by Lam Pui Wan Final Report Bachelor of Engineering ...eeserver.ee.polyu.edu.hk/FYP/FYP_201718/PT_ext/PT...T HE HONG KONG POLYTECHNIC UNIVERSITY DEPARTMENT OF ELECTRICAL ENGINEERING

THE HONG KONG POLYTECHNIC UNIVERSITY

DEPARTMENT OF ELECTRICAL ENGINEERING

1

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]

𝑉𝑠: Power grid voltage



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DUT: Electrical device under test

𝑖𝑢: Output current from the device which is controlled by the former AC-DC converter

𝑉𝑢: Output voltage from the device which is controlled by former AC-DC converter

𝑉𝑑𝑐: Input DC voltage to latter DC-AC inverter

𝑉𝑖: Output AC voltage to power grid

𝑖𝑟: 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,𝑣𝑑, can be obtained by:

𝑣𝑑 = 𝑣𝑃𝑁

= 𝑣𝑃𝑛 − 𝑉𝑁𝑛

= 𝑣𝑎𝑛 − 𝑣𝑏𝑛

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 𝑣𝑜 =𝑀𝑉𝑖𝑛

2 𝜔𝑀𝑡 + 𝐻𝑖𝑔𝑕𝑒𝑟 𝑂𝑟𝑑𝑒𝑟 𝐻𝑎𝑟𝑚𝑜𝑛𝑖𝑐𝑠

And Modulation Index (M) =𝑉�̂�

𝑉�̂�=

2𝑉�̂�

𝑉𝑖𝑛

It utilizes the PWM technique that the output voltage is compared with a

high frequency carrier triangle (𝑉𝑐) and a sine wave (𝑉𝑀).



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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 = 𝐴𝑜𝑛𝑋 + 𝐵𝑜𝑛𝑌

In off-state, the main diode of the converter conducts for a duty ratio of (1-

D). The state-space equation is

X = 𝐴𝑜𝑓𝑓𝑋 + 𝐵𝑜𝑓𝑓𝑌

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

�̇� = 𝐴𝑜𝑛𝑋 + 𝐵𝑜𝑛𝑌

�̇� = 𝐴𝑜𝑓𝑓𝑋 + 𝐵𝑜𝑓𝑓𝑌

By combining the above two equations,

�̇� = [𝐷𝐴𝑜𝑛 + (1 − 𝐷)𝐴𝑜𝑓𝑓]𝑋 + [𝐷𝐵𝑜𝑛 + (1 − 𝐷)𝐵𝑜𝑓𝑓]𝑌

2. Linearizing the state-space equations with small signal variation d to

D causing small variation of x of X,

D = 𝐷+d

X = 𝑋+x

�̇� + �̇� = [(𝐷 + d)𝐴𝑜𝑛 + (1 − 𝐷 − d)𝐴𝑜𝑓𝑓](𝑋 + 𝑥) + [(𝐷 + d)𝐵𝑜𝑛

+ (1 − 𝐷 − d)𝐵𝑜𝑓𝑓]𝑌

Neglecting high order small signal variation,

�̇� = 𝐴𝑥 + 𝐹𝑑

where A = 𝐷𝐴𝑜𝑛 + (1 − 𝐷) 𝐴𝑜𝑓𝑓



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F = (𝐴𝑜𝑛 − 𝐴𝑜𝑓𝑓)𝑋 + (𝐵𝑜𝑛 − 𝐵𝑜𝑓𝑓)𝑌

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.

𝑥

𝑑= [𝑠𝐼 − 𝐴]−1𝐹

where I is a unit matrix. [𝑠𝐼 − 𝐴]−1 is the inverse of [𝑠𝐼 − 𝐴]; 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 α and β 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 α, β plane [7]

The current error is defined as:

𝑖𝑒 = 𝑖 − 𝑖𝑟𝑒𝑓

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 α, β 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. 𝐾𝑃: 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑎𝑙 𝑔𝑎𝑖𝑛, 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑖𝑛𝑔 𝑡𝑕𝑒 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒

2. 𝐾𝑑: 𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑔𝑎𝑖𝑛, 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑖𝑛𝑔 𝑡𝑕𝑒 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛𝑠

3. 𝐾𝑃: 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 𝑔𝑎𝑖𝑛, 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑖𝑛𝑔 𝑟𝑒𝑚𝑜𝑣𝑒 𝑠𝑡𝑒𝑎𝑑𝑦 − 𝑠𝑡𝑎𝑡𝑒 𝑒𝑟𝑟𝑜𝑟

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



24

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:

𝑈𝑜

𝑈𝑖=

1

1 − 𝐷

Where D =𝑡𝑜𝑛

𝑇 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,

(𝑈𝑖 − 𝑖𝐿𝑟)𝐷𝑇 = (𝑈0 − 𝑈𝑖 + 𝑖𝐿𝑟)(1 − 𝐷)𝑇



26

𝑈0

𝑈𝑖=

𝐷

(1 − 𝐷 +𝑟𝑅)

By solving the above two equations, it has

𝑈0

𝑈𝑖=

1

(1 − 𝐷)(1 +𝑟

𝑅(1 − 𝐷)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):

𝐿𝑑𝑖𝐿𝑑𝑡

= 𝑈𝑖 − 𝑖𝐿𝑟

Cdu𝐶

dt= −

𝑢𝐶

𝑅



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(𝑖�̇�𝑢𝑐

* = (−

𝑟

𝐿0

0 −1

𝑅𝐶

,(𝑖𝐿𝑢𝐶

* + (1

𝐿0+𝑈𝑖 ≡ �̇� = 𝐴𝑜𝑛𝑋 + 𝐵𝑜𝑛𝑌

For off-state refer to Fig.19,

Fig.19 Off state of Conventional boost DC/DC converter



= 𝑈𝑖 − 𝑖𝐿𝑟 − 𝑢𝐶

Cdu𝐶

dt= 𝑖𝐿 −

𝑢𝐶

𝑅


* = (−

𝑟

𝐿−

1

𝐿1

𝐶−

1

𝑅𝐶

,(𝑖𝐿𝑢𝐶

* + (1

𝐿0+𝑈𝑖 ≡ �̇� = 𝐴𝑜𝑓𝑓𝑋 + 𝐵𝑜𝑓𝑓𝑌

Averaging and linearizing the above state-space equations,

(𝑖�̇̂�𝑢�̂�

* = (−

𝑟

𝐿−

1 − 𝐷

𝐿1 − 𝐷

𝐶−

1

𝑅𝐶

,(𝑖�̂�𝑢�̂�

* + (

𝑢𝐶

𝐿

−𝑖𝐿𝐶

,𝑑 ≡ �̇� = 𝐴𝑥 + 𝐹𝑑

Solving with Laplace Transform, it gives



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𝑥

𝑑=

(𝑖�̇̂�𝑢�̂�

*

𝑑=

𝑎𝑑𝑗[𝑠𝐼 − 𝐴]𝐹

det [𝑠𝐼 − 𝐴]=

(𝑠 +

1𝑅𝐶

−1 − 𝐷

𝐿1 − 𝐷

𝐶𝑠 +

𝑟𝐿

)(

𝑢𝐶

𝐿

−𝑖𝐿𝐶

)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

Hence, the frequency responses of the boost converter are as shown below:

Control to output voltage transfer function:

𝑢�̂�

𝑑=

1 − 𝐷𝐿𝐶

𝑢𝐶 −𝑖𝐿𝐶

(𝑠 +𝑟𝐿)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

Control to inductor current transfer function:

𝑖�̂�𝑑

=(𝑠 +

1𝑅𝐶) (

𝑢𝐶

𝐿 ) + (1 − 𝐷

𝐿)(𝑖𝐿𝐶)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

Where,

𝑖𝐿 =𝐼𝑜

1 − 𝐷=

𝑢𝑐

(1 − 𝐷)𝑅

𝑢𝐶 =𝑈𝑖

(1 − 𝐷)(1 +𝑟

𝑅(1 − 𝐷)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



29

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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𝑈𝑜

𝑈𝑖=

𝐷

1 − 𝐷

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.



31

Fig.22 Conventional boost DC/DC converter with component loss

By the volt-second principle,

(𝑈𝑖 − 𝑖𝐿𝑟)𝐷𝑇 = (𝑈0 + 𝑖𝐿𝑟)(1 − 𝐷)𝑇

𝑖𝐿(1 − 𝐷) =𝑈0

𝑅

By solving the above two equations, it has

𝑈0

𝑈𝑖=

𝐷

(1 − 𝐷 +𝑟𝑅)

By small-signal modeling of it in continuous mode and using state-space

average technique,

For on-state refer to Fig.



32

Fig.23 On-state of Conventional boost DC/DC converter



= 𝑈𝑖 − 𝑖𝐿𝑟

Cdu𝐶

dt= −

𝑢𝐶

𝑅


* = (−

𝑟

𝐿0

0 −1

𝑅𝐶

,(𝑖𝐿𝑢𝐶

* + (1

𝐿0+𝑈𝑖 ≡ �̇� = 𝐴𝑜𝑛𝑋 + 𝐵𝑜𝑛𝑌

For off-state refer to Fig.24,



33

Fig.24 Off-state of Conventional boost DC/DC converter



= −𝑖𝐿𝑟 − 𝑢𝐶

Cdu𝐶

dt= 𝑖𝐿 −

𝑢𝐶

𝑅


* = (−

𝑟

𝐿−

1

𝐿1

𝐶−

1

𝑅𝐶

,(𝑖𝐿𝑢𝐶

* + (00)𝑈𝑖 ≡ �̇� = 𝐴𝑜𝑓𝑓𝑋 + 𝐵𝑜𝑓𝑓𝑌

Averaging and linearizing the above state-space equations,

(𝑖�̇̂�𝑢�̂�

* = (−

𝑟

𝐿−

1 − 𝐷

𝐿1 − 𝐷

𝐶−

1

𝑅𝐶

,(𝑖�̂�𝑢�̂�

* + (

𝑢𝐶 + 𝑈𝑖

𝐿

−𝑖𝐿𝐶

,𝑑 ≡ �̇� = 𝐴𝑥 + 𝐹𝑑

Solving with Laplace Transform, it gives

𝑥

𝑑=

(𝑖�̇̂�𝑢�̂�

*

𝑑=

𝑎𝑑𝑗[𝑠𝐼 − 𝐴]𝐹

det [𝑠𝐼 − 𝐴]=

(𝑠 +

1𝑅𝐶

−1 − 𝐷

𝐿1 − 𝐷

𝐶𝑠 +

𝑟𝐿

)(

𝑢𝐶 + 𝑈𝑖

𝐿

−𝑖𝐿𝐶

)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

Hence, the frequency responses of the buck-boost converter are as shown

below:




34

𝑢�̂�

𝑑=

1 − 𝐷𝐶

(𝑢𝐶 + 𝑈𝑖

𝐿) −

𝑖𝐿𝐶

(𝑠 +𝑟𝐿)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶


𝑖�̂�𝑑

=(𝑠 +

1𝑅𝐶) (

𝑢𝐶 + 𝑈𝑖

𝐿 ) + (1 − 𝐷

𝐿)(𝑖𝐿𝐶)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

Where,

𝑖𝐿 =𝐼𝑜

1 − 𝐷=

𝑢𝑐

(1 − 𝐷)𝑅

𝑢𝐶 =𝑈𝑖𝐷

(1 − 𝐷 +𝑟𝑅)

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



35

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

1−D

240

48=

1

1 − 𝐷

D= 0.8

2. The input ripple current can be derived by the inductance

equation as:

Ld𝑖𝐿dt

= 𝑢𝐿

Hence, ∆𝑖𝐿 =𝑢𝐿

𝐿∆𝑡 =

𝑈𝑖𝐷𝑇𝑠

𝐿

As 𝑛𝑖 =∆𝑖𝐿

𝑖𝐿 , L =


𝑖𝐿𝑛𝑖

Therefore, L=6.8mH

3. The output ripple voltage can be derived by the capacitance

equation as:

Cd𝑢𝑜

dt= 𝑖𝑐

Hence, ∆𝑈𝑜 =1

𝐶𝑖𝐶∆=

𝐼𝑜𝐷𝑇𝑠

𝐶

As 𝑛𝑢 =∆𝑈𝑜

𝑈𝑜 ,



36

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,

𝑈𝑜

𝑈𝑖=

D

1−𝐷

48

240=

𝐷

1 − 𝐷

D= 0.17

2. The input ripple current can be derived by the inductance

equation as:



37

Ld𝑖𝐿dt

= 𝑢𝐿

Hence, ∆𝑖𝐿 =𝑢𝐿

𝐿∆𝑡 =


𝐿

As 𝑛𝑖 =∆𝑖𝐿

𝑖𝐿 , L =


𝑖𝐿𝑛𝑖

Therefore, L=36mH

3. The output ripple voltage can be derived by the capacitance

equation as:

Cd𝑢𝑜

dt= 𝑖𝑐

Hence, ∆𝑈𝑜 =1

𝐶𝑖𝐶∆=

𝐼𝑜𝐷𝑇𝑠

𝐶

As 𝑛𝑢 =∆𝑈𝑜

𝑈𝑜 ,

Therefore, C=9.4uF

Regarding to the transfer functions of the boost converter,

G𝑖𝑑 (𝑠)𝑎𝑛𝑑 G𝑣𝑑 (𝑠) 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

𝑖𝐿 = 8𝐴



38

𝑢𝐶 = 240𝑉

G𝑣𝑑 (𝑠)

=𝑢�̂�

𝑑=

1 − 𝐷𝐿𝐶

𝑢𝐶 −𝑖𝐿𝐶

(𝑠 +𝑟𝐿)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

=

1 − 0.86.8 × 10−3 × 11 × 10−6 240 −

811 × 10−6 (𝑠 +

06.8 × 10−3)

𝑠2 +𝑠

150 × 11 × 10−6 +𝑠 × 0

6.8 × 10−3 +0

𝑅𝐶𝐿+

(1 − 0.8)2

6.8 × 10−3 × 11 × 10−6

=0.64 × 109 − 0.73 × 106𝑠

𝑠2 + 606𝑠 + 534760

G𝑖𝑑 (𝑠)

=𝑖�̂�𝑑

=(𝑠 +

1𝑅𝐶) (

𝑢𝐶

𝐿 ) + (1 − 𝐷

𝐿)(𝑖𝐿𝐶)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

= 35294𝑠 + 1212

𝑠2 + 606𝑠 + 534760

By using Matlab, the bode plot have been obtained as shown below.

For control to output voltage transfer function

G𝑣𝑑 (𝑠)



39



40

For control to inductor current transfer function



41

G𝑖𝑑 (𝑠)



42

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



43

loop is necessary for improving the stability of the system.

Similarly, regarding to the transfer functions of the buck-boost converter,

G𝑖𝑑 (𝑠)𝑎𝑛𝑑 G𝑣𝑑 (𝑠) 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

𝑖𝐿 = 1.6𝐴

𝑢𝐶 = 48𝑉


𝑢�̂�

𝑑=

1 − 𝐷𝐶

(𝑢𝐶 + 𝑈𝑖

𝐿) −

𝑖𝐿𝐶

(𝑠 +𝑟𝐿)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

=706 × 106 − 170 × 103𝑠

𝑠2 + 2955𝑠 + 2 × 106


𝑖�̂�𝑑

=(𝑠 +

1𝑅𝐶)(

𝑢𝐶 + 𝑈𝑖

𝐿 ) + (1 − 𝐷

𝐿)(𝑖𝐿𝐶)

𝑠2 +𝑠𝑅𝐶

+𝑠𝑟𝐿

+𝑟

𝑅𝐶𝐿+

(1 − 𝐷)2

𝐿𝐶

=8000𝑠 + 27.6 × 106

𝑠2 + 2955𝑠 + 2 × 106

For control to output voltage transfer function



44

G𝑣𝑑 (𝑠)



45

For control to inductor current transfer function

G𝑖𝑑 (𝑠)



46



47

The bode plots reflect that the loop phase shift at 180o at high frequency.



48

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,

G𝑐(𝑠) is error compensate transfer function

G𝑀(𝑠) is PWM modulation transfer function

G𝑖𝑑 (𝑠) is control to inductor current transfer function

K is current sampling constant

By adopting conventional PI controller for the error compensator,

𝐺𝑐(𝑠) = 𝐾𝑝 +𝐾𝑖

𝑆

𝐾𝑝= 0.115 and 𝐾𝑖 = 10 by ziegler-nichols method



49

While PWM modulation transfer function is

𝐺𝑀(𝑠) =1

𝑉𝑀

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,



50

G𝑐(𝑠) is error compensate transfer function

G𝑀(𝑠) is PWM modulation transfer function

G𝑉(𝑠) is control to output voltage transfer function

K is current sampling constant

By adopting conventional PI controller for the error compensator,

𝐺𝑐(𝑠) = 𝐾𝑝 +𝐾𝑖

𝑆

𝐾𝑝= 0.0176 and 𝐾𝑖 = 68.1 by ziegler-nichols method

While PWM modulation transfer function is

𝐺𝑀(𝑠) =1

𝑉𝑀

The control diagram would become as a bidirectional DC-DC converter



51

The voltage controller:

5. Result

By combining the above two converters, a DC regenerative electronic load

is obtained.

The diagram is as shown below:



52

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



53

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. Mejía. "Design of a simple

electronic load controlled with configurable load profile." Entre Ciencia E Ingenierãa

7.13(2013):9-13.

[3] 曲畅. 电流断续型直流电子负载的设计与实现. Diss. 哈尔滨工业大学, 2011.

[4] 党三磊, 丘东元, and 张波. "能量回馈型电子负载的原理介绍." 中国电源学会全国电源技术年会

2007.

[5] Jerry Hu. “Advanced Power Electronic”, HK Polytechnic University, 2017

[6] Roncero, Carlos, et al. "Controllable electronic load with energy recycling capability." Przeglad

Elektrotechniczny 87.4(2011).



54

[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] Reljić, Dejan, et al. "A COMPARISON OF PI CURRENT CONTROLLERS IN FIELD ORIENTED

INDUCTION MOTOR DRIVE." (2006).

Documents

by Lam Pui Wan Final Report Bachelor of Engineering ...eeserver.ee.polyu.edu.hk/FYP/FYP_201718/PT_ext/PT...T HE HONG KONG POLYTECHNIC UNIVERSITY DEPARTMENT OF ELECTRICAL ENGINEERING