A combined algorithm approach for PD location estimation using RF antennas

J. M. Fresno, G. Robles, J. M. Martínez-Tarifa and B. G. Stewart, “A combined algorithm approach for PD location estimation using RF antennas,” 2017 IEEE Electrical Insulation Conference (EIC), Baltimore, MD, USA, 2017, pp. 384-387.
doi: 10.1109/EIC.2017.8004695
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8004695&isnumber=8004594

Abstract— To locate the positions of partial discharge sources in free space at least four RF antennas are arranged in a suitable
spatial geometry to detect the radiated electromagnet energy from the discharge. The time-difference-of-arrival (TDOA) between the signals from each antenna are then used within multi-lateration equations to determine the position of the source. The iterative Hyperbolic Least Squares (HLS) method and the non-iterative Maximum Likelihood Estimator (MLE) method are two common techniques used in the literature to solve the multi-lateration equations. This paper investigates the ability of combining MLE and HLS to improve location accuracy and maintain fast location computation time. To this end HLS, MLE and the combined MLEHLS method are evaluated in terms of location accuracy and computation performance for three spatial antenna configurations, namely Square, Pyramidal and Trapezoidal arrangements. The location accuracies for each method are evaluated for theoretical TDOA values and also for the case when a finite sampling rate of 10G samples-per-second is considered; the latter is implemented through appropriate rounding up of TDOA values by one sample time. It is shown that MLE-HLS produces improved location accuracy compared with HLS and MLE for both theoretical and finite sampled TDOA values. In addition, it is shown that MLE-HLS improves significantly the computation time over the iterative HLS method.

Keywords— Antenna theory; Mathematical model; Maximum likelihood estimation; Partial discharges; Position measurement; location algorithms; partial discharges; radio-frequency localization

Characterization of Peltier cells for energy harvesting applications (III)

As demonstrated in the former post, the equivalent voltage source of the cell depends on the temperature difference of the surfaces and takes a value of V_o = 0.0245 \cdot \Delta T and the internal series resistor is R_s = 2.24~\Omega. Therefore, there would be different power outputs considering the resistor load and the temperature difference. The next plot shows the delivered power to a set of loads and four temperature differences \Delta T =[5,~10,~15,~20] degree Celsius. The maximum power given by the cell is delivered to a load that equals the internal resistor, R_s=R_L and takes a value of:

P_{max}=\frac{V_o^2}{4R_L}&s=1 W


If a difference of temperatures of 20 ºC is achieved the voltage at the load would be 245 mV and it would draw a current of 109.4 mA, the maximum power would reach 26.8 mW when connecting a load of 2.24~\Omega. Of course, all these data are hypothetical since the assumptions are in the most optimistic side considering that R_s=R_L. Even under these circumstances a voltage booster would be needed to increase the voltage to a level according to the requirements of the MCU. For instance, the ultralow power STM32L432 ARM Cortex M4 requires at least a power supply of 1.71 V. There are two options to increase the voltage, using voltage multipliers or using DC-DC converters.

Voltage multipliers

These circuits use a combination of diodes and capacitors that allows to duplicate the voltage at the input in every stage. A common setup is the Cockcroft-Walton configuration as the shown in this paper to multiply the voltage obtained from events that create pulses that can reach peaks of 1 V or more. In the case of one or two Peltier cells connected in series, this circuit is out of the question since the Schottky diodes with the lowest forward voltage drop are close to 250 mV so they would consume the voltage provided by the cell or cells.


Voltage boosters

Voltage boosters or DC-DC step-up converters would be the most feasible solution. The working principle is easy. The inductance L is charged closing switch S storing a magnetic field. This field will maintain the current flowing towards load R when S is opened. Since the inductance is giving energy to the load the voltage at L is effectively reversed and added to v_i(t) increasing the voltage at the output, v_o(t). The switching should be done fast to avoid a total magnetic discharge of the coil when S is open and a total depletion of capacitor C when S is closed. The diode D prevents the capacitor from discharging through S.Booster.png

This idea has been implemented in integrated circuits (IC) that scavenge small quantities of energy from the source, in our case the Pletier cell, to drive the switch and are able to increase the voltage at the output upto 3.3 V or 5 V depending on the MCU connected. Some examples of these IC and their behavior under real conditions are shown in the next post.



Characterization of Peltier cells for energy harvesting applications (II)

With the setup described in the last post, the temperature of one of the surfaces of the cells can be controlled with an electrical current, the other surface is cooled passively with a heatsink. The resistors and the two temperature sensors are connected to the same voltage source taking advantage of the wide range of voltages supported by the LM35. The outputs of the LM35 are connected directly to two multimeters to measure the differences of temperature achieved between the two surfaces. Now, the process is easy: the resistors are heated with different currents and the output voltages of the cell and the temperatures are registered. This will solve the voltage source of the equivalent electric circuit of the cell in open circuit or the Thévenin voltage. The results are represented in the next Figure showing a perfect linearity between temperature and voltage.


I_s = [0.49~0.59~0.69~0.79] A
V_s = [12.3~14.6~17.3~20] V

V_o = [62.4~140.5~252.5~414~580~775] mV

T_h = [24.8~30.2~38.4~55.0~66.5~82.7] degree Celsius
T_c = [22.5~24.5~28.0~38.0~42.9~51.0] degree Celsius

Where, I_s and V_s are the current and voltage applied by the power supply to the resistors, respectively; V_o is the output of the cell and T_h and T_c are the temperatures of the hot and cold sides of the cell, respectively. The plot shows that V_o = 0.0245 \cdot \Delta T with the slope in V / ºC.

The next test will determine the equivalent series resistance, R_s, of the cell loading it with a known resistor, R_L = 13.5~\Omega. In this case, the current given by the cell provokes a voltage drop in the internal resistor R_s so the voltage applied to R_L, V_L, is smaller than the open circuit voltage, V_o > V_L.  A new set of measurements is conducted injecting the same current to the heating resistors to determine this voltage and, then, the internal resistance of the cell:

V_L = [51.9~121.1~ 211.7~ 344.1~ 486~ 639] mV

T_h = [27.6~ 33.2~ 40.7~ 53.0~ 65.0~ 79.3] degree Celsius
T_c = [25.5~ 27.7~ 30.7~ 36.7~ 41.9~ 48.6] degree Celsius


The blue plot represents the voltage in open circuit, V_o, and the red plot the voltage at the load, V_L. Dividing this voltage by the load resistor yields the current given by the cell, I_L. Therefore, the internal resistor is calculated applying Ohm’s Law knowing that the voltage drop is V_o - V_L and the current is I_L. This is done for several points along the experimental results in the plot giving a constant value for the resistor, R_s = 2.24~\Omega. The same process is repeated for another cell of the same type and the result for R_s differ from the first cell giving R_s = 4.75~\Omega. Even when the former internal resistor is double the latter one, the results have been re-checked and confirmed and are in agreement to other results found in the literature.

Once the cell has been characterized, it is possible to determine the current that it will give to a known load. The next step is to devise a method to store the energy delivered by the cell or to explore the possibility of boosting the voltage to drive an MCU (microcontroller unit) directly. This will be explained in the next post.

Characterization of Peltier cells for energy harvesting applications (I)

Módulo Peltier, 32.8W, 6A, 8.8VPeltier cells are usually applied to cool surfaces when connected to an electric power supply but they can also convert differences of temperature between their sides into a voltage, known as the Seebeck effect. Therefore, it is possible to have a voltage at the ends of the wires of a Peltier cell by applying heat to one of the sides and attaching a heatsink to the other side. In terms of energy harvesting, the heat should come from a residual source such as an electrical or mechanical machine or, simply, the sun using Fresnel lenses. The cooling of the other side should be passive to minimize the energy consumption, hence the use of a heatsink. It is important to know how much energy can be obtained with a single cell as a function of the difference of temperatures, for this reason, the characterization of the cell must be the first step in the design of applications scavenging energy.

20170324_162157.jpgThe mounting scheme is shown in the side Figure where the heatsink is clearly seen on top of the cell. This is hidden by some pieces of thermal insulating foam but the two wires are visible. Finally, an aluminium plate has been adhered to the cell with a thermal conductive bonding paste.

The aim of this work is to obtain the Thévenin equivalent of an Adaptive ETH-071-14-15 Peltier cell but the process is valid for any other type of cell. The datasheet details the working curves when the cell is used as load but nothing is said about its characteristics when used as a source. The characterization requires the application of a known difference of temperatures, ΔT, and this is achieved injecting current to a pair of ceramic resistors  of 47 Ω in parallel attached to the aluminium plate with silicone.


20170324_161932_001Two LM35 temperature sensors read the temperature of the aluminium plate and the heatsink. Notice that, once the plate and the heatsink are attached to the cell, its sides are no longer reachable so the sensors have to be connected to the closest surfaces to the cell. There will be an uncertainty in the measurements but we can asume that it is negligible or, at least, that it affects the two sensors in the same manner so the difference of temperatures is the same as in the surfaces of the cell. The mounted cell is enclosed in methacrylate box coated with thermal insulating panels ensuring that, once a constant difference of temperatures, ΔT, is achieved, it is maintained along the experiment so the output voltage can be directly related to the selected ΔT.

Next: Measurements.