Flexible load management in Smart
Student report
Eloy Rodríguez Moldes
Flexible load management in
Smart-grids
Master Thesis for Msc Energy Technology
Project report, May 2013
Title:
Semester:
Semester theme:
Project period:
ECTS:
Supervisor:
Project group:
Flexible load management in Smart-grids
10th
Master Thesis
01.09.12 to 29.05.13
50
Pukar Mahat
WPS4-1052
SYNOPSIS:
Eloy Rodriguez Moldes
Copies:
Pages, total:
Appendix:
This report describes the implementation
of a demand side management system in
a residential area. A study on washing
machine and refrigerator operation is conducted, as well as the use pattern design. The optimal control of the appliances is done using the Matlab Optimization Toolbox for the purpose of minimizing
the losses in the distribution lines, and the
final price of the electrical energy for the
customers. Finally the optimal operation
pattern for the appliances is implemented
in a model of the grid in DIgSILENT, to
validate the line losses reduction an control
the power quality.
3
82
14
By signing this document, the author confirms that he has participated
in the project work and thereby he is liable for the content of the report.
Preface
This Master Thesis project report, called Flexible load management in Smart-grids
is written by Eloy Rodríguez Moldes in the period 1th of September 2012 to 29th
of May 2013.
Reading Instructions
• Figures are numbered sequentially in their own chapter. For example Figure
1.3 is the third figure in the first chapter.
• Equations are numbered in the same way as figures but they are shown in
brackets.
• References are specified in the text in square parentheses according to Harvard
method. The bibliography is on page 43.
i/vi
Acknowledgements
The author of this report would like to thank Pukar Mahat for his excellent guidance
as a supervisor for this project.
iii/vi
iv/vi
Contents
Preface
i
Acknowledgements
iii
Contents
v
1 Introduction
1
1.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Solutions approach . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.3
Prior work in the field . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4
Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.5
Key assumption and limitations . . . . . . . . . . . . . . . . . . . . .
4
2 Flexible loads
2.1
5
Introduction to Demand Side Management . . . . . . . . . . . . . .
5
2.1.1
DSM methods . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
Residential electricity demand . . . . . . . . . . . . . . . . . . . . . .
8
2.3
Study cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
3 Appliances
3.1
3.2
13
Washing Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3.1.1
Use Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
Refrigerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
4 Optimization
4.1
25
Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
v/vi
25
4.2
Energy cost function . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.3
Losses function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.4
Optimization using Matlab Optimization Toolbox . . . . . . . . . . .
28
4.4.1
Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
4.4.2
Solver Functions . . . . . . . . . . . . . . . . . . . . . . . . .
29
Optimization results . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4.5
5 Modeling
35
5.1
System description . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
5.2
Implementation of optimal results
. . . . . . . . . . . . . . . . . . .
35
5.3
Energy Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
6 Conclusion and future work
41
Bibliography
43
vi/vi
Chapter
1
Introduction
1.1
Background
According to the Energy Strategy 2050 of the Danish Ministry of Climate and
Energy, 30% of total electricity is to be covered by renewable energy consumption
by 2020.
During last years the Danish Power system has moved from a centralized model
supported by large power production plants to a decentralized system. This change
has been motivated by the introduction of renewable energy resources like wind
and photovoltaic. However, the increases of this kind of generation facilities turn
into in a stochastic energy supply system due to the high weather reliance.
One of the main problems in electricity networks, which becomes even bigger in
grids with large renewable resources, is the load balancing. The imbalance between
electricity production and consumption leads to the necessity of power plants with
fast response (as CHP) and storage systems (as batteries), which are able to compensate random renewable generation. However, even with this solution, there is
still a need for the conventional power plants which should run during the period
of lower availability of renewable energy.
Other possibility is the actions on the demand side. The Demand Side Management (DSM) is load profile variation in order to change the consumption with
production. By this management, it is possible to shift electricity consumption with
respect to production or prices considerations, or both. Thereby, it is possible to
take advantage of a possible prices policy with different time-variant tariff schemes.
Various tariff schemes are discussed in detail in reference [1].
The adaptation to power production becomes of special interest in Smart-Grids
where the energy available is not only limited, but also fluctuating. Furthermore,
the energy efficiency can also be improved in large system with smart grid. That
improvement bases on more efficient distribution, since the consumption power
peak decreases, and consequently the losses should decreases too. Besides, it is
possible to flatten the load profile, which leads to a better use and exploitation of
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1.1. Background
Introduction
the production systems, avoiding need of over-sizing.
Another use of DSM is the real-time response to fast variations on the production, which could be originated by wind gusts or any other stochastic generation.
The dynamic response of thermal storage appliances as freezers and air conditioning
could help to manage these by frequency regulation.
The objective with DSM is not to decrease the amount of energy consumed
at a dwelling, but to increase the utilization and efficiency of the production, and
transportation systems and decrease the total cost for the user [4].
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1.2. Solutions approach
1.2
Solutions approach
This project starts with a literature study in following fields:
• Study of Demand Side Management methods and relevance in Danish electrical system.
• Modeling of appliances and Time of use patterns.
• Programing optimization.
The next step is to fulfill the objectives in the problem formulation.
1.3
Prior work in the field
The optimal control of different scenarios of variable energy production in combination with a battery storage system has been presented in [8].
The current status for Demand Side Management and their challenges for integration in the network has been presented in [5].
Many pilot DSM projects have been developed around the world, reference [13]
makes a comprehensive study on them.
Surveys referents to people time of use have been conducted in many countries in
recent years [9].
Linear and nonlinear programing optimization is highly studied in [27].
1.4
Problem Statement
Demand side management (DSM) is able to adapt the electrical energy consumption
by acting on the behavior of the loads. Today the control of loads is based in
different tariff schemes to motivate the customer to move its consumption. Smart
grids make possible monitoring and control of those individual electrical loads. The
implementation of these systems improves the use of renewable energy, distribution
system and can help to the customers to decrease the electrical bill.
The objective for this Project is to develop a demand side management based
on household appliances. The specific objectives are as follows:
Objective 1: Identify and simulate two of the most important appliances in a
household, dividing in subtasks;
Objective 2: Design an optimal control to manage the loads according to cost
and electrical requirements;
Objective 3: Develop a realistic model of the system in DIgSILENT and test the
controls designed according to voltage and frequency requirements;
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1.5. Key assumption and limitations
1.5
Key assumption and limitations
In order to simplify the calculations only active power is considered.
Flexible pricing have not been considered.
Calculations are based on the combination of UK time use survey, and data from
a residential area in Denmark.
The same washing program have been considered for all the washing machines.
Refrigerator opening doors is not considered, and food mass is taken as a constant
value.
Communication infrastructure between utility company and final user is not considered.
4/45
Chapter
2
Flexible loads
As mentioned before, the Danish Power System’s evolution has led to a decentralized power production scenario, contributing to significant power production of
renewable resources. According to the annual report of the Danish Energy Agency,
in 2011, the generation from RE was of 14% of the total energy production, and
shows a growing trend in the use of this kind of energy.
The following table 2.1 summarizes the share of final energy consumption in
Denamrk.
Table 2.1: Electrical Sectors in Denmark in 2011[6]
Concept
Total supply
Exports
Danish Consumption
Households
Total industries (transport, industry and services)
Losses
Energy in GWh
45456
10375
35081
10156
22537
2388
Percent
100%
29%
64.2%
6.8%
From the table above 2.1, it is seen that third part of energy is used to domestic
supply. It is interesting indicate that the residential electricity has experienced a
growth of 17% in EU-27 between the period 1999 to 2008, whereas in Denmark, it
has even decreased [3]. Nevertheless it is a very significant part of the total Danish
electrical system, and becomes of a special interest to apply a DSM, in order to
decrease costs for end-user and losses in the distribution system.
2.1
Introduction to Demand Side Management
According to [2] “demand side management is is the planning, implementation,
and monitoring of those utility activities designed to influence customer use of
electricity in ways that will produce desired changes in the utility’s load shape”.
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2.1. Introduction to Demand Side Management
Flexible loads
This definition covers the reduction in total energy consumption, but also the load
shifting and customer generation, getting a more beneficial load profile. These
benefits include economical and efficiency improvements, from generation utilities
as well as distribution system or final consumer. In general a DSM considers loads
able to react to external parameters. This consideration introduces the concept of
flexible load with which, an utility will be able to adapt its consumption within a
certain constraints.
The correct implementation of a DSM should maintain the same final services
that the electrical grid provides to the users today. However, it is also possible to
change the user habits, while maintaining the same comfort label.
In addiction, the security of supply is improved by DSM when renewable energy
such as wind or solar are used. These type of electrical generation is associated with
a high temporal variability since it can not be reliably dispatched or accurately
predicted. Due to this, match generation and consumption becomes of a special
interest. A correct combination of valley filling and peak shaving could aid to
reduce this problem.
By using DSM programs, it is possible change the load profile shape as shown
in Figure 2.1. The most common applications of DSM are as follow:
Peak shaving: Concerns the reduction of energy usage during intervals of high
demand.
Valley filling: Refers to the increment of consumption during off-peak periods.
Load Shifting: Peak usage rescheduled to fit under lower threshold.
Other load-shape objectives are detailed in [2], Strategic conservation, Strategic
load growth and Flexible load shape.
peak
off-peak
Peak
shaving
off-peak
Valley
filling
Load
Shifting
Figure 2.1: Load profile shapes
The peak reduction concerns the use of energy in critical periods. A reduction
on power demand leads to a decrement in power losses. Higher the total demand,
larger the transmission losses. Furthermore, other advantage of peak shaving, is
a lower dependence of peak generators. This may be motivated by a economic
6/45
Flexible loads
2.1. Introduction to Demand Side Management
reasons so as to, decrease the usually high operating costs and fuel dependence of
generators during critical periods.
A proper load management could help to flatten the load profile, avoiding effects of intermittent generation and improving the efficiency of the system. The
modification of the load shape by increasing the consumption in off-peak periods
results in a better use of base generators. In that periods, the cheap energy from
renewable sources or from sources with high disconnection costs, such as nuclear
power plants, could be used.
DSM are intended to benefit both customers and suppliers. While the suppliers try to maximize profits by saving cost on production and distribution, the
customers try to minimize invoice amount by using more efficient loads and adapting consumption with a price schedule. In this report, both problems have been
considered. On one hand, the losses in the distribution line will be minimized by
adjusting the loads and, on the other hand the cost of consumption will also be
minimized by the rescheduling different process within some specific load.
2.1.1
DSM methods
The different methods of DSM are defined according to the interaction level between
consumer and supplier [10], some of the most common methods are summarized
below.
1. Energy saving and Load efficiency
It refers to efficiency improvements in electrical equipment, which results to a
reduction in energy consumption. New control is required once the new equipment
has been installed. The effects on the electrical demand are indirect, since it focuses
on power reduction regardless of consumption schedule.
2. Pricing models
It bases on energy regulation by means of price incentives. The main idea
is the introduction of various energy prices at different periods during the day.
The differences in price might be adequate both in quantity and time, to motivate
customers to vary its consumption habits [1]. That prices can be established in
advance, for example in the energy supply contract, or it can be daily updated or
even in real time, basis on many parameters factors. Three of these managements
are briefly explained in next paragraphs.
Time of use tariff (TOU): This method is based on the definition of time blocks
with different prices, which reflect the average energy cost during these periods. For example lowest prices during the night.
Critical peak pricing (CPP): The high prices are allocated in periods where
the generation cost is very high, usually due to a lack in generation or an
excessive consumption. The objective is to promote a peak shaving (Figure
2.1).
Real time pricing (RTP): This kind of tariff reflects the variations in the market, usually in hourly periods. For example fluctuations in fuel price. This
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2.2. Residential electricity demand
method moves the prices uncertainty from the supplier to the final user.
3. Direct load control
A centralized control system is able to connect or disconnect a specific load.
This method requires a direct communication between client and supplier. DLC
is normally used for loads of the same type. The most suitable appliance to implement this method are those with a thermal inertia, due to the possibility of be
disconnected for some time and still keep its temperature in an adequate range [28].
4. Demand side bidding
This concept refers to the offers of energy reduction from the customers to
the suppliers. It opens a new market with energy offers from both sides. The
possibilities to sell energy from distributed generation systems, like solar panels,
already exist, but demand side bidding will enable a new way of interaction.
5. Frequency control
The frequency represents very effective method to measure power imbalances.
From a nominal value of 50 Hz, a decrement means a decrement in production,
which should be properly compensated with a reduction in the consumption, and
conversely.
6. Energy storage
Different systems of energy storage are used to balance the power. The main
idea is to store energy when there is excess of production or the price is low,
and discharge the energy when the production is low or the price of electricity is
high. This kind of systems includes for example chemical batteries, appliances with
thermal inertia or large hydroelectric power plants with pumping systems.
In general this activities involves the introduction of power monitoring (measurement), control and actuation systems such smart meters, which exceeds the
scope of the present report. Apart from that, the policies to assist the development
and implantation of DSM are not considered.
2.2
Residential electricity demand
The Energy consumption of domestic appliances has been widely measured in European countries. The following table 2.2 shows the results of a study conducted
in 2007 in EU-15 [7]. The table includes the most common appliances in EU and
its contribution to annual electrical consumption. The power rating is also summarized, however this data is based on [20], which includes a concrete model for
each appliance and may vary for different models and types (e.g. Filament bulbs
or fluorescent tube are included on lights). Nevertheless the values fit with other
publications such as [4].
According to [7], lights and appliances represent more than 50% of the electrical consumption of which 33% corresponds to refrigerators and washing machines.
Many reports which describe a DSM in household appliances make a group differentiation on it according to the use priority [4], [11]. That means the possibility to
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2.2. Residential electricity demand
Table 2.2: Household appliances consumption[7][20]
Appliance type
Residential electric heating (c)
Refrigerators (c)
Miscellaneous
Lighting
Electric storage water heater (p)
Consumer electronics and
standby equipment
Electric hobs (c)
Central heating circulation pumps
Washing Machines (p)
TV-on mode
Electric ovens (c)
Dishwashers (p)
Driers (p)
Office equipment
Room air-conditioners (c)
Relative
contribution (%)
21.3
14.5
13.3
10.8
9.2
6.4
Power Rating
(Watts)
2200
177
60
2000
-
5.3
4.3
3.7
2.8
2.1
2
1.8
1.4
1
2509
2056
130
2500
2200
2700
-
defer the start of a concrete appliance according to the characteristics of the task
which it does. If the running of an appliance could be postponed, the electrical
consumption which corresponds to that particular machine could also be shifted,
helping to adapt the load profile to any requirements considered.
The ability of an appliance to be postponement is indicated on the table 2.2 by
(p). These appliances are washing machines, dishwashers and drier machines. The
large consumption corresponds to the washing machine and it is also a more common appliance than drier or dishwasher [7]. A detailed study of washing machine
management and division in subtasks is presented in chapter 3. Other devices as
electronic chargers could be also included, however the impact in terms of energy is
too low in comparison to the three mentioned before. One of the most interesting
management ways is the subdivision of the profile, in different tasks as proposed
in [12]. It is also important to consider the maximum deferrable time, according
to user choices or to the necessity of be completed to run other appliance after the
first one (e.g. drier after washing machine).
The table 2.2 also provides information about less flexible equipment. This
refers to utilities which are used continuously, indicated by (c). However some of
them may have some possibilities to shift as briefly explained before. The electrical
heaters, coolers and refrigerators are appliances which have the biggest impact in
load consumption, as it can be seen in the relative contribution from table 2.2.
These appliances have, in common, the function of a temperature maintenance,
which could be assumed as a thermal storage [14]. Hobs and ovens, although are
not running at all time, can be also considered as an adaptive device. The main
advantage of implement a DSM on these devices, is the possibility of activate and
deactivate the appliance, and at the same time keep the temperature in an acceptable range. The refrigerator is one of the most appropriate device to implement a
9/45
2.3. Study cases
DSM due to the relatively big range of temperatures for the food to be preserved.
The third group of appliances includes those that are not possible to shift, and
any change in their power consumption profile could affect to its operation. This
group includes appliances like lights, TV or some office equipment.
2.3
Study cases
For this project, a residential area in Aalborg has been considered. The place
consists of 15 houses in three streets. A 10.5/0.42 kV transformer, whose main
characteristics are included in table 2.3, supplies the power into the grid. The grid
is made of 15 PVC and 4 paper distribution lines, the reference number, length and
resistance are listed in table 2.4. Figure 5.1, in Chapter 5 shows the modeled grid
in DIgSILENT.
Table 2.3: Transformer data
Nominal Power
High voltage side
Low Voltage side
Frequency
Internal Impedance
400 kVA
10.5 kV
420 V
50 Hz
4.0 %
Table 2.4: Distribution lines
Reference number
Line 1
Line 2
Line 3
Line 4
Line H1
Line H2
Line H3
Line H4
Line H5
Line H6
Line H7
Line H8
Line H9
Line H10
Line H11
Line H12
Line H13
Line H14
Line H15
Length (meters)
28.4
50.3
86.6
130.7
31.8
38.5
16.9
20.9
28.1
34.8
15.1
20.3
14.1
28.4
20.3
45.9
63.6
26.2
22.3
Resistance (ohms)
0.0055
0.0097
0.0167
0.0252
0.0062
0.0075
0.0033
0.0041
0.0055
0.0068
0.0029
0.0040
0.0028
0.0055
0.0040
0.0090
0.0124
0.0051
0.0043
The dwellings consumption have been calculated from the Danish hourly consumption for houses without electrical heating, and the measured annual energy
10/45
2.3. Study cases
consumption for each household. The load profile for the whole system is shown in
Figure 2.2.
Total Power [kW]
30
25
20
15
10
5
0
Figure 2.2: Total Power profile for the system
11/45
2.3. Study cases
12/45
Chapter
3
Appliances
As explained before, two of the most appropriate appliances, in a household, for
DSM according to the amount of energy consumption, are washing machines and
refrigerators. This chapter provides an analysis of both devices, in order to understand their operation and decide a correct management of flexible consumption.
3.1
Washing Machine
The first considered domestic appliance for DSM has been the washing machine.
It is seen from the table 2.2 that the annual energy consumption of the washing
machine represents the largest among the deferrable appliances.
Basically, there are two different types of washing machines (horizontal axis
and vertical axis) which have been produced by leading manufacturers for the last
years. The main difference between them is the drum rotational axis direction.
However, nowadays the vertical axis is not popular due to the biggest water and
energy consumption [15]. As a result of the low energy consumption, horizontal
axis is the most used in Europe and all the models considered as the most energy
efficient household washing machines are with horizontal axis [16].
The basic design of a horizontal axis washing machine consists on an electrical
motor, connected to the drum where the laundry is washed, and a water heater.
As it is explained in next paragraphs, during a wash cycle, high and fast variations
occur in the drum. Thus it needs a motor capable of satisfying these requirements.
One of the motors, which can be easily used to this purpose and also generally used
in washing machines is an induction motor [19] [17].
In a normal washing cycle, three different processes occur, wash mode, rinse
mode and spin mode [18]. These mode are briefly explained in the next section in
order to get a better understanding of the washing process. These modes can be
different for each manufacturer and program.
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3.1. Washing Machine
Appliances
1. Wash mode
The objective of this mode is to remove the dirt of the laundry. The drum speed
for a wash mode is typically 30-45 rpm [17]. During this mode hot water is supplied
at the chosen temperature program. As it is shown in the load profile (Figure 3.3),
the water heater increases the energy consumption compared to rinse and spin
modes, and it is the main energy consumer. The wash mode uses a small amount
of water which generates high torque in the load when wet and heavy clothes drop
from the drum’s highest point [17][18].
2. Rinse mode
During this process, the cleaner is removed from the clothes by using cold water.
The speed is the same as in wash mode however the torque decreases as shown in
Figure 3.1. It is because of the greater use of water. The maximum torque is
developed when the laundry drops from the drum’s highest point to the bottom.
During this cycle the drop distance is decreased due to the bigger water height in
comparison with wash mode, and therefore the torque is less. It is not necessary to
heat the water; consequently the energy consumption for this mode is smaller than
in wash mode.
Torque
WASH
SPIN
Speed
Figure 3.1: Comparison of the wash mode and the spin mode[18]
3. Spin mode
During this mode, the water is removed from the laundry due to high speed
drum revolution. The spinning speed varies for different programs, however for ten
of the most efficient washing machines in Europe, the maximum spin speed are
between 1400 and 1800 rpm [16] . During this mode the high speed precludes the
laundry drop due to centrifugal force, therefore the torque developed by the motor
is smaller than in other modes. This explains the low energy consumption in Figure
3.3. The maximum speed is raised by steps of lower speed as shown in Figure 3.2.
Figure 3.3 shows the energy consumption measured for a washing machine at
1200 rpm maximum spin speed and 40◦ C water temperature for the wash mode
[20].
In order to develop a flexible demand for the washing machine the understanding
of the whole cycle is necessary. From the Figure 3.3, it can be seen that during
wash mode the heater is working continuously for 20 minutes and the drum turns
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Appliances
3.1. Washing Machine
Washing Machine Algorithm
RPM
800
000
600
40
-40
Wash
Rinse
Spin
TIME
Figure 15. Speed Profile of the Washing Cycle
Figure 3.2: Speed Profile of the Washing Cycle[17]
4.1
Tumble-Wash Cycle
The tumble-wash phase is typical with low drum speeds reversing the direction of the drum rotation every
few turns. Because there are short intervals of rotation, the drum must reach a stable rotational speed in
under two seconds. This requirement necessitates applying a high torque to the washer drum to make it
move. A high-generated torque is one of the key requirements in this operating mode. The speed of the
drum for a tumble wash is typically 30–45 rpm. The exact speed depends on the type of clothes being
washed and is determined by the washing program. The drum speed is low and the clothes rise in the drum
and fall down when they reach the highest point. Wet and heavy clothes are periodically bumped in the
drum, generating high torque ripples to the motor. The control algorithm of the drive needs to have enough
dynamics to eliminate those ripples. Error in the speed should not exceed limits of ± 2 RPM. These
requirements can be satisfied where there is a PID controller for a speed control loop and an inner PI
current control loop.
4.2
Out-of-Balance Detection
The out-of-balance detection and load displacement phase is performed prior to the washer going into a
spin-dry. The clothes in the drum must be properly balanced to minimize centrifugal forces causing a
waggling of the washer. In the first step, the imbalance is detected. The speed of the drum is increased by
2500
a ramp up to the value
at which the clothes become centrifuged to the
inner side of the drum. The algorithmSpin
Wash
Rinse
performs an integration of the motor torque ripple per one cycle. The integral value estimates the size of
the load imbalance. If the imbalance is lower than the safety limit, the drum speed increases and goes into
2000
a dry-spin. If the imbalance is higher than the safety limit, the drum speed decreases and the rotation
direction is reversed. The algorithm performs a new load displacement at the reversed speed. At the end
1500
of a load displacement interval, the rotation is reversed and out-of-balance detection is executed again. The
1000
Washing Machine Three-Phase AC-Induction Direct Vector Control, Rev.1
500
20
Freescale Semiconductor
0
0:01
0:04
0:07
0:10
0:13
0:16
0:19
0:22
0:25
0:28
0:31
0:34
0:37
0:40
0:43
0:46
0:49
0:52
0:55
0:58
1:01
1:04
1:07
1:10
1:13
1:16
1:19
1:22
1:25
1:28
[Watts]
Washing Machine Profile
Figure 3.3: Consumption of a washing machine cycle in Watts and modes
15/45
3.1. Washing Machine
Appliances
have a low influence in the energy consumption. However in raise and spin modes
the drum turn consume all the energy in four peaks between 250W and 568W. That
indicates three turns at maximum speed in rinse and one in spin mode.
In order to develop a flexible demand for the washing machine the consumption
profile has been divided in according to the three cycles, also shown in Figure 3.3:
Cycle 1: 30 minutes, 2056W peak consumption, 730Wh.
Cycle 2: 50 minutes, three peaks of 250W, 78.5Wh.
Cycle 3: 10 minutes, 568W peak , 60Wh.
The subdivision in three cycles does not introduce any problem in the total wash
since, as explained they are different processes, with different objectives, which start
in a specific time and have a discrete duration. Also almost all the washing machines
include a stop function which is able to halt the cycle and restart it again after some
time. Usually the wash is restarted from the beginning of the cycle (Zanussi ZWI
71201 WA), but some of them are able to restart from the same point into the
cycle within a restart time less than 10 minutes (Whirlpool W10468366A). For
this project, the possibility of introduce a delay of 30 minutes between cycles is
considered. This is a similar option to the technology Tumble Fresh Option of
Whirpool which provides a periodic tumbling after a wash when the laundry is not
unloaded.
3.1.1
Use Pattern
The system is implemented in the test scenario in Aalborg as explained before,
however it is not realistic that all the houses use the washing machine at the same
time. In this section the most probably time to wash for each of the 15 dwellings
is studied.
According to the directive 2010/30/UE, which is the regulation followed to
determine the yearly consumption of appliances in the European Union, a washing
machine performs 220 cycles/year. Base on this assumption, the probability of
wash on a normal day is 0.65. For the considered case in Aalborg with 15 houses,
the number of houses which uses the washing machine per day is 10. This high
number of washes is not only justified by different loads for color and white clothes,
but also because around 85% of the washes are not a full load cycle [15].
The behavior of a typical home washing machine and its effects as a flexible
load has been analyzed in previous section. An efficient DSM should try to adapt
the behavior of the appliances to operate in a most proficient schedule, without
depending on the habits of the users. It should adapt its operation within the
range between users’ preferred start and finish time. For example if a user runs the
washing machine at 24:00, it is possible to run the wash during the whole night,
since it is very likely that the clothes are not need before the morning. In order
to determine the most probably washing time for each household, a study on the
washing habits is necessary.
16/45
Appliances
3.1. Washing Machine
Models to predict the load profile of a dwelling has been widely studied [21],[22],[23].
Most of these methods are based on time of use surveys, by relating a particular
activity with the use of an appliance. Some of the most complete time of use surveys have been conducted in Sweden, Norway or UK. Reference [9] reviews most of
these reports. In Denmark, the ELMODEL-bolig forecast model has collected data
for the last 30 years, however the unavailability of data in English is a limitation for
use. In this project, the UK time use survey conducted in 2000 has been provided
by the UK Data Archive, University of Essex, and it has been considered.
The Time Use Survey (TUS) shows how people use their time in a 24 hours
basis, with ten minutes resolution. Two different data are obtained according to
weekdays and weekend days. The TUS indicates, each 10 minutes, the proportion
of households where at least one occupant is engaged in a particular activity (in
that case using the washing machine). From this data, the most probable time for
wash is calculated, and represented in Figure 3.4.
6%
5%
4%
3%
2%
1%
00:00
01:00
02:00
03:00
04:00
05:00
06:00
07:00
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0%
Figure 3.4: Houses using the washing in a week day from TUS
From Figure 3.4, it is not easy to see clearly tendency in washing times due
to the large discontinuity in daily profile between 7:00 and 16:00. The number of
houses, using the washing machine in a specific time, are lower than 5% of the total
houses in the best cases, and values adjacent to these maximum points have a large
deviation from them. Therefore, it seems to be difficult to extract a clear trend
with the available data.
Some papers, which develop models for daily electricity consumption, based in
user practices, obtain a high correspondence with measured values; however they
identify the washing machine profile as the most critical predictable appliance.
In general, deferrable activities, denoted in table 2.2 by (p), introduce the most
frequently discrepancies [22].
The accumulative frequency graphic shown in Figure 3.5 represents the proportion of wash cycles which have been started by a specific time, and it is a good
indicator to establish a use pattern basis on the most probably wash time during
each wash cycle.
17/45
3.1. Washing Machine
Appliances
10 wash cycle
9 wash cycle
8 wash cycle
7 wash cycle
6 wash cycle
5 wash cycle
4 wash cycle
3 wash cycle
2 wash cycle
1 wash cycle
Figure 3.5: Accumulative frequency graphic for 10 washes
However, this information is not enough to determine the start time. With the
aim of improve the accuracy for washing time prediction, another relation between
washing machine use and household occupancy level, is considered. The use of
some kind of appliances is not related with people’s habits, for example the refrigerator is running regardless of the user. However, other appliances usage pattern,
is strongly related to the occupied period. For example, when people are not at
home, microwave is not be used. The washing machine start is included in the
second group [24].
In order to obtain a more detailed simulation, the households have been divided
in five different occupancy patterns as proposed in [24]. The unoccupied periods
have been based in job time and child care considerations. Table 3.1 summarizes
the unoccupied periods for each kind of household.
Table 3.1: Occupancy pattern for a three-person household [24]
Pattern
a
b
c
d
e
Unoccupied period
9:00-13:00
9:00-16:00
9:00-18:00
13:00-18:00
Always occupied
The occupancy profile is not included in the TUS, however some studies on
this database have determined the occupancy level by using sophisticated methods
basis on Markov-Chain technique [25]. Moreover the relation between household
occupancy and watching TV activity has been considered. The connection of these
parameters have been analyzed by the Pearson correlation coefficient (r). It provides
a measurement about the degree of linear relationship between two parameters,
regarding the goodness of fit. Pearson correlation coefficient leads in a strong
correlation of 0.8. The determination factor (R2 ) indicates how much variance of
the data is explained by the linear regression, and for this case it is of 64%. These
values shows a high relation between dwelling occupancy evolution and watching
18/45
Appliances
3.1. Washing Machine
TV activities. Moreover, the TV using is a easily measurable factor, and could
be used for a real time implementation of the system based on smart meters and
communication systems.
Watching TV values cannot be assumed as occupancy levels, since it is possible
be at home without watch the TV. However the proportion of houses watching TV
and the proportion of occupancy experiment a similar evolution [25], consequently
TV watching activities has been used to compare occupancy at different times.
According to Table 3.1, it is assumed that there is full occupancy from 18:00.
Relating a 100% occupancy on this time with the average of TV-watching for the
same period, it is possible to obtain the unoccupancy level as the difference between
this value and the value of people watching TV in a specific time. The results of
these calculations and the association with the 15 households considered are shown
in table 3.2.
Table 3.2: Unoccuped houses
Period
18:00-0:00
9:00-13:00
13:00-16:00
16:00-18:00
TV watching (%)
73.6%
39.4%
41.4%
47.6%
Unoccupied houses
0%
46.5%
43.7%
35.3%
nr of houses
0
7
7
5
From this data it is possible to define the following equations:
A+B+C =7
A+B+D =7
A+D =5
where A, B, C and D represents the number of houses which follow the occupancy pattern a, b, c and d respectively. Since there must be at least one for every
pattern, the constraints below have been also considered:
A + B + C + D ≤ 14
A≥1
B≥1
C≥1
D≥1
The feasible solutions for the equation system are shown in Table 3.3. The first
solution has been randomly taken. It leads in the less number of dwellings with
full occupancy (26.7%). This solution results in a 6.6% of houses of type a, 13.3%
of type b and 26.7% of types c, d and e. Figure 3.6 summarizes the occupancy
level for each household, where the continuous line represents the occupancy. The
houses 1 to 10 are those which use the washing machine.
Finally, the accumulated frequencies, presented in Figure 3.5, are used to determine which house uses the washing machine, placing the start time for a wash
19/45
3.1. Washing Machine
Appliances
Table 3.3: Occupancy pattern for a three-person household [24]
A=1
B=2
C=4
D=4
A=2
B=2
C=3
D=3
A=3
B=2
C=2
D=2
A=4
B=2
C=1
D=1
house 15
house 14
house 13
house 12
house 11
house 10
house 9
house 8
house 7
house 6
house 5
house 4
house 3
house 2
house 1
Figure 3.6: House occupancy pattern
in a period of occupancy. For example, it is not possible start a wash at 10:00 in
house 1, since Figure 3.6 shows that the house is not occupied. The exact time has
been determined by calculating the most probable time from TUS data, for each
accumulated period. The finish time is the first time when the house is occupied
again after an unoccupied period, or the duration of the total wash cycle (90 minutes) plus 1 hour (30 minutes between each mode). The possible time for use for
the washing machine for the 10 houses are shown in Figure 3.7.
house 10
house 9
house 8
house 7
house 6
house 5
house 4
house 3
house 2
house 1
Figure 3.7: Washing machine using time
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3.2. Refrigerator
3.2
Refrigerator
Refrigerators and freezers represent the second largest energy consumption in a
household (Table 2.2). In this category, chest freezers, fridge freezers, upright
freezers and refrigerators are included. The most common freezer appliance is
the fridge with refrigerator and chest freezer [20], however for this project a simple
refrigerator has been considered due to simplicity reasons. Moreover, the simulation
of a fridge freezer is based on the same principles than a refrigerator, but considering
two cooling devices: refrigerator and chest freezer. Another limitation for the model
is the temperature variation due to number of door openings. Variations in food
stored is neither considered.
In recent years, the improvement in refrigerators design has made possible a
consumption of 156 kWh/year [16]. However most of the refrigerators reviewed
consume between 200 and 300 kWh/year with a rated power around 90 and 150
W. This amount of peak power is not very significant, however the possibility of
coordinating various refrigerators of different households, becomes interesting in
order to adapt consumption in real time [4]. The use of a thermal storage device
to DSM has been already studied in the literature [29] [30], based on this idea
the thermal characteristics of a refrigerator are studied, and related with its load
profile.
The function of a refrigerator is to preserve the aliments in a correct temperature, which usually is between 3 and 8◦ C [31]. The operation to maintain the
temperature in the desired range is shown in Figure 3.8, and it consists of basically in running the compressor when the superior temperature is reached; stop the
cooling at inferior limit, and keep off the cooling until the temperature increases
again.
The DSM is done by changing the temperature limits (which always should be
included in the original limits, set between 3 and 8◦ C) according to the necessities
of the system. That is, when an optimal point (according to economic and energetic
considerations) is reach, it is possible turn off the refrigerator, decreasing the total
cost and power losses in moments with high prices, and high power request. In the
case of a reduction in energy price or consumption decrement the refrigerator is
turned on.
A very important factor in the energy consumption is the temperature of the
room where the refrigerator is placed and the number of times of door opening [32].
For this project the room temperature is assumed as constant in 21◦ C, since the
freezer is usually placed at kitchens, and it is the standard temperature for a house
[31]. As mentioned, the effect of door opening is not taken into account.
The temperature evolution related with electrical power required has been described by [33] and is characterized by equation 3.1.
T (t + 1) = ε · T(t) + (1 − ε)(Tamb (t) −
η · P (t)
)
A
(3.1)
The parameters are described in table 3.4. In [30] the differential equations
from 3.1 are presented in order to obtain the temperature evolution for warming or
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3.2. Refrigerator
Temperature [ºC]
10
8
6
4
2
0
20
40
60
80
100
120
140
160
180
120
140
160
180
Power [W]
150
100
50
0
0
20
40
60
80
100
Figure 3.8: Power vs Temperature evolution in the refrigerator for 180 minutes
22/45
3.2. Refrigerator
cooling. This equations determines when the compressor is switched on 3.2 or off
3.3.
T1 (t) =
T1 (t1 ) − TON (t1 )
A
−m
t1
c
e
where TON (t) = Tamb (t) −
T2 (t) =
A
(3.2)
A
(3.3)
e− mc t + TON (t)
η·P (t)
A
T2 (t1 ) − Tamb (t1 )
A
−m
t1
c
e
e− mc t + Tamb (t)
where,
Table 3.4: Refrigerator parameters
ε
η
A
mc
Tamb
factor of inertia
coefficient of performance
thermal insulation
thermal mass
ambient temperature
3
6 W/◦ C
1500 J/◦ C
22 ◦ C
From equations the system has been simulated in Matlab. The scrpit, allows
the introduction of a switching schedule, in order to obtain the power profile. The
numerical values used for the simulation are included in table 3.4. This values, used
in [29], represent a good approximation to the refrigerator dynamics. Figure 3.8
presents a 3 hours simulation from the Matlab model. As can be seen a complete
cycle takes 95 minutes. The considered refrigerator has a nominal power consumption of 177 W during 18 minutes. For simplification reasons the complete cycle will
be considered as 100 minutes and the working time per cycle of 20 minutes. This
assumption leads in an energy demand of 59 Wh for a complete cycle.
The model runs autonomously, keeping the temperature in the limits, and provides the power profile as shown in Figure 3.8. However, it is able to respond to an
external order. If an increment in consumption is required, the refrigerator power
output will increase if the temperature is decreasing, and similar process is followed
for a consumption decrement. However, if an increment is required and the compressor is already running, or the temperature is in the lower limit, no modification
will occur. This phenomenon occurs in the minute 135 of the Figure 3.8, when an
increment in consumption is required. After the temperature hits the lower limit,
the compressor switches off and the temperature increases until 8◦ C.
Although the refrigerator is a continuous run appliance, some modifications can
be done in its load profile in order to obtain a better performance. As mentioned
before, the variations are based in an external signal which activates or deactivates
the compressor. This idea is based on direct load control (DLC). By this management, it is possible to introduce the optimal control schedule for the refrigerator.
For this project, two different scenarios has been considered to manage the
refrigerator. The first one refers to a normal operation, where the temperature
23/45
3.2. Refrigerator
never exceeds 8◦ C. However, it is possible to move the cooling periods within the
time range in order to obtain a better performance in price or energy losses. For
example it is possible bring forward a cooling period, as shown in Figure 3.8 in
minute 135, if there is a lower price at that time.
The extension of the temperature range, results in a larger cycle duration. This
management makes possible to maintain the refrigerator in on or off during continue periods of more than 20 or 80 minutes respectively. It is because, decrease
from a temperature greater than 8◦ to 3◦ needs more energy, and consequently a
larger on period. In contrast it is possible maintain the refrigerator in off during
more time starting from 3◦ C, until a temperature greater than 8◦ C. The benefit of
longer periods in on or off is to take advantage of time intervals, where running
the refrigerator entails a lower price or energy losses, and on the contrary avoid
unfavorable periods.
Due to simplicity reasons, in order to match up the time intervals from power
consumption with the washing machine use pattern, the activation periods are of 10
minutes durations. A increment of temperature from 8◦ C, during an extra period
of 10 minutes, results in a maximum temperature of 10.5◦ C. This second scenario
considers a cycle duration of 150 minutes and 30 running minutes. The optimal
control will be obtained for both cases and compared with the original management.
24/45
Chapter
4
Optimization
In order to achieve the minimum losses in distribution lines, and electricity cost
for final user, an optimization of the washing machine and refrigerator use has
been conducted. This chapter provides a detailed explanation of how the grid is
modeled in Matlab. Chapter 3 focused on the behavior of the washing machine
and refrigerator from the point of view of technical operation and time of use.
These characteristics and limitations are used here to model the electrical system
according to operation requirements.
4.1
Problem Formulation
The representation of the power system, presented in section 2.3, can be simplified
as a power source (the transformer) connected to multiple loads (the houses). For
each household, five different loads have been considered. Four of them are variable
loads, which corresponds to the three washing cycles and one to the refrigerator, as
Figure 4.1 clarifies. This design have been chosen in order to consider loads with
the same power consumption along the time, and implement an on/off actuator
in that loads. Finally the last load represents the remaining household energy
consumption.
HOUSEHOLD 2
CYCLE
3
(spin)
REFRIG
CYCLE
2
(rinse)
CYCLE
1
(wahs)
OTHER
ENERGY
SOURCE
(Transformer)
OTHER
CYCLE
1
(wahs)
CYCLE
2
(rinse)
CYCLE
3
(spin)
REFRIG
HOUSEHOLD 1
OTHER
CYCLE
1
(wahs)
CYCLE
2
(rinse)
CYCLE
3
(spin)
HOUSEHOLD 15
Figure 4.1: Block diagram of smart grid system
25/45
REFRIG
4.1. Problem Formulation
Optimization
The washing machine pattern limits the time of use from around 8:00 to 0:00
Figure 3.7, in order to simplify the optimization system and reduce the calculation
time this has been considered as the optimization period. The analysis resolution
(time steps) is determined by the smallest operation time of the appliances, in this
case it is 10 minutes, which corresponds to the last washing cycle (spin). A smaller
resolution will result in a better control of the temperature in the refrigerator,
since increments of 1◦ C or even 0.5◦ C could be considered. However it implies an
increase in the number of studied steps, which results in a much higher run time of
the optimization algorithm.
Therefore 96 steps of ten minutes has been considered from 8:00 to 23:50. Hence
for each of the variable loads represented in Figure 4.1, a vector of 96 elements is defined. According to the on/off control technique, the values are limited to one when
the specific load is activated, and zero otherwise. This vector is denoted by xapp ,
where app represents the considered appliance (wash, rinse, spin or refrigerator).
xapp =
x1app , x2app , . . . x96
app
(4.1)
The load profile of a particular appliance is then calculated with equation 4.2,
where Papp symbolizes its rated power. On the other hand if the energy consumption
Eapp is multiplied element by element to the activation vector, the sum of the result
is the total energy consumption from 8:00 to 0:00 (equation 4.3).
Appliance power profile = xapp · Papp =
Total energy =
96
X
1 , P 2 , . . . P 96
Papp
app
app
(4.2)
(4.3)
xapp · Eapp
i=1
The extension of this vector xapp , to include all the flexible loads, leads in a
5670 elements vector which contains all the desing variables for the smart power
system. Consequently, this is the solution to the optimization problem.
house1
z
x1 . . . x96
|
{z
wash
}|
x97 . . . x192
}
|
{z
rinse
x193 . . . x288
}
|
{z
spin
{
x289 . . . x384
}
|
{z
ref rigerator
}
. . . x5670
(4.4)
Once the electrical network has been mathematically modeled, next step is to
define objective functions for the optimization problem. Next sections describe the
energy cost function as well as the power losses function.
26/45
4.2. Energy cost function
4.2
Energy cost function
The energy cost function refers to the total price that the customers pay for use the
washing machine and refrigerator. The appropriate activation and deactivation of
appliances is directly related with the spot market, so that the activation occurs at
a minimum, while the user requirements are not modified. The energy cost function
is formulated as follows:
C=
15 X
96
X
(xwash hi · Ewash + xrinse hi · Erinse + xspin hi · Espin + xref hi · Eref +) · P ricei
h=1 i=1
4.3
(4.5)
Losses function
The studied scenario, presented in 2.3, corresponds to a radial network. Consequently the real power loss has been calculated according to the equation 4.6
presented in [34], but leaving out the imaginary part as explained in limitations.
PLoss =
N
N X
X
αmn · Pm · Pn
(4.6)
m=1 n=1
where: αnm =
rmn
Vm ·Vn cos(δm
− δn )
variables:
• PLoss = Power loss on the distribution lines.
• Pm , Pn = Power at bus m, n.
• N = number of busses.
• rmn = resistive part of the element m, n in the impedance matrix of the system.
• Vm , Vn = Voltage at bus m, n.
• δm , δn = Phase angle at bus m, n.
The adaptation of the general power loss equation to the study case results in
equation 4.7.
PLoss =
96 X
20 X
20
X
i
αmn (Pm
+ xwash im + xrinse im + xspin im + xref im )
i=1 m=1 n=1
·(Pni + xwash in + xrinse in + xspin in + xref in )
27/45
(4.7)
4.4. Optimization using Matlab Optimization Toolbox
Although the voltage and phase angle change with power variations, it remains
almost constant because it may not vary much, and consequently α has been considered as constant. The values of V and δ have been obtained from a load flow
conducted in the DIgSILENT model, which is presented in Chapter 5.
The result of equation 4.7 does not represent any final result for minimization,
since it is the sum of power loss for each period. However, it represnets the total
power loss, and it is an effective value to account for the minimization of total energy
losses. The real value of energy loss will be calculated by using the DIgSILENT
model.
4.4
Optimization using Matlab Optimization Toolbox
For this project, the optimization solvers implemented in Matlab are used. Matlab
Optimization Toolbox includes several optimization methods, which can be used
according to the specific requirements and characteristics of each problem. These
algorithms allows users to solve constrained and unconstrained continuous and discrete optimization problems. Functions for linear, nonlinear, quadratic, integer and
multiobjective programing are included. The standard form, for a minimization
problem in the optimization toolbox [35], is as follows:
min
x f (x)
(4.8)
subject to
Gi (x) = 0 : equality constraints evaluated at x
Gi (x) ≤ 0 : inequality constraints evaluated at x
xlow , xupper : parameter bounds
It is seen from equations 4.5 and 4.7, that the cost minimization is defined by
a linear function, while the power loss function is nonlinear. The explanation of
the mathematical model of section 4.1, shows that a integer programing with 0-1
boundaries is required.
4.4.1
Constraints
Equality and inequality constraints have been designed for both washing machine
and refrigerator. The main constraints refer to the total energy consumption per
appliance. The implementation of this equation has been already presented in 4.3.
This expression includes the design parameter vector x, which corresponds with
activation periods. Consequently its sum results in the total time when a specific
appliance is running. According to Figure 3.3, these times are 30, 50 and 10 minutes
for wash, rinse and spin respectively. However the refrigerator activation time
depends of the total period considered (16 hours) but also of the initial temperature.
For this project three different temperatures has been considered: 3, 5.5 and 8◦ C.
These values have been randomly assigned for each of the 15 households. Hence this
consideration leads on three total running times of 18, 19 and 20 minutes, which
have been calculated using the Matlab script for the refrigerator dynamics.
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4.4. Optimization using Matlab Optimization Toolbox
Besides the general energy constraints, other particular limitations have to be
considered for each kind of appliance. For the washing machine, it can have only
one cycle at a time and maintain the correct order of operation (wash, rinse and
spin). In addition, the cycles cannot be broken.
Finally, the constraints necessary for the refrigerator have been designed depending on the initial temperature, and the maximum temperature which could be
reach for each individual refrigerator. The upper bound temperature can be chosen
from the scenarios described in section 3.2, a normal operation on 8◦ C (scenario 1)
or 10.5◦ C (scenario 2). While the initial temperature has been randomly assigned
to each refrigerator, the temperature range leads in two different kind of inequality
constraints.
The bounds have been set according to the use pattern calculation (Figure 3.7)
for the washing machine, while for the refrigerator the whole period is considered as
feasible, and the limitations are introduced exclusively by the constraints equations.
4.4.2
Solver Functions
As conclusion the minimization problem includes the following requirements:
• Integer boundaries solution set (binary).
• Linear Cost function.
• Nonlinear Loss function.
• Inequality linear constraints.
• Equality linear constraints.
However any of the solvers present in Matlab Optimization Toolbox fulfills all
the requirements. In order to achieve a proper optimization, the minimization
problem has been divided in two subproblems. First refers to the cost optimization,
which has been processed by using the bintprog solver. This algorithm is based in
dual-simplex and branch&bound methods. Dual-simplex is a common method to
solve linear functions, widely explained for example in [27]. Branch&bound method
is an iterative optimization algorithm which finds the best integer solution for a
given problem, based in a tree structure of feasible solutions [36]. The bounds are
0-1 non selectable.
On the other hand, the loss power function has been solved using the optimizer
fmincon. Fmincon solves nonlinear functions, with linear and nonlinear constraints,
within a selectable range of bounds. This solver uses gradient based search methods.
That means that the minimum is obtained by computing the values pointed by the
gradient of the objective function, until a minimum is found. This method is based
on the knowledge that the gradient vector points in the direction of maximun
29/45
4.4. Optimization using Matlab Optimization Toolbox
increase of a function [37]. Hence one of the task of the optimizer is to calculate
the search direction. Some methods can be chosen in fmincon solver, in this project
the interior point method has been used due to a smaller run time in contrast with
other methods with a better accuracy but much longer run time.
Gradient search methods need an initial point from where the gradient is calculated. The initial point for fmincon is the optimal for a minimum energy cost
(result of the cost optimization with bintprog). However the result is not an integer
solution.
The noninterger result is actually a weighted solution of the optimal integer
point. It means that each single objective value has a significant value for the
minimum result, and the greater numbers represent the most beneficial activation
intervals. The proposed methodology carries several optimizations using fmincon,
and after each optimization the solution and the boundaries are improved.
It is done by fixing to 1 (activate) the biggest value of the solution, and adapt
the boundaries according to the characteristics of this point. For example if it
corresponds to a spin cycle all the other points for this cycle are set to 0. This
iterative optimization procedure is repeated until an integer solution is obtained.
Figure 4.2 presents a overview of the optimization process, the complete code
as well as the constraint construction is included in Annexes. In summary, a linear
optimization based in Dual-simplex method is conducted for minimize the price of
the energy that the user pays. Based on that solution several nonlinear gradient
search optimizations, find the closest activation schedule to the cost optimization,
which makes minimum the power losses on the system. It is important to note
that while the optimal solution for cost is a global minimum, the result from losses
optimization may not be. This is because a nonlinear function is not necessarily
convex, and consequently the solution point can be a local minimum.
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4.5. Optimization results
LOAD WASHING
LIMITS AND INITIAL
TEMPERATURE
Boundaries &
Constraints
definition
COST
OPTIMIZATION
(bintprog)
Construction of
initial point
Iterative
Optimization
LOSS ENERGY
OPTIMIZATON
(fmincon)
Optimization
finished
Adaptation of
boundaries
NO
Fix the maximun
value
YES
COST
COMPARATION
PRINT RESULTS
Figure 4.2: Flow Chart general algorithm
4.5
Optimization results
This section presents the results of the optimization process explained in Figure
4.2. The specific study place has been described in 2.3, as well as the power profile
and the transmission lines characteristics, which are necessaries to compute the
power losses in equation 4.7. The use pattern of the washing machine is deduced
in Figure 3.7. The behavior of the refrigerator has led in two different scenarios of
maximum temperature (8◦ C and 10.5◦ C) described in 3.2.
Finally the price evolution of the spot market from 8:00 to 23:00 is shown in
figure 4.3.
Table 4.1 shows the time interval where the washing machine can be used, as
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4.5. Optimization results
Energy Price [DKK/kWh]
0,7
0,6
0,5
0,4
0,3
0,2
Figure 4.3: Spot Market price for electricity
well as the total duration of this interval. The initial temperature for each house is
also included. Finally, the optimal schedule times for each washing cycle is shown.
The results are for the Scenario 1, however the schedule for Scenario 2 is similar,
except in four houses, where the variations are less than 30 minutes, and it is not
shown.
House
Start
INPUTS
Finish
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
9:20
11:00
12:10
15:10
8:10
13:30
9:20
9:50
16:10
18:00
11:50
18:00
18:00
17:40
18:00
16:00
11:50
12:20
18:40
20:30
Duration
2:30
7:00
5:50
2:30
9:50
2:30
2:30
2:30
2:30
2:30
Initial
temperature
3
5.5
8
3
5.5
8
3
5.5
8
3
5.5
8
3
5.5
8
Wash
OUTPUTS
Rinse
Spin
10:00
15:20
15:10
15:10
15:10
14:10
15:10
10:40
16:10
18:00
10:40
16:10
15:40
15:40
15:40
14:40
15:40
11:10
16:40
19:10
11:30
17:00
17:00
16:30
16:40
15:40
16:30
12:00
17:30
20:10
Table 4.1: Optimization inputs and washing time results (Scenario 1)
Figure 4.4 presents a comparison of the refrigerator temperature of house 1,
for the three cases. In this case the solution for the Scenario 2 never decreases to
3 ◦ C, it is a good example about how the optimization algorithm maintains the
temperature in the range between 3 and 10.5 ◦ C. However, the optimal activation
to decrease cost and energy losses results in frequent activations of small duration
during peak hours, which keeps the temperature between around 6 and 8 ◦ C, but
still inside the temperature range for Sceanrio 2.
32/45
4.5. Optimization results
12
Temperature [⁰C]
10
8
Original
6
Scenario 1
4
Scenario 2
2
0
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
Time [Hour]
Figure 4.4: Temperature in refrigerator of house 1 for the three scenarios
As seen in table 4.1 above, the new washing times have been placed in the
cheapest periods of energy price in Figure 4.3. The total prices for each house,
before (Original) and after the optimization for scenarios 1 and 2, are shown in
Figure 4.5.
0,7
0,8
0,6
Price [DKK]
0,7
Price [DKK]
0,6
0,5
0,5
Original
0,4
Scenario 1
0,3
Scenario 2 Original
0,4
0,2
Scenario 1
0,3
0,1
Scenario 2
0,2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
House
0,1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
House
Figure 4.5: Prices per house for each Scenario
For the Scenario 1 the total price reduction is 3.9%, while for Scenario 2 the
reduction is of 6.0%. The annual amount of money saved is 116.67 DKK and
177.23 DKK respectively. However, it is important to remark that the real amount
is bigger than the current, since the simulation is conducted from 8:00 to 24:00,
and a 24 hours simulation will result in a higher amount of money saved, since 8
hours more will be computed. Besides, that result is based in the spot market price,
while the price for the final user is higher. As conclusion the algorithm presented
conducts a successful minimization of the price paid for the final user. As expected
the scenario 2 presents a profitable result. Figure 4.6 summarizes this results.
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4.5. Optimization results
Total price reduction
0,8
100%
0,7
98%
0,6
2954 DKK
94%
2837 DKK
92%
90%
Original
Scenario 1
Price [DKK]
96%
0,5
0,4
2776 DKK
0,3
0,2 Scenario 2
Figure 4.6: Annual prices for each scenario
Despite the fact that the total amount of the price reduction is not very significant, the investment required to implement the optimal control will not be that
much in the future. This is due to the fact that the houses will be equipped with
smart meters and some smart flexible devices in the future. Furthermore according
to [38] demand response is one of the main drivers for introduction of smart meters
in Denmark. However, demand response itself is not economically profitable.
34/45
Chapter
5
Modeling
This chapter provides a description of the topology and modeling of the network
in DIgSILENT Power Factory. The model is used to obtain the necessary data
to implement the power loss function as well as to compare the results after the
optimal management with the original case.
5.1
System description
The test system is based on Section 2.3. The external grid supplies the energy
necessary for the households. The control is based in a DLC (direct load control)
model of flexible loads. Hence two different load elements represent each household.
A fix load represents the normal power profile, while a variable load implements
the optimal consumption of washing machine and refrigerator. Figure 5.1 shows
the DIgSILENT implementation.
The values included in the model are the result from a power flow simulation,
conducted with average power consumption values, in order to obtain V and δ for
each bus (section 4.3).
5.2
Implementation of optimal results
The optimal control calculated in Chapter 4 has been implemented in the model.
Figure 5.2 presents a comparative of the total active power, supplied by the main
grid, for each scenario. The resultant curve for both scenarios, 1 and 2, shows
how the optimal control of the appliances leads in a flatten curve than the original.
Moreover, the peaks have been reduced or avoided.
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5.2. Implementation of optimal results
Modeling
External Grid
0,02 MW
-0,00 ..
1,00
10,5000
1,0000
0,0000
GridTerminal 10.5 kV
0,02
-0,00
4,05
Transformer
-0,02
0,00
4,05
Terminal 0
0,4200
1,0000
-0,0696
0,02
-0,00
7,92
Line (1)
Line (2)
-0,02
0,00
7,92
0,01
-0,00
4,83
-0,01
0,00
4,83
Terminal 2
Terminal 1
0,4198
0,9995
-0,0824
0,00
-0,00
0,92
0,00
-0,00
0,89
0,00
-0,00
0,69
Line H2
0,00
-0,00
0,66
Line H4
-0,00
0,00
0,89
M5
0,4198
0,9994
-0,0840
House 2
-0,00
0,00
0,92
0,00
-0,00
House 1
0,00
-0,00
0,93
0,00
-0,00
0,19
0,00
-0,00
0,4198
0,9995
-0,0830
0,00
-0,00
Flex App 2
Line H3
House 4
Line H5
0,00
-0,00
0,00
-0,00
0,00
-0,00
Flex App 1
House 3
0,4195
0,9989
-0,0978
0,00
-0,00
House 6
-0,00
0,00
0,54
M8
0,4198
0,9995
-0,0829
Line H8
-0,00
0,00
0,62
Line H7
0,00
-0,00
0,00
-0,00
Flex App 6
House 8
-0,00
0,00
0,19
M1
0,00
-0,00
M4
0,4195
0,9989
-0,0969
0,00
-0,00
Flex App 3
House 5
0,00
-0,00
0,00
-0,00
Flex App 5
House 7
0,4196
0,9990
-0,0963
0,00
-0,00
Flex App 7
Line (3)
Line (4)
-0,01
0,00
2,59
0,00
-0,00
1,21
-0,00
0,00
1,21
Terminal 3
0,4194
0,9985
-0,1090
Terminal 4
0,00
-0,00
0,19
0,00
-0,00
0,64
0,00
-0,00
0,16
Line H10
0,4192
0,9981
-0,1181
0,00
-0,00
0,42
0,00
-0,00
-0,00
0,00
0,42
0,4193
0,9984
-0,1099
0,4193
0,9984
-0,1099
House 10
House 9
0,4194
0,9985
-0,1091
0,00
-0,00
Line H11
E3
-0,00
0,00
0,19
E1
0,00
-0,00
0,00
-0,00
0,00
-0,00
0,47
0,00
-0,00
0,30
Flex App 10
0,00
-0,00
0,00
-0,00
Flex App 9
House 11
-0,00
0,00
0,16
0,4193
0,9985
-0,1092
-0,00
0,00
0,30
Line H13
E4
T 10
0,00
-0,00
0,00
-0,00
House 12 Flex App 12
E5
0,00
-0,00
0,00
-0,00
Flex App 11
House 13
-0,00
0,00
0,47
0,4192
0,9980
-0,1196
0,4192
0,9981
-0,1185
House 14
Line H15
0,00
-0,00
Flex App 14
0,00
-0,00
0,00
-0,00
Flex App 13
House 15
Figure 5.1: Grid modeled in DigSilent
36/45
0,00
-0,00
0,47
Line H14
Line H12
-0,00
0,00
0,64
E2
Line H9
M6
M2
Flex App 4
-0,00
0,00
0,69
0,00
-0,00
0,62
Line H6
-0,00
0,00
0,93
M 10
M3
0,4198
0,9994
-0,0838
0,00
-0,00
0,54
0,01
-0,00
2,59
-0,00
0,00
0,66
Line H1
0,00
-0,00
0,4196
0,9990
-0,0962
-0,00
0,00
0,47
T 12
0,4192
0,9981
-0,1186
0,00
-0,00
Flex App 1..
0,4196
0,9989
-0,0968
0,00
-0,00
Flex App 8
Modeling
5.2. Implementation of optimal results
60
Scenario 2
50
Original
Scenario 1
Power [kW]
40
30
20
10
0
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
Time [hours]
Figure 5.2: Power profile of the system for each scenario
As expected, a better performance on the power profile results in less voltage
droops. Figures 5.3 and 5.4 shows the voltage in pu for the houses nearest and the
furthest from the transformer respectively, houses 3 and 13.
1,0000
Original
Scenario 1
0,9995
Voltage [pu]
Scenario 2
0,9990
0,9985
0,9980
0,9975
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 00:00
Time [hours]
Figure 5.3: Voltage in house 3
37/45
0:00
5.3. Energy Losses
1
Voltage [pu]
0,998
0,996
0,994
Original
Scenario 1
0,992
Scenario 2
0,99
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 00:00
Time [hours]
Figure 5.4: Voltage in house 13
5.3
Energy Losses
The power loss profiles from DIgSILENT is shown in Figure 5.5, for each scenario.
The energy losses for each case, and the percent of reduction respect the original
case, are summarized in table 5.1. Again, it is important to remark that this values
of energy losses only represent the period between 8:00 to 0:00, and consequently,
the daily value should be greater.
0,3
Scenario 2
0,25
Original
Scenario 1
Power [kW]
0,2
0,15
0,1
0,05
0
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
Time [hours]
Figure 5.5: Power loss in the network
Table 5.1: Energy Losses for each scenario
Case
Enegy Losses [KWh]
Reduction
Original
0.4524
0%
Scenario 1
0.4323
4.45%
Scenario 2
0.4088
9.65%
38/45
20:00
21:00
22:00
23:00
0:00
5.3. Energy Losses
The simulation results show that the method proposed is able to decrease the
energy losses for both scenarios.
39/45
5.3. Energy Losses
40/45
Chapter
6
Conclusion and future work
The objective of this project was to develop an intelligent management system for
residential loads. The project includes the study of residential loads, use pattern,
optimization and modeling.
The distribution of residential electricity energy consumption in different loads
have been studied, and the most convenient appliances to implement a DSM have
been presented. A way to convert washing machine and refrigerator in flexible
loads, has been developed. Two different methods have been proposed: so that the
user experience does not change and increasing the temperature of the refrigerator
during some periods.
An optimization was conducted to find the best operation for the washing machine and refrigerator. The operation results show the benefits of the DSM. The
price that the user pays for the electrical energy and in the energy losses in the distribution system have been properly reduced. The results of the simulations show
that the energy quality, measured by the voltage drop, experiment a significant
improvement.
As future work this report recommends, to investigate the control of other
appliances. A real time control for the refrigerator based on frequency variations
could be studied. Finally a longer simulation period will lead on a more accurate
result.
41/45
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