rooftop storage collocated solar Tset Preferable room temperature in oC
power generations. In view with this, the present article Minimum and maximum allowable room
Tmin , Tmax
illustrates a multi-objective real time residential load temperature
management topology considering random variation in μtb , μts Binary status of power purchase (sell) from (to) the
rooftop solar power and distribution grid energy price. local utility, 1- YES, 0- NO
Initially the problem is developed as a time average stochastic ρtb , ρts Main distribution grid energy buying and selling
price in $/kWh
optimization problem which is further simplified to a mixed
Pt b , Pt s Amount of power purchase (sell)
integer linear programming by utilizing the idea of Lyapunov
optimization. Ocular and thermal discomfort minimization are Pl ,i Pi AC Rated power requirement of lights and AC in kW
attached with the energy cost minimization objective to lower ,
the discomfort level due to real time load management actions. Pt PV Solar generation at time t in kW
The proposed technique is validated on a real life residential Power demand at time t other than lighting and AC
data and it has been established that the derived strategy can Pt CL
loads in kW
optimally control the domestic loads in real time. The controls Battery energy and power at time t in kWh and kW
Etbat Pt bat
for the residential loads are also realized using internet of , respectively
things (IoT) based controller. P bat Battery power rating in kW
bat
Emin bat
Emax Lower and upper limits of the battery energy level
Keywords—Illuminance, internet of things (IoT), Lyapunov , in kWh
optimization, ocular discomfort, thermal discomfort. Maximum allowable power exchange with main
P max
distribution grid in kW
NOMENCLATURE
I. INTRODUCTION
HEC Home energy controller
MILP Mixed integer linear programming Since last few decades, energy sector is experiencing a
AC Air-conditioners paradigm shift from the excessive utilization of fossil fuels
H Total number of rooms, indexed by i in the power generation to renewable power generation to
l Index for lighting loads present in a room avoid huge carbon emission. Therefore, to mitigate the effect
I T ,t , i Indoor illuminance level
of global warming, renewable energy generations are
I D ,t ,i Average indoor illuminance due to daylight at time penetrating in the modern power grid to match the energy
t in lux supply and demand profiles with less carbon footprint.
I l ,t ,i Indoor illuminance due to light l in room i at time t Again, exponential population growth rapidly increases the
in lux
Outside illuminance at time step t in lux power requirement in residential, commercial and industrial
I O ,t sectors. However, intermittency present in the renewable
ξw Parameter defining window glass transmission energy resources creates real time supply demand
Aw,i total window area at room ‘i’ in m2 unbalancing. Demand response programs are becoming
popular in recent times to fight with this unavoidable demand
φ Angle in degree between window and sky
increment by regulating the loads according to the available
As ,i Room surface area in m2 generation to minimize the effect of renewable generation
r Coefficient defining indoor average reflectance uncertainty. In 2016, International Energy Agency revealed
level that residential consumers had almost 32% share in the total
ϕl ,t ,i Lumens output from the light l load demand [1]. Therefore, in smart grid era residential load
management with the help of two-way communication
Pl ,t ,i Power absorbed by light l at time t in kW
facilities is gaining interest in world wide. However, wide
λl Lighting load’s luminous efficacy in lumens/kW variety of residential devices having non-identical
Lighting load utilization factor operational characteristics makes the domestic demand
U l ,i response strategies challenging. Logenthiran et al. [2]
M l ,i Lighting load maintenance factor proposed day-ahead centralized load shifting method on
Comfort level illuminance inside the room flexible residential devices to minimize the gap between
I set ,i
forecasted and objective load curve. Paterakis et al. [3]
I min,i , I max,i Minimum and maximum illuminance level designed a day-ahead load management of household
appliances by neighborhood coordination. Nguyen et al. [4]

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2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

literatures mainly developed single-objective energy

management problems aiming to reduce only the electricity
cost. In contrast with the aforementioned articles, the present
state of art proposes a real time HEMS by controlling the
lighting and air-conditioning loads. The specific
contributions are as follows-
1. A multi-objective optimization portfolio is proposed to
minimize the occupants’ total discomfort (ocular and
thermal) and electricity cost simultaneously by
controlling the consumption of lighting sources and
ACs.
2. The complete formulation is developed as an MILP by
linearizing all the non-linearity related to objective
functions and constraints.
3. Solution process is suggested as a Lyapunov
Fig. 1. Internal framework of the considered smart home. optimization strategy to eliminate the complexity
regarding time average stochastic formulation.
propounded a centralized day-ahead optimal bidding 4. An IoT based controller is designed to realize the real
strategy for a residential building by controlling the heating, time control of the residential loads.
ventilation and air-conditioning loads. In case of previously The remaining article is organized as: Section II
illustrated centralized approaches, users cede the load formulates the energy management problem followed by the
management process completely on the network operator solution strategy in Section III. Section IV deals with the
and have no other option than obeying the decision. design descriptions of the IoT based controller. A detailed
Therefore, these strategies breach the privacy issues related case study with necessary simulation results is portrayed in
to the home occupants and that motivates the demand Section V. Finally the article is concluded in Section VI.
response strategy designers to move on towards
decentralized strategies. II. REAL TIME SMART HOME ENERGY MANAGEMENT
Home energy management system (HEMS) or load PROBLEM FORMULATION
management of individual residential unit is a sub-set of the
decentralized demand response strategies. The aim of HEMS In this section, the energy management problem
is to schedule the deferrable home appliances to minimize corresponding to the smart home is formulated. In order to
electricity cost and to maximize the comfort level [5]. An develop the mathematical model of the home energy
MILP based day ahead domestic load management was management problem, the objective functions related to the
prescribed in [6], where air-conditioning and other shiftable comfort measurement of the occupants and total electricity
domestic loads were managed to keep the total power cost of the home is described first followed by the
consumption below a certain limit. Three non-identical operational constraints of the home. The smart home is
HEMS based on MILP, continuous relaxation and fuzzy equipped with a home energy controller (HEC), responsible
logic were designed by Wu et al. [7]. The benefit of day- for controlling the lighting and ACs at real time to lower the
ahead bi-directional power flow management of electric total consumption of the home against real time energy price
vehicles and stationary storages along with the domestic load and rooftop solar power generation.
scheduling were explored in literature [8]. Zhao et al. [9]
proposed water heater load management strategy for A. Objective Functions
minimizing the total energy cost by heating water from The objective of HEC is to simultaneously minimize the
renewable power sources and optimizing the operation of ac long-term operational cost and the discomfort experienced
and dc loads. The previously mentioned literatures have by the occupants due to control of lighting and air-
mainly aimed to develop the deterministic offline solution of conditioning loads in the home.
the residential energy management. However, these 1) Ocular Discomfort Minimization
strategies are not capable to handle any uncertainty in day Indoor illuminance level is maintained at the day time
ahead input parameters like energy price, renewable by both lights and the daylight. However, at nights it is
generation etc. To avoid such deficiency, merger of maintained only by the lighting loads. Uniform distribution
regression study and artificial neural network was deployed
of the daylights coming from the window is considered in
in [10] to mitigate the uncertainty effect of solar power
generation on home load management. Home energy this study (non-uniformity is left for the future study). It is
management as a stochastic optimization portfolio were worthy to mention that the ocular discomfort is measured by
designed in [11] and [12] by generating scenarios from the indoor illuminance level. However, at daytime control
probability distribution of uncertain parameters using over the illuminance of the lighting sources by exploiting
roulette wheel and two point estimation methods maximum possible daylight can provide the visual comfort
respectively. A risk constrained home energy management to the occupants with less electricity consumption. Hence,
based on conditional value at risk method was proposed by indoor illuminance at time ‘t’ is written as follows,
Paul and Padhy in [13]. I T , t , i = I D , t , i + ¦ I l ,t , i (1)
As per the previous literature review, a wide number of l

researches for the last 5/6 years are dedicated to develop Now, indoor average illuminance caused from daylight can
efficient day-ahead HEMSs. Day ahead algorithms are either be written as,
suffering from lack of uncertainty handling capability, [6]- I D ,t ,i = DFavg ,i I O ,t (2)
[9], or need exact probability distribution functions of the Here, DFavg is defined as the average daylight factor [14].
random parameters, [10]-[13], to develop stochastic
formulations, which is a cumbersome job. Again, the DFavg = ξ w Aw,iφ ª¬ As ,i (1 − r 2 ) º¼ % (3)

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2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

Now, indoor illuminance caused by lights is as follows, 1 T −1

Min ¦ E ª¬ F ( Ω ) º¼
lim (10)
I l ,t ,i = (ϕl ,t ,iU l ,i M l ,i ) As ,i (4) Ω T →∝ T t = 0

Where, ϕl ,i ,t = Pl ,t ,i λl . Here, E[.] denotes expectation value.

Now, ocular discomfort can only be minimized if the B. Constraints
indoor illuminance level will remain close to the comfort The objective function (10) should be minimized keeping
level. Therefore the ocular discomfort minimization following constraints in mind:
objective is as follows,
I min,i ≤ IT ,t ,i ≤ I max,i and 0 ≤ Pl ,t ,i ≤ Pl ,i (11)
Min f1 = ¦ abs ( IT ,t ,i − I set ,i ) (5)
i∈H

Where, abs(.) is the absolute function. Tmin ≤ Tt in,i ≤ Tmax and 0 ≤ Pt ,AC
i ≤ Pi
AC
(12)
2) Thermal Discomfort Minimization
Purpose of the air-conditioning unit is to keep the indoor Etbat = Etbat
−1 + Pt
bat
Δt (13)
temperature within the comfort level, preferred by the home
− P bat ≤ Pt bat ≤ P bat and Emin
bat
≤ Etbat ≤ Emax
bat
(14)
occupants. The indoor temperature can be represented as a
function of power consumed by the AC unit as written in
equation (6) [12].
(μ P − μts Pt s ) + Pt bat + Pt PV = Pt CL + ¦ Pt ,AC
b b
t t i + ¦ ¦ Pl , t , i
i∈H i∈H l

T in
t +1,i =T e
t ,i
Δt
in − τ
(
+ 1− e
− Δt
τ
) ª¬T
t
amb
+R P AC
eq t , i
º¼ (6)
μtb + μts ≤ 1
(15)
(16)
where, τ = Req Cair , Δt is the gap between two consecutive
time steps and Req = ( Rwall Rwin ) ( Rwall + Rwin ) Pt b , Pt s ≤ P max (17)
Therefore, thermal discomfort minimization objective is Equation (11) denotes that the illuminance in the room
given by, should be within the specified limit by limiting the power
(
Min f 2 = ¦ abs Tt in+1,i − Tset
i∈H
(7) ) consumption of each lighting source below its rated value.
Equation (12) depicts the boundaries of the indoor
1) Electricity Cost temperature and power absorbed by the AC unit. Equation
Residential energy demand of the smart home is met (13) shows the energy updating expression of the battery
from both local distribution grid and rooftop energy storage storages, which is having 100% efficiency in this study.
collocated solar panel. Therefore, home occupants have to Power and energy limiting boundaries of batteries are shown
pay the distribution network operator for their grid energy in equation (14). Utilization of two extra binary variables
usage. Again, they will receive incentives from the utility corresponding with charging/discharging operations can
after selling their excess solar power to the upper grid. easily reformulate the equation (13) with battery efficiency.
Hence, the net monetary payment at time step t can be Power balance inside the home at each time step is restored
expressed as, by the equation (15). Equation (16) denotes that the power
exchange with the main distribution grid is unidirectional at
(
Ct = μtb ρtb Pt b − μts ρts Pt s Δt (8) ) any particular time step t. Power exchange between the upper
2) Overall Objective Function distribution grid and the home is bounded by the inequality
Full satisfaction level can be restired if both ocular and (17).
thermal comfort levels are achieved simultaneously in less
electricity cost. However, monetary payment reduction and III. PROPOSED SOLUTION PROCESS
discomfort minimization are contradictory with each other. Before beginning the solution process, nature of the
Minimization of one will lead to maximization of the other. formulated problem needs to be investigated. As can be seen
Hence, a pareto optimal decision should be made by revising from expressions (5) and (7), presence of mod function
the objective function as a weighted average one as makes it non-linear. Again, multiplication of binary and
mentioned below. continuous variables converts the objective (8) and
F ( Ω ) = γ ( ς 1 f1 + ς 2 f 2 ) + (1 − γ ) Ct , 0 ≤ γ ≤ 1 (9) constraint (15) to a non-linear expression having integer
variables. Thus, the derived problem is a mixed integer non-
Where, Ω = ª¬ Pl ,t ,i , Pt AC , Pt b , Pt s , Pt bat º¼ , ς is a positive valued convex one. Again, presence of time average objective
parameter used to represent the ocular and thermal function (10) makes the solution process further complex. As
discomfort as an economic loss to the HEC and γ is the MILP guarantees convergence to the global optimal result
[7], the entire problem needs a proper linearization and
weight parameter between both objective functions. revision to eliminate non-linearity and time average
Now, as consumption of the lighting and AC loads are equation.
regulated separately at each time. Hence, individual cost
analysis at each time step may lead to costlier solution. A. Linearization Techniques
Therefore, long term value of the objective function (9)
needs to be minimized for obtaining maximum benefit. 1) Elimination of absolute (abs) Function from (5) and
Knowledge regarding future scenarios is absence in case of (7)
real time optimization process but it is the prime Equations (5) and (7) takes the form of
requirement for minimization of the long term objective. Min f = ¦ abs ( xi − yi ), xi ≥ 0, yi ≥ 0 (18)
i
Therefore, in this article the objective function is rewritten
Now expression (18) can be written as,
as a time average stochastic expression (10), as given below.
f = ¦ ª¬ Fi ,1 + Fi ,2 º¼ (19)
i

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2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

Fig. 3. MQTT protocol-based control.

The conditional Lyapunov drift at each time gap is as

follows,
Fig. 2. IoT based controller for controlling the residential loads.
Δ (Yt bat ) = E ª ℑ ( Yt bat
+1 ) − ℑ ( Yt
bat
) Ytbat º¼ (27)
¬
Subject to the following constraints,
( xi − yi ) + Fi ,1 − Fi ,2 = 0 (20) Minimization of this drift will surely limit the dynamic
change in the battery energy level by minimizing its
Fi ,1 , Fi ,2 ≥ 0 (21) operation but that will indeed increase the discomfort level
Due to constraint (20), Fi ,1 and Fi ,2 are linearly dependent and also the operational cost. This will rise a multi-objective
optimization portfolio with the objective function defined as,
and always takes positive values due to constraint (21).
Therefore, in equation (19) either Fi ,1 or Fi ,2 will take Qt = Δ (Yt bat ) + W ⋅ E ª¬ F ( Ω ) Yt bat º¼ ,W > 1 (28)
positive value at a time and other will be zero.
2) Linearization with Auxiliary Variables Where, W is a positive trade-off constant.
As can be seen from expressions (8) and (15) that, they Lemma 1: For each time slot t, Qt will be upper bounded by,
comprise of non-linearity having terms as a created due to
multiplication two variables among which one is binary and Qt ≤ ℜ + Yt bat E ª¬ Pt bat Δt Yt bat º¼ + W ⋅ E ª¬ F ( Ω ) Yt bat º¼
other is continuous in nature as shown below,
G = α P, P min ≤ P ≤ P max (22)
Where, ℜ = 0.5 ( P bat ) Δt 2
2
(29)
Where, Į and P are binary and continuous variables
respectively. Proof: In Appendix
The above terms can be simplified by defining auxiliary
variable, z = α P such that Now minimization of this upper bound will apparently
reduce the original objective function defined in (28).
P − P max (1 − α ) ≤ z ≤ P − P min (1 − α ) (23)
Therefore the new revised real time optimization problem for
P minα ≤ z ≤ P maxα (24) controlling the lighting and AC loads in the home is given
by,
B. Problem Simplification Using Lyapunov Optimization
The solution process of the new revised real time Min U ( Ω ) = (Yt bat Pt bat Δt ) + W ⋅ F ( Ω ) (30)
Ω
optimization process is still complex due to the presence of
time average stochastic objective function (10). Long-term Subject to the linearized counter parts of the constraints
value of (9), is highly dependent on the charging/discharging (11)-(17) and constraint (25).
operation of the battery unit to lower both discomfort and the
operation cost. However, in real time decision process, IV. INTERNET OF THINGS (IOT) BASED CONTROL
knowledge regarding peak/off-peak price hours and the For control of the residential loads, an IoT based platform is
sudden change in renewable generation is not available. used. Similar control is used in the past for appliance load
Therefore, to precisely operate the battery unit, its operation monitoring applications effectively [16]. The control mainly
needs to be limited by making the energy status of the battery aims at operation of loads in ON/OFF mode using the
stable. Lyapunov optimization process can handle this type
proposed strategy. For this purpose, a laboratory scale
of dynamic behaviors efficiently by implementing queueing
experimental prototype is made with Wi-Fi enabled
theory [15]. In regards of that, a virtual queue Yt bat is defined ESP8266 controller. The controller supports IoT structure
here to accumulate the battery power exchange data at each with a dashboard. The control is carried out with commands
time step. This queue starts from Y0bat = 0 and evolves as, stored in an Atmega based pre-processing microcontroller
which can communicate with the ESP board. Operating
Yt bat
+1 = Yt
bat
+ Pt bat Δt (25) commands can be sent through a dashboard installed
preferably in a smartphone for controlling loads. The
Battery queue takes information same as battery energy
structure for the IoT based control is shown in Fig.2.
variable and updates with each charging/discharging
operation. Therefore, the Lyapunov function corresponding In the proposed control, a multi-layer hierarchical
to battery queue id given by, communication structure is used for controlling of different
loads. This communication structure where information
ℑ (Yt bat ) = 0.5 (Yt bat )
2
(26) exchange takes place is based on a protocol known as
message queueing telemetry transport or MQTT as shown

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2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

Fig. 4. Smart home input data for case study: outdoor illuminance and PV
generation on (a) clear sky day, (b) overcast sky day, (c) outdoor
temperature on both days, (d) critical demand and real time energy price.

in Fig.3. Based on the optimization results, the data is stored

in a cloud server from where the data is processed via the
Atmega based microcontroller. This processed data is
compared with the real time data obtained from the loads on
the basis of discomfort and cost. Based on the above
information, the loads can be turned ON/OFF. For this
purpose, a relay module is used. The ON/OFF commands Fig. 5. Simulation outputs for clear sky and overcast sky days- (a) total
can be sent via a smartphone where a controlling dashboard illuminance from lighting sources, (b) indoor temperature, (c) power
is preinstalled. The dashboard has controller interface which demand of lighting sources and AC, (d) grid power, (e) battery power, (f)
is securely programmed for controlling of loads in particular energy level in battery.
household. The simulation results are depicted in Fig. 5 by giving
equal importance to both discomfort and cost
V. CASE STUDY SIMULATION minimization objectives. Fig. 5(a) and 5(c) represent the
total indoor illuminance and power absorption of the
A rectangular shape home of 10 m length, 3 m height
lights on both days. It is noted that at morning and mid-
and 8 m width is considered here to demonstrate the
day hours (8 am to 2 pm or intervals 9 to 15) as the
efficacy of the developed home energy management outdoor illuminance is high, therefore lighting sources
topology. The room has two windows each of 1 m length are turned off at both conditions. However, at early
and 0.7 m height. The room consists of 20 lighting morning (5 am to 7 am) and evening (3 pm to 6 pm)
sources each of 60 W (0.06 kW) rating with luminous hours lighting loads are kept ON due to low outdoor
efficacy of 90 lm/watt and two ACs each of 3 kW rating. illuminance on the overcast sky day but on the clear sky
Indoor air heat capacity and equivalent thermal day, the lights are OFF at the mentioned hours due to
resistance of the room are 0.525 kWh/o C and 18 oC/kW presence of sufficient sunlight. In both the cases
respectively. The value of Ȣ1 and Ȣ2 are 0.1$/lux and 0.1$/ consumption of the lights are regulated according to the
o
C respectively. Utilization factor of the lighting loads available daylight to keep the indoor illuminance close
are fixed to 0.9. Again, maintenance factor of lighting to visible limit. Fig. 5(b) and 5(c) portray the inside room
loads are set to 0.9 too. Preferable illuminance and temperature and the power absorbed by the AC for
temperature inside the room is 300 lux and 22oC keeping the room temperature near to the preferable set
respectively. However, tolerance level of indoor point. It is noted that the power consumption of the air-
illumination in absence of day light and temperature are conditioning unit is regulated successfully by the HEC
±20 lux and ±2 oC respectively. Outside illuminance and and the room temperature is always kept close to the
temperature on a clear sky and an overcast sky days of comfort level. However, on the overcast sky day AC
consumes less power compared to the clear sky day
summer season along with the solar generation from a
because of the low outdoor ambient temperature on the
practical 8 kW panel on the respective days are depicted overcast sky day. This helps the AC to maintain the
in Fig. 4(a) and 4(b). Ambient temperature of the indoor temperature with less power. Power purchase/sell
concerned two days is shown in Fig. 4(c). Real time from/to the main distribution grid, battery power
energy demand of the room other than lighting and AC transactions at each time step and battery energy level
loads on both days is graphed in Fig. 4(d) along with the are depicted in Fig. 5(d), 5(e) and 5(f) respectively. It is
real time energy purchase price taken from [17]. Real noticed from the above-mentioned curves that during
time energy selling price is considered to be 60% of the peak solar power generation hours on both concerned
real time energy purchase price. The battery unit days, before selling the excess renewable power to the
associated with the rooftop solar panel is of 8kWh-3kW upper grid after meeting the required load demand, HEC
rating. The battery is allowed to discharge up to 30% of prefers to charge the battery. This stored battery energy
its energy rating. Initially its energy level is at 4kWh is further utilized at peak energy price hours (i.e. evening
(50%). Transmission of glasses at windows are 0.9, φ is time) to minimize the monetary expenditure due to
90 o and reflectance coefficient of the room is 0.5. energy purchase. However, more revenue is generated
on clear sky day due to more solar power generation and
The simulation is performed by using “intlinprog”
hence more energy sold back to the upper utility.
solver present at MATLAB 2016b software platform
Therefore, net electricity cost of the two concerned days
installed in a 64-bit, i7, 16GB RAM personal computer.
are 0.778$ (clear sky) and 1.1960$ (overcast sky).

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2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)

TABLE I
SIMULATION OUTCOME FOR DIFFERENT ROOM SIZE
(Y ) − (Y ) ≤ 2Y P Δt + ( P ) Δt
bat 2
t +1 t
bat 2
t
bat
t
bat bat 2 2

Size Electricity cost ($) Solution time (Sec) Hence, ℑ (Y ) − ℑ (Y ) ≤ Y P Δt + 0.5 ( P )

bat
t +1 t
bat
t
bat
t
bat bat 2
Δt 2
10×8×3 0.778 0.3
12×8×3 0.937 0.31 Introducing the term W ⋅ F ( Ω ) at both side of the above
10×10×3 0.954 0.3
12×10×3 1.128 0.32 equation and taking the conditional expectation, the upper
bound (29) can be proved.
Under the above-mentioned computation facility, the
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Now, the above expression can have an upper bound at [Online]. Available: https://hourlypricing.comed.com/live-prices.

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