Masterexamen med huvudområdet elektronik Master of Science with a major in Electronics
Modeling and Simulation of Solar Energy Harvesting Systems with Artificial Neural Networks
Florian Gebben
MID SWEDEN UNIVERSITY Department of Electronics Design (EKS)
Examiner: Bengt Oelmann, bengt.oelmann@miun.se Supervisor:Sebastian Bader, sebastian.bader@miun.se Author:Florian Gebben, florian.gebben@gmail.com Degree programme: Master of Science
Main field of study:Electronics Semester, year: Spring 2016
Simulations are a good method for the verification of the correct operation of solar- powered sensor nodes over the desired lifetime. They do, however, require accurate models to capture the influences of the loads and solar energy harvesting system.
Artificial neural networks promise a simplification and acceleration of the modeling process in comparison to state-of-the-art modeling methods. This work focuses on the influence of the modeling process’s different configurations on the accuracy of the model. It was found that certain parameters, such as the network’s number of neurons and layers, heavily influence the outcome, and that these factors need to be determined individually for each modeled harvesting system. But having found a good configuration for the neural network, the model can predict the supercapacitor’s charge depending on the solar current fairly accurately. This is also true in comparison to the reference models in this work. Nonetheless, the results also show a crucial need for improvements regarding the acquisition and composition of the neural network’s training set.
Abstract iii
List of Figures vii
List of Tables ix
Acronyms xi
1 Introduction 1
1.1 Background and problem motivation . . . 1
1.2 Overall aim . . . 2
1.3 Problem statement . . . 2
1.4 Thesis outline . . . 3
2 Theory 5 2.1 Wireless sensor networks . . . 5
2.2 Energy harvesting . . . 5
2.2.1 Solar panel . . . 6
2.2.2 Harvesting circuit . . . 7
2.2.3 Energy storage . . . 8
2.3 Modeling techniques . . . 9
2.3.1 Equivalent circuit modeling . . . 10
2.3.2 Artificial neural networks . . . 11
3 Methodology 15 3.1 Artificial neural network model . . . 18
3.2 Reference models . . . 20
3.3 Discharge models . . . 20
3.4 Performance determination . . . 20
4 Representation of the Solar Energy Harvesting Systems 23 4.1 Solar harvesting design . . . 23
4.1.1 Load emulation . . . 24
Contents
4.1.2 On-board monitoring . . . 25
4.2 Deployment . . . 25
4.3 Real-world data set . . . 26
5 Synthetic Data Set Generation 29 5.1 Setup . . . 29
5.2 Data sets . . . 30
5.3 Limitations . . . 31
6 Artificial Neural Network Model 37 6.1 Implementation . . . 37
6.2 Discharge model . . . 38
6.3 Results . . . 40
6.3.1 Comparing different architectures . . . 40
6.3.2 Varying the sampling interval . . . 42
6.3.3 Varying the input currents in the training set . . . 43
6.3.4 Correlation between evaluation and simulation error . . . 45
6.3.5 Normalized vs. unnormalized data . . . 47
6.3.6 Best models . . . 48
7 Reference Models 53 7.1 Equivalent circuit . . . 53
7.1.1 Implementation . . . 53
7.1.2 Results . . . 56
7.2 Lookup table . . . 59
7.2.1 Implementation . . . 59
7.2.2 Discharge model . . . 60
7.2.3 Results . . . 60
8 Discussion 63
9 Conclusion 65
Bibliography 67
A Schematics 71
vi
2.1 Typical structure of a solar energy harvesting system . . . 6
2.2 Cross section of a solar cell . . . 7
2.3 IV-curve of a solar panel . . . 8
2.4 Single-diode equivalent circuit of a solar cell . . . 10
2.5 Equivalent circuit of a boost converter . . . 10
2.6 Equivalent circuit of a supercapacitor . . . 11
2.7 Structure of a neuron in an artificial neural network . . . 12
2.8 Structure of an artificial neural network . . . 12
3.1 Modeling concept . . . 15
3.2 Modeling and simulation workflow for data-driven modeling methods 17 3.3 ANN modeling workflow . . . 19
3.4 Discharge curves . . . 21
3.5 Harmonizing different sampling intervals . . . 22
4.1 Real-world deployment of the solar energy harvesting systems . . . 25
4.2 Simulation data BQ25504 . . . 27
4.3 Simulation data LTC3129 . . . 28
5.1 Setup to generate ANN training data . . . 29
5.2 Synthetic training sets . . . 32
5.3 Real-world data distribution . . . 33
5.4 BQ25504 evaluation sets . . . 34
5.5 LTC3129 evaluation sets . . . 35
6.1 Structure of an artificial neural network in MATLAB . . . 37
6.2 Comparison between models with and without low-current filter . . . . 39
6.3 BQ25505 performance diagram for different ANN architectures . . . 40
6.4 LTC3129 performance diagram for different ANN architectures . . . 41
6.5 BQ25504 performance diagram for different sampling intervals . . . 42
6.6 LTC3129 performance diagram for different sampling intervals . . . 43
6.7 BQ25504 performance diagram for different numbers of charging cycles in the training set . . . 44
List of Figures
6.8 LTC3129 performance diagram for different numbers of charging
cycles in the training set . . . 45
6.9 Relationship between evaluation and simulation performance . . . . 46
6.10 BQ25505 modeling duration . . . 47
6.11 BQ25505 modeling performance . . . 47
6.12 Simulation with the best performing BQ25504 model . . . 49
6.13 Simulation with the best performing LTC3129 model . . . 50
6.14 Zoom in on the discharge behavior to show the influence of the low-current filter . . . 51
7.1 Equivalent circuit model . . . 53
7.2 Equivalent circuit: Harvesting IC . . . 54
7.3 Equivalent circuit: Supercapacitor . . . 55
7.4 Equivalent circuit: Boost-converter . . . 55
7.5 Equivalent circuit: Load . . . 56
7.6 Equivalent circuit simulation BQ25504 . . . 57
7.7 Equivalent circuit simulation LTC3129 . . . 58
7.8 Lookup table model . . . 59
7.9 Lookup table simulation BQ25504 . . . 61
7.10 Lookup table simulation LTC3129 . . . 62
viii
2.1 Power densities of harvesting technologies . . . 6
2.2 Comparison between a supercapacitor and a Li-Ion battery . . . 9
4.1 Configurations of the solar harvesting systems . . . 24
6.1 MATLAB training settings . . . 38
6.2 Configurations of best performing ANN models . . . 48
7.1 Excerpt from the BQ25504 lookup table . . . 60
8.1 Comparison of different modeling techniques (BQ25504) . . . 64
8.2 Comparison of different modeling techniques (LTC3129) . . . 64
ANN Artificial Neural Network
EDLC Electric Double-Layer Capacitor IC Integrated Circuit
Li-Ion Lithium-Ion
MOSFET Metal-Oxide-Semiconductor Field-Effect Transistor MPPT Maximum Power Point Tracking
MAE Mean Absolute Error MSE Mean Square Error RMSE Root Mean Square Error RNG Random Number Generator SEHS Solar Energy Harvesting System SoC State of Charge
SPICE Simulation Program with Integrated Circuit Emphasis WSN Wireless Sensor Network
1.1 Background and problem motivation
Wireless Sensor Networks (WSNs), which have the ability to sense, compute and send data and signals, help to gather information about their deployment envi- ronment and understand ambient events in order to be able to react to these.
While this is also true for remote and hostile environments, a higher reliability from the system is demanded here as continuous maintenance is more difficult and not desired [1].
In this context a reliable system is able to handle the defined tasks for the desired amount of time without disruption. Disruptions may occur due to an insufficient suitability to the demands regarding environment or tasks, or due to power outages.
As the amount of energy stored in a node is limited and in order to extend the time until such an outage occurs, Solar Energy Harvesting Systems (SEHSs) can be used to scavenge ambient energy to power the system or charge a battery.
For some low-energy systems the harvested energy might be sufficient to ensure a perpetual operation, other more energy-intensive systems deplete their energy resources sooner, which can lead to a power-outage and, thus, a system failure.
In order to be able to prognosticate which system can survive under which con- ditions it is important to model the system and be able to simulate its behavior under the given conditions. Many state-of-the-art modeling methods strive to de- scribe each of the system’s components as accurately as possible to obtain the full model by a combination of submodels [2]. This approach is logical as the model’s structure will follow the structure of the physical system. For simple harvesting architectures this relatively quick and straight-forward approach is sufficient and likely the most efficient modeling method.
However, many harvesting system incorporate more complex components, such as specialized Integrated Circuits (ICs), that help to increase the efficiency. These components demand either a simplification of their behavioral description or a
1 Introduction
higher modeling effort. Therefore, other modeling approaches that aim to see the system as a unit rather than breaking it down into subcomponents can be useful.
1.2 Overall aim
The aim of this work is to gain insight into how the method of Artificial Neural Networks (ANNs) can be used for the modeling of solar energy harvesting. ANNs have the ability to learn behaviors by inspecting input and output data to identify their relationships and have already been used extensively for different modeling and forecasting tasks (see Chapter 2). Using ANNs promises to speed up the process of developing the model and to give the developer a method that can easily be adapted to different harvesting architectures as there is no need to model the individual components [3].
This work will provide insight on important parameters and steps in the process of generating an accurate and universal ANN-model, as well as determine how this approach compares to other modeling methods.
1.3 Problem statement
The objectives of this research can be described as follows:
First, the influence of training set parameters on the model’s performance and the duration of training and simulation will be identified. Included in these parameters are the sampling interval of the data and the overall amount of data used to train the model. The training set will be generated synthetically in a laboratory in order to obtain it within a short timeframe.
Furthermore, it is necessary to identify, which ANN-architecture is the most suit- able with respect to good simulation results and whether or not this can be gen- eralized. Two main characteristics define the architecture: the number of hidden layers and the number of neurons in each layer (see Section 2.3.2).
In order to contextualize the results from the ANN-modeling, it will be compared to two reference models: another data-driven model (a lookup table) and an equiv- alent circuit model, which is the state-of-the-art technique for electronic systems.
The comparisons will include the aspects accuracy, modeling effort, and simulation duration.
2
1.4 Thesis outline
The thesis is organized into nine chapters as follows:
• Chapter 1 defines the problem that this work addresses.
• Chapter 2 provides necessary background information along with examples of modeling methods and their implementation in the literature.
• Chapter 3 deals with the methods and the workflow of this work.
• Chapter 4 introduces the solar energy harvesting systems that have been used in this work.
• Chapter 5 covers the acquisition of a synthetic data set.
• Chapter 6 addresses the modeling of the solar energy harvesting systems using artificial neural networks.
• Chapter 7 describes the implementation and results of two reference modeling methods.
• Chapter 8 discusses the results of the three different modeling methods.
• Chapter 9 closes the thesis by summarizing the findings and suggesting fur- ther actions.
2.1 Wireless sensor networks
The term WSN describes a collection of interconnected embedded sensing devices, so-called nodes, which measure ambient values, such as temperature, humidity and vibration, and transfer these values to other members of the network. In many cases, these tasks only take a small percentage of the total run time. In the meanwhile, the nodes are usually in sleep mode to preserve energy. The relation between the active time tact and the total period T (active + sleep mode) is called duty cycle (see Equation 2.1).
D= tact
T ∗100 % (2.1)
Wireless Sensor Networks increase in popularity due to their potential in a wide range of applications, such as environmental [4] and industrial monitoring [5], motion tracking [6] and health care [7]. Another reason for this trend can be seen in recent technological advances, resulting in decreased costs and component sizes and, thereby, increased usability and profitability.
2.2 Energy harvesting
The lifetime of individual nodes in a WSN has a substantial influence on the reliability and robustness of the network as a whole. Depending on its topology, a single node’s failure may jeopardize the functionality of the entire network.
In order to prevent this from happening, it has to be ensured that each node reaches at least its projected lifetime. This can be done by maintaining the system regularly, which involves charging or changing the battery, but this often contra- dicts the reason for using WSNs: the “deploy-and-forget” principle. In order to decrease the need for maintenance and prolong the lifetime of nodes, a number of
2 Theory
actions can be taken. Energy efficient components with low power consumption and different energy modes are beneficial on the node-level, while on the network- level the implementation of energy aware routing protocols will ensure an even distribution of the communication workload and a low energy overhead [8]. How- ever, these measures will only prolong the lifetime of the nodes, but not prevent the node from ultimately running out of energy. The only way to do this is by incorporating an energy harvesting system.
Energy harvesting systems convert energy from ambient sources into electrical energy, which is made available to the sensor node. Common energy harvesting methods and their power densities are listed in Table 2.1. The table shows that among the listed harvesting technologies, solar energy harvesting offers the highest energy density. Furthermore, solar energy is largely predictable [9], which can increase the reliability of the SEHS. These advantages make solar energy the main source for harvesting ambient energy for WSNs.
Table 2.1: Power densities of harvesting technologies [10]
Harvesting technology Power density Solar cells (outdoors at noon) 15 mW cm−2 Piezoelectric (shoe inserts) 330 µW cm−2 Vibration (small microwave oven) 116 µW cm−3 Thermoelectric (10◦C gradient) 40 µW cm−3 Acoustic noise (100 dB) 960 nW cm−3
Figure 2.1 shows a typical structure of a SEHS that supplies a node in a WSN. In the following the individual components are explained.
Solar energy harvesting system
Solar panel Harvesting circuit
Energy
storage DC/DC MCU
Sensor
Wireless transceiver
Wireless sensor node
Solar radiation
Figure 2.1: Typical structure of a solar energy harvesting system
2.2.1 Solar panel
While other components in an SEHS may be optional, a solar panel is indispens- able. It is responsible for converting the solar energy from the sun into electrical
6
energy. This is a result of the photoelectric effect, which frees electron-hole pairs with the help of the photonic energy of the solar radiation (see Figure 2.2). One solar panel incorporates multiple solar cells. The number of parallel and serial con- nected solar cells defines the rated output voltage and power of the solar panel.
Figure 2.2: Cross section of a solar cell1
2.2.2 Harvesting circuit
The harvesting circuit is responsible for passing the electrical energy to the storage or load of the system. In the simplest case, the harvesting circuit is a diode between solar panel and energy storage to prevent discharge of the energy storage in times the voltage across the solar panel is lower. But this system is only applicable, if a supercapacitor is used as storage and if the nominal voltages of solar panel and supercapacitor match. In other cases, there could be undesirable effects, such as a low energy efficiency and destroyed components.
In such cases, a DC/DC converter is necessary to match the voltage to the nom- inal voltage of the energy storage. Furthermore, certain batteries like Li-Ion bat- teries need a protection circuit to ensure a safe charge and discharge process. A method that is often used to improve efficiency of the energy harvesting process is Maximum Power Point Tracking (MPPT).
The goal of MPPT is, as the term implies, to find the point in the IV-curve of the solar panel, at which the power extraction is the highest (see Figure 2.3). There are various techniques of different complexity and accuracy available. An evaluation of the main MPPT techniques can be found in [11].
1https://www.redarc.com.au/how-do-solar-panels-work
2 Theory
0 V
MP V
OC
Voltage 0
PMAX
IMP
ISC
Current, Power
IV-curve of a solar cell
Figure 2.3: IV-curve of a solar panel
2.2.3 Energy storage
In order to save the harvested electrical energy an energy storage has to be used.
There are only a few applications that make no use of any energy storage. These so-called harvest-use systems consume the generated power directly [12].
Most systems, however, make use of the harvest-use-store architecture. Systems with such an architecture store energy that exceeds the demanded energy for the usage in times, when the harvested energy is lower than the energy demand.
The most common energy storages in SEHS and energy harvesting in general are Electric Double-Layer Capacitors (EDLCs), also known as supercapacitors, and batteries like the Lithium-Ion (Li-Ion) battery. Table 2.2 shows a comparison between these two components.
The table illustrates why supercapacitors are so popular in SEHS. Their high cycle life allows them to be undergo an extensive number of charge and discharge cycles without losing their function. This is important as these cycles occur on a daily basis and an energy storage losing its functionality results in a decreased system reliability and an increased demand for maintenance. Furthermore, EDLCs can
8
Table 2.2: Comparison between a supercapacitor and a Li-ion battery [13]
Category Li-Ion battery Supercapacitor
Manufacturer Emmerich Samwha
Model ICR-18650 NQ-JI28 GreenCap DS
Nominal voltage [V] 3.7 2.7
Operational range [V] 3.0 to 4.2 0 to 2.7 Temperature range [◦C]
charge 0 to 45 −40 to 60
discharge −20 to 60 −40 to 60
Typical capacity 2600 mA h 50 F
Internal resistance [mΩ] 150 15
Cycle life 300 500,000
operate in a higher temperature range and need a less complex circuitry, while allowing a quicker discharge due to their higher specific power.
Li-Ion batteries, however, provide a longer run-time for medium loads, as they outperform EDLCs in terms of energy density. Besides, they have a relatively stable output voltage throughout the operational range, whereas the voltage of the supercapacitor is linear to the state-of-charge.
2.3 Modeling techniques
Modeling can be described as the “representation, often mathematical, of a process, concept, or operation of a system, often implemented by a computer program”.2 Modeling is an important step in the development of an electronic system as it helps the developer to make sure that the designed system operates as desired and meets the necessary requirements. There can be several models that describe the same system, each of which is designed to represent a certain behavior of the system. When thinking of modeling a car, it is possible to have separate models to simulate the car’s aerodynamic behavior and its motion.
There are several methods to model a system. Which method is chosen largely depends on the system and which behavior of the system one is interested in.
In the following, two methods including examples of how they are used in the modeling of SEHS are presented.
2http://www.dictionary.com/browse/modeling
2 Theory
2.3.1 Equivalent circuit modeling
An equivalent circuit is the theoretical representation of an electronic circuit that contains all relevant electrical characteristics of the real circuit. Figures 2.4, 2.5, and 2.6 show exemplary equivalent circuits for a few components in an SEHS: solar panel, boost-converter, and supercapacitor.
In [14], the authors show that a single-diode equivalent circuit (compare Figure 2.4) can model a solar panel with good accuracy. Equivalent circuit models of power converters, among others buck and boost converters like the one shown in Fig- ure 2.5, are presented in [15]. EDLC models have been in the focus of [16]. The authors do not only use the simple model shown in Figure 2.6, but also more complex models and their utilization for a range of components.
D RSH
RS
Iph V
ID ISH
Figure 2.4: Single-diode equivalent circuit of a solar cell
D
RL
VS
IC
C L
S
VO
Figure 2.5: Equivalent circuit of a boost converter
Various tools can be used to implement an equivalent circuit. One is to use the circuit simulator Simulation Program with Integrated Circuit Emphasis (SPICE) or one of its adaptions, like PSPICE. Also several IC manufacturers have developed their own SPICE-based tools (e.g. TINA by Texas Instruments or LTspice by Linear Technology). The advantage of these tools is that often accurate component models are provided by the manufacturer. Mathwork’s Simscape Power Systems is another tool that offers component libraries. It provides, for example, a generic EDLC model3 that includes basic parameters such as the serial resistance and serial and parallel capacitance but also allows more complex settings.
3http://mathworks.com/help/physmod/sps/examples/supercapacitor-model.html
10
ESR ISC
C0 RP
IC0
ILe ak
Figure 2.6: Equivalent circuit of a supercapacitor
Another modeling alternative is converting the equivalent circuit into a math- ematical model. Therefore, equations need to be extracted from the equivalent circuit. Next, the model can be implemented in MATLAB Simulink. [17] presents the implementation of the single-diode model for a solar panel as a mathematical model in MATLAB Simulink, which was also the tool of choice for implement- ing the converter models in [15]. Here, the authors point out the low simulation time, something that was also mentioned in [18]. The latter study models a bat- tery/supercapacitor hybrid energy storage in Simulink.
Which of these tools one chooses largely depends on the goal of the simulation.
SPICE and Simscape Power Systems are exceptional for detailed transient analysis, whereas the mathematical models can often offer a lower simulation time.
2.3.2 Artificial neural networks
ANNs are a subdiscipline of machine learning and as such belong to the family of artificial intelligence. The concept is derived from the biological neural network, which is a network of computational cells, so-called neurons. These neurons process signals coming form their inputs (dendrites) to send a new signal over their outputs (axons) to other neurons.
Figure 2.7 shows the structure of a neuron in an ANN. A possible limitless number of signals is weighted individually and added up along with a bias value, before a transfer function defines the neuron’s output. The neuron’s output can be calcu-
2 Theory
∑
w1
w2
w3
wn
f(s)
i1
i2
i3
in
b
s o
Activation function
Figure 2.7: Structure of a neuron in an artificial neural network
lated as follows:
output= f(Xn
i=1
(wn∗ in) + b) (2.2)
A network of such neurons forms an ANN. The example network in Figure 2.8 has one input layer with two inputs and one output layer with one output. The number of neurons in these layers corresponds to the number of inputs and outputs.
Furthermore, there are two hidden layers. Each hidden layer contains a certain number of parallel neurons. The possible number of hidden layers and their neurons is indefinite.
Hidden layers Output layer Input layer
Input 1
Input 2
Output
Figure 2.8: Structure of an artificial neural network
Just like the biological neural network, ANNs possess the ability to learn. That means that the weights and biases of each neuron can be set individually in order to produce a certain network behavior. The process of updating the weights and biases is called training.
Necessary for the training is a training set. This is a set of data that contains all the information that the network is supposed to learn. This data is presented to a learning algorithm, which uses this data to continuously update the weights and
12
biases in an optimization procedure.
Artificial Neural Networks can be used to carry out various tasks. Their ability to solve classification problems can be used in the medical sector to aid in the diag- nosis of breast cancer [19, 20]. Another application area for ANNs is the modeling of systems in order to understand their behavior or forecast events. [21] reviews 51 hydrological ANN-models and comes to the conclusion that this method is well suited for that field, but standardization is needed to increase its feasibility. Also stock market behavior has been suggested to be modeled through ANNs with an accuracy that is similar to more complex methods [22].
ANNs have also been used in the modeling of components in a Solar Energy Har- vesting System. [23] presents the modeling of the specific capacitance of a newly- developed Neem-based supercapacitor using an ANN. Their results are promising and the authors suggest to increase the amount of model inputs in order to sta- bilize its performance. In [24] the authors use ann ANN-based model of a solar cell to predict the parameters of an equivalent circuit based on temperature and solar irradiance. The results show that the ANN-aided model outperforms the conventional model in the prediction of the solar panel’s power-voltage-curves.
Also electrical energy storages have been in the focus of research: An ANN com- bined with an extended Kalman filter was used in [25] for modeling Lithium- Ion batteries and estimating the state-of-charge. The authors of [26] show that ANN-models can predict the State of Charge (SoC) of batteries and battery- supercapacitor hybrids with good accuracy.
In [27] an approach is presented that uses ANNs to model a solar energy harvesting system consisting of a solar panel and a supercapacitor. The results show promis- ing results for the given architecture. However, the authors recommend further studies with different systems and an investigation of the influence of the ANN’s structure.
The general concept of the SEHS-models in this work is shown in Figure 3.1. The models are designed in such a way that they will take the momentary values of input_current and output_voltage as model input to predict the next value of output_voltage, which consequently will be, along with the next input_current- value, the next model input. input_current is the current that flows from the solar panel of the SEHS to the harvesting controller, whereas output_voltage is the voltage across the supercapacitor.
output_voltage(t+1)
Discharge Model Charge Model
output_voltage(t) input_current(t)
Sum
Figure 3.1: Modeling concept
As mentioned in Chapter 1, the training set for the ANN-modeling will be obtained in a laboratory environment. This is due to the fact that the training set needs to include all necessary behaviors of the system that is to be modeled. Obtaining this kind of data set in a real-world deployment is a long and possibly unsuccessful process, as it is possible the data will only reflect the deployment’s environment.
A measuring setup in the laboratory allows controlling the input to the system and thereby the dimensions and form of the training set itself.
However, this approach has a downside. Building an accurate setup for the gen- eration of a data set that shows the relationship between the solar radiation and the supercapacitor’s voltage is either laborious or costly, as a fully-dimmable solar simulator would be required, which is able to replicate the spectrum of the sun exactly. Therefore, we decided to use the current from the solar panel instead of the solar radiation as input to the model.
Figure 3.1 also shows that there are separate models for charge and discharge.
One could think that needing two separate models is a disadvantage, as it seems
3 Methodology
to require more effort to create the individual models. But this additional step has several positive aspects, such as creating the training set for the ANN-model is a lot easier if the focus is on the charging process alone. This is due to the need to show all possible cases to the ANN training algorithm. An ANN is good at interpolating between known data, but is not able to extrapolate beyond that (think of the behavior of a cubic function, which interpolates monotonically decreasing data points, outside the scope of the given data).
Even in the simple case of a solar-powered sensor node with a constant load, which is an unrealistic scenario in a WSN, the amount of time needed to collect the necessary data increases, as the charging process slows down. With an even more complex load, such as a schedule-triggered measurement/communication or, even more demanding, triggered by an external signal (node or event), the number of cases that need to appear in the training set is too high and the effort to obtain the data too great for that data acquisition to still be reasonable.
Furthermore, even if we were able to obtain a complete training set for such con- ditions, this model would only apply to the specific system in question and could not easily be adapted to a slightly different system. This kind of flexibility can only be archived with separate models for charge and discharge.
In this work three different charge models are used, but the main focus lies on the ANN-model, which will be compared against a lookup table model and an equivalent circuit that is implemented as mathematical model. The following steps are necessary in this process:
1. Designing the SEHS 2. Generating artificial data 3. Obtaining real-world data 4. Implementing the ANN-model 5. Implementing the reference models
After designing the two SEHSs and testing their functionality, an experimental setup is built with the goal to generate the synthetic data set, which consists of both training and evaluation set.
Furthermore, both systems will be installed in a real-world deployment to measure input and output along with solar irradiance. This data set will later be used as simulation set to test all models on accuracy.
16
Modeling
Lab-generated data set
(T=1s)
Real-world data set
(T=60s)
Preprocessing &
interpolation Preprocessing &
interpolation
Evaluation
Simulation
Simulation set (T=2s) Evaluation set
(T=2s) Training set
(T=2s)
Figure 3.2: Modeling and simulation workflow for data-driven modeling methods
3 Methodology
3.1 Artificial neural network model
The generation of the ANN-model is done with the help of MATLAB and its Neural Network Network Toolbox. The toolbox provides functions to create, train and evaluate neural networks. Furthermore, it provides a graphical user interface that assists the user in the first steps without requiring detailed knowledge of the algorithm. During the process of implementing custom ANNs, however, usage of lower-level functions is necessary.
Figure 3.2 show the workflow of the ANN modeling. First, the synthetic training set is used to model the data, followed by an evaluation of the model with data that has also been generated synthetically. Finally, the simulation tests the model behavior on real-world data.
The ANN modeling process is a subprocess, which is pictured in Figure 3.3. First, the architecture of a ANN is defined. This includes the inputs and outputs, the number of layers and neurons, as well as the transfer function and the fundamental training setting, such as the training algorithm. After that, the network’s weights and biases are initialized. As the outcome of the training can vary strongly with different initial values, multiple trials are run for the same architecture. This way, we can see how much the results fluctuate.
When MATLAB trains the ANN, the training set is split into three sets: training, validation and testing. This is to avoid overfitting, an effect that occurs if an ANN possesses low generalization and is, thus, unable to accurately predict values outside the training set.1 The training data is used to iteratively update all weights and biases. Meanwhile, the network is validated against the second part of the data and the error is calculated. If this validation performance does not increase five calculations in a row, or if the gradient of the training is below a certain threshold, the training has reached its stop condition. In the following step, the ANN is tested with the third fraction of the training set, the test set, by computing the error.
In order to avoid overfitting it is important that the three sets are not identical, as the calculation results would not be conclusive in that case. In this work, when the term training set is used, it refers to the data, before MATLAB divides it into the three parts.
When MATLAB has run all trials, the models can be evaluated and simulated (see Section 3.4).
1https://de.mathworks.com/help/nnet/ug/improve-neural-network-generalization-and-avoid- overfitting.html
18
Define ANN architecture
Initialize weights & biases
Train the ANN
Calculate & store performance
Restore best- performing ANN
All trials trained?
No
Yes
Figure 3.3: ANN modeling workflow
3 Methodology
3.2 Reference models
Both the modeling by lookup table and the mathematical model is performed in MATLAB Simulink. MATLAB provides extensive functions for matrix calcula- tions, whose result can be used in Simulink blocks to create the lookup table. This combination of tools is very convenient for this modeling.
As for modeling the equivalent circuit, it would be possible to use the SPICE- adaptions LTspice (Linear Technology) and PSICE, as models for the harvesting ICs that we used in this work are provided for theses tools. However, these models need a tremendous amount of simulation time. For instance, the exemplary cir- cuit provided by Texas Instruments uses a 1 µV supercapacitor and is rated with a simulation time of 45 min for the transient simulation only. As the great accu- racy for the IC’s transient behavior is not necessary for this work, we decided to implement the equivalent circuit as mathematical model in MATLAB Simulink.
Before implementing the mathematical model the SEHS’s equivalent circuit will be created. This is followed by the determination of the electrical characteristics, gathered from the components’ data sheets.
3.3 Discharge models
In order to model the discharge behavior of the two systems, a complete discharge curve has been selected from real-world data for each model. The discharge curves can be seen in Figure 3.4.
The implementation of the discharge models depend on the method that has been used for the charge model, as they need to complement each other. The discharge of the ANN model will be represented by a regression, while the lookup table model will use each one lookup table for charge and discharge. The equivalent circuit models the discharge as Simulink blocks, which describe the behavior of the boost-converter and the resistor and which determine the discharge current.
3.4 Performance determination
Performance means the accuracy with which a model is able to predict the output for a given input. In other words, it is the difference between simulation and target values. There are several ways to measure the performance. A few of the most
20
0 500 1000 1500 2000 2500
Sampling intervals [1T=60s]
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Supercapacitor voltage [V]
(a) BQ25504
0 500 1000 1500 2000 2500 3000 3500 4000
Sampling intervals [1T=60s]
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Supercapacitor voltage [V]
Discharge curve LTC3129
(b) LTC3129
Figure 3.4:Discharge curves
common ones are the Mean Absolute Error (MAE), the Mean Square Error (MSE), and the Root Mean Square Error (RMSE).
In this work the RMSE has been used for all performance determinations, both for the evaluation of the ANN-models and the simulation of all models. Its unit is the original unit of the values and compared to the MSE larger errors have a higher influence on the performance (see Formula 3.1).
RM SE =
v u u t1
n
n
X
i=1
(Vtarget(i) − Vsim(i))2 (3.1)
In order to be able to correctly use a model, it is important to harmonize the
3 Methodology
sampling interval (the time between two data points in a time-series of data) of all data streams that are used in the modeling process (see Figure 3.5). In the case of the ANN-model this means that the time distance between two values in the training, evaluation and simulation set must have the same length. The defined sampling interval will always be between the sampling intervals of the artificial and the real-world data set.
In order to do this harmonization, the sampling interval of the training set will be increased by skipping the appropriate number of values, while the sampling interval of the simulation set will be decreased by interpolating between two values.
Defined sampling interval:
Training set:
Simulation set:
T_model T_trainingSet T_simulationSet
Figure 3.5: Harmonizing different sampling intervals
22
Energy Harvesting Systems
4.1 Solar harvesting design
For the purpose of this project two SEHS have been designed. For both systems to be comparable, they fulfill the same function: charging an EDLC with a rated volt- age of 2.7 V and a capacitance of 35 F by harvesting solar energy with a 1 W solar panel with a nominal voltage of 5 V. Therefore, two ICs have been selected that are developed for energy harvesting applications and match these specifications.
Texas Instruments’ BQ255041 is an ultra power DC/DC boost converter with the capability of charging supercapacitors and various kinds of batteries. The same applies to the LTC3129 by Linear Technology.2 Both components include a basic MPPT-functionality. This means that by connecting the appropriate pins to a resistor divider, the chips will control the input voltage to operate with improved efficiency. The BQ25504 also allows for the MPPT to be implemented externally to further improve the efficiency by using a more complex method.
Throughout this work, the model number of the harvesting chip (BQ25504 or LTC3129) will be used to refer to the harvesting board that contains this chip.
1http://www.ti.com/product/BQ25504
2http://www.linear.com/product/LTC3129
4 Representation of the Solar Energy Harvesting Systems
Table 4.1: Configurations of the solar harvesting systems
Module Implementation
Solar panel POW111D2P, 80 mm × 100 mm, 1 W, 5 V Harvesting IC BQ25504 / LTC3129
Energy storage Supercapacitor 2.7 V, 35 F Boost converter TPS61070
Load 137.5 µA constant drain
Monitor LTC2990
The boost-converter TPS61070 by Texas Instruments is used to convert the voltage of the EDLC to a constant voltage of 3.3 V. It operates down to the minimum input voltage of 0.9 V and is rated with an efficiency of 90 %. The output of this boost-converter is the output of the SEHS.
Table 4.1 shows all components of the harvesting board. The complete circuit is shown in Appendix A.
4.1.1 Load emulation
The harvesting board offers a load emulation to test different load scenarios with- out the need to attach a real sensor node. Therefore, three MOSFETs can be switched individually to connect one resistor each to the output of the TPS61070 boost-converter. This way, the user can assign each resistor to emulate a specific task (e.g. sensing, communicating). Additionally, one fixed and non-switchable re- sistor can be installed to mimic a constant load. The latter has been made use of in this project. A resistance of 24 kΩ, which translates to a constant current of 137.5 µA, is slowly discharging the supercapacitor.
This constant load corresponds to a duty cycle of 0.64 % for the example of the commercial wireless measurement system MICAz by Crossbow,3 which is a sys- tem created for embedded sensor networks and which is equipped with an IEEE 802.15.4 transceiver. In this example the active current is defined by the consump- tion of an active microcontroller and the transceiver sending data with a power level of −10 dB m, while in sleep mode both components are set to the lowest possible energy mode.
3http://www.openautomation.net/uploadsproductos/micaz_datasheet.pdf
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Knowing the currents in active mode and sleep mode and assuming that these are constant, the duty cycle can be calculated with Equation 4.2.
Iavg = Iactive∗ tactive+ Isleep∗(T − tactive)
T (4.1)
D= tactive
T = Iaverage− Isleep
Iactive− Isleep (4.2)
4.1.2 On-board monitoring
On the harvesting board the voltages across the solar panel and across the su- percapacitor as well as the input and charge current are monitored. This task is executed by the LTC2990 by Linear Technology.4 This IC is able to measure the values with an accuracy of 1 % and a resolution of 14 bit.
4.2 Deployment
The harvesting board has an interface to the SENTIO-em, a sensor platform de- veloped at Mid Sweden University [28]. Attached to the the sensor platform is an XBee 2.4GHz module that is running an IEEE 802.15.4 communication protocol.
Furthermore, the Pyranometer 6450 Solar Radiation Sensor by Davis Instruments5 is in place to measure the solar radiation.
SENTIO-em (data collection)
Raspberry Pi (data storage)
Remote Computer Currents
Voltages Irradiance Pyranometer
6450
SSH- connection
LTC3129 system
Currents Voltages Irradiance BQ25504
system
Currents Voltages
Figure 4.1:Real-world deployment of the solar energy harvesting systems
4http://cds.linear.com/docs/en/datasheet/2990fd.pdf
5http://www.davisnet.com/product_documents/weather/spec_sheets/6450_SS.pdf
4 Representation of the Solar Energy Harvesting Systems
The ARM Cortex-M3 microcontroller on the SENTIO-em triggers the measure- ments of voltage, current and solar radiation with a sampling rate of 1/60 Hz, that is one measurement every minute. After each measurement the data is sent over the communication interface to a Raspberry Pi, which is responsible of storing all data. The data can be accessed over an SSH-connection by a computer on the same network.
This setup has been placed in a permanent deployment in Sundsvall (Sweden) with the solar panels orthogonal to the ground to prevent them from being covered after snowfall.
4.3 Real-world data set
Figure 4.2 shows segments from the real-world data set obtained using the BQ25504- system. The LTC3129-system collected the data segments shown in Figure 4.3. For each of the systems, two segments (one collected in summer and one in winter), have been chosen to serve as simulation set to determine the performance of each model that is created later in the process (see Chapter 6 and 7).
The Swedish winter is characterized by long periods of darkness, while the sun sets only for a short time in summer. This is why there are two quite different curves for the supercapacitor voltage of each system.
One phenomenon that stands out in the LTC3129 system is that the voltage across the EDLC drops every time the input current rises after the night and when the state of the harvesting system is supposed shift from discharging to charging. This behavior is yet to be investigated.
Remarkable is also that there is little difference in the level of the input current when comparing the summer and winter segments for the LTC3129 system. This is caused by a current regulation within the IC, which will also be mentioned later on in Chapter 5.
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0 0.02 0.04 0.06 0.08 0.1 0.12
Input current [A]
0 0.5 1 1.5 2 2.5 3
Input voltage [V]
BQ25504 Simulation Data - Summer
(a) Summer
0 500 1000 1500 2000 2500 3000
Sampling intervals [T] (1T = 60s) 0
0.02 0.04 0.06 0.08 0.1 0.12
Input current [A]
0 0.5 1 1.5 2 2.5 3
Input voltage [V]
BQ25504 Simulation Data - Winter
(b) Winter
Figure 4.2: Simulation data BQ25504
4 Representation of the Solar Energy Harvesting Systems
0 500 1000 1500 2000 2500 3000
Sampling intervals [T] (1T = 60s) 0
1 2 3 4 5 6 7 8
Input current [A]
#10-3
0 0.5 1 1.5 2 2.5 3
Input voltage [V]
LTC3129 Simulation Data - Summer
(a) Summer
0 500 1000 1500 2000 2500 3000
Sampling intervals [T] (1T = 60s) 0
1 2 3 4 5 6 7 8
Input current [A]
#10-3
0 0.5 1 1.5 2 2.5 3
Input voltage [V]
LTC3129 Simulation Data - Winter
(b) Winter
Figure 4.3: Simulation data LTC3129
28
5.1 Setup
Figure 5.1 shows the experimental setup that was used to obtain the synthetic data set, which will be the basis for the ANN model.
Voltmeter Agilent 34410a MATLAB
Instrument Control
Harvesting Controller Current Source
HM 8143
Amperemeter
Agilent 34410a EDLC
Figure 5.1: Setup to generate ANN training data
Two Agilent 34410a are used to measure the input current and supercapacitor voltage. The Hameg HM8150 Arbitrary Function Generator is connected to both of the multimeters’ external triggers to be able to trigger the measurements with a steady frequency. When measurements are triggered, the Agilent 34410a stores the values into the internal memory, which needs to be read out frequently to avoid memory overflow and data loss. The values are stored with an accuracy of nine digits.
5 Synthetic Data Set Generation
The center of the setup is a computer running MATLAB R2016a that is connected to all devices over USB interfaces. A MATLAB script controls the whole exper- imental setup by configuring the instruments, initiating the process, reading out the memory of multimeters and storing the data.
Starting with a discharged capacitor, the Hameg HM8143 is used as a current source to feed constant currents to the SEHS and, thus, mimic the solar panel.
The input current and voltage across the EDLC are monitored over the complete charging process with a constant sampling interval defined by the user. This process is repeated in 1 mA-steps for the whole range of possible input currents, which is defined by the power rating of the solar panel. This way the whole charging process is captured in a data set consisting of multiple time-series for both input current and output voltage.
This setup does not include any load, apart from the self-discharge of the super- capacitor during the charging process.
5.2 Data sets
The above described setup was used with the SEHSs presented in Chapter 4 to generate two synthetic data sets that will be used as training sets for the ANN- modeling of the two systems. Each data set includes 200 charging cycles, from 1 mA till 200 mA with a step size of 1 mA. The condition for ending one charging cycle has been defined as follows: a linear regression of the past 10 values of the supercapacitor voltage is conducted after each new measurement. If the slope of this regression was less than 1 µV, the MATLAB script stopped the charging cycle, discharged the supercapacitor and initiated the next cycle.
Figure 5.2 shows the two obtained data sets. The first data set (IC: BQ25504) shows a very even distribution of the individual data points between the super- capacitor’s maximum voltage of 2.7 V and the current source’s maximum current of 200 mA. It can also be observed that the low currents of 1 mA and 2 mA are not able to fully charge the supercapacitor before reaching the cycle termination point.
The second system’s data set (IC: LTC3129) is not as evenly distributed as the previously described data set. This is due to the behavior of the charging IC, which limits the input current. The current increases with a rising supercapacitor voltage.
If that voltage exceeds approximately 2.5 V, the input current drops rapidly, until the capacitor is fully charged.
30
Figure 5.3 shows the input current against the supercapacitor voltage (note: the dense part of the data has been thinned out to make the figure more lightweight). It illustrates the idea behind using a synthetic training set: many system states that could occur during the operation do not appear in the real-world data set, which, thereby, might only represent a fraction of the information needed if one strives to create a model that is valid for a broad range of applications and environments.
The evaluation sets can be seen in Figure 5.4 and 5.5. All diagrams show the supercapacitor voltage as a response to the defined input current curves, defined as follows:
1. linear increasing current (5.4a and 5.5a)
2. triangular waveform overlaid with a linear increasing current (5.4b and 5.5b) 3. periodically increasing and decreasing current (5.4c and 5.5c)
These evaluation sets emulate three hypothetical charging scenarios. It becomes clear that the two SEHSs react differently to the same settings of the constant current source, which is because of how the two harvesting ICs work. While it can be observed that the general course of the supercapacitor voltage is similar, the voltage of the LTC3129 system rises faster. Moreover, the LTC3129 harvesting ICs utilizes an input current control, which could cause the current to be reduced throughout the charging and which lets the current drop to a minimum, when the EDLC is fully charged (compare training set in Figure 5.2.
5.3 Limitations
This setup uses a constant current source as a replacement for the solar panel.
However, a current source does not mimic the solar panel’s behavior perfectly, as this is characterized by a unique non-linear IV-curve, which is defined by the open circuit voltage VOC, the short circuit current ISC and a maximum power point PM AX (see Figure 2.3). Using the constant current source together with a charging IC that includes MPPT will make the IC maintain a power point, which is likely to deviate from the solar panel’s maximum power point.
5 Synthetic Data Set Generation
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
0 0.05 0.1 0.15 0.2 0.25
Input current [A]
Training set BQ25504
(a) BQ25505
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
0 0.05 0.1 0.15 0.2 0.25
Input current [A]
Training set LTC3129
(b) LTC3129
Figure 5.2: Synthetic training sets
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0 0.5 1 1.5 2 2.5 3 Supercapacitor voltage [V]
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Input current [A]
BQ25504 real-world data distribution
(a) BQ25505
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Input current [A]
LTC3129 real-world data distribution
(b) LTC3129
Figure 5.3: Real-world data distribution
5 Synthetic Data Set Generation
0 20 40 60 80 100 120 140 160 180 200
Sampling Intervals [T] (1T = 60s) 0
0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
BQ25504 evaluation set 1
(a) Evaluation set 1
0 100 200 300 400 500 600 700
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0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
BQ25504 evaluation set 2
(b) Evaluation set 2
0 100 200 300 400 500 600
Sampling Intervals [T] (1T = 60s) 0
0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
BQ25504 evaluation set 3
(c) Evaluation set 3
Figure 5.4: BQ25504 evaluation sets
34
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0 0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
LTC3129 evaluation set 1
(a) Evaluation set 1
0 100 200 300 400 500 600 700
Sampling Intervals [T] (1T = 60s) 0
0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
LTC3129 evaluation set 2
(b) Evaluation set 2
0 100 200 300 400 500 600
Sampling Intervals [T] (1T = 60s) 0
0.05 0.1 0.15 0.2 0.25
Input Current [A]
0 0.5 1 1.5 2 2.5 3
Supercapacitor voltage [V]
LTC3129 evaluation set 3
(c) Evaluation set 3
Figure 5.5: LTC3129 evaluation sets
6.1 Implementation
Input Input
1 Input Input
1
b W
W
Hidden 1 Hidden 1
10
b W
Output Output
1
Output Output
1
Figure 6.1: Structure of an artificial neural network in MATLAB
Figure 6.1 shows the structure of the ANN that models the charge process. Even though this figure suggests that the output is not fed back to the input, it is.
The feedback has been implemented manually and is, thus, not represented in the structure of the ANN. This was necessary, because the output discharge model has to be taken into account.
The ANN in the figure has a single hidden layer with ten parallel neurons and an output layer. The neurons in both layers are, except for their number, identical.
They all include a weight for each input, a bias input and a transfer function, which is implemented as log-sigmoid transfer function.
This specific transfer function has been chosen because of the data normalization that has been used. The training data, as well as evaluation data and simulation data, is scaled between 0 and 1, where 0 is the lowest and 1 is the highest value of the training set. This promises a faster and possibly more precise training out- come [29]. For this normalization the log-sigmoid transfer function is well-suited as the function’s output range and the normalization’s range match. Thereby, the ANN’s output is automatically limited to this range.
6 Artificial Neural Network Model
Before MATLAB trains an ANN, the weights and biases are set to random values based on the state of the Random Number Generator (RNG). In order to be able to reproduce training sessions, the RNG can be seeded prior to training. Thereby, it is set to a known state, which can be restored at any time. In these experiments, the RNG is always seeded according to the same pattern: the first trial is seeded with the value 1, the second with the value 2 and so forth.
Table 6.1 displays the full list of settings of the training process.
Table 6.1: MATLAB training settings
Category Name MATLAB
Training algorithm Levenberg-Marquardt backpropagation trainlm
Transfer function Log-sigmoid logsig
Ratio train/val/test Interleaved data division divideint
6.2 Discharge model
The discharge model that supplements the ANN model is implemented as a fit- ting curve with a third-degree polynomial function, also know as cubic function (see Equation 6.1). Knowing the current supercapacitor voltage, it is possible to compute the corresponding derivative for that value in the fitted discharge curve.
y= p1∗ x3+ p2∗ x2+ p3∗ x+ p4 (6.1) The outputs of the charge and discharge model are determined simultaneously, with one exception. If the input current is lower than the minimum input cur- rent of the training set, the charge model is not taken into account. The reason is that at times, when the EDLC should clearly discharge, the ANN model regu- larly predicted values that outweigh the influence of the discharge model, which resulted in a never discharging capacitor in the simulation. This behavior is shown in Figure 6.2.
38
0 1 2 3 4 5 6 7 8
Sampling intervals [T] (1T = 5s) #104
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Supercapacitor voltage [V]
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Supercapacitor voltage [V]
BQ25504 simulation without low-current filter
Real data Simulation output
(a) Without low-current filter
0 1 2 3 4 5 6 7 8
Sampling intervals [T] (1T = 5s) #104
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Supercapacitor voltage [V]
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Supercapacitor voltage [V]
BQ25504 simulation with low-current filter
Real data Simulation output
(b) With low-current filter
Figure 6.2:Comparison between models with and without low-current filter
