SlideShare a Scribd company logo
1 of 1
One challenge of integrating renewable energy generation into the
electric grid is that it may induce deviations in the frequency of power
resulting in instability in the electrical service quality. This has the
potential to damage equipment and lead to power outages. We propose a
method that uses frequency as a signifier of the current state of the grid
and regulates this quantity by way of deferrable ‘smart’ loads employed at
the residential level. These loads can be directly controlled to mediate the
frequency excursion by deferring consumption whilst preserving their
respective duty cycles. Here, we discuss the characterization of potential
‘smart’ loads as well as the design and implementation of embedded
systems that perform the logic to control load behavior and sense
frequency in a home-built test micro grid. Thermal loads, refrigerators
and water heaters, were selected for their energy storage and their
regulation will not cause a noticeable disruption in service. We measure
frequency of the mains power using a microcontroller that transmits data
wirelessly to a single-board computer for processing. Once data is
analyzed, an ancillary algorithm rooted at the specified deferrable load
responds to queries and commands from the computer to advance or
postpone power usage. This manner of demand regulation allows the test
bed to successfully stabilize frequency and improve the state of the power
delivered with no disturbance to the consumer. Furthermore, this test bed
can be modified for other investigations when direct implementation into
the grid is neither practical nor an available resource.
Introduction
The utility service is responsible for ensuring that the supplied electricity is
constantly in balance with the electricity in demand. To guarantee that the
grid can accommodate for the increase or decrease in power generation
due to renewable sources, frequency must be regulated to stay with in a
threshold of 60 ± 0.01 Hz.
Renewable Energy Generated in CA ISO service area
• Frequency of AC power is an indicator of balance between power
generation from generators and power withdrawal from loads.
• When generation and consumption are not in balance, the frequency
changes at the rate of
∆𝜔 =
𝑃𝑔 − 𝑃𝑙
𝑀
• 𝑃𝑔 is the power provided by the generators
• 𝑃𝑙 is power consumed by loads
• M is the system’s inertia
• ∆𝜔 is the change in angular Frequency
Acknowledgements
Hartnell College Advanced Technology Center
Jack Baskin School of Engineering at U.C. Santa Cruz
Zachary Graham , Mentor
Tela Favaloro , Mentor
This publication was developed with support from a
Hispanic Serving STEM & Articulation program funded by
the U.S. Department of Education
Load Characterization Smart Load Result
Andres Aranda
Electrical Engineering, UCSC, Salinas, CA 93901
Zachary W. Graham and Tela Favaloro, Center for Sustainable Energy and Power
Systems, UCSC, Santa Cruz, CA 95064
For further information
Optimal candidates for the deferral of consumption for frequency regulation
have the means of energy storage and thus do not directly affect the
consumer
• We identified two residential loads for use as frequency controlled
reserve: a water heater and a refrigerator.
• These appliances have the means to store electricity as thermal energy
and thus defer consumption
• The necessity to make these deferrable loads smart, allows control to the
grid to accommodate for fluctuation in frequency
• Smart control and response is implemented through microcontrollers with
temperature sensor attached to a relay switch within each deferrable load
[refer to next section]
Designing Smart Demand for Frequency Regulation in a Micro-Grid Test Bed
Algorithm/Design
Abstract
Please contact the following:
zwgraham@soe.ucsc.edu
tela@soe.ucsc.edu
Reference papers:
Kondoh, J.; Ning Lu; Hammerstrom, D.J., "An evaluation of the
water heater load potential for providing regulation
service," Power and Energy Soc., IEEE , pp.1,8, 24-29 2011
Andres Aranda is an Electrical Engineering major at University of
California, Santa Cruz
XBEE Command
Smart Response
• Arduino Mega, Node XBEE, temperature sensor and heating element are connected in an
integrated circuit
• Base XBEE configured on the single board computer commands Node XBEE wirelessly through
Arduino ‘s serial monitor
• Arduino algorithm analyzes command received, and Node XBEE responds with data accordingly
• Algorithm controls Water Heater’s turn on/off within a threshold of its assigned set point.
• Implementation of design permits manipulation of the water heater relay, regulating duty cycle
• Further development will allow water heater to be completely independent and self-regulating
allowing direct response to a change in frequency .
• Additional expansion includes applying concepts of smart loads into more deferrable thermal
appliances as well as electrical storage, such as an electric vehicle battery
𝐶𝑚𝐿
𝑑𝑇
𝑑𝑡
= 𝑃𝑒 − 𝑃𝑎𝑖𝑟 − 𝑃𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑
• C = heat capacity of substance
• m = mass of object
• L = volume
• T = temperature
• t = time
• 𝑃𝑒 = energy drawn from heating element
• 𝑃𝑎𝑖𝑟 = energy lost to outside surroundings
• 𝑃𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 = energy lost to water being used by consumer
This equation illustrates the amount of energy supplied vs energy
lost over time. The period it takes to reach 37 percent of its original
heat is represented by τ.
𝑃𝑎𝑖𝑟 =
𝐶𝑚𝐿(𝑇𝑖 − 𝑇𝑓)
τ
This equation was used to find our rate of decay to our particular
water heater. Our τ was found to be 6 and half hours.
• Graph above illustrates power consumption of chosen appliances
• The typical duty cycle for these appliances is ~35% and can be used for
both normal reserve and disruptive reserve scenarios

More Related Content

What's hot

Statcom control scheme for power quality improvement of grid connected wind e...
Statcom control scheme for power quality improvement of grid connected wind e...Statcom control scheme for power quality improvement of grid connected wind e...
Statcom control scheme for power quality improvement of grid connected wind e...Kinnera Kin
 
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...IJECEIAES
 
New academic final year projects for btech and mtech
New academic final year projects for btech and mtechNew academic final year projects for btech and mtech
New academic final year projects for btech and mtechAsoka Technologies
 
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...IAES-IJPEDS
 
Capacitor bank and improvement of power factor
Capacitor bank and improvement of power factorCapacitor bank and improvement of power factor
Capacitor bank and improvement of power factorAhshan Kabir
 
Introducing Rrs
Introducing RrsIntroducing Rrs
Introducing Rrsrichardrs
 
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...Power System Operation
 
All digital energy sensing for minimum energy tracking
All digital energy sensing for minimum energy trackingAll digital energy sensing for minimum energy tracking
All digital energy sensing for minimum energy trackingI3E Technologies
 
Power electronics control of an energy regenerative mechatronic damper
Power electronics control of an energy regenerative mechatronic damperPower electronics control of an energy regenerative mechatronic damper
Power electronics control of an energy regenerative mechatronic damperI3E Technologies
 
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...I3E Technologies
 
Iaetsd power-quality improvement of grid interconnected
Iaetsd power-quality improvement of grid interconnectedIaetsd power-quality improvement of grid interconnected
Iaetsd power-quality improvement of grid interconnectedIaetsd Iaetsd
 
Power factor correction
Power factor correctionPower factor correction
Power factor correctionJamilah Abbas
 

What's hot (16)

Statcom control scheme for power quality improvement of grid connected wind e...
Statcom control scheme for power quality improvement of grid connected wind e...Statcom control scheme for power quality improvement of grid connected wind e...
Statcom control scheme for power quality improvement of grid connected wind e...
 
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...
Multi Units of Three Phase Photovoltaic using Band Pass Filter to Enhance Pow...
 
New academic final year projects for btech and mtech
New academic final year projects for btech and mtechNew academic final year projects for btech and mtech
New academic final year projects for btech and mtech
 
Ppt phase-2
Ppt phase-2Ppt phase-2
Ppt phase-2
 
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...
Open-Switch Fault-Tolerant Control of Power Converters in a Grid-Connected Ph...
 
Capacitor bank and improvement of power factor
Capacitor bank and improvement of power factorCapacitor bank and improvement of power factor
Capacitor bank and improvement of power factor
 
Introducing Rrs
Introducing RrsIntroducing Rrs
Introducing Rrs
 
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...
A STATCOM CONTROL SCHEME FOR POWER QUALITY IMPROVEMENT OF GRID CONNECTED TO W...
 
All digital energy sensing for minimum energy tracking
All digital energy sensing for minimum energy trackingAll digital energy sensing for minimum energy tracking
All digital energy sensing for minimum energy tracking
 
Power electronics control of an energy regenerative mechatronic damper
Power electronics control of an energy regenerative mechatronic damperPower electronics control of an energy regenerative mechatronic damper
Power electronics control of an energy regenerative mechatronic damper
 
Smart grid
Smart gridSmart grid
Smart grid
 
Vasudevan JNTUH
Vasudevan JNTUHVasudevan JNTUH
Vasudevan JNTUH
 
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...
A multi input bridgeless resonant ac-dc converter for electromagnetic energy ...
 
Iaetsd power-quality improvement of grid interconnected
Iaetsd power-quality improvement of grid interconnectedIaetsd power-quality improvement of grid interconnected
Iaetsd power-quality improvement of grid interconnected
 
H41015660
H41015660H41015660
H41015660
 
Power factor correction
Power factor correctionPower factor correction
Power factor correction
 

Similar to Updated2015Poster

144624132-Sizing-a-PV-system-ppt.ppt
144624132-Sizing-a-PV-system-ppt.ppt144624132-Sizing-a-PV-system-ppt.ppt
144624132-Sizing-a-PV-system-ppt.pptBlessyJoy18
 
Energy Efficiency in Electrical Systems.pptx
Energy  Efficiency in Electrical Systems.pptxEnergy  Efficiency in Electrical Systems.pptx
Energy Efficiency in Electrical Systems.pptxPoojaAnupGarg
 
AI Battery Power Management
AI Battery Power ManagementAI Battery Power Management
AI Battery Power Managementvishnu746522
 
Implementation of a grid-tied emergency back-up power supply for medium and l...
Implementation of a grid-tied emergency back-up power supply for medium and l...Implementation of a grid-tied emergency back-up power supply for medium and l...
Implementation of a grid-tied emergency back-up power supply for medium and l...IJECEIAES
 
IRJET- Level of Service & Throughput Maximization at Operational Toll Plazas
IRJET- Level of Service & Throughput Maximization at Operational Toll PlazasIRJET- Level of Service & Throughput Maximization at Operational Toll Plazas
IRJET- Level of Service & Throughput Maximization at Operational Toll PlazasIRJET Journal
 
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...IRJET- Different Control Strategies for Power Control of Voltage Source Conve...
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...IRJET Journal
 
A CONTROL APPROACH FOR GRID INTERFACING INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...
A CONTROL APPROACH FOR GRID INTERFACING  INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...A CONTROL APPROACH FOR GRID INTERFACING  INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...
A CONTROL APPROACH FOR GRID INTERFACING INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...IJMER
 
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...Pradeep Avanigadda
 
Electrical power system management
Electrical power system managementElectrical power system management
Electrical power system managementAkshay Awadhani
 
Impacts of Distributed Generation on Power Quality
Impacts of Distributed Generation on Power QualityImpacts of Distributed Generation on Power Quality
Impacts of Distributed Generation on Power QualityParth Patel
 
Site Acceptance Test for Solar PV System of Bronzeville Community Microgrid
Site Acceptance Test for Solar PV System of Bronzeville Community MicrogridSite Acceptance Test for Solar PV System of Bronzeville Community Microgrid
Site Acceptance Test for Solar PV System of Bronzeville Community MicrogridPower System Operation
 
Load shedding and load scheduling (ppt)
Load shedding and load scheduling (ppt)Load shedding and load scheduling (ppt)
Load shedding and load scheduling (ppt)GehlotDarshan1
 
Advance Technology in Application of Four Leg Inverters to UPQC
Advance Technology in Application of Four Leg Inverters to UPQCAdvance Technology in Application of Four Leg Inverters to UPQC
Advance Technology in Application of Four Leg Inverters to UPQCIJPEDS-IAES
 
Artificial Intelligence techniques
Artificial Intelligence techniquesArtificial Intelligence techniques
Artificial Intelligence techniquesPavan Kumar Talla
 
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...IRJET Journal
 

Similar to Updated2015Poster (20)

144624132-Sizing-a-PV-system-ppt.ppt
144624132-Sizing-a-PV-system-ppt.ppt144624132-Sizing-a-PV-system-ppt.ppt
144624132-Sizing-a-PV-system-ppt.ppt
 
Energy Efficiency in Electrical Systems.pptx
Energy  Efficiency in Electrical Systems.pptxEnergy  Efficiency in Electrical Systems.pptx
Energy Efficiency in Electrical Systems.pptx
 
AI Battery Power Management
AI Battery Power ManagementAI Battery Power Management
AI Battery Power Management
 
G046033742
G046033742G046033742
G046033742
 
G1101045767
G1101045767G1101045767
G1101045767
 
D011122934
D011122934D011122934
D011122934
 
Implementation of a grid-tied emergency back-up power supply for medium and l...
Implementation of a grid-tied emergency back-up power supply for medium and l...Implementation of a grid-tied emergency back-up power supply for medium and l...
Implementation of a grid-tied emergency back-up power supply for medium and l...
 
IRJET- Level of Service & Throughput Maximization at Operational Toll Plazas
IRJET- Level of Service & Throughput Maximization at Operational Toll PlazasIRJET- Level of Service & Throughput Maximization at Operational Toll Plazas
IRJET- Level of Service & Throughput Maximization at Operational Toll Plazas
 
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...IRJET- Different Control Strategies for Power Control of Voltage Source Conve...
IRJET- Different Control Strategies for Power Control of Voltage Source Conve...
 
A CONTROL APPROACH FOR GRID INTERFACING INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...
A CONTROL APPROACH FOR GRID INTERFACING  INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...A CONTROL APPROACH FOR GRID INTERFACING  INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...
A CONTROL APPROACH FOR GRID INTERFACING INVERTER IN 3 PHASE 4 WIRE DISTRIBUT...
 
ROLE OF POWER ELECTRONICS IN NON-RENEWABLE AND RENEWABLE ENERGY SYSTEMS
ROLE OF POWER ELECTRONICS IN NON-RENEWABLE AND RENEWABLE ENERGY SYSTEMSROLE OF POWER ELECTRONICS IN NON-RENEWABLE AND RENEWABLE ENERGY SYSTEMS
ROLE OF POWER ELECTRONICS IN NON-RENEWABLE AND RENEWABLE ENERGY SYSTEMS
 
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...
 
Gr3412151231
Gr3412151231Gr3412151231
Gr3412151231
 
Electrical power system management
Electrical power system managementElectrical power system management
Electrical power system management
 
Impacts of Distributed Generation on Power Quality
Impacts of Distributed Generation on Power QualityImpacts of Distributed Generation on Power Quality
Impacts of Distributed Generation on Power Quality
 
Site Acceptance Test for Solar PV System of Bronzeville Community Microgrid
Site Acceptance Test for Solar PV System of Bronzeville Community MicrogridSite Acceptance Test for Solar PV System of Bronzeville Community Microgrid
Site Acceptance Test for Solar PV System of Bronzeville Community Microgrid
 
Load shedding and load scheduling (ppt)
Load shedding and load scheduling (ppt)Load shedding and load scheduling (ppt)
Load shedding and load scheduling (ppt)
 
Advance Technology in Application of Four Leg Inverters to UPQC
Advance Technology in Application of Four Leg Inverters to UPQCAdvance Technology in Application of Four Leg Inverters to UPQC
Advance Technology in Application of Four Leg Inverters to UPQC
 
Artificial Intelligence techniques
Artificial Intelligence techniquesArtificial Intelligence techniques
Artificial Intelligence techniques
 
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...
IRJET - The Power Quality Improvement with Harmonic Reduction and Stabilizing...
 

Updated2015Poster

  • 1. One challenge of integrating renewable energy generation into the electric grid is that it may induce deviations in the frequency of power resulting in instability in the electrical service quality. This has the potential to damage equipment and lead to power outages. We propose a method that uses frequency as a signifier of the current state of the grid and regulates this quantity by way of deferrable ‘smart’ loads employed at the residential level. These loads can be directly controlled to mediate the frequency excursion by deferring consumption whilst preserving their respective duty cycles. Here, we discuss the characterization of potential ‘smart’ loads as well as the design and implementation of embedded systems that perform the logic to control load behavior and sense frequency in a home-built test micro grid. Thermal loads, refrigerators and water heaters, were selected for their energy storage and their regulation will not cause a noticeable disruption in service. We measure frequency of the mains power using a microcontroller that transmits data wirelessly to a single-board computer for processing. Once data is analyzed, an ancillary algorithm rooted at the specified deferrable load responds to queries and commands from the computer to advance or postpone power usage. This manner of demand regulation allows the test bed to successfully stabilize frequency and improve the state of the power delivered with no disturbance to the consumer. Furthermore, this test bed can be modified for other investigations when direct implementation into the grid is neither practical nor an available resource. Introduction The utility service is responsible for ensuring that the supplied electricity is constantly in balance with the electricity in demand. To guarantee that the grid can accommodate for the increase or decrease in power generation due to renewable sources, frequency must be regulated to stay with in a threshold of 60 ± 0.01 Hz. Renewable Energy Generated in CA ISO service area • Frequency of AC power is an indicator of balance between power generation from generators and power withdrawal from loads. • When generation and consumption are not in balance, the frequency changes at the rate of ∆𝜔 = 𝑃𝑔 − 𝑃𝑙 𝑀 • 𝑃𝑔 is the power provided by the generators • 𝑃𝑙 is power consumed by loads • M is the system’s inertia • ∆𝜔 is the change in angular Frequency Acknowledgements Hartnell College Advanced Technology Center Jack Baskin School of Engineering at U.C. Santa Cruz Zachary Graham , Mentor Tela Favaloro , Mentor This publication was developed with support from a Hispanic Serving STEM & Articulation program funded by the U.S. Department of Education Load Characterization Smart Load Result Andres Aranda Electrical Engineering, UCSC, Salinas, CA 93901 Zachary W. Graham and Tela Favaloro, Center for Sustainable Energy and Power Systems, UCSC, Santa Cruz, CA 95064 For further information Optimal candidates for the deferral of consumption for frequency regulation have the means of energy storage and thus do not directly affect the consumer • We identified two residential loads for use as frequency controlled reserve: a water heater and a refrigerator. • These appliances have the means to store electricity as thermal energy and thus defer consumption • The necessity to make these deferrable loads smart, allows control to the grid to accommodate for fluctuation in frequency • Smart control and response is implemented through microcontrollers with temperature sensor attached to a relay switch within each deferrable load [refer to next section] Designing Smart Demand for Frequency Regulation in a Micro-Grid Test Bed Algorithm/Design Abstract Please contact the following: zwgraham@soe.ucsc.edu tela@soe.ucsc.edu Reference papers: Kondoh, J.; Ning Lu; Hammerstrom, D.J., "An evaluation of the water heater load potential for providing regulation service," Power and Energy Soc., IEEE , pp.1,8, 24-29 2011 Andres Aranda is an Electrical Engineering major at University of California, Santa Cruz XBEE Command Smart Response • Arduino Mega, Node XBEE, temperature sensor and heating element are connected in an integrated circuit • Base XBEE configured on the single board computer commands Node XBEE wirelessly through Arduino ‘s serial monitor • Arduino algorithm analyzes command received, and Node XBEE responds with data accordingly • Algorithm controls Water Heater’s turn on/off within a threshold of its assigned set point. • Implementation of design permits manipulation of the water heater relay, regulating duty cycle • Further development will allow water heater to be completely independent and self-regulating allowing direct response to a change in frequency . • Additional expansion includes applying concepts of smart loads into more deferrable thermal appliances as well as electrical storage, such as an electric vehicle battery 𝐶𝑚𝐿 𝑑𝑇 𝑑𝑡 = 𝑃𝑒 − 𝑃𝑎𝑖𝑟 − 𝑃𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 • C = heat capacity of substance • m = mass of object • L = volume • T = temperature • t = time • 𝑃𝑒 = energy drawn from heating element • 𝑃𝑎𝑖𝑟 = energy lost to outside surroundings • 𝑃𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 = energy lost to water being used by consumer This equation illustrates the amount of energy supplied vs energy lost over time. The period it takes to reach 37 percent of its original heat is represented by τ. 𝑃𝑎𝑖𝑟 = 𝐶𝑚𝐿(𝑇𝑖 − 𝑇𝑓) τ This equation was used to find our rate of decay to our particular water heater. Our τ was found to be 6 and half hours. • Graph above illustrates power consumption of chosen appliances • The typical duty cycle for these appliances is ~35% and can be used for both normal reserve and disruptive reserve scenarios