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Project ID:PT_ext08
Regenerative Electronic Load
by
Lam Pui Wan
14112954D
Final Report
Bachelor of Engineering (Honours)
in
Electrical Engineering
Of
The Hong Kong Polytechnic University
Supervisor: Dr. W.L. Chan Date:31/3/2018
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Abstract
Electricity is inevitable and necessary nowadays in our daily life. Due to the
flourishing development of technology and science, new power devices are
released and designed every day. To ensure their reliability and quality,
manufacturers are always used an electronic load to test the devices before
promoting to the market. The electronic load is able to emulate the desired
values from the devices so that the characteristic can be obtained. However,
the conventional electronic loads are usually resistive that the power would
be dissipated during the test. This causes a kind of waste of energy. To
eliminate the energy loss, a regenerative electronic load has been promoted in
order to recover the testing energy back to the power grid or to be stored in a
rechargeable battery. The configuration of the regenerative electronic load
would be reviewed and the system of regenerative electronic load would be
designed in this paper. The main content and results of this paper are
presented as follow.
At first, the background of regenerative electronic load would be reviewed
including its principle, modeling and control method. After that, a DC
electronic load would be designed by a boost converter and a buck-boost
converter.
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Finally, a simulation model in MATLAB/Simulink environment would be set
up.
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Table of Content
1. Introduction.................................................................................................................... 5
2. Objective .................................................................................................................. 7
3. Background .................................................................................................... 8
3.1Overview of the regenerative electronic load ............................................. 8
3.1.1 Working principle of the AC regenerative electronic load .............. 8
3.1.2 Working principle of the DC regenerative electronic load .......... 13
3.2 Modeling of converters ......................................................................................... 14
3.3 Control of converters ............................................................................................. 17
3.3.1 Current control method ................................................................................... 17
3.3.2 Hysteresis band current control ................................................................. 18
3.3.3 PID Controller ........................................................................................................ 21
4. Methodology .................................................................................................... 21
5. Result .............................................................................................................. 51
6. Conclusion ........................................................................................... 52
7.Reference list .................................................................................. 53
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1. Introduction
Electrical equipment is conventionally required to be tested its
characteristics and functions, for example, electrical performance test,
protection test or reliability test before releasing to the market. Most of the
tests are conducted under a load. Instead of using fixed-resistor banks of
different sizes, manufacturers would also use electronic loads to simulate
various power states. To eliminate the inconveniences of the use of fixed-
resistor banks, the electronic load can provide an easier way and a much
higher throughput for varying loads. The electronic load is comprised of a
bank of power electronic which governs the amount of current by the
equipment drawn from the power source on test.
Restrepo et al. [1] proposed that using a microcontroller with different load
profiles to generate different load values in order to achieve the dynamic
response and static performance of the tested equipment as shown on
Fig.1.
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Fig.1 General Structure of Electronic load [2]
This is the conventional electronic load system. The load profile is normally
a sequence of load values with digital format. The microcontroller consists
of Digital to Analog (D/A) converter is used to control and program the
load values from the load profile so as to provide the reference value for
testing the load. The MOSFET transistor is operated in ohmic region
allowing for a varying of drain current (Id) as well as the voltage between
gate and source (VGS). Basically, the power source would be discharged by
the electronic load in particular ways. In fact, the current from power
source would be changed according to the change of load. Therefore, the
electronic load can be used to control the current and thus emulate the
condition.
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Fig.2 Power and control diagram of the electronic load [3]
However, both of the loads are resistive so that the energy would be
dissipated in the form of heat loss. The equipment would either be aging
and deteriorated quickly. Moreover, it is hard to simulate the dynamic
response of the equipment since the rating or characteristic of the resistive
load is normally fixed. In order to overcome the above weaknesses,
regenerative electronic loads are currently proposed to be used.
For the regenerative electronic load, it is divided into two parts, the circuit
of load and the circuit of regeneration. For the circuit of load, it adopts the
concept of conventional electronic load while for the circuit of
regeneration; it is usually comprised of converters to send back the energy.
This project is to study the topologies and characteristics of regenerative
electronic load.
2. Objective
This project aims
To realize the characteristics of regenerative electronic load.
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To review the design methods of conventional regenerative electronic
load.
To design and implement a regenerative electronic load.
3. Background
3.1Overview of the regenerative electronic load
3.1.1 Working principle of the AC regenerative electronic
load
Fig.3 AC regenerative electronic load system [4]
๐๐ : Power grid voltage
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DUT: Electrical device under test
๐๐ข: Output current from the device which is controlled by the former AC-DC converter
๐๐ข: Output voltage from the device which is controlled by former AC-DC converter
๐๐๐: Input DC voltage to latter DC-AC inverter
๐๐: Output AC voltage to power grid
๐๐: Grid-connected current
The AC regenerative electronic load system has been presented as shown
on Fig.1. Two converters are connected between the output of the
electrical device under test (DUT) and the power grid. The former AC-DC
converter is used to emulate the desired load profile by draining the
current based on the desired values from the DUT while the latter DC-AC
inverter is used to regenerate the energy absorbed during the test back to
the grid with unity power factor.
These two types of converter are adopted because both of them are
current controlled. It means that the harmonic and unbalanced load
current can be compensated. Therefore, it can work with and emulate any
type of load (Rafael, ).
For the working principle of a three-phase AC-DC converter, it is based on
diodes conducting principle.
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Fig.4 Three-phase AC-DC converter[5]
The diodes conducting principle is that there are always and only two
diodes conducting at any moment. As shown on Fig.4, the one with
highest voltage is conducted for the upper diodes while the one with
lowest voltage is conducted for the bottom diodes.
Fig.5 Three-phase voltage waveform and Output DC voltage waveform [5]
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The output DC voltage,๐ฃ๐, can be obtained by:
๐ฃ๐ = ๐ฃ๐๐
= ๐ฃ๐๐ โ ๐๐๐
= ๐ฃ๐๐ โ ๐ฃ๐๐
For the working principle of DC-AC inverter, it is usually company with
Sinusoidal Pulse-width Modulation (SPWM), for example, SPWM Single-
phase half-bridge inverter as shown on Fig. 6.
Fig.6 SPWM Single-phase half-bridge inverter diagram [5]
Where ๐ฃ๐ =๐๐๐๐
2 ๐๐๐ก + ๐ป๐๐๐๐๐ ๐๐๐๐๐ ๐ป๐๐๐๐๐๐๐๐
And Modulation Index (M) =๐๏ฟฝฬ๏ฟฝ
๐๏ฟฝฬ๏ฟฝ=
2๐๏ฟฝฬ๏ฟฝ
๐๐๐
It utilizes the PWM technique that the output voltage is compared with a
high frequency carrier triangle (๐๐) and a sine wave (๐๐).
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Carlos et al. [6] also suggested using two electronic converters with a
common DC-bus as shown on Fig.7 for a controllable electronic load for
high power tests with the function of recycling of the energy to the grid.
Fig.7 Active electronic load with energy recycling scheme [6]
The left inverter is for demanding a load current from the grid while the
right inverter is for recycling energy back to the grid.
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Fig.8 Active electronic load with energy recovery topology
Base on the above topology, the left inverter is a controllable AC-DC
converter while the right inverter is a three-phase full-bridge inverter.
The average DC voltage can be controlled from a positive maximum to a
negative minimum value in continuous manner. There is also
bidirectional power flow. In rectifier mode, power flows from ac to dc
side. In inverter mode, power is transferred from the dc to ac side.
3.1.2 Working principle of the DC regenerative electronic
load
Fig.9 Topology of Regenerative Electronic Load [3]
The system of DC regenerative electronic load is similar with AC
regenerative electronic load. A DC-DC converter and a DC-AC inverter are
connected between the output of the DC electrical device under test and
the power grid for emulating the desired load profile and regenerating the
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energy respectively as well. In order to regenerate the power into the grid,
the output voltage of DC/DC side must be stepped up to high level.
Therefore, for electronic load circuit, it is usually adopted a DC/DC boost
converter. The circuit is as shown below.
Fig. 10 DC-DC boost converter diagram [5]
3.2 Modeling of converters
As regenerative electronic loads are conventionally comprised of
converters, in order to design and analysis suitable converters for the
electronic load, it is usually modeling of converters under steady state
condition with open-loop control. Therefore, the control of converters can
be decided afterward. The converter has run for a considerable time to
settle down to a stable condition with their regular gate signals. The steady
state analysis is actually for designing the converters. However, practical
converters are rare to work in open-loop. By comparing to open-loop
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control, closed-loop control is frequently used so that the parameters, such
as, output voltage, output current and input current, can be regulated to
desired levels all the time even with the change of conditions, for example,
variation of load, input voltage and voltage drop from power loss.
Regarding to design a closed-loop control system, dynamic models of the
converter has to be obtained in the first place which are mathematical
models, in the form of transfer functions, with the response characteristic
from applying small-signal. DC/DC converters are highly non-linear and
have the features of both analogue and digital systems. They are controlled
by digital type of duty ratio of gate signals for most converters and by
phase difference of gate signals for phase shift converters. As a result, state-
space average technique is usually used for dynamic modeling. It is also
focused on two states, on-state and off-state. In on-state, the transistor of
the converter conducts for a ration of D of a switching period. The state-
space equation in on-state is
X = ๐ด๐๐๐ + ๐ต๐๐๐
In off-state, the main diode of the converter conducts for a duty ratio of (1-
D). The state-space equation is
X = ๐ด๐๐๐๐ + ๐ต๐๐๐๐
where X is the state-space variable such as a set of capacitor voltage and
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inductor current in the form of matrix. Aon and Bon, and Aoff and Boff are
the state-space matrices of the converter during on-state and off-state,
respectively. Y is the input variable such as input voltage, Vin.
There are several steps to obtain the control model. For example,
1. Averaging the state-space equations with on-state DTs, off-state (1-
D)Ts
๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐ + ๐ต๐๐๐
๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐๐ + ๐ต๐๐๐๐
By combining the above two equations,
๏ฟฝฬ๏ฟฝ = [๐ท๐ด๐๐ + (1 โ ๐ท)๐ด๐๐๐]๐ + [๐ท๐ต๐๐ + (1 โ ๐ท)๐ต๐๐๐]๐
2. Linearizing the state-space equations with small signal variation d to
D causing small variation of x of X,
D = ๐ท+d
X = ๐+x
๏ฟฝฬ๏ฟฝ + ๏ฟฝฬ๏ฟฝ = [(๐ท + d)๐ด๐๐ + (1 โ ๐ท โ d)๐ด๐๐๐](๐ + ๐ฅ) + [(๐ท + d)๐ต๐๐
+ (1 โ ๐ท โ d)๐ต๐๐๐]๐
Neglecting high order small signal variation,
๏ฟฝฬ๏ฟฝ = ๐ด๐ฅ + ๐น๐
where A = ๐ท๐ด๐๐ + (1 โ ๐ท) ๐ด๐๐๐
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F = (๐ด๐๐ โ ๐ด๐๐๐)๐ + (๐ต๐๐ โ ๐ต๐๐๐)๐
The state-space equation of the converter becomes a linearized equation. It
can be solved by Laplace Transform to give a transfer function as shown
below.
๐ฅ
๐= [๐ ๐ผ โ ๐ด]โ1๐น
where I is a unit matrix. [๐ ๐ผ โ ๐ด]โ1 is the inverse of [๐ ๐ผ โ ๐ด]; s=jw
The control-to-output small-signal transfer function of a converter has
been obtained.
3.3 Control of converters
After modeling of converters, there is more information for deciding the
control method of converters in order to obtain the desired values.
There are two main control methods, voltage control method and
current control method.
3.3.1 Current control method
The current control methods are important in power electronic circuit
since they are able to force the current vector in the (three phase) load
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according to a reference trajectory.
3.3.2 Hysteresis band current control
For the current control method, a hysteresis band current control is
usually adopted. The advantages of adopting the hysteresis band current
control are its fast response current loop ad simplicity of
implementation; the disadvantage of it is that PWM frequency may vary
with the band because peak-to-peak current ripple is required to be
controlled at all points of the fundamental frequency wave []. Therefore,
the hysteresis band must be programmed as function of load to optimize
the PWM performance. The principle of hysteresis band current control
is to compare the actual phase current with the tolerance band around
the reference current associated with that phase. It derives the
switching signals from the comparison of the current error with a fixed
tolerance band. There are two hysteresis band current control methods
of three-phase voltage source inverter, hexagon hysteresis based control
and square hysteresis based control. For hexagon hysteresis based
control, the purpose is to maintain the actual value of the currents with
its hysteresis bands all the time. Refer to the graph below, three phase
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currents are transformed into ฮฑ and ฮฒ coordinate system due to their
dependence. The actual value of the current i must be kept within the
hexagon area. The inverter will be switched if i reach and exceed the
border of the hexagon.
Fig.11 Hysteresis hexagon in ฮฑ, ฮฒ plane [7]
The current error is defined as:
๐๐ = ๐ โ ๐๐๐๐
For square hysteresis based control, it is similar to hexagon that the
current i is controlled within the square.
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Fig.12 Square hexagon in ฮฑ, ฮฒ plane [7]
In practical, the hysteresis band current controller is used to track the
reference load current with minimum error as shown below.
Fig.13 Hysteresis Band Current Controller [6]
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3.3.3 PID Controller
A proportional-integral-derivative (PID) controller is always used in
feedback loops control. It can be used to achieve desired performance
criteria, for example, steady state error, reference tracking and quick
response. It is usually used in closed-loop system such as, voltage control
loop and current control loop [8].
There are three parameters of PID controller
1. ๐พ๐: ๐๐๐๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐, ๐๐๐๐๐๐ ๐๐๐ก๐๐๐ ๐ก๐๐ ๐ ๐๐๐๐ ๐๐ ๐๐๐ ๐๐๐๐ ๐
2. ๐พ๐: ๐๐๐๐๐ฃ๐๐ก๐๐ฃ๐ ๐๐๐๐, ๐๐๐๐๐๐ ๐๐๐ก๐๐๐ ๐ก๐๐ ๐๐ ๐๐๐๐๐๐ก๐๐๐๐
3. ๐พ๐: ๐๐๐ก๐๐๐๐๐ ๐๐๐๐, ๐๐๐๐๐๐ ๐๐๐ก๐๐๐ ๐๐๐๐๐ฃ๐ ๐ ๐ก๐๐๐๐ฆ โ ๐ ๐ก๐๐ก๐ ๐๐๐๐๐
There are three types of PID controller.
1. Proportional Control
2. Proportional-Derivative (PD) Control
3. Proportional-integral-derivative (PID) Control
4. Methodology
The scope of this project is to exam the regenerative electronic load. In
order to achieve the purpose, DC regenerative electronic load with
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recycling power to a rechargeable battery would be studied.
The topology would be as shown below.
Fig.14 Topology of DC regenerative electronic load [4]
By using DC regenerative electronic load, the output of DC power supply
would connect the input of electronic load and thus test the supply. The
output of electronic would connect a rechargeable battery to recycle the
tested power. Basically, the DC regenerative is comprised of three parts,
electronic load circuit, DC bus capacitor and regenerative circuit as shown
on Fig.7. Therefore, this project would study and analysis their principles
and thus design the model. The electronic load circuit is for emulating the
actual load. Since the output current from the DC power supply is decided
by the load and the load characteristic is current related, the testing can be
achieved if the value of the current in the electronic load system is equal to
the output current. A reference value of current based on the power supply
output would be calculated and the input current in the electronic load
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would chase the reference value quickly in order to achieve the
characteristic.
In DC electronic load system, the load simulation is comprised of the
testing DC power supply and DC/DC converter. There are two functions of
DC/DC converter. The first one is to step up the voltage and the second one
is to control the input current with the reference value. Therefore, boost
converter is adopted to use. Regarding to the second function, the
electronic load is required to be able to work as constant current mode and
constant resistance mode. Under the constant current mode, the output of
the DC power supply would be limited and regulated to the desired
constant level. Under the constant resistance mode, the desired constant
resistance value would be emulated. It is equal to the situation that the DC
power supply connects to the constant resistive load. In fact, in order to
fully realize the testing DC power supply, the electronic load is also
required to be able to have dynamic load responses.
Therefore, it has to select a suitable DC/DC converter as well as an
appropriate controller.
DC/DC converter selection
To ensure the inverting process can be preceded smoothly, it should be
adopted a high step-up DC/DC converter. As there are several boost DC/DC
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converters, they would be studied and analyzed.
1. Conventional boost DC/DC converter
The structure of conventional boost DC/DC converter is as shown on
Fig.15.
Fig.15 Conventional boost DC/DC converter [4]
Assumed that the inductance L and capacitance C are large to ensure the
output voltage Uo is constant. Under the ideal case, namely, no energy loss,
and steady-state operation mode, by considering the volt-second balance,
its voltage conversion ratio is:
๐๐
๐๐=
1
1 โ ๐ท
Where D =๐ก๐๐
๐ is a duty ratio; ton is on-state over an on-off period; T is an
on-off period.
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Fig.16 Voltage conversion ratio of boost DC/DC converter [5]
It shows that Uo/Ui >1 and depends solely on D. Ideally, it can be infinite
when D=1. However, it is limited by the component loss in a practical
circuit. Hence, the component loss can be treated as a resistor, r, and series
to inductor.
Fig.17 Conventional boost DC/DC converter with component loss [4]
By the volt-second principle,
(๐๐ โ ๐๐ฟ๐)๐ท๐ = (๐0 โ ๐๐ + ๐๐ฟ๐)(1 โ ๐ท)๐
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๐0
๐๐=
๐ท
(1 โ ๐ท +๐๐
)
By solving the above two equations, it has
๐0
๐๐=
1
(1 โ ๐ท)(1 +๐
๐
(1 โ ๐ท)2)
By small-signal modeling of it in continuous mode and using state-space
average technique,
For on-state refer to Fig.18,
Fig.18 On-state of Conventional boost DC/DC converter
By Kirchhoffs Voltage Law (KVL) and Kirchhoffs Current Law (KCL):
๐ฟ๐๐๐ฟ๐๐ก
= ๐๐ โ ๐๐ฟ๐
Cdu๐ถ
dt= โ
๐ข๐ถ
๐
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(๐๏ฟฝฬ๏ฟฝ๐ข๐
* = (โ
๐
๐ฟ0
0 โ1
๐
๐ถ
,(๐๐ฟ๐ข๐ถ
* + (1
๐ฟ0+๐๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐ + ๐ต๐๐๐
For off-state refer to Fig.19,
Fig.19 Off state of Conventional boost DC/DC converter
By Kirchhoffs Voltage Law (KVL) and Kirchhoffs Current Law (KCL):
๐ฟ๐๐๐ฟ๐๐ก
= ๐๐ โ ๐๐ฟ๐ โ ๐ข๐ถ
Cdu๐ถ
dt= ๐๐ฟ โ
๐ข๐ถ
๐
(๐๏ฟฝฬ๏ฟฝ๐ข๐
* = (โ
๐
๐ฟโ
1
๐ฟ1
๐ถโ
1
๐
๐ถ
,(๐๐ฟ๐ข๐ถ
* + (1
๐ฟ0+๐๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐๐ + ๐ต๐๐๐๐
Averaging and linearizing the above state-space equations,
(๐๏ฟฝฬฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
* = (โ
๐
๐ฟโ
1 โ ๐ท
๐ฟ1 โ ๐ท
๐ถโ
1
๐
๐ถ
,(๐๏ฟฝฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
* + (
๐ข๐ถ
๐ฟ
โ๐๐ฟ๐ถ
,๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐ฅ + ๐น๐
Solving with Laplace Transform, it gives
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๐ฅ
๐=
(๐๏ฟฝฬฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
*
๐=
๐๐๐[๐ ๐ผ โ ๐ด]๐น
det [๐ ๐ผ โ ๐ด]=
(๐ +
1๐
๐ถ
โ1 โ ๐ท
๐ฟ1 โ ๐ท
๐ถ๐ +
๐๐ฟ
)(
๐ข๐ถ
๐ฟ
โ๐๐ฟ๐ถ
)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Hence, the frequency responses of the boost converter are as shown below:
Control to output voltage transfer function:
๐ข๏ฟฝฬ๏ฟฝ
๐=
1 โ ๐ท๐ฟ๐ถ
๐ข๐ถ โ๐๐ฟ๐ถ
(๐ +๐๐ฟ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Control to inductor current transfer function:
๐๏ฟฝฬ๏ฟฝ๐
=(๐ +
1๐
๐ถ) (
๐ข๐ถ
๐ฟ ) + (1 โ ๐ท
๐ฟ)(๐๐ฟ๐ถ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Where,
๐๐ฟ =๐ผ๐
1 โ ๐ท=
๐ข๐
(1 โ ๐ท)๐
๐ข๐ถ =๐๐
(1 โ ๐ท)(1 +๐
๐
(1 โ ๐ท)2)
For regenerative circuit, a buck-boost converter is adopted to use. It is
because the buck-boost converter has an output voltage magnitude that is
either greater than or less than the input voltage magnitude. It can produce
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a range of output voltages. As the step up ratio of conventional boost
converter is normally 5 to 6 times, the buck-boost converter can further
step up the input voltage to reach the voltage level of rechargeable
batteries under boost mode if the DC power testing equipment has
relatively low input. Similarly, if the voltage level of the adopted
rechargeable batteries is lower than the DC power testing equipment, the
buck-boost converter can be operated in buck mode to fulfill the batteries.
The structure of conventional boost DC/DC converter is as shown on
Fig.20.
Fig.20 Conventional buck-boost DC/DC converter [5]
The output voltage is of the opposite polarity than the input. Under the
ideal case, namely, no energy loss, and steady-state operation mode, by
considering the volt-second balance, its voltage conversion ratio is:
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๐๐
๐๐=
๐ท
1 โ ๐ท
Where D=ton/T is a duty ratio; ton is on-state over an on-off period; T is an
on-off period.
Fig.21 Voltage conversion ratio of buck-boost DC/DC converter [5]
Therefore, it looks like a product of the conversion ratio of buck and boost
converters. Similarly, there is also component loss in a practical circuit.
Hence, the component loss can be treated as a resistor, r, and series to
inductor.
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Fig.22 Conventional boost DC/DC converter with component loss
By the volt-second principle,
(๐๐ โ ๐๐ฟ๐)๐ท๐ = (๐0 + ๐๐ฟ๐)(1 โ ๐ท)๐
๐๐ฟ(1 โ ๐ท) =๐0
๐
By solving the above two equations, it has
๐0
๐๐=
๐ท
(1 โ ๐ท +๐๐
)
By small-signal modeling of it in continuous mode and using state-space
average technique,
For on-state refer to Fig.
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Fig.23 On-state of Conventional boost DC/DC converter
By Kirchhoffs Voltage Law (KVL) and Kirchhoffs Current Law (KCL):
๐ฟ๐๐๐ฟ๐๐ก
= ๐๐ โ ๐๐ฟ๐
Cdu๐ถ
dt= โ
๐ข๐ถ
๐
(๐๏ฟฝฬ๏ฟฝ๐ข๐
* = (โ
๐
๐ฟ0
0 โ1
๐
๐ถ
,(๐๐ฟ๐ข๐ถ
* + (1
๐ฟ0+๐๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐ + ๐ต๐๐๐
For off-state refer to Fig.24,
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Fig.24 Off-state of Conventional boost DC/DC converter
By Kirchhoffs Voltage Law (KVL) and Kirchhoffs Current Law (KCL):
๐ฟ๐๐๐ฟ๐๐ก
= โ๐๐ฟ๐ โ ๐ข๐ถ
Cdu๐ถ
dt= ๐๐ฟ โ
๐ข๐ถ
๐
(๐๏ฟฝฬ๏ฟฝ๐ข๐
* = (โ
๐
๐ฟโ
1
๐ฟ1
๐ถโ
1
๐
๐ถ
,(๐๐ฟ๐ข๐ถ
* + (00)๐๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐๐๐๐ + ๐ต๐๐๐๐
Averaging and linearizing the above state-space equations,
(๐๏ฟฝฬฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
* = (โ
๐
๐ฟโ
1 โ ๐ท
๐ฟ1 โ ๐ท
๐ถโ
1
๐
๐ถ
,(๐๏ฟฝฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
* + (
๐ข๐ถ + ๐๐
๐ฟ
โ๐๐ฟ๐ถ
,๐ โก ๏ฟฝฬ๏ฟฝ = ๐ด๐ฅ + ๐น๐
Solving with Laplace Transform, it gives
๐ฅ
๐=
(๐๏ฟฝฬฬ๏ฟฝ๐ข๏ฟฝฬ๏ฟฝ
*
๐=
๐๐๐[๐ ๐ผ โ ๐ด]๐น
det [๐ ๐ผ โ ๐ด]=
(๐ +
1๐
๐ถ
โ1 โ ๐ท
๐ฟ1 โ ๐ท
๐ถ๐ +
๐๐ฟ
)(
๐ข๐ถ + ๐๐
๐ฟ
โ๐๐ฟ๐ถ
)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Hence, the frequency responses of the buck-boost converter are as shown
below:
Control to output voltage transfer function:
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๐ข๏ฟฝฬ๏ฟฝ
๐=
1 โ ๐ท๐ถ
(๐ข๐ถ + ๐๐
๐ฟ) โ
๐๐ฟ๐ถ
(๐ +๐๐ฟ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Control to inductor current transfer function:
๐๏ฟฝฬ๏ฟฝ๐
=(๐ +
1๐
๐ถ) (
๐ข๐ถ + ๐๐
๐ฟ ) + (1 โ ๐ท
๐ฟ)(๐๐ฟ๐ถ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
Where,
๐๐ฟ =๐ผ๐
1 โ ๐ท=
๐ข๐
(1 โ ๐ท)๐
๐ข๐ถ =๐๐๐ท
(1 โ ๐ท +๐๐
)
For the sake of convenience to simulate the result, it is assumed that the
above DC regenerative electronic load is used to test a solar PV panel.
Normally, the panels are working under the voltage 48V and the current 8A
and thus the watt is around 380W. It is also assumed that
1. The output voltage (Uo)= 240v
2. Switching frequency (Fs)=50kHz
3. The percentage of input ripple current (ni)=2%
4. The percentage of output ripple voltage (nv)=1%
5. The output resistance=150 ohm
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By solving the equations mentioned in the part of boost converter for
selecting the values of boost converter, they give,
1. For voltage conversion ratio,
Uo
Ui=
1
1โD
240
48=
1
1 โ ๐ท
D= 0.8
2. The input ripple current can be derived by the inductance
equation as:
Ld๐๐ฟdt
= ๐ข๐ฟ
Hence, โ๐๐ฟ =๐ข๐ฟ
๐ฟโ๐ก =
๐๐๐ท๐๐
๐ฟ
As ๐๐ =โ๐๐ฟ
๐๐ฟ , L =
๐๐๐ท๐๐
๐๐ฟ๐๐
Therefore, L=6.8mH
3. The output ripple voltage can be derived by the capacitance
equation as:
Cd๐ข๐
dt= ๐๐
Hence, โ๐๐ =1
๐ถ๐๐ถโ=
๐ผ๐๐ท๐๐
๐ถ
As ๐๐ข =โ๐๐
๐๐ ,
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Therefore, C=11uF
Similarly, it is assumed that a 48V rechargeable battery pack is used for
storing the regenerative energy.
1. The output voltage=48V
2. Switching frequency (Fs)=50kHz
3. The input current=1.6A
4. The percentage of input ripple current (ni)=2%
5. The percentage of output ripple voltage (nv)=1%
6. The output resistance = 36 ohm
By solving the equations mentioned in the part of buck-boost converter for
selecting the values of buck-boost converter, they give,
1. For voltage conversion ratio,
๐๐
๐๐=
D
1โ๐ท
48
240=
๐ท
1 โ ๐ท
D= 0.17
2. The input ripple current can be derived by the inductance
equation as:
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Ld๐๐ฟdt
= ๐ข๐ฟ
Hence, โ๐๐ฟ =๐ข๐ฟ
๐ฟโ๐ก =
๐๐๐ท๐๐
๐ฟ
As ๐๐ =โ๐๐ฟ
๐๐ฟ , L =
๐๐๐ท๐๐
๐๐ฟ๐๐
Therefore, L=36mH
3. The output ripple voltage can be derived by the capacitance
equation as:
Cd๐ข๐
dt= ๐๐
Hence, โ๐๐ =1
๐ถ๐๐ถโ=
๐ผ๐๐ท๐๐
๐ถ
As ๐๐ข =โ๐๐
๐๐ ,
Therefore, C=9.4uF
Regarding to the transfer functions of the boost converter,
G๐๐ (๐ )๐๐๐ G๐ฃ๐ (๐ ) are represented as control to output voltage transfer
function and control to inductor current transfer function respectively,
Assume there is no component loss,
r = 0 ohm
๐๐ฟ = 8๐ด
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๐ข๐ถ = 240๐
G๐ฃ๐ (๐ )
=๐ข๏ฟฝฬ๏ฟฝ
๐=
1 โ ๐ท๐ฟ๐ถ
๐ข๐ถ โ๐๐ฟ๐ถ
(๐ +๐๐ฟ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
=
1 โ 0.86.8 ร 10โ3 ร 11 ร 10โ6 240 โ
811 ร 10โ6 (๐ +
06.8 ร 10โ3)
๐ 2 +๐
150 ร 11 ร 10โ6 +๐ ร 0
6.8 ร 10โ3 +0
๐
๐ถ๐ฟ+
(1 โ 0.8)2
6.8 ร 10โ3 ร 11 ร 10โ6
=0.64 ร 109 โ 0.73 ร 106๐
๐ 2 + 606๐ + 534760
G๐๐ (๐ )
=๐๏ฟฝฬ๏ฟฝ๐
=(๐ +
1๐
๐ถ) (
๐ข๐ถ
๐ฟ ) + (1 โ ๐ท
๐ฟ)(๐๐ฟ๐ถ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
= 35294๐ + 1212
๐ 2 + 606๐ + 534760
By using Matlab, the bode plot have been obtained as shown below.
For control to output voltage transfer function
G๐ฃ๐ (๐ )
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For control to inductor current transfer function
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G๐๐ (๐ )
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The bode plots reflect that the phase shift is large and lead or lag
compensation will make the system to be unstable. Hence, an inner current
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loop is necessary for improving the stability of the system.
Similarly, regarding to the transfer functions of the buck-boost converter,
G๐๐ (๐ )๐๐๐ G๐ฃ๐ (๐ ) are represented as control to output voltage transfer
function and control to inductor current transfer function respectively,
Assume there is no component loss,
r = 0 ohm
๐๐ฟ = 1.6๐ด
๐ข๐ถ = 48๐
Control to output voltage transfer function:
๐ข๏ฟฝฬ๏ฟฝ
๐=
1 โ ๐ท๐ถ
(๐ข๐ถ + ๐๐
๐ฟ) โ
๐๐ฟ๐ถ
(๐ +๐๐ฟ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
=706 ร 106 โ 170 ร 103๐
๐ 2 + 2955๐ + 2 ร 106
Control to inductor current transfer function:
๐๏ฟฝฬ๏ฟฝ๐
=(๐ +
1๐
๐ถ)(
๐ข๐ถ + ๐๐
๐ฟ ) + (1 โ ๐ท
๐ฟ)(๐๐ฟ๐ถ)
๐ 2 +๐ ๐
๐ถ
+๐ ๐๐ฟ
+๐
๐
๐ถ๐ฟ+
(1 โ ๐ท)2
๐ฟ๐ถ
=8000๐ + 27.6 ร 106
๐ 2 + 2955๐ + 2 ร 106
For control to output voltage transfer function
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G๐ฃ๐ (๐ )
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For control to inductor current transfer function
G๐๐ (๐ )
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The bode plots reflect that the loop phase shift at 180o at high frequency.
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Hence, a voltage control loop with lead-lag compensation is suggested to
use.
Based on the above result, the block diagram of closed-loop current control
of the electronic load circuit (boost converter) is as shown,
Fig.
Where,
G๐(๐ ) is error compensate transfer function
G๐(๐ ) is PWM modulation transfer function
G๐๐ (๐ ) is control to inductor current transfer function
K is current sampling constant
By adopting conventional PI controller for the error compensator,
๐บ๐(๐ ) = ๐พ๐ +๐พ๐
๐
๐พ๐= 0.115 and ๐พ๐ = 10 by ziegler-nichols method
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While PWM modulation transfer function is
๐บ๐(๐ ) =1
๐๐
The control diagram would become
Similarly, the block diagram of closed-loop voltage control of the
regenerative circuit (buck-boost converter) is as shown below,
Fig.
Where,
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G๐(๐ ) is error compensate transfer function
G๐(๐ ) is PWM modulation transfer function
G๐(๐ ) is control to output voltage transfer function
K is current sampling constant
By adopting conventional PI controller for the error compensator,
๐บ๐(๐ ) = ๐พ๐ +๐พ๐
๐
๐พ๐= 0.0176 and ๐พ๐ = 68.1 by ziegler-nichols method
While PWM modulation transfer function is
๐บ๐(๐ ) =1
๐๐
The control diagram would become as a bidirectional DC-DC converter
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The voltage controller:
5. Result
By combining the above two converters, a DC regenerative electronic load
is obtained.
The diagram is as shown below:
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The currents and voltages are able to be control in the desired values.
6. Conclusion
The regenerative electronic load is reviewed and the system has been
simulated by MATLAB/Simulink. Although the result showed that the
currents and voltages are controlled in which means those DC electrical
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device can be tested, there are also many improvements on the
regenerative system, such as, response time, better performance of
converters and so on.
7. Reference list
[1] Klein, R. L, A. F. De Paiva, and M. Mezaroba. Regenerative AC electronic load with LCL filter.
2012.
[2] Alvarez, Andres Fernando Restrepo, J. A. R. Gutierrez, and E. F. Mejรญa. "Design of a simple
electronic load controlled with configurable load profile." Entre Ciencia E Ingenierรฃยญa
7.13(2013):9-13.
[3] ๆฒ็
. ็ตๆตๆญ็ปญๅ็ดๆต็ตๅญ่ด่ฝฝ็่ฎพ่ฎกไธๅฎ็ฐ. Diss. ๅๅฐๆปจๅทฅไธๅคงๅญฆ, 2011.
[4] ๅ
ไธ็ฃ, ไธไธๅ
, and ๅผ ๆณข. "่ฝ้ๅ้ฆๅ็ตๅญ่ด่ฝฝ็ๅ็ไป็ป." ไธญๅฝ็ตๆบๅญฆไผๅ
จๅฝ็ตๆบๆๆฏๅนดไผ
2007.
[5] Jerry Hu. โAdvanced Power Electronicโ, HK Polytechnic University, 2017
[6] Roncero, Carlos, et al. "Controllable electronic load with energy recycling capability." Przeglad
Elektrotechniczny 87.4(2011).
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[7] Milosevic, Mirjana, G. Andersson, and S. Grabic. "Decoupling Current Control and Maximum
Power Point Control in Small Power Network with Photovoltaic Source." IEEE Pes Power
Systems Conference and Exposition IEEE, 2006:1005-1011.
[8] Reljiฤ, Dejan, et al. "A COMPARISON OF PI CURRENT CONTROLLERS IN FIELD ORIENTED
INDUCTION MOTOR DRIVE." (2006).