Bruno Exposto
email: bruno.exposto@algoritmi.uminho.pt

J G Pinto

João L Afonso
email: joao.l.afonso@algoritmi.uminho.pt

Power Outage Detection Methods for the Operation of a Shunt Active Power Filter as Energy Backup System

Keywords: Shunt Active Power Filter, Energy Backup, Power Quality, Power Outage Detection, Kalman Filter

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Smart Grids will become a reality in the future. Efforts are being made to pursue this objective in several countries of the world [START_REF] Platform | SmartGrids -Strategic Deployment Document for Europe's Electricity Networks of the Future[END_REF], [START_REF] Fang | Smart Grid, The New and Improved Power Grid: A Survey[END_REF]. The implementation of this new technology implies massive resources deployment, i.e., it must be implemented, study and regulated different parts that will constitute the smart grid. In the technical point of view, Smart Grids generically will integrate three major systems: infrastructure system, smart management system and smart protection system [START_REF] Fang | Smart Grid, The New and Improved Power Grid: A Survey[END_REF]. This technical global vision, although that can change according with the definition of each one point of view and work scope, provides a framework for what can be studied in the Smart Grid context. In terms of infrastructure it must be studied new ways of delivering energy, with the maximum quality, efficiency, reliability and controllability. To achieve these goals, it must be studied new types of power electronics devices, extend the existing power electronics devices capabilities and inherently study new types of control systems.

To achieve good Power Quality indexes, future Smart Grid probably will have to integrate different Power Quality Conditioners [START_REF] Pinto | Analysis of the Features of a UPQC to Improve Power Quality in Smart Grids[END_REF], [START_REF] Javadi | Series active conditionners for reliable Smart grid: A comprehensive review[END_REF]. Today are available several types of Power Quality Conditioners, namely shunt conditioners [START_REF] Singh | A review of active filters for power quality improvement[END_REF], series condition-ers [START_REF] Javadi | Series active conditionners for reliable Smart grid: A comprehensive review[END_REF], and the integrated approach known as Unified Power Quality Conditioners (UPQC) [START_REF] Javadi | Series active conditionners for reliable Smart grid: A comprehensive review[END_REF], [START_REF] Fujita | The unified power quality conditioner: the integration of series and shunt-active filters[END_REF]. Besides these types of Power Quality Conditioners, exist also in the literature, several references to other devices that have Power Quality compensation capabilities [START_REF] Reddy | Utility-Interactive Hybrid Distributed Generation Scheme With Compensation Feature[END_REF].

Shunt Active Power Filters (SAPFs) are shunt connected with the electrical power grid to compensate current problems. This type of Power Quality Conditioners usually is designed to mitigate the current harmonics, the current unbalances, low power factor and the neutral currents [START_REF] Exposto | Three Phase Four Wire Shunt Active Power Filter from Theory to Industrial Facility Tests[END_REF].

SAPFs are generally constituted by an inverter that can be single-phase or three-phase, voltage-source or current source. There are more defining characteristics that can be applied to the inverters that are used in SAPF, but the focus in this work is three-phase voltage-source inverters [START_REF] Singh | A review of active filters for power quality improvement[END_REF].

In normal grid operation, the SAPF is compensating the load currents, but when a power outage occurs, the load and the SAPF will be disconnected due to lack of energy. If the process that is being executed by the load is critical, the placement of an SAPF upstream of the load will not useful to deal with the situation of a power outage. In this situation will be necessary to deploy backup equipment like Uninterruptible Power Supplies (UPS). If the power line problems are outages, blackouts or losses of the utility line with time bigger than 10 ms, sags or dips, or even short under-voltages with lasting time less than 16 ms or even overvoltages with lasting time inferior to 16 ms, the Off-line UPS can be a good solution [START_REF] Gurrero | Uninterruptible power supply systems provide protection[END_REF]. Considering that the power converters of a three phase offline UPS is very similar to the SAPF hardware, it would be advantageous combine the two functionalities in the same equipment.

Given this, in this paper is proposed a topology of SAPF that combines the functionalities of current compensation, when connected to the power grid, with the UPS functionalities, to feed the loads that are downstream in case of an power outage.

The combination of the two functions can result in a shorter payback time, so this solution has several advantages. This paper presents some preliminary results from a PhD work related with the development of devices to the compensate Power Quality problems. The paper describes the hardware topology of the Shunt Active Power Filter, the control system as well as the energy backup control scheme. Also it describes power outage detection schemes. The behavior of the SAPF with energy backup capability is analyzed, and simulation results are presented.

Relationship to Collective Awareness Systems

Future Smart Grids will have several features: digitalization, flexibility, intelligence, resilience, sustainability, and customization [START_REF] Jiang | A vision of smart transmission grids[END_REF]. Those combined features will allow extending the capabilities of the conventional electrical grids, to levels never thought before. The intelligence of Smart Grids will rely always on data. In fact, to reach collective awareness in a complex system is necessary have large data provided by a network of sensors and devices [START_REF] Pitt | Transforming Big Data into Collective Awareness[END_REF]. The Smart Grid will have these two providers of data associated with the capability of change in a real time the behavior of the devic-es. Given this, the study of methods to obtain information, at the same time that are used devices that have the capability to interact with the grid present several advantages in the future Smart Grids. If we consider that the topology of an off-line UPS has some touching points with the topology of the SAPF, combining the two features will result in a device that is capable of increasing the overall Power Quality at the same time that protects the load of power outages and other aforementioned events.

The collection of data, the increase of Power Quality in the grid and the change of behavior of the devices connected to the grid will be addressed in the PhD work so this is a good contribution to the Smart Grid issue and to the collective awareness systems.

Shunt Active Power Filter with Energy Backup

The topology of the SAPF is composed by a three-phase four wire shunt converter, with three IGBT legs and a split capacitor in the DC-link (Fig. 1). This topology was chosen because enables the compensation of the three-phases plus the neutral, using only six IGBTs. The main disadvantage is the difficulty in the correct regulation of the DC-link voltages i.e. the difficulty in maintain the voltage of the two capacitors (C 1 and C 2 ) equal. The power inverter is connected to the power grid trough three LCR passive output filters to eliminate the switching noise. In the DC-link of the SAPF is connected a reversible DC-DC power converter. This power converter provides an interface with the backup battery pack. When the SAPF is operating in a normal mode, the DC-DC converter charges the battery pack. If a power outage occurs and the energy backup mode is triggered, the DC-DC converter transfers energy from the battery pack to the DC-Link and insures that the voltage in this point is always equal to the predefined reference value. The control of the SAPF is divided in several independent algorithms interacting in an integrated way. To the operation as SAPF, is implemented a control algorithm based in the p-q Theory. Also it was implemented a digital phase locked loop (PLL), that is used in conjunction with the p-q Theory. The detection of the power outage sag or dips is done using a Kalman filter based RMS calculator. The control system is also in charge of the voltage and current control, in both of the operating modes of the SAPF, and the resynchronization after the normal power restoration.

Control System

In the SAPF mode the determination of the compensation currents is done using the p-q theory. This time domain approach has been largely used in SAPFs and Unified Power Quality Conditioners and has the advantages of requiring less processing capability [START_REF] Akagi | Instantaneous power theory and applications to power conditioning[END_REF], [START_REF] Afonso | Active filters with control based on the pq theory[END_REF].

If the grid voltages are distorted, it is not possible generate compensating reference currents that aim to have sinusoidal source currents, because the p-q Theory will generate reference currents that when injected in the grid and in conjunction with the load currents, will ensure constant power at the source. In this case exists a modification of the p-q Theory that instead of constant instantaneous power at source, results in sinusoidal currents at the source, even with distorted power grid voltages. This modification consists in using the positive sequence of the fundamental voltages instead of the real voltages [START_REF] Afonso | Active filters with control based on the pq theory[END_REF], [START_REF] Monteiro | Compensation algorithms based on the pq and CPC theories for switching compensators in micro-grids[END_REF]. To determine the positive sequence of the voltages, in this work was implemented a digital PLL in the α-β reference frame. In sum, the use of the digital PLL in conjunction with the control algorithm based in the p-q Theory results in sinusoidal source currents. In Fig. 2 is showed the implementation of the p-q Theory algorithm. The topology of the inverter composed by a three-phase four wire shunt converter, with three IGBT legs and a split capacitor in the DC-link. In this topology it's necessary that the DC-link capacitors have the same voltage value, or at least an approximated value. To ensure this, is necessary to control these voltages in a separated way. In this work the control of those voltages is done using two (proportional-integral) PI controllers (1). If, for example, v a_pll ≥0 (calculated through the inverse Clark transform of v α_pll and v β_pll ) the top capacitor voltage (V DC_pos ) is regulated using i rega , oth-erwise is the regulated the bottom capacitor voltage (V DC_neg ). This is done for all the three-phases of the SAPF. In ( 2) and ( 3) is possible to see how is done this regulation. Finally, the reference compensation current generated by the p-q Theory algorithm (i cx *) and the regulation current (i rx ) are used to calculate the inverter reference current (3).

∫

- + - = ) ( 1 ) ( _ * _ _ * _ _ x DC x DC i x DC x DC p x reg V V k V V k p (1)        < + + ≥ + + = 0 , 0 , _ 2 _ 2 _ 2 _ _ _ _ 2 _ 2 _ 2 _ _ _ pll x pll c pll b pll a pll x neg reg pll x pll c pll b pll a pll x pos reg rx v v v v v p v v v v v p i ( 2
)
rx cx x ref i i i - = * _ (3)

Outage Detection Methods

In this work, the power outage detectors are responsible for evaluate the RMS values of the grid voltages and determine SAPF operation mode. If the system doesn't detect sag, swell or a power outage, the SAPF will operate in the normal mode compensating the load currents. Otherwise, the SAPF will stop the compensation of the loads and operate n backup mode. The event detection algorithm must be as fast as possible so that the transfer time between normal mode and backup mode be very short. In Moschitta, et al. [START_REF] Moschitta | Performance Comparison of Advanced Techniques for Voltage Dip Detection[END_REF] the authors make a comparison of several sag and power outage detection methods. Their comparison showed that a Kalman filter can be used with success in the detection of sags and power outages decreasing the detection time. The authors propose and discuss other methods but the Kalman filter method has a good performance, is relatively simple to implement and is fast. In this work were implemented three Kalman filters, one per phase. The estimation of the RMS values of the voltages is done using the values obtained in the Kalman filters outputs through the following equation:

2 ] [ ] [ ˆ2 2 n q n s V RMS + = . (4)
Where ] [ ˆn s and ] [ ˆn q are the estimated values, of voltage and its quadrature respectively. Using the RMS values calculated using the Kalman filters the control system monitors the grid voltages continuously, to determine the operating mode of the SAPF. The control system of the SAPF changes its behavior in a situation where exists a sag higher than 20% of the nominal voltage, or a power outage. In this situation is activated the energy backup mode of the SAPF and the current control of the inverter is changed to voltage control (the reference voltages are generated using the PLL). Also the loads and the SAPF are isolated from the power grid.

After the restoration of the normal state of the grid, the control system resynchronizes with the grid and after this, reconnects the load to the grid and returns to the normal mode. In Fig. 3 is possible to see the full operating diagram of the SAPF.

Simulation Models and Simulation Results

The simulation model is composed by the topology showed in Fig. 1. The simulations were performed using PowerSim PSIM software. In Table 1 is possible to see the simulation parameters values of the model. In the simulations, the SAPF starts to compensate the loads (Fig. 4 a) and is possible to see that the source currents (i sx ) are sinusoidal and in phase with the voltages (v sx ). At t=0.5 s the source voltages are removed and then the SAPF acts as energy backup (Fig. 4 b) maintaining the load voltages (v lx ) with the nominal RMS value. The load stays some time being fed by the SAPF for a certain period of time. Then at t=0.8 s (Fig. 4 c) the source voltages are restored and the SAPF starts the resynchroni-zation of the load voltages (v lx ) and the source voltages (v sx ). When the resynchronization is complete (t=0.815 s), the load and the SAPF is reconnected to the grid and the SAPF returns to normal mode.

Conclusions and Future Work

This paper presents a Shunt Active Power Filter (SAPF) that is able to compensate Power Quality problems and that also serves as energy backup system during power outages. The papers also discuss some methods of power outage detection. The simulation results show that the SAPF can successfully compensate the current harmonics, the current unbalances and the power factor. The simulation results also show that the SAPF can be used as energy backup system in case of a power outage. Also the power presented outage detection scheme performs correctly.

Fig. 1 .

 1 Fig. 1. Topology of the proposed Shunt Active Power Filter with energy backup.

Fig. 2 .

 2 Fig. 2. p-q Theory algorithm implementation.

Fig. 3 .

 3 Fig. 3. Shunt Active Power Filter operation diagram.

Fig. 4 .

 4 Fig. 4. Simulation results of the SAPF: (a) Operating in normal mode; (b) Operating in backup mode; (c) During transference to backup mode; (d) During transference to normal SAPF mode.

Table 1 .

 1 Shunt Active Power Filter simulation model parameters.

	Parameters Values Units
	R sx	10	mΩ
	L sx	100	µH
	C fx	25	µF
	R fx	4	Ω
	C x	10	mF
	L bt	2	mH
	C bt	1	mF

v sa v sb v sc i sa i sb i sc i sn v la v lb v lc i la i lb i lc i ln i fa i fb i fc i fn

  Nevertheless further tests are needed, namely with different loads and power outage conditions.

			v sa	v sb	v sc				(a)								v sa v sb	v sc				(b)
	Voltage (V)	-250 0 250 500														Voltage (V)	5 00 -2 50 0 2 50
	Current (A)	0.3 -500 -50 0 50 100	i sa	0.31 i sb	0.32 sc i i sn	0.33	0.34	0.35 T ime (s)	0.36	0.37	0.38	0.39	0.4	Current (A)	-50 0 50 0.46 -5 00 1 00	i sa	0.47 i sb	0.48 i sc i sn	0.49	0.5	0.51 T ime (s)	0.52	0 .53	0.5 4	0.55
	Voltage (V)	0.3 -100 -250 0 250 500	v la	0.31 v lb	0.32 v lc		0.33	0.34	0.35 T ime (s)	0.36	0.37	0.38	0.39	0.4	Voltage (V)	-2 50 0 2 50 0.46 -1 00 5 00	v la	0.47 v lb	v lc	0.48	0.49	0.5	0.51 T ime (s)	0.52	0 .53	0.5 4	0.55
	Current (A)	0.3 -500 -50 0 50 100	i la	0.31 i lb	0.32 i lc	i ln	0.33	0.34	0.35 T ime (s)	0.36	0.37	0.38	0.39	0.4	Current (A)	-50 0 50 0.46 -5 00 1 00	i la	0.47 i lb	i lc	0.48 i ln	0.49	0.5	0.51 T ime (s)	0.52	0 .53	0.5 4	0.55
		0.3 -100		0.31	0.32		0.33	0.34	0.35	0.36	0.37	0.38	0.39	0.4		0.46 -1 00		0.47		0.48	0.49	0.5	0.51	0.52	0 .53	0.5 4	0.55
	Currente (A)	-50 0 50 100	i fa	i fb	i fc	i fn			T ime (s)						Currente (A)	-50 0 50 1 00	i fa	i fb	i fc	i fn			T ime (s)
		0.3 -100		0.31	0.32		0.33	0.34	0.35	0.36	0.37	0.38	0.39	0.4		0.46 -1 00		0.47		0.48	0.49	0.5	0.51	0.52	0 .53	0.5 4	0.55
									T ime (s)														T ime (s)
										500
									Voltage (V)	-250 0 250
										0.76 -500	0.77	0.78	0.79	0.8	0.81	0.82	0.83		0.84	0.85	0.86
																T ime (s)
										100
									Current (A)	-50 0 50
										0.76 -100	0.77	0.78	0.79	0.8	0.81	0.82	0.83		0.84	0.85	0.86
																T ime (s)
										500
								(c)	Voltage (V)	-250 0 250
										0.76 -500	0.77	0.78	0.79	0.8	0.81	0.82	0.83		0.84	0.85	0.86
																T ime (s)
										100
									Current (A)	-50 0 50
										0.76 -100	0.77	0.78	0.79	0.8	0.81	0.82	0.83		0.84	0.85	0.86
																T ime (s)
										100
									Currente (A)	-50 0 50
										0.76 -100	0.77	0.78	0.79	0.8	0.81	0.82	0.83		0.84	0.85	0.86
																T ime (s)

Acknowledgment. This work is financed by FEDER Funds, through the Operational Programme for Competitiveness Factors -COMPETE, and by National Funds through FCT -Foundation for Science and Technology of Portugal, under the projects FCOMP-01-0124-FEDER-022674 and PTDC/EEA-EEL/104569/2008. Bruno Exposto is supported by the doctoral scholarship SFRH/BD/87999/2012 granted by FCT -Foundation for Science and Technology of Portugal.


Maratovich Maksim

Igor Sergeevich Habibullin

Viktor Nikolaevich Pavlov

Stanimir Mescheryakov

Valtchev

Maksim Maratovich

Igor Sergeevich Pavlov

Viktor Nikolaevich Mescheryakov

Stanimir Valtchev

Active Power Filter with Relay Current Regulator and Common DC Link for Compensation of Harmonic Distortion in Power Grids

Keywords: Non-linear load, Quality of electric energy, Total harmonic distortion, Relay current control, DC-link, Active power filter

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Power Quality

Less than twenty years ago the harmonic components of current and voltage in the electric alternating current were negligible and their impact on the grid could be ignored. Currently, in most countries the level of harmonic components in power grids has increased in several times. The tendency for further growth is here to stay [START_REF] Nejdawi | Harmonic Trend in the USA: A Preliminary Survey[END_REF]. The high level of harmonic components should be considered seriously because it has a negative impact both on the grid and its users.

The reason for the growth of the harmonic current and voltage is the growing number of electricity customers that use non-linear load, both in the industrial and domestic sectors. The main negative effect of the non-linear load consists in the specific nature of the harmonics in the consumed current from the grid. The harmonic components frequencies can be so high that they provoke electromagnetic disturbance but the low frequency harmonics are also a problem because their filtering requires large reactive elements. Currently, 60 % of the electrical consumption is due to the nonlinear load and now the requirements for power supply quality from the grid is one of the main tasks of the electrical energy industry [START_REF] Bojarskaja | The influence of the harmonic content of the currents and voltages on energy efficiency[END_REF].

The existence of higher harmonic contents in the grid current results in significant economic damages. These include the additional losses in rotating electrical machines, the loss in transformers, vibration in electric machine systems, single-phase ground short circuit, capacitor breakdowns, insulation aging, disruption and failure of high-precision measuring instruments, protective gears, control systems and microprocessor-based systems, interference and distortion of signals in telecommunication networks and systems. In addition, the nonlinear load has high level of reactive energy circulation; hence the losses in the energy transport system rise, as well as the overloading of generators, transformers and transmission lines. Oscillations of system voltage are then more probable. In general, the quality of the supplied energy goes downward [START_REF] Zhezhelenko | The higher harmonics in power systems of industrial enterprises[END_REF].

Outlining the Research Question and its Motivation

The harmonic components in the power network variables are produced in the consumer environment and they are originated by the load characteristics. This means that the consumers must themselves control the influence exercised by their equipment onto the grid.

The most characteristic behavior of the power grid working on active-inductive load has been modeled in Matlab in order to analyze the influence of a nonlinear load application. The above mentioned load is connected to a three-phase classical uncontrolled semiconductor bridge rectifier. The adopted for this simulation parameters As it is seen in Fig. 1 (a), the current and the voltage waveforms show a certain phase difference. The load requires reactive power from the supplying network and the THD i is higher than normally is [START_REF]IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems[END_REF]. The usually applied equipment to correct the electric power quality parameters of the consumed power have been the passive power filters of high order harmonics, the compensating capacitor batteries and synchronous compensators. Based on the achievements in power electronics, it became possible to solve this issue by means of active power filters (APF) [START_REF] Moran | Using active power filters to improve power quality[END_REF], [START_REF] Sandeep | Importance of Active Filters for Improvement of Power Quality[END_REF], [START_REF] Meshherjakov | The active filter-compensating devices for systems controlled dc drive[END_REF]. The APF that is currently applied consists of a voltage converter (with fully controlled power switches) and a capacitor battery in a dedicated DC link. However, the most non-linear consumers, having a rectifier incorporated, already possess a capacitor in their output DC link. It is suggested therefore that a new type of APF will use this already existing DC link: the converter of the filter is connected to the DC output voltage tank. This will reduce the number of circuit elements and simplify the control system of the APF [START_REF] Meshherjakov | The active harmonic filter adapted to the alternating current[END_REF]. The chosen control system is based on the relay (bangbang) current controller. This control system is characterized by simplicity, stable performance, high speed and high accuracy [START_REF] Kazmierkowski | Current control techniques for three-phase voltage source PWM converters: A survey[END_REF], [START_REF] Chen | Review of the control strategies applied to active power filters[END_REF], [START_REF] Xiaobo | Hysteresis Current Control Strategy for Three-phase Three-wire Active Power Filter[END_REF].

The APF is supposed to operate as a step-up converter, i.e. the output voltage (the output filter's DC link voltage) will be always higher than the voltage applied to the APF converter (the damaged voltage that is necessary to correct). The main task in the development of this APF is the construction of the control system based on the balance of the power consumed by the nonlinear load from the AC supply and the power injected into the DC link. The other task is the control of the voltage level at the output of the APF converter in order to correspond to the consumed power.

Relationship to Collective Awareness Systems

The increase in the number and the power of non-linear loads is due to the rapid development of the modern electronics. From the point of view of the economy, the power electronics made the energy use more efficient. Unfortunately the electronic devices applied in the energy sector have led to quality problems of the power grid. Those problems our society needs to solve by the effort of both the energy producers and the electric power consumers.

In the industry, the modern static power converters and the frequency controllers for motor drives made possible by the high-power IGBT transistors and other emerging devices to facilitate the control of the induction motors, the cheapest and most common type of electric motors. The application of electronic devices brought certain effects in the general electric network: massively the controlled AC drives have been upgraded by introducing a frequency controlled converters in already existing power system and this distorted the consumed current.

In the domestic applications the switching power supplies increased dramatically in number. The switched power converter is highly efficient but the massive use of it created problems. For example, the millions of laptops, tablet PCs and mobile phones, the necessary servers, routers, etc., all of these electronic devices operate at a constant voltage supply, but they are connected to the AC mains. The converters from the AC to DC in the millions of devices and other equipment represent a non-linear load. As a final result, the quality parameters of the AC grid deteriorated.

In fact, it is not possible to avoid the non-linear load in the energy system. A promising solution to this problem is the use of APF in order to compensate the damage made to the grid parameters. This filtering is also a must for the interconnections between the numerous generators and consumers in the future smart grids. If a simple and reliable solution like the proposed one will be adopted, the manufacturers of electronic equipment will produce massively equipment that will be more easily made compact and cheap.

The consumers connected to the mains will be able to have their nonlinear influence compensated: the APF will be cheaper and more acceptable to be used in massive number to compensate for harmonic distortion. This will contribute to the development of Collective Awareness Systems, where the price of the nonlinear load compensation will be equally divided between the consumers and the producers of electric energy.

Theoretical bases

The schematic diagram of the proposed APF is shown in Fig. 2 (a). A transformer is used as the matching element between the APF converter output (here it is an inverter) and the electric grid. (1)

The "Ideal" current, flowing from the mains, is defined by the power that the DC consumer requires.

The active power 1 P at the input should correspond to that DC power, and 1 P is:

1 k1 kL k k 1 P 3 U I cos ∞ = = ⋅ ⋅ ⋅ ϕ ∑ , (2)
where kL I is the current drawn from the grid by the uncontrolled rectifier, k1 U is the AC input voltage, k ϕ is the phase shift between the voltage and current (in fact, the first harmonic of the input current is the only harmonic contributing to the DC output power!). The reactive power 1 Q at the input is:

1 k1 kL k k 1 Q 3 U I sin ∞ = = ⋅ ⋅ ⋅ ϕ ∑ . ( 3
)
The apparent power 1 S at the uncontrolled rectifier input is:

FA i 3L L A U B U C U LA i LB i LC i FB i FC i D i D C L L L R C U 2 2 1 1 1 S P Q = + . ( 4
)
According to the required (and expected) result from the filtering, it is assumed that the phase angle between the current and the voltage will be zero ( 0 ϕ = ). Then the total power at the input of the scheme is:

1 1 1 1 L Q 0; S P 3 U I . = = = ⋅ ⋅ (5)
The power 2 P that is expected to be consumed by the load is:

2 u 1 d P k U I = ⋅ ⋅ , (6)
where u k 1.35 = is the DC/AC voltage ratio of the full bridge rectifier, and d I is the DC current drawn by the load. The power balance between 1 P and 2 P will be:

1 2 P P P = + ∆ , (7) where P ∆ represents the total losses in the APF, the rectifier and the transformer. In general, the lost part P ∆ can be represented as a function of the current d I multiplied by the coefficient P k ∆ . Then the balance of power is:

1 L u 1 d P d 3 U I k U I k I ∆ ⋅ ⋅ = ⋅ ⋅ + ⋅ . ( 8
)
The peak value of the "ideal" current consumed from the grid is:

L * d P u 1 I k I k U 3 ∆   = +     . ( 9
)
The instantaneous values of the "ideal" phase currents are:

* d P LA u 1 * d P LB u 1 * d P LC u 1 I k i (t) k sin( t); U 3 I k i (t) k sin( t 120 ); U 3 I k i (t) k sin( t 120 ). U 3 ∆ ∆ ∆   = + ⋅ ω       = + ⋅ ω + °      = + ⋅ ω - °    (10)
As a general outlook, the APF control circuit is shown in Fig. 2 (b). The relay current control (RCC) is configured by adjusting the hysteresis value in order to determine the precision by which to process the signal from the current sensors. The difference between the "ideal" and real current is delivered to the RCC together with the signal from the DC current feedback i D . The RCC block calculates and compares continuously the instantaneous "ideal" load currents and the real load currents. The control signals for the converter (it is an inverter in Fig. 2 are generated by RCC. These signals are aimed to form the APF output current instantaneous value. The instantaneous values of APF output currents are supplied to a step-up transformer. The secondary of the transformer supplies the missing instantaneous current continuously and thus compensates for the non-sinusoidal waveforms of the consumed current in the load. As a result, the current that the grid supplies to the whole circuit, becomes sinusoidal with a reasonable precision. The physical basis of this current waveform shaping, as in all the active filter circuits, is the temporary energy storage implemented by passive reactive devices. The particular difference in this method is the use of the output voltage: the filter capacitor or the battery, and not constructing a separate DC link as it is usually done.

Simulation Results

Following the described operation principle of this APF, a computer model has been developed in Matlab. The connection to the nonlinear load corresponds to the shown in Fig. 2 (a). The simulation parameters are:

U 380 = V, f 50 = Hz, L R 4.5 = Ohm, L L 0.1 = mH, d C 30 = mF, 3L L 0.1 = mH.
The results shown in Fig. 3 demonstrate the current, supplied to the uncontrolled rectifier, having a sinusoidal form and a phase coincident with the mains voltage phase. As a result, no reactive power is consumed from the grid and the level of harmonic distortion of the current (THD i ) is close to ideal. This is illustrated by Fig. 3 (b) where THD i = 2.43%.

Experimental Results

The APF control system (RCC) was experimented in a real implementation. The parameters of the experimental study are: U 24 = V, f 50 = Hz, R 0 20 = -Ohm, L 0.1 = mH. In Fig. 4 a general view of the construction is shown. The power module is "Mitsubishi PS22054" connected to a "Mitsubishi 1200V DIP IPM (PS2205X) EVALUATION BOARD", used for debugging converter circuits. The module "Piccolo TMDX28069USB" of Texas Instruments" is a DSP controller, used here as the RCC. The module "CSLA1CH" of Honeywell is a linear current sensor (for measurement of the current in the load circuit). The waveforms were observed by oscilloscope "HANTEK DSO8060" and the values were measured by multimeter "MASTECH M890F". The power supply was a regulable block supplying 24 V at a maximum current of 2A) is connected to converter input. A single-phase load is experimented being a combination of a resistor and an inductive coil, connected to the power converter output. As it is verified from the waveform in Fig. 5 (a,b) and the multimeter readings, the load current (DC) is corresponding to the sinusoidal input current from the grid at a correct magnitude, phase and frequency. The variation of the load (resistance of the variable resistor) across a range of values left the waveforms always correctly corresponding to the frequency, phase and amplitude required from the energy qualiy point of view.

Conclusions and Future Work

According to the results from the theoretical analysis, mathematical modelling, and experiments, the proposed APF based on the power rectifier filter capacitor as a DC link is designed and verified. The APF control based on RCC and limited calculation based on "ideal" load current was investigated. According to the simulation results, the uncontrolled rectifier combined with the new APF system is an effective means of compensation for harmonic current distortion and reactive power. For the experimental verification the APF set-up has been designed, and it confirmed the good performance of the simple "bang-bang" RCC control of the APF. The application of the proposed APF control system to non-linear power converters will improve the electromagnetic compatibility of the "naturally" nonlinear consumers and the power grids. It will have a positive influence on the power system and its customers. It provides increased reliability and energy efficiency. This will be especially important for the future smart grids construction. Further work on the APF will be in experimental studies of "uncontrolled rectifier -APF" to improve the construction and control system of the proposed APF.

  simulation results are presented in Fig.1 (a, b).

Fig. 1 .

 1 Fig. 1. (a) Waveforms of phase A current (solid line) and phase A voltage (dotted line); (b) Spectral contents of the phase A current, THD i = 34.27.

Fig. 2 .

 2 Fig. 2. APF: (a) its connection to the load and grid; (b) its control system. The operation of the suggested APF control system is planned to compensate for the difference L I ∆ between the real L I and the ideal L * I load current that passes

Fig. 3 .

 3 Fig. 3. Current in the phase A of the uncontrollable rectifier: (a) Graphically compared (solid line) to the phase A voltage (dashed line); (b) The spectral composition of the current.

Fig. 4 .

 4 Fig. 4. General view of set up to research RCC.The mathematical model of the RCC based APF control system as shown in Fig.2(b) was first implemented as a simulation in Matlab 8.1 and then was loaded to the DSP controller. The RCC control was supposed to maintain a sinusoidal current at a frequency 50 Hz and amplitude of 1.2 A. This task and the width of the hysteresis gap of the RCC were programmed in the DSP controller and the program was not changed during the experiment. The current feedback obtained from the current sensor placed in series with the load was introduced to the DSP controller too (analogue input). The signal processing speed is 3 MSPS. The "bang-bang" operation produced by the RCC control resulted in driving signals applied to the power converter of the APF. The signals depend on the programmed task, the width of the hysteresis gap and the signal from the current feedback. The driving signals from the DSP controller were sent to the power converter switches (through drivers). The correct waveforms from the experiments are shown in Fig.5 (a, b).

Fig. 5 .

 5 Fig. 5. Operation of the RCC: (a) Waveform and numerical value of the load current; (b) closer view of the signal of the load current sensor.


Ivo M Martins

Sónia J A Silva

Ferreira Pinto

Isménio E Martins

Ivo M Martins

Fernando A Silva

Sónia F Pinto

Isménio E Martins

Transformer and LCL Filter Design for DPFCs

Keywords: FACTS, DFACTS, UPFC, DPFC

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Nowadays the electrical network is facing increasing congestion and loss of reliability. Under this contingency, it is essential to improve the performance of existing power lines and optimize power flow. Flexible AC Transmission systems (FACTS) can be used for power flow control, both in static and dynamic conditions, making transmission systems more flexible 1. Although FACTS devices offer several benefits, they have not seen widespread commercial acceptance due to a number of reasons 2. As an alternative approach, the concept of distributed FACTS devices (DFACTS) has been proposed as a lower cost and higher reliability solution 2. However, since the Distributed Static Series Compensator (DSSC) has no power source, it can only adjust the line impedance and is not as powerful as UPFC.

Using the concept of DFACTS devices, a new concept of distributed power flow controller (DPFC) has been proposed 3 to achieve the same functionality as the UPFC. The DPFC is derived from the UPFC but eliminates the common DC link between the shunt and series converters. As UPFC, DPFC devices give the possibility to control system parameters, such as line impedance and power angle.

After stating the Contribution to Collective Awareness System (section 2) this paper details the operation principle and configuration of DPFC devices (section 3). In section 4 the design of a coupling transformer that extracts electromagnetic energy from the transmission line is presented and in section 5 the design of a third-order LCL filter is shown. Simulation results are presented and discussed in section 6, using switching models of converters connected to the transformer secondary.

Contribution to Collective Awareness Systems

This work follows previous research where sliding-mode controllers, based on switched state-space models, to achieve cross-decoupled (independent) control of active and reactive power flow were presented and two different DPFC series converter topologies were proposed 4, 5. This paper proposes a power transformer and a third-order LCL filter to be part of a DPFC device. DPFC devices can contribute to sustainability of electrical power. This research work on energy management and smart grids might benefit from future collective awareness systems in order to implement cooperative control, or perform informed decision making or the effective involvement of the electrical or sustainable energy systems.

Distributed Power Flow Controller

DPFC devices can be used for power flow control in existing transmission lines. Multiple DPFC devices are distributed along the transmission line, cooperating together allowing cross-decoupled control of active and reactive power flow. Each DPFC device (Fig. 1) consists of a power IGBT full-bridge single-phase converter, with a DC capacitor capable to provide the required DC voltage, a series clamp-on transformer to be used in the connection to the transmission line and a low pass filter to reduce the switching frequency harmonics injected into the grid by the converter. From the conceptual viewpoint each DPFC device can be represented by two controllable voltage sources, connected in series with the transmission line. Each voltage source generates voltage at a different frequency, one at fundamental frequency, v o,1h , and the other at the third-harmonic frequency, v o,3h , so that the converter output voltage is ݒ = ݒ ,ଵ + ݒ ,ଷ . The voltage source v o,1h injects a voltage vector with controllable magnitude and phase angle at fundamental frequency, allowing cross-decoupled control of the active and reactive power flow (P 1h and Q 1h ). The voltage source v o,3h is responsible to maintain the DC bus voltage (U dc ) of the DPFC converter by using the third-harmonic frequency power. Therefore, using the third-harmonic line current, a controllable voltage vector is injected in series with the line, absorbing or generating active power from the third-harmonic current (P 3h ).

Transformer Design

Operation Principle

A clamp-on transformer (COT) is used 6 to use the electromagnetic energy of the transmission line. The COT comprises two halves of a cylindrical torus magnetic core surrounding the power line, as shown in Fig. 1. The power line carrying the current i p acts as the single-turn primary winding of the transformer (݊ = 1), being the secondary winding with n s turns coiled around the magnetic core. The low pass filter and the AC/DC converter are connected to the transformer secondary terminals.

Transformer Design

Assuming linear operation and neglecting resistive and leakage voltage drops, the main transformer design equation, which relates the voltage V p across the primary winding having n p turns, given the maximum magnetic flux density B max , frequency f s and core section effective area A fe , is

fe p h p h s p B A V V f n π ≥ + 6: max ,1 ,3 2 (3 ) 6
Selecting the transformer magnetic material and establishing the allowed maximum transformer B max value, knowing V p,1h , V p,3h and frequency f s , since ݊ = 1, the core section effective area A fe can be then calculated.

The transformer primary winding voltage V p,1h , V p,3h is the voltage injected in series with the transmission line by the DPFC device and must be established according to specifications. For design purposes, consider a 220 kV, 300 MVA transmission line with a total of 4500 DPFC devices (1500 devices distributed along one phase) with 0.20 pu line power flow control capability. Each DPFC device must handle ܵ ௗ = 13.3 kVA. This means that the DPFC maximum output voltage at fundamental frequency is ܸ ,ଵ = √3ܵ ௗ ܼ ܸ ൗ = 3.1 V, where Z line and V n are the transmission line impedance and phase-to-phase voltage at fundamental frequency. Since the maximum line current is ܫ ,ଵ = 787 A, the DPFC output apparent power is ܵ ଵ = ܸ ,ଵ ܫ ,ଵ = 2.45 kVA. Considering the phase angle δ of the output voltage V p,1h as ߜ = ± ߨ 2 ⁄ ± 10%, the maximum active power generated by the DPFC is ܲ ଵ = ܵ ଵ cosሺߜሻ = 383 W. This active power generated at fundamental frequency must be equal (neglecting losses) to the active power P 3h absorbed at the third-harmonic frequency. Considering the transformer losses, low-pass filter and DPFC converter, it is assumed ܲ ଷ = 1.5 × ܲ ଵ = 574 W, where ܲ ଷ = ܸ ,ଷ ܫ ,ଷ . To guarantee a low harmonic distortion of the transmission line current, the injected third-harmonic current I line,3h should not exceed 10% of the line nominal current ܫ( ,ଷ = 0.1 × ܫ ,ଷ ). Thus, from the above conditions, the DPFC maximum output voltage at third-harmonic frequency is ܸ ,ଷ = 7.3 V.

To start the transformer design from equation ( 1), the B m value must be established according to the core magnetic material characteristics. Normally this value is chosen from the material magnetization curve as the highest B m value before the saturation zone. Assuming a transformer core using M4 grade Grain-Orientation (GO) 3% Silicon Steel (Si-Fe) laminations, this value is estimated as ܤ = 1.8 T. Thus, given the required output voltages V p,1h and V p,3h , asthe primary number of turns is ݊ = 1 and the fundamental frequency ݂ ௦ = 50 Hz, the core section effective area can be calculated as ܣ = 13.9 × 10 ିଷ m ଶ .

For the calculated A fe value, the size and shape of the core is designed to minimize the total weight of the transformer (magnetic core and copper windings). To start the design, the secondary winding number of turns n s is set according to the maximum current and voltage values in the secondary side of the transformer. Making ݊ ௦ = 18 and considering the maximum current density ܬ ௨ = 4 A/mm ଶ , the section of the secondary winding wires is chosen as 10 mm 2 . Therefore, the cross-sectional area of the secondary winding is ܣ ௪ଶ = 180 mm ଶ . Taking into account the section of the power line cable ܣ ௪ଵ = 500 mm ଶ , the total area of copper in the transformer window is ܣ ௪ = ܣ ௪ଵ + ܣ ௪ଶ = 680 mm ଶ . Given the window space factor is nearly ܭ ௪ = 0.33, calculated by the empirical formula ܭ ௪ = 10 ሺ30 + ܸܭ ௩ ሻ ⁄ , where KV hv is the voltage of the secondary winding expressed in kV, the transformer window area is calculated as

ܹ = ܣ ௪ ܭ ௪ ⁄ = 2.1 × 10 ିଷ m ଶ .
This means that a transformer core with 5.1 cm inner diameter is needed. The core cross-section width around the power line cable and the transformer length can be now sized to optimize the total weight of the transformer. Representing the transformer core dimensions by the core average magnetic path length M gl , the weight of the magnetic core and secondary winding as function of M gl is presented in Fig. 2. As shown, the optimum value for M gl is in the range 19-20 cm. Making ܯ = 19.67 × 10 ିଶ m the core outer diameter is 7.4 cm. Given the calculated core section effective area, a 1.2 m long transformer is obtained.

LCL Filter

In grid-connected applications reduced levels of harmonic distortion are required to comply with IEEE 519-1992 standard. Therefore, a low pass output filter is used to Optimum Zone for Mgl connect the DPFC device to the electric power system (Fig. 1), to reduce the switching frequency harmonics injected to the grid by the DPFC converter.

Since between the filter and the grid a transformer is used, which inserts a leakage inductance seen by the grid, the output filter comprises an LC filter plus the transformer leakage inductance (ߣ ௧ ᇱ ), which can be seen as an LCL filter but with constant leakage inductance L f2 on the output. Neglecting parasitic resistances and considering the output equivalent impedance ܼ = ܴ + ܮݏ seen from the transformer, for the low pass third-order order filter the transfer function is:

1 2 1 2 3 2 2 1 2 1 2 (s ) ( ) ( ) ( ) ( ) ( ) o o f f f o o o f f o o o PW M f o f f f o f f f o L R C L L L L V s L L L R R V s s s s L L C L L L C L L L + + = + + + + + + + + (2)
While the numerator of the transfer function ( 2) has one real zero set by the output impedance ݖ( ଵ = ܴ ܮ ⁄ ), the denominator has one real pole (p 1 ) and two complex conjugate poles and can be represented by the polynomial

݀ሺݏሻ = ሺݏ +  ଵ ሻሺݏ ଶ + 2ߦω ݏ + ω ଶ ሻ
, where ξ is the damping factor and ω p the angular passband edge frequency. Equating the denominator coefficients from ( 2) with the polynomial d(s), the filter parameters may be calculated from:

2 2 1 1 1 2 1 1 1 2 1 2 2 1 2 (2 ) 2 , , ( 2 ) 2

Damped Filter Design

Since passive LCL filters have low damping characteristics at resonant frequency, they can cause instability. Therefore, the filter should be damped to avoid resonances without reducing attenuation at the switching frequency or affecting the fundamental. Several passive damping topologies can be used, each one having its particular properties 7. Fig. 3 illustrates two practical approaches to damp the LCL low-pass filter. A damping resistor R d can be added in series with the shunt capacitor C f as shown in Fig. 3a. Since at the resonant frequency the impedance of the filter is zero, the aim of the damping is to insert impedance at this frequency to avoid oscillation. The main drawback of this damping method is that its transfer function contains a highfrequency zero ݖ( ଶ = 1 ሺܥ ܴ ௗ ሻ ⁄

). The addition of R d degrades the slope of the highfrequency asymptote, from -40 dB/decade to -20 dB/decade, reducing the filter attenuation above the resonant frequency. Hence, R d must be chosen so that the value of z 2 is significantly greater than ω r . This condition can be expressed as

ܴ ௗ ≪ 1 ሺܥ ω ሻ ⁄
. Setting the damping resistor impedance at a third of the capacitance at the resonant frequency then ܴ ௗ = 0.77 Ω. The damping factor is now ߦ = 0.167 and the resonant peak ܯ| | = 9.6 dB. Fig. 4 illustrates how addition of the damping resistor modifies the magnitude of the transfer function, reducing oscillations in 54.2 dB, but also reducing the filter attenuation above the resonant frequency from -40 dB/decade to -20 dB/decade.

To avoid significant power dissipation in R d , an inductor L d can be placed in parallel with the damping resistor providing a low frequency bypass, as shown in Fig. 3a. To allow R d to damp the filter, at the resonant frequency the inductor L d should have an impedance magnitude sufficiently greater than R d . However, increasing the inductance L d increases weight and energy stored. Thus, the inductor is selected as

ܮ ௗ = 4 ܴ ௗ ω ⁄ = 0.67 mH.

Series R d , L d and C d Damping in Parallel with the Shunt Capacitor

Another approach to damp the filter is to add resistor R d in parallel with the shunt capacitor, as illustrated in Fig. 3b. The resistor results in increased power losses, therefore just by itself it is not a practical solution. To obtain the same damping factor as the previous method the resistor is calculated from: 6.9

(p 2 )( ) C f o d f p f o f o L L R C L L R ξω + = = Ω + + - (4)

Results

The presented transformer and filter with parallel R d and L d damping in series with the shunt capacitor has been modeled and simulated in Matlab/Simulink environment, considering the implementation of the DPFC devices in a transmission network. The simulations values were obtained for a power system consisting of the sending and receiving end voltages V s and V R , connecting the load R load , L load through a transmission line R line , L line , with 4500 DPFC devices (1500 devices per phase). Fig. 5a shows the PWM voltage v PWM injected by the converter and its reference v oref . The reference voltage is calculated according to the specified levels of active and reactive power. Fig. 5b shows the primary and secondary winding voltages v p and v s , where v s is divided by the secondary winding number of turns n s . As can be noted the effective transformer turns ratio is not exactly n s /n p , due to windings and leakage voltage drops.

Conclusions

In this paper a power transformer and a third-order LCL filter to be part of a DPFC device was presented. To couple the DPFC device to the transmission line, the transformer is clamped in series with the power line, avoiding galvanic contacts. The LCL low-pass filter interfaces the transformer with the single-phase full-bridge IGBT based converter, to reduce the high frequency switching harmonics. For the designed filter, two passive damping methods were presented. Simulation results were presented showing the effectiveness of the designed transformer and filter.

Fig. 1 .

 1 Fig. 1. DPFC configuration

Fig. 2 .

 2 Fig. 2. Transformer weight optimization

  Usually ξ and ω p are set according to the desired filter characteristics, the pole p 1 is used to cancel z 1 and should be placed as near as possible from z 1 (ideally  ଵ = ݖ ଵ ) to reduce the filter attenuation |ܣ|( = 20 log ଵ ሺ ଵ ݖ ଵ ⁄ ሻ) bellow ω p . However, to fulfill the condition ܮ ଶ > 0 in (3), for a given ω p , the values of ξ and p 1 are constrained by ߦ < ሺܴ -ܮ  ଵ ሻ ሺ2ܮ ω ሻ ⁄ and  ଵ < ܴ ܮ ⁄ . Setting L f2 as the transformer leakage inductance (ߣ ௧ ᇱ = 1.55 μH) then ξ and p 1 can be established from ߦ = ሺܴ - ଵ ሺܮ ଶ + ܮ ሻሻ ሺ2ω ሺܮ ଶ + ܮ ሻሻ ⁄ and  ଵ < ܴ ሺܮ ଶ + ܮ ሻ ⁄ and pole  ଵ = 0.9ܴ ሺܮ ଶ + ܮ ሻ ⁄ , the filter parameters are obtained (ܴ = 0.15 Ω and ܮ = 4.9 mH) as ܮ ଵ = 0.55 mH and ܥ = 91.6 μF. At the resonant frequency ω = ω ඥ1 -2ߦ ଶ = 4.7 kHz the damping factor of the filter is ߦ = 3.2 × 10 ିସ and the resonant peak ܯ| | = 20 log ଵ ൫1 ൫2ߦඥ1 -2ߦ ଶ ൯ ⁄ ൯ = 63.8 dB. The magnitude bode plot of the undamped filter is presented in Fig. 4.

Fig. 3 .

 3 Fig. 3. Practical approaches to the damping of the LCL filter: a) Parallel R d and L d in series with the shunt capacitor. b) Series R d , L d and C d in parallel with the shunt capacitor

Fig. 4

 4 Fig. 4 illustrates how the parallel damping resistor reduces filter oscillations at the resonant frequency without reducing attenuation above this frequency. One practical solution to significantly reduce the power dissipation in R d is to add a tuned L d -C d circuit in series with R d , as illustrated in Fig. 3b. To allow R d to damp the filter, the value of the high-frequency blocking inductor L d and the DC blocking capacitor C d are chosen such that, at the filter resonant frequency, the impedance of the damping branch is dominated by the resistor R d . Therefore, the inductor is selected as ܮ ௗ = ܴ ௗ ω ⁄ = 1.5 mH and the capacitor from ܥ ௗ = 1 ሺω ଶ ܮ ௗ ሻ ⁄ = 31 μF.

Fig. 4 .

 4 Fig. 4. Magnitude bode plot of the LCL filter

Fig. 5 .

 5 Fig. 5. a) Converter PWM output voltage. b) Transformer winding voltages.

Acknowledgments. This work was supported by Portuguese national funds through FCT -Fundação para a Ciência e a Tecnologia, under project PEst-OE/EEI/LA0021/2013.


Jorge Luis

Stanimir Valtchev

Fernando Coito

Resonant Power Conversion through a Saturable Reactor

Keywords: Magnetic amplifier, mag amp, saturable reactor, wireless power transfer

The resonant converter control is usually implemented by electronic circuits that regulate the parameters of the necessarily produced energy pulses of circulating in the resonant circuit. In the same time the power circuit is characterized by fixed (or uncontrollably varying) parameters. In this article a research is described that shows a long time ago forgotten techniques: the magnetic amplifier that controls the power circuit parameters and as a result, changes the resonant frequency depending on the needs of control. The inductance that is made to vary its value in a controllable, continuous and linear mode would be a perfect (non-dissipative) regulator for the power converter. This can be achieved through a DC magnetization applied as a control command to the magnetic core. By varying this magnetization current and hence the magnetic parameters of the core, the inductance L is possible to be adjusted to a desired value. This operation is similar to the principle of the (long ago) well known "magnetic amplifier" or the "saturable core reactor" as it is often called. The magnetic amplifier usually has an AC source in series with the load and with its primary while in the secondary the DC control signal is applied. The application of a regulated inductance device in the Wireless Power Transfer (WPT) will guarantee a simple way to adjust the frequency of the transmitter and/or the receiver to achieve the required impedance adaptation and efficient energy transfer.

Introduction

The resonant converter control technique is more developed now compared to some decades ago, but still it is very complex and costly to implement. In search for new simple and reliable methods of control, this work is aimed to demonstrate the possible use of the magnetic amplifier principles in the control of the (power) resonant circuit.

The inductance that is capable to vary its value in a continuous and linear mode would be a perfect (non-dissipative) regulator for the power converter, especially if the switching frequency will be kept constant. This can be achieved through a DC current applied as a control. By varying the current and hence the magnetic flux, the value of the resonant inductor L will be regulated [START_REF] Steffen | Lieutenant Commander[END_REF], [START_REF] Platt | Magnetic Amplifiers -Theory and Application[END_REF].

This principle is similar to the functioning of the "magnetic amplifier" or the "saturable reactor core" as they are often called. This circuit was invented by E. F. W. Alexanderson in 1916, USA, and was used during long time for the theatre light dimming [START_REF] Steffen | Lieutenant Commander[END_REF].

During the World War II, the German scientists gave a big boost to those circuits, by using them in the V2 missiles and in the airplanes' navigation equipment. The magnetic amplifier has the AC source and the load in series with the primary winding while in the secondary a DC control signal is applied. To avoid that the powerful AC signal appears in the secondary of that "transformer" and provoke problems in the control system, it is necessary to use a special "three legs transformer". This type of connection gives a possibility to isolate the two circuits: the control circuit and the power (source) circuit [START_REF] Steffen | Lieutenant Commander[END_REF] [START_REF] Platt | Magnetic Amplifiers -Theory and Application[END_REF].

The application of this type of circuit that provides regulation of the inductance, in the Wireless Power Transfer (WPT) will make possible to adjust the frequency of the transmitter and/or the receiver. This will permit to obtain impedance adaptation in order to achieve a maximum energy transfer.

The limit of the proposed method is set by the highest achievable frequency that is determined mostly by the eddy current losses in the core material.

Relationship to Collective Awareness Systems

The resonance based energy transfer is important solution for efficient energy application in electric and hybrid vehicles, very fast trains, embedded medical systems, home automation, biomedical systems and the emerging field of Internet of Things that includes also the energy transport. By the proposed resonant frequency adjustment through simple and robust regulation, it will be possible to achieve a widely spread and massive production of cheap wireless energy transmission equipment. The developed regulated inductive element would be useful also in the power quality compensation which is the main concern of the modern society and in particular, the emerging Smart Grids.

Saturable Reactor

The saturable reactor is a magnetic device that consists of a single magnetic core, having two windings. One is connected to AC source and the (power) load, normally designated by "load coil" and another is connected to a DC source namely "control coil". The idea is to control of the load current and voltage by the control coil, similarly to what is done in a transistor or another electronic device. In Fig. 1 (left) is shown a saturable reactor. In the left side of the magnetic core is the DC control winding (a variable resistance is representing the regulator). In the right side of the core are shown the AC power source and the load connected in series. When the control current is varied, the impedance of the load winging is changing, once the permeability of the magnetic circuit varies, producing a change of the inductance. However, in this basic circuit, exists a problem: it is the mutual induction between the DC and AC windings that provokes interaction between both circuits. The power current in the AC winding will induce undesirable feedback to the DC side.

One way to solve this problem is the circuit presents in Fig. 1 (right), with two cores construction that separates the cores and the windings.

This circuit, having two separate cores with series control and series load windings, makes possible to cancel the induced voltages and to minimize the unwanted effects. The saturable reactor is based on magnetization curve of the applied magnetic core material. A generic magnetization curve is shown in Fig. 2.

H B µ m m = (1)
It is the slope of a straight line drawn starting in the origin. A similar line drawn tangent to the curve at its "knee" is called the maximum permeability and its value is:

H B µ ' ' m = (2)
The slope H B 0 0 of the normal induction at the origin (enlarge in Fig. 2) is the permeability for very low induction value B 0 ; it is called initial permeability and it is usually much lower than µ m [2].

The most common saturable reactor consists of a three legged core as it will be shown in Fig. 5, where each coil is wound on separate magnetic "leg". The two AC coils in Fig. 6 should have relatively low and equal number of turns and the middle coil usually has much higher number of turns. This gives the possibility of amplification: through lower control current to obtain control over powerful circuits. Because of this in many cases the (regulated) saturable is used as a "Magnetic Amplifier".

In open circuit condition of the control circuit, the imaginary part of the complex impedance value is much higher than the real part of the impedance (the winding DC resistance). It must be recalled that a relatively small amount of direct current flowing into the control winding of the core reactor, because of the high number of turns and in case of no air gap, is easily capable to produce core saturation. Thus, the reactance of the core reactor may be varied by a small amount of DC power. In this way, the AC winding of the core regulates the amount of power delivered to the load by the AC source, controlled by a small amount of DC power flowing in the DC winding.

Usually, when one winding of the core reactor is used to control the power in the other winding through reactance variation, the magnetic device is called a saturable reactor [2], [START_REF] Lufcy | A survey of Magnetic Amplifier[END_REF], [START_REF] Woodson | Magnetic Amplifier Analysis Using a generalized Model for the Saturable Reactor Core[END_REF]. The concept is the same for the magnetic amplifier: the lower DC component of the impedance permits regulation of the permeability. The main difference between a magnetic amplifier and a saturable core reactor is that the magnetic amplifier uses a half of the magnetic loop and the amplifier uses the complete magnetic loop. Because of this the term "Saturable Core" is often substituted by the term "Magnetic Amplifier".

Basically a saturable reactor consists of three essential elements (Fig. 3): Direct current source, Magnetic core with windings and Alternating current source. These three elements, when connected together, form the essentials of the Saturable reactor. Its operation is based upon the above mentioned principle: the current flowing in the coil wound on the magnetic core can be regulated by varying the core saturation [START_REF] Woodson | Magnetic Amplifier Analysis Using a generalized Model for the Saturable Reactor Core[END_REF], [START_REF] Ing-Ien | Modelling of Control Loop Behaviour of MagAmp Post Regulators[END_REF], [START_REF] Yoshnao | Variable Gain Magnetic Amplifier and Application for Power Invariance Control System[END_REF]. In order to optimize the magnetic amplifiers, the choice of magnetic core is very important. It is also important to choose which part of the core is more convenient to saturate.

The main goal of any magnetic core is to supply an easy path for the magnetic flux in order to guarantee the flux linkage (magnetic coupling), between two or more elements. The energy storage in a magnetic core is an undesired parasitic effect. In order to minimize this problem, the choice of a magnetic material with high permeability and thin hysteresis loop is the right option.

Today, the wound magnetic cores used in practice are made by amorphous metal alloy. These cores are used in SMPS (Switch Mode Power Supply) application up to 100-200kHz, and especially in magnetic amplifiers [START_REF] Yoshnao | Variable Gain Magnetic Amplifier and Application for Power Invariance Control System[END_REF], [START_REF]International Commission on Non-Ionizing Radiation Protection (ICNIRP) -"Guidelines for Limiting Exposure to Time-varying Electric[END_REF].

As it was shown, the magnetic amplifier is a relatively simple device. However, this simplicity is very misleading when mathematical analysis of its operation is attempted, because of the extremely nonlinear characteristics of the core material. The linear circuit theory may be applied only to carefully selected parts of its operation regimes. In order to simplify the analysis the common practice is to make the assumptions of perfect core material. As it was mentioned before, the AC winding voltage will induce undesired voltage in the DC winding. This influence may short circuit the DC winding if the impedance of the DC winding is low and by this, it would effectively short circuit the AC voltage in the power winding. This difficulty might be overcome by using high impedance in the DC control circuit [START_REF] Grilo | O TRANSDUTOR[END_REF], [START_REF] Mali | Magnetic Amplifiers -Principles and Applications[END_REF].

In Fig. 4 (a) a common solution is shown, in which two reactor cores are used. The DC current is applied in opposite direction in each winding. The AC current is applied in the same direction in both coils. A similar solution is shown in Fig. 4 (b).where the connection is parallel in order to reduce the necessary AC voltage [2], [START_REF] Lufcy | A survey of Magnetic Amplifier[END_REF]. When there is zero direct current in the control winding of Fig. 4, both reactor impedances are large and prevent any load current except a small exciting current to flow in the AC loop in the lower parts of the voltage sinusoids. When non-zero direct current is applied to the control winding, the impedance remains large for the first part of a cycle, until the saturation flux density is reached. Then the reactor impedance is reduced and larger load current may flow. In Fig. 5 a three-leg magnetic core is shown. The current in the DC coil will produce a change in the total flux and hence a change of inductance [START_REF] Mali | Magnetic Amplifiers -Principles and Applications[END_REF], [START_REF] Platt | Magnetic Amplifiers -Theory and Application[END_REF]. This core has one DC coil and two AC coils and the total AC and DC flux is a changing sum: alternatively in each of the lateral legs it is either sum or difference of the fluxes. The figure shows the virtual paths for the AC and DC fluxes. The number of turns of the AC half-windings is equal and symmetric. The equal number of turns in the AC coils will provoke equal AC magneto-motive force, which will be cancelled in the centre leg and cause fluxes to flow as indicated by solid line. In consequence, no fundamental AC voltage is induced in the DC coil, but the DC flux is injected in both outer legs as indicated by the dotted lines. Fig. 6 shows the magnetization and permeability curves for the saturable core reactor with the ideal operating point indicated (point "O"). It is important to notice that this point is located on the "knee" of the magnetization curve. The "knee" of the curve corresponds to the maximum curvature. Saturable core reactor and magnetic amplifier should operate on this "knee" of the magnetization curve [START_REF] Mali | Magnetic Amplifiers -Principles and Applications[END_REF], [START_REF] Platt | Magnetic Amplifiers -Theory and Application[END_REF].

When the saturable core reactor is set at the "knee" of the magnetization curve, any small increase in control current will cause a large increase of load current, and any small decrease in control current will cause a large decrease of the load current. This is why the point "O" is the ideal operating point: the small changes in control current will cause large changes of load current, in other words, the saturable core reactor can better and efficiently amplify the control current [START_REF] Mali | Magnetic Amplifiers -Principles and Applications[END_REF], [START_REF] Platt | Magnetic Amplifiers -Theory and Application[END_REF].

The saturable reactor AC winding inductance depends on the flux provoked by the DC winding (-s). The inductance depends also on the geometry of the magnetic core and its permeability, having in mind that the effective permeability depends on the DC control winding function [START_REF] Steffen | Lieutenant Commander[END_REF]. In simplified form and in case of flux concentrated only in the core, the equation of the inductance is:

[ ]

H 10 µ l A N π 4 L -7 2 × × = (3)
Once the geometry of the core is fixed by the manufacturing, the unique variable is the permeability µ. In this case the permeability will control the inductance L.

Results Presentation

In this section the results obtained from measurements during the experimentation are shown. The circuit that was used as a basis for different tests is the one shown in Fig. 5. The experiment was executed in circuit corresponding to the one in Fig. 7: This circuit (Fig. 7) consists of two parts. The one in blue (external coil), is the signal coil with 10 turns, another is the resonant circuit, shown in red (internal coil). This coil has 30 turns two capacitors 0,1µF each, connected in series. The inductance of the resonant coil (shown in red) was measured and the (initial) value of mH 58 , 7 L = has been obtained. In these conditions the calculated resonant frequency is:

kHz 175 , 8 10 50 10 58 , 7 π 2 1 C L π 2 1 f 9 _ 3 _ r = × × × = × = (4)
In fact, this value was confirmed when the experiments were executed, i.e. close to 8,2 kHz. The magnetic amplifier was constructed on a tree legs transformer, where the middle leg (control) have a coil of 30 turns and the two legs (one on each side) form two half-coils in series with 20 turns each.

In Fig. 8 the schematic diagram of the three legs transformer is represented. The "green" coils are the AC half-coils, A1 and A2, and the "red" coil, C, is the control coil, connected to the variable DC. The graphic shown in Fig. 9 presents the values obtained during the tests of the magnetic amplifier.

L [mH]

0,000 0,500 The illustration in Fig. 10 shows the series connection between a fixed inductor (4,7 mH) and the regulated inductance of the magnetic amplifier. The values obtained are shown in Fig. 11.

Conclusions and Future Work

A confirmation was found that the magnetic amplifier gives the possibility to adjust the inductance L, by a DC current control The correct starting point for the regulation (zero DC control current) of the power should be the in which the inductance guarantees the minimum output power. All the other points of operation will be achieved by the non-zero current of the DC coil. By some value of a fixed (initial) and applying a regulated additional inductance, the resonant circuit will obtain the necessary capacity to regulate its resonant frequency and thus to regulate the power of the resonant converter.

The future work should involve the study of magnetic cores applied to optimize this circuit in terms of frequency and maximum allowed AC current along with the large spectrum of frequencies. The necessary electronic circuits should be constructed to control the completed system

Fig. 1 .

 1 Fig. 1. Simple saturable reactor circuit (left); Saturable reactor having two cores (right).

Fig. 2 .

 2 Fig. 2. Generic magnetization curve. The relation of B to H at any point on the curve is the normal permeability for that value of B. For the maximum flux density B m the normal permeability is:

Fig. 3 .

 3 Fig. 3. Three essential elements of the saturable reactor.

Fig. 4 .

 4 Fig. 4. Magnetic amplifier structures: (a) series; (b) parallel [2].

Fig. 5 .

 5 Fig. 5. Three legs transformer applied to magnetic amplifier [2].

Fig. 6 .

 6 Fig. 6. Variation of flux and permeability with magnetization force.

Fig. 7 .

 7 Fig. 7. The circuit base to the different tests.

Fig. 8 .

 8 Fig. 8. Schematic of three legs transformer.

Fig. 9 .

 9 Fig. 9. The values obtained during the tests of the magnetic amplifier.

Fig. 10 .

 10 Fig. 10. Schematic of the tests on the saturable reactor in series with the resonant circuit inductor.

Fig. 11 .

 11 Fig. 11. The values obtained with Saturable reactor in series with resonant circuit.


Nuno Mancelos
email: n.mancelos@campus.fct.unl.pt

Joana Correia
email: jm.correia@campus.fct.unl.pt

Luís Miguel Pires
email: l.pires@campus.fct.unl.pt

Luís B Oliveira

João P Oliveira

Piezoelectric Energy Harvester for a CMOS Wireless Sensor

Keywords: Energy harvesting, Piezoelectric transducers, Self-powered, Microsystems, Smart systems, Wireless sensor nodes, MEMS, WSN

The emerging of collective awareness platforms opened a new range of driven forces that will converge to more sustainable systems. To achieve this task, these platforms have to support an increasing number of more sophisticated remote sensors and actuators that will need to cooperate smartly and strongly with each other in a mesh type of intelligent interconnectivity. These remote smart miniaturized nodes can add noninvasive intelligence but suffer from lifetime performance due to the small quantity of energy available in micro batteries. Therefore, harvesting energy from the environment is a promising technique. This work presents the study and experimental evaluation of a flexible piezoelectric material to validate the use of a piezoelectric harvester in a CMOS wireless actuator/sensor node.

Introduction

The recent advances in ultra-low-power device integration, communication electronics and Micro Electro-Mechanical Systems (MEMS) technology have fuelled the emerging technology of Wireless Sensor Networks (WSNs). The spatial distributed nature of WSNs often requires batteries to power the individual sensor nodes. One of the major limitations on performance and lifetime of WSNs is the limited capacity of these finite power sources, which must be manually replaced when they are depleted. Moreover, the embedded nature of some of the sensors and hazardous sensing environment make battery replacement very difficult and costly. The process of harnessing and converting ambient energy sources into usable electrical energy is called energy harvesting. Energy harvesting raises the possibility of self-powered systems, which are ubiquitous and truly autonomous, and without human intervention for energy replenishment. Among the ambient energy sources such as solar energy, heat, and wind, mechanical vibrations are an attractive ambient source mainly because they are widely available and are ideal for the use of piezoelectric materials, which have the ability to convert mechanical strain energy into electrical energy.

Contributions of this paper are summarized as follows. Section 2 presents the relationship to Collective Awareness Systems. In Section 3, state of the art of energy harvesting transducers is presented. In Section 4 the concept of synergy between piezoelectric energy harvesters and WSN is justified and a block diagram of the proposed self-powered Wireless Actuator/Sensor Node is presented. Section 5 presents experimental evaluation of the piezoelectric harvester. Finally some conclusions are drawn in section 6.

Relationship to Collective Awareness Systems

Nowadays, the emergence of collective awareness systems is pushing the performance of end user interactive objects. The support framework based in a interconnected objects and things (Internet of Things, IoT) is the bridge that combines technologies and components from micro-systems (miniaturized electric, mechanical, optical and fluid devices) with knowledge, technology and functionality from several areas of research.

However, Harbor Research [START_REF]Harbor Research: Machine-to-Machine (M2M) an Smart Systems Forecast[END_REF] defines smart systems as a new generation of systems architecture (hardware, software, network technologies, and manage services) that provides real-time awareness based on inputs from machines, people, video streams, maps, new feeds, sensors and more that integrate people, process, and knowledge to enable collective awareness and decision making.

WSN provide endless opportunities, but at the same time pose formidable challenges, such as the fact that energy is a scarce and usually non-renewable resource. However, as part of WSN, micro-systems could provide advances in low power Very Large Scale Integration (VLSI), embedded computing, communication hardware, and in general, the convergence of computing and communications, are making this emerging technology a reality. Likewise, advances in nanotechnology and MEMS are pushing toward networks of tiny distributed sensors and actuators.

As mentioned in the previous section, energy harvesting can dramatically extend the operating lifetime of nodes on WSN. Finally, this technology enables battery less operation and reduces the operation costs of WSN, which are mainly due to battery replacement.

Energy Harvesting from the Surroundings

Energy harvesting techniques developed for micropower generators deal with the challenge of scavenging and making use of residual energy present in ambient sources, usually energy in the form of light, Radio Frequency (RF) electromagnetic radiation, thermal gradients and many sources of motion, namely rotation, vibration and fluid flow. Energy harvesting transducers that make use of energy in the form of motion are called Electromechanical and are separated in three different groups: electromagnetic, electrostatic and piezoelectric transducers. Piezoelectric transducers make use of the piezoelectric effect, which refers to the accumulation of an electrical charge in some solid materials, like crystals and certain ceramics, when a mechanical stress is applied to them. The effect is reversible, which means that movement, in the form of oscillation, can occur for the resonance frequency of the particular piezoelectric material to which an electrical charge is applied. These transducers are usually designed to harvest energy from vibration sources. Their harvesting optimization highly depends on the success of the characterization of the vibration from which the energy is to be harvested.

The three electromechanical transducer types are very different from each other. In general, power efficiency of a mechanical transducer could be considered as the ratio between the electrical power it delivers and the mechanical power it receives from the motion source. However, comparing different transducers is not trivial.

In [START_REF] Mitcheson | Green: Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices[END_REF], a variant of harvester effectiveness performance indicator is introduced, the Volume Figure of Merit (VFM), which is used to compare the performances of energy harvesting electromechanical transducers as a function of their size. The devices chosen for the actual comparison are electromechanical transducers of the three types mentioned above. Table 1 contains the two best results achieved for each of the transducer types. The main conclusion taken from the presented results is that piezoelectric transducers achieve reasonable values for power efficiency, when compared to the other electromechanical energy harvesting transducers.

Table 1. VFM for the Three Transducers Types (Extracted from [START_REF] Mitcheson | Green: Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices[END_REF]).

Transducer type Reference VFM[%]

Electromagnetic [3] 0.52 [START_REF] Ching | A lasermicromachined multi-modal resonating power transducer for wireless sensing systems[END_REF] 0.64 Electrostatic [START_REF] Despesse | High damping electrostatic system for vibration energy scavenging[END_REF] 0.06 [START_REF] Arakawa | Micro seismic electrets generator using electrets polymer film[END_REF] 0.68 Piezoelectric [START_REF] Fang | Fabrication and performance of MEMS-based piezoelectric power generator for vibration energy harvesting[END_REF] 1.39 [START_REF] Roundy | Energy scavenging for wireless sensor networks[END_REF] 1.74

Synergy between Piezoelectric Energy Harvesters and Wireless Sensor Networks

Wireless Actuator/Sensor Nodes represent a wide range of devices with different functionalities and characteristics with an estimated power consumption level that can be retrieved from the data available in [START_REF] Yoon | A Study of Piezoelectric Harvesters for Low-Level Vibrations in Wireless Sensor Network[END_REF]. Some commercially available actuator sensor nodes, namely Crossbow MICAZ, Intel Mote 2 and Jennie JN5139, have power consumption levels of 2.8 mW, 12 mW and 3 mW, respectively. In [START_REF] Huang | Ultra Low Power Wireless and Energy Harvesting Technologies -An Ideal Combination[END_REF], the power consumption of a wireless sensor node based on the Nordic RF24L01 wireless transceiver is analysed. The conclusion reached is that the RF transceiver is responsible for 74% of the power consumption, the rest being associated with the power consumptions of the microcontroller, the power management module, sensors, actuators and Analog to Digital Converter (ADCs).

The power supplied by a piezoelectric energy harvester depends greatly on the piezoelectric transducer's characteristics and the vibration conditions it is submitted to. Furthermore, for each piezoelectric transducer setup there are optimal vibration conditions, which should match the resonance frequency of the piezoelectric material, and its optimal acceleration, which is directly related to the vibration amplitude. Considering an optimized energy harvesting setup regarding the transducer and the characterisation of the vibration frequency, the circuit responsible for rectification and eventual voltage supply regulation must be designed and implemented. It should be noted that this circuit has a power efficiency associated to it. As an optional component in the power management part of the system, and depending, once again, on the vibration predictability, an energy storage device might be considered.

Two examples of piezoelectric energy harvesters implemented with optimal vibration characteristics and resistive loads that maximize the power output are given in [START_REF] Yoon | A Study of Piezoelectric Harvesters for Low-Level Vibrations in Wireless Sensor Network[END_REF] and [START_REF] Zhou | A Self-powered Wireless Sensor Node for Structural Health Monitoring[END_REF]. In the first case, a power output of 3 mW was achieved, while in the second work a value of 4.4 mW was also experimentally verified. For the first implementation, a Volture V22BL piezoelectric transducer was used, with vibration characteristics of 50 Hz and 1g. The second example makes use of a Piezo Systems T226-A4-503X piezoelectric transducer, with vibration characteristics of 50 Hz and 0.5 g. It should be noted that the power outputs are achieved using optimized resistive loads for each of the situations.

Although power consumption and power output levels do not match, energy harvesting solutions can be made possible using a duty cycling technique, making use of a battery or a supercapacitor. This technique consists in switching periodically the sensor node on and off. Since the wireless sensor node doesn't have to be constantly communicating, the energy harvested by the transducer is used in the communication time interval of the sensor node and stored in the battery (or capacitor) during the rest of the cycle (switched off time interval). In [START_REF] Mitcheson | Green: Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices[END_REF], a duty cycle of 1.6% is used for a solution using a piezoelectric energy harvester powering a custom designed radio transceiver that requires 12 mW when transmitting. The power consumption values previously presented, from [START_REF] Yoon | A Study of Piezoelectric Harvesters for Low-Level Vibrations in Wireless Sensor Network[END_REF], are based in operating conditions of 1% communication, 10% processing and 89% sleeping. The proposed block diagram of a self-powered actuator/sensor node is presented in Fig. 1.

Experimental Evaluation of the Piezoelectric Energy Harvester

The chosen piezoelectric energy harvester Midé Volture™ V21bl [12], designed for vibration energy harvesting, is presented in Fig. 2. It uses the piezoelectric characteristics of its specific piezoceramic material to produce electrical charge when mechanically stimulated [START_REF]Datasheet: Volture Products -Material Properties[END_REF] and consists in a package of piezoelectric materials in a protective skin, with four pre-attached electrical leads. The piezoelectric harvester includes two electrically isolated piezo wafers, which may be used independently or in one of two possible combinations. These combinations can be optimised for increased output voltage (series configuration) or increased output current (parallel configuration). For this implementation, and since the desired output voltage is relatively low compared to the range of typical output voltages of the piezoelectric harvester, the parallel configuration is used, in order to maximize the output current needed to charge the capacitor. Fig. 3 presents the final equivalent circuit of the parallel configuration of the two wafers.

A block diagram of the test setup is shown in Fig. 4, which comprises three complementary parts:

1. a test vibration module which is formed by an audio amplifier (LM386) and vibration speaker coupled to the piezoelectric transducer; 2. a rectifying diode bridge plus a fast charge capacitor; 3. a data-acquisition subsystem, consisting of a 10-bit ADC and a Microcontroller (MCU) connected to both a Liquid Crystal Display (LCD) Module (HD44780 module, 16X2 LCD Panel) and a USB connection to a computer. A picture taken of the test setup is shown in Figure 5.

The energy stored in the capacitor is calculated using the standard equation given by, (1) For the Energy calculation, the actual capacitance of the parallel of capacitors was set to 2100 µF. In fact, this energy was calculated using the discharge time of the capacitor (from 1.3 V to 0 V), which is approximately 21 seconds, Fig. 6 a). Using this discharge time, the resistance value of the RC circuit (2 KΩ) and the RC time constant approximation, the actual capacitance of the capacitor can be calculated. Using this value, the estimated stored energy in the capacitor is 1.77 mJ, for 1.3 V. Two different methods of vibration were used during the tests: the manually induced and the one produced by the small amplitude vibration speaker. The optimal vibration frequency was found for the second case.

For the manually induced movement test, a constant oscillation frequency was emulated. Given the equivalent circuit of the piezoelectric harvester, previously presented in Fig. 3, the expected behaviour of the charging circuit is described by, [START_REF] Mitcheson | Green: Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices[END_REF] where is the instant voltage across the capacitor while depends on the open circuit voltage of the piezoelectric harvester. The charging time was approximately 68 seconds, Fig. 6 b). After some testing using a speaker, the optimal vibration frequency for energy harvesting purposes was found to be 58 Hz. Three tests were run with this vibration frequency, following the same procedure. The charging process was interrupted when the capacitor reached 1.3 V, after which the capacitor is connected to a 2 kΩ resistor. Fig. 6 a) shows the results of these three tests. The charging time of the capacitor (from 0 V to 1.3 V) is approximately 125 seconds (medium value). It is greater than the one achieved with the first test (the manually induced movement test), proving that the tip-to-tip displacement amplitude, related to the vibration acceleration, is an important factor in the energy harvesting implementation, using this particular piezoelectric energy harvester.

Using non-optimal vibration frequencies for the vibration speaker case, the time the piezoelectric harvester takes to charge the capacitor up to the same voltage level is greater. To prove this, two non-optimal frequencies were chosen: 60 Hz, which is above the optimal frequency, and 56 Hz, which is below. The charging times for these tests are approximately 250 seconds for the first one and 180 seconds for the second. Both of them are greater than the one achieved for the optimal vibration frequency, 125 seconds. Table 2 shows practical results of this work.

Conclusions

The main conclusion of the present work is that it is possible to implement an energy harvesting solution using the piezoelectric energy harvester Midé Volture™ V21bl for low voltage applications, even if the vibration conditions applied to the harvester are not optimal. Comparing the vibration speaker case and the test involving manually induced oscillation, it is possible to conclude that the tip-to-tip displacement amplitude is a very important factor in terms of energy generated by the piezoelectric device, more so than the actual selection of the right frequency for the oscillation.

For each configuration of the mechanical vibration method, there is an optimal vibration frequency, which is 58 Hz, in the described case.

Applying this study to a microsensor node makes energy-harvesting operation a possibility for microsensor networks [START_REF] Calhoun | Design considerations for ultra-low energy wireless microsensor nodes[END_REF] based on CMOS technology.

Fig. 1 .

 1 Fig. 1. Block diagram of a Piezoelectric-powered WSN.

Fig. 2 . 3 .

 23 Fig. 2. Midé Volture™ V21bl [12]. Fig. 3. Parallel equivalent circuit.

Fig. 4 .

 4 Fig. 4. Block diagram of the test setup.

Fig. 5 .

 5 Fig. 5. Photograph of the implementation.

Fig. 6 .

 6 Fig. 6. a) Three tests for the optimal vibration frequency -58 Hz; b) manually induced movement test.

Table 2 .

 2 Summary of the experimental results.

	Vibration type	Vibration frequency	Charging time (from 0V to 1.3V)	Energy stored in time the capacitor after charging	Used capacitor
		58 Hz	125 s
	Vibration Speaker	56 Hz 60 Hz	180 s 250 s	1.77 mJ	2100 μF
	Manual	-	68 s