Optimizing Energy Hub Operation Using Modified Firefly Algorithm

Optimal Sizing and Operation of
Energy Hubs Using Firefly
Algorithm
Eng/ Alaa M Eladl 1

Eng/ Alaa M Eladl 2
Our Research aims to
Minimize the total energy cost and CO2 emission amount of
the energy hub.
Maximizing the cost of electrical and heating energy sold
back to the network.
Research Objective:
Customer
Network

Eng/ Alaa M Eladl 3
Our Research achieved the following:
 Modification for Standard Firefly Algorithm (MFFA).
 Solving Energy Hub Problem by using MFFA.
 Sizing for Energy Hub components by using MFFA.
 Bi-directional Energy.
The new in our Research

Today We’ll Discuss….
 ENERGY HUB
¤ Energy Hub Concept. ¤ Energy Hub Components.
¤ Energy Hub Model.
 Cooling Combined Heat and Power (CCHP).
¤ Cogeneration Definition. ¤ Cogeneration Advantages.
¤ Cogeneration Model.
Optimization techniques.
¤ Optimization types . ¤ Standard Firefly Algorithm.
¤ Modified Firefly Algorithm.
 Application or case Study.
Eng/ Alaa M Eladl 4

Research OBJECTIVES
• Energy Hub System aims to design, develop,
install and assess energy and environmental
benefits of a new integrated concept of
interconnectivity between buildings, Distributed
Energy Resources (DER).
Eng/ Alaa M Eladl 5

ELECTRICITY Grid
Very expensive
More Losses
Not Scalable
less reliability
Not Flexibility
Eng/ Alaa M Eladl 6

Not Scalable
less reliability
Not Flexibility
Natural Gas
Eng/ Alaa M Eladl 7

OPTIMIZATION
Eng/ Alaa M Eladl 9

OPTIMIZATION
Eng/ Alaa M Eladl 10
Scalable
reliability
Flexibility
Low losses
Not expensive

• Energy Hub is a unit where multiple energy carriers can be converted, conditioned.
• It represents an interface between different energy infrastructures and/or loads
• Energy hubs consume power at their input ports connected to ,e.g., electricity and
natural gas infrastructures, and provide certain required energy services such as
electricity, heating, and cooling.
Energy HUB Concept
Energy
HUB unit

Energy Hub Elements
energy hub contains
 Transformer,
 CHP
 Auxiliary Boiler
 Absorption Chiller

CHP Technologies and Applications
What’s
CHP ?
Combined Heat & Power (CHP) is a form of Distributed Generation
CHP is …
! An Integrated System
! Located At or Near a Building/Facility
! Provides at Least a Portion of the Electrical Load and
! Recycles the Thermal Energy for
– Space Heating / Cooling
– Process Heating / Cooling
– Dehumidification

What’s
CHP ?
Prime Mover
Heat Exchanger
Thermal System
Generator (fuel input)
100
%
Qin
Natural Gas
 Prime Mover generates mechanical energy
 Generator converts mechanical energy into electrical energy
 heat exchangers that capture and recycle the heat from the prime
mover
 Thermal Utilization equipment converts the recycled heat into
useful heating, cooling, and/or dehumidification
 Operating Control Systems insure the CHP components function
properly together
Qout
Qout
Wout
35%
electricity
50%
thermal
15%
waste

What’s
CHP ?

CHP Benefits
Source: ICF International

CHP Benefits

CHP
Application
The great majority of CHP applications can be grouped into three categories:
 Industrial
 commercial/institutional
o Manufacturing
o Food Processing
o Ethanol
 Municipalities
o Hospitals
o Schools
o Office Buildings
o Data Centers
o Landfills
o Wastewater Treatment Facilities

What’s
CCHP ?
 Cooling Combined heat and Power

What’s
CCHP ?
 An absorption chillers are coupled to a CHP
plant to produces chilled water and hot water
for air conditioning or alternatively the heat is
used to heat a swimming pool.

CHP Model
Pg
Natural Gas
Thermal
Electricity
Lh
Le ξ
η
𝐿𝑒 = 𝑃𝑔 ∗ ξ
𝐿ℎ = 𝑃𝑔 ∗ η

CCHP Model
Pg
Natural Gas
Cooling
Electricity
Lh
Le ξ
η
𝐿𝑒 = 𝑃𝑔 ∗ ξ
𝐿ℎ = 𝑃𝑔 ∗ η
Cooling
Combined Heat
and Power
CCHP
Thermal
Lc μ
𝐿𝑐 = 𝑃𝑔 ∗ μ

Energy Hub Model

Energy Hub Model
CCHP UNIT

Energy Hub Model
ENERGY HUB UNIT

L=C*P
Energy Hub Model
C
P

min 𝑓 = 𝐶1 − 𝐶2
𝐶1 = 𝐶𝐶𝐻𝑃 + 𝐶𝐵 +
𝑡=1
𝑁
(𝐶1𝑒 ∗ 𝑃𝑒−𝑖𝑛 𝑡 + 𝐶𝑔 ∗ 𝑃
𝑔 𝑡 )
𝐶2 =
𝑡=1
𝑁
(𝐶2𝑒 ∗ 𝑃𝑒−𝑜𝑢𝑡 𝑡 + 𝐶ℎ ∗ 𝑃ℎ 𝑡 )
Objective Function
A. Objective Function
Theobjectiveoftheproposedalgorithmistominimizethefollowingfunction
-Where

η𝑔𝑒 𝑆𝐶𝐻𝑃 + 𝑃𝑒
𝑚𝑎𝑥 ≥ 𝐿𝑒
𝑚𝑎𝑥
B. Operational Constraints
1)PowerDispatchConstraints
Objective Function
η𝑔ℎ 𝑆𝐶𝐻𝑃 + 𝑆𝐵 ≥ 𝐿ℎ
𝑚𝑎𝑥
+ 𝐿𝑐
𝑚𝑎𝑥/η𝑔𝑐
0 ≤ 𝑣 𝑡 ≥ 1 𝑣 𝑡 𝑃
𝑔(𝑡) ≤ 𝑆𝐶𝐻𝑃
𝑃
𝑔
𝑚𝑖𝑛 ≤ (1 − 𝑣 𝑡 )η𝑔𝑃
𝑔(𝑡) ≤ 𝑆𝑔
𝑃𝐵
𝑚𝑖𝑛
≥ 𝑇𝑅𝐵𝑆𝐵

𝐿𝑒 𝑡 + 𝑃𝑒−𝑜𝑢𝑡 𝑡 = 𝑃𝑒−𝑖𝑛 𝑡 + 𝑣 𝑡 η𝑔𝑒𝑃
𝑔(𝑡)
B. Operational Constraints
2)PowerBalanceConstraints
Objective Function
𝐿𝑐 𝑡 = ηℎ𝑐𝑃ℎ𝑐(𝑡)
𝐿ℎ 𝑡 + 𝑃ℎ𝑐 𝑡 + 𝑃ℎ 𝑡 = 𝑣 𝑡 η𝑔ℎ𝑃
𝑔 𝑡 + (1 − 𝑣 𝑡 ) η𝐵𝑃
𝑔(𝑡)

Optimizing The Energy
Hub System Using FFA

Mathematical Optimization
Deterministic Methods
Iterative
Methods that
produce same
set results
every time as:
• Newton’s Method.
• Sequential quadratic
programming SQP.
• Interior Point
Method.
• Gradient Descent
Method.
Stochastic
methods that
converge to an
approximate
solutions such
as:
• Ant Colony
• Simulated Annealing.
• Genetic Algorithm.
• Particle Swarm.
• Firefly Method.
Stochastic Methods

Stochastic Optimization
Heuristic algorithms
Metaheuristic algorithms
• Heuristic algorithm finds solutions
in a reasonable amount of time
but there is no guarantee that
optimal solutions are reached.
• intend to be suitable for local
optimization.
• Metaheuristic uses certain tradeoff
a randomization and local search,
provides a good way to move away
from local search to the search on
global scale.
• intend to be suitable for global
optimization.

Metaheuristic
Optimization
Local Search Algorithm
• One type of search
strategy is an
improvement on
simple local search
algorithms.
• A well known local
search algorithm is
the hill
climbing method
which is used to find
Global Search Algorithm
• Global search that are not
local search-based are
usually population-based.
• Such algorithms for Global
search ant colony
optimization, evolutionary
computation, particle
swarm optimization,
and genetic algorithms.

Metaheuristic
Optimization
• Single Solution [Simulated
Annealing] and population based
[Genetic Algorithm, Particle Swarm,
FFA,..etc ].
• Methods that can be hybridized and
other memetic.
• Methods that can be solved using
Parallel Processing.
Other
Classifications:

Metaheuristic
Optimization
Nature-inspired metaheuristics:
Simulated
Annealing.
Particle
swarm
optimization.
Artificial bee
colony
algorithm.
Genetic
Algorithm.
Firefly
Algorithm.

Firefly Algorithm
Strategy
And Test of
FFA

Basic Firefly Algorithm
• Firefly algorithm is a kind of optimization algorithm based on the
firefly social features.
• This algorithm is similar with other intelligent algorithms, it is
relatively simple both in theory and implementation.
• The algorithm is very effective in dealing with a lot of optimization
problem.

• The core of this algorithm is to use the absolute brightness of fireflies
on behalf of the objective function value.
• The location of the fireflies is the solution.
• The relative brightness of the fireflies is obtained by comparison.

• Fireflies are attracted by brighter companion.
• 𝛽0 is the biggest appeal
𝑥𝑖 𝑘 + 1 = 𝑥𝑖 𝑘 + 𝛽𝑖𝑗 𝑟𝑖𝑗 𝑥𝑖 − 𝑥𝑗 + 𝛼𝜀𝑖
𝛽𝑖𝑗(𝑟𝑖𝑗) = 𝛽0𝑒−𝛾𝑟2
𝑟𝑖𝑗 = 𝑥𝑖 − 𝑥𝑗 =
𝑘=1
𝑑
(𝑥𝑖,𝑘 − 𝑥𝑗,𝑘)2
𝑟𝑖𝑗 is the Cartesian distance between fireflies and found by this
relationship,

There are two important parameters in the location updating formula:
The light absorption coefficient 𝛾
The random coefficient.𝛼
𝛾 is the absorption coefficient, controlling the change of light
intensity and deciding the convergence of the algorithm.
𝛼 is the random coefficient , controlling the
random movement of fireflies.

γ∈ 0, ∞ ,
For γ0 , there is β = βo
The attenuation light intensity without distance
, fireflies can be seen any where in the space
and global search is very easy to do.
For γ  ∞ , there is β(r) = δ(r)
The attraction between fireflies is close
to 0, and each firefly is similar to have
random movement .

• The smaller 𝛾 is,
with faster
algorithm
convergence the
larger the
attraction between
fireflies is.
The light
absorption
coefficient
𝛾
𝒙𝒊 𝒌 + 𝟏 = 𝒙𝒊 𝒌 + 𝜷𝒊𝒋 𝒓𝒊𝒋 𝒙𝒊 − 𝒙𝒋 + 𝜶𝜺𝒊
𝜷𝒊𝒋(𝒓𝒊𝒋) = 𝜷𝟎𝒆−𝜸𝒓𝟐

• The bigger the 𝛼 is
with slower
algorithm
convergence the
greater random
motion range of
fireflies
The
random
coefficient.
𝛼
𝒙𝒊 𝒌 + 𝟏 = 𝒙𝒊 𝒌 + 𝜷𝒊𝒋 𝒓𝒊𝒋 𝒙𝒊 − 𝒙𝒋 + 𝜶𝜺𝒊
𝜷𝒊𝒋(𝒓𝒊𝒋) = 𝜷𝟎𝒆−𝜸𝒓𝟐

Modified Firefly Algorithm
These modification to improve strategy of attraction and rate of
convergence.
 change of variance to adaptively change 𝜶 𝒂𝒏𝒅 𝜸.
 Move all fireflies attracted to the best firefly.

M.FFA ------change of variance to adaptively change 𝛼 𝑎𝑛𝑑 𝛾:
A. Design of the adaptive adjustment parameters:
B. Design of the autonomous flight.
• Best Solution don’t move and less optimum only search space.
C. Design of the random movement step.
𝛾𝑖 = 𝛾𝑏 + 𝑒−𝑘𝜎𝐼
2
𝛾𝑒 − 𝛾𝑏 𝛼𝑖 = 𝛼𝑏 −
1
𝑒𝑘𝜎𝐼
2 𝛼𝑒 − 𝛼𝑏
𝑥𝑖 𝑘 + 1 = 𝑥𝑖 𝑘 + 𝛽0𝑒−𝛾𝑟2
𝑥𝑖 − 𝑥𝑗 + 𝛼 × 𝑟𝑖𝑗 × 𝑟𝑎𝑛𝑑 − 0.5

M.FFA -----Move all fireflies attracted to the best firefly:
𝑥𝑖 𝑘 + 1 = 𝑥𝑖 𝑘 + 𝛽0𝑒−𝛾𝑟2
𝑥𝑖 − 𝑥𝑗 + 𝛽0𝑒−𝛾𝑟𝑏𝑒𝑠𝑡
2
𝑥𝑏𝑒𝑠𝑡 − 𝑥𝑖 + 𝛼 × 𝑟𝑎𝑛𝑑 − 0.5
The Cartesian distance becomes:
𝑟𝑖𝑗 = 𝑥𝑖 − 𝑥𝑗 = 𝑘=1
𝑑
(𝑥𝑖,𝑘 − 𝑥𝑗,𝑘)2
𝑟𝑖,𝑏𝑒𝑠𝑡 = (𝑥𝑖 − 𝑥𝑏𝑒𝑠𝑡)2 + (𝑦𝑖 − 𝑦𝑏𝑒𝑠𝑡)2

In this modification we used three modification:
• Autonomous motion of firefly this means the best firefly don’t move unless other found.
• The random motion is function of the Cartesian distance from the optimum solution, this
means the far one moves faster as (r>>) and the near to optimum moves slowly as (r<<).
• The motion towards the global optimum and there is no trapping in any local minimum.
𝑥 𝑖, :
= 𝑥 𝑖, : + 𝛽0 × 𝑒−𝛾𝑟2
× 𝑥 𝑗, : − 𝑥 𝑖, : + 𝛽0 × 𝑒−𝛾𝑟2
× 𝑥𝑏𝑒𝑠𝑡 − 𝑥 𝑗, :
+ 𝛼 × 𝑓(𝑟) × (𝑟𝑎𝑛𝑑 − 0.5)

Case Study (1)

Energy Hub Case [1].
This case solve only single objective for cost minimization and to clarify
the result with GA algorithm.
Extension of the case will be added later for multi-objective case with
the following [ minimum cost, minimum emission and minimum losses].

• 𝐿 =
𝐿𝑒
𝐿ℎ
=
2
5
where L is
the energy demand.
# INPUT
DATA #

# SOLUTION
#

0 20 40 60 80 100 120 140 160 180 200
44
45
46
47
48
49
50
51
52
Iteration
Best
Cost
#
SIMULATION
#

The solution was carried out using both
genetic algorithm (GA) and firefly algorithm
(FA). The results of both algorithms are
compared with those of the conventional
mathematical method .
#
SIMULATION
#

Case Study (2)

Many hospitals also proactively look
for cost effective energy solutions
because of their energy costs.
The potential to meet the high power
quality and reliability needs with a
CHP system is also of great interest
to hospitals.

The hospital which is considered as case study.
 10,000 square-meters
 The hospital operates 24 hours a day all year
round (8760 hours per year).
Required :
 increase the energy efficiency

Energy Hub Case [2].  Energy load profiles:
The electrical, heating and cooling loads during in a normal Summer day

Energy Hub Case [2].  Energy price:
The electrical and Natural gas loads during in day

Problem Model:
Energy
Hub
Model
Pe
Pg-CHP
Pg-Boiler Lc-Cooling
Lh-heating
Le-electrical

 The CHP size is selected from the available sizes of SOKRATHERM cogeneration units.
 The sizes available for these types of CHP start from 50 kw to 532 kw electrical output.
 These types of CHP have gas/electricity efficiency ranging from 34% up to 39% and gas/heat
efficiency from 50% up to 57%.
 In our case average efficiencies of 35% and 54% are considered as given in table .
 CCHP Selection:

 The boiler size is selected from the available sizes of Melbury HE boilers .
 The sizes available for these types of Boiler start from 530 kW to 10000 kW heating output.
 Boiler Selection:

THE FOLLOWING TABLE
 THE CHP UNITS, BOILERS AND
COOLING CHILLERS COST
 PERFORMANCE
CHARACTERISTICS OF CCHP
AND AUXIL-IARY BOILER.

 Optimal sizing and dispatch at
peak load
 The convergence characteristics of the objective
value are shown .
 The FFA resulted in CHP size of 337 kW and
boiler size of 6300 kW.
 The optimal dispatch resulted in
 electrical power input Pe= 1065.5 kW,
 gas power input to CHP of 956kW
 gas power input to Boiler of 6514.7 kW.
In the first layer of solution

 Optimal sizing and dispatch
during 24 h
 The convergence characteristics of the objective
value are shown .
 The FFA resulted ‘as the same for peak load’ in
CHP size of 337 kW and boiler size of 6300 kW.
 The optimal dispatch resulted in
In the Second layer of solution

 The peak values of these powers are
 The electrical power (Pe-in) = 1065.5 kW
 The gas power input to CHP (Pg1) = 956 kW
 Gas power input to the boiler (Pg2) = 6140.6 kW
 Optimal sizing and dispatch
during 24 h
In the Second layer of solution

Energy Hub Case [2].  Optimal sizing and dispatch
exported to the network
In the Third layer of solution
 The electrical power exported to the
network during the day .
 At the time of peak load stayed at its value
of 0.1519 kW and there was no excess heat
power to be exported to the network.

Our Research achieved the following:
 Modification for Standard Firefly Algorithm (MFFA).
 Solving Energy Hub Problem by using MFFA.
 Sizing for Energy Hub components by using MFFA.
 Bi-directional Energy.
The new in our Research

Optimizing Energy Hub Operation Using Modified Firefly Algorithm

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