1

Control Transition Mode from Voltage Control to

MPPT for PV Generators in Isolated DC Microgrids

V. Fernão Pires1,3,4

, Armando Cordeiro2,3,4

, Daniel Foito1,4,5

, J. Fernando Silva 3,6

1 ESTSetúbal, Instituto Politécnico de Setúbal, Setúbal, Portugal

2 ISEL, LCEC, Instituto Politécnico de Lisboa, Lisboa, Portugal

3 INESC-ID Lisboa, Portugal

4 Sustain.RD, Instituto Politécnico de Setúbal, Setúbal, Portugal

5 Uninova - Universidade Nova de Lisboa, Lisboa

6 Instituto Superior Técnico - Universidade de Lisboa, Lisboa

Corresponding Author:

Professor Daniel Foito

Electrical Engineering Department

ESTSetúbal, Instituto Politécnico Setúbal

Campus do IPS - Estefanilha

2914-761 Setúbal, PORTUGAL

Tel: +351-265 790 000 (ext. 4315)

email: daniel.foito@estsetubal.ips.pt

Abstract - The integration of photovoltaic (PV) power sources on a large scale into grid-tied and islanded

solutions is now a reality. Despite the fluctuating characteristics of solar energy, the direct current (DC) nature

of PV sources is highly compatible with DC microgrids compared with AC solutions. However, as more PV

sources are being installed, challenges related to the control of DC microgrids are also increasing, especially for

islanded applications. To ensure an appropriate transition from the maximum power point to DC bus voltage

regulation of DC microgrids, novel control strategies must be designed, and this aspect is particularly critical

when these grids operate without energy storage systems. We therefore propose a new control strategy for a PV

generator for islanded DC microgrids without storage systems. Our approach allows for smooth switching from

the maximum power point mode to the voltage control regulation mode (V control) when the available PV power

is excessive, thus limiting the generated PV power and returning to maximum power point operation when all

the available power is required. This allows us to control a DC microgrid without a storage system and provides

a new alternative that offers a cost-effective solution for rural and deprived regions. Our solution combines the

maximum power point tracking algorithm with a proportional integral compensator for V control and minimises

undervoltage/overvoltage problems in the DC bus. The behaviour of the isolated DC microgrid under different

conditions, for example in the case of transitions, perturbations, and different types of loads, is also studied and

verified. The performance of the proposed control strategy is confirmed by several simulation and experimental

tests.

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Keywords - Photovoltaic systems, maximum power point tracking, constant power, quadratic Boost converter,

DC microgrids.

I. INTRODUCTION

Over recent years, the increasing development and integration of new small-scale renewable energy sources (RES) in

the context of electrical distribution networks has given rise to the related concept of microgrids. Microgrids have been

highlighted as a very promising future solution [1] that will allow for the high penetration of RES into AC grids. From the

perspective of distributed generation (DG), microgrids have several interesting characteristics, such as distributed power

system management, advanced monitoring and diagnostics, optimisation/self-optimisation capabilities, operation in both

grid-connected and islanded modes, and demand response/energy management support [2]. The study and development

of microgrids have focused not only on AC but also on DC distribution networks. Microgrids based on DC distribution

networks usually allow for the simple integration of RES and offer improved efficiency and direct connection to

community energy storage (CES) systems like such as supercapacitors and/or batteries [3, 4].

The concept of DC microgrids based on RES, especially using photovoltaic (PV) generators, has evolved significantly

over the last few years. In DC microgrids supplied by PV generators, several design concepts are typically involved, such

as the DC - DC power converter topology, voltage regulation and control of the DC bus. Many DC - DC converters have

been proposed, studied, and implemented in order to interconnect PV generators with a DC bus. Boost converters [5-9]

are one of the most widely adopted topologies for such applications. These converters offer suitable characteristics , such

as a high input-output voltage gain and a continuous input current, which is essential to extend the lifetime of PV

generators. The boost topology, which is associated with the SEPIC converter [10], has also been extended to bipolar DC

microgrids. However, due to inductor and semiconductor losses, the input -output voltage gain of the boost converter is

usually limited to around four in practice [5]. Several modified topologies to increase the voltage gain of this converter

have been proposed: some have been based on the integration of two classical DC - DC converters [11-15], while others

have included the use of switched-capacitor or switched-inductor structures to extend the voltage gain [16-20]. One of the

most interesting solutions that achieves high-voltage gain while preserving the simplicity of the boost converter is the

quadratic boost converter [21-27]; this topology is based on the classic boost converter with only one active

semiconductor and can provide continuous input current and quadratic gain. Since PV generators are characterised by a

relatively low output voltage, this converter may be an interesting solution for interfacing PV generators with DC

microgrids. However, these converters have non-minimum phase dynamic characteristics, meaning that it is difficult to

develop a controller using only the output voltage for feedback purposes [28]. Two-loop current mode controllers are

therefore typically applied for regulation of these converters , and the converter output voltage is regulated via the control

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of the inductor current [29]. A variety of control methods have been proposed with the purpose of regulating the output

voltage, such as current programmed control [30], robust control based on the Hammerstein identification [31],

loop-shaping [32], and sliding mode control (SMC) [33-35]. Controllers based on the simplified parallel-damped

passivity-based approach have also been proposed [36]. The authors of [37] presented a modified voltage-mode control

law for the regulation of a quadratic boost converter, which employed an integral action based on the normalised output

voltage error. All these methods demonstrate the importance of voltage control for these converters.

As mentioned above, another important issue associated with the use of DC microgrids is voltage regulation of the DC

bus, and this problem has been investigated for networks with several RES and CES. Two main approaches for

controlling the DC bus voltage have been proposed: the master-slave and the droop control methods [38, 39]. In the

master-slave technique, a master unit such as a large storage system is responsible for controlling the DC bus voltage.

The disadvantage of this approach is that the stability of the system is highly dependent on the performance of this master

unit [40, 41]. In contrast, the droop control technique is based on the detection of the current or output power [42].

Despite certain advantages, this technique has some limitations when used with different power sources, such as PV,

wind, and storage systems with different sets of state-of-charge (SoC) parameters [43]. An alternative control technique

approaches have therefore been proposed in [44, 45]. Another problem arises if the microgrid is mainly supplied by RES

such as PV generators without storage systems. In this situation, it is necessary to significantly curtail the generation of

PV power, meaning that the PV generators often operate well below their maximum power point (MPP). Several works

have explored the control of PV generators operating at the MPP or another specific power point below the MPP [46],

and a range of strategies have been proposed, for example constant power generation (CPG) based on a power control

method [47], CPG based on a current limit method [48] and CPG based on the perturb and observe (P&O) algorithm

[49]. It should be clarified that most proposed DC microgrids consist of multiple power sources, meaning that a primary

control element is always required, such as a mechanism for load power sharing within the microgrid [47]. In addition,

most studies in the literature [38]-[50] have been carried out in the context of DC microgrids connected to AC grids

where there is a limit on the active power injected into the AC grid.

Although several works have been presented regarding the transition between, for example, CPG and MPPT, solutions

for isolated DC microgrids that are supplied only by PV generators (without storage systems) have rarely been

investigated. Another aspect that has been almost overlooked in studies in this area relates to the behaviour of this type of

isolated network supplied by only PV generators. To demonstrate such limitations regarding these issues several relevant

works were examined in the literature [51-55], showing in this way, the opportunity for additional developments in the

control of PV generators in isolated DC microgrids. In future, the proposed solution could be used in rural and deprived

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regions; storage systems are very expensive, meaning that this could be a very economical solution in regions that often

do not require a permanent supply of electrical energy. There are several rural applications in which energy is only

required during the day, namely for water pumping and small loads that can be connected to small facilities (small

support houses or warehouses). There are also other situations in which this can be a reality. For example, when the

network is supplied by a diesel or biofuel generator. Concerning this conventional source, seen as backup power for

small-scale microgrids, the diesel generator is mostly used due to its several advantages, such as low investments, ease of

move and compatible combination with other energy sources. However, by one side its response speed is slow and the

starting time lasts several seconds to reach stable output power. Therefore, due to the slow dynamic behaviour of the

generator, the compensation for sudden load power changes must be ensured by the PV generator. On the other side, to

avoid wasting energy, during the day the diesel may not be operated in continu ous-running mode. Finally, situations in

which there is a failure or maintenance in the storage systems and is intend to maintain the system operating only with the

PV generator. Hence, there is a need for a control system with a different approach, i.e. one that requires voltage control

of the DC microgrid in normal mode but can also operate in MPPT mode during transitions and perturbations. In this

context, the novel contribution of the current work relates to the DC bus voltage control of DC microgrids solely supplied

by a unique PV generator, operating in islanded mode and without the use of energy storage systems. For this kind of DC

microgrid, the transition from voltage control to MPPT mode to regulate the bus voltage of the DC microgrid has rarely

been investigated. We explore the problem of DC bus voltage control in a DC microgrid supplied solely by a PV

generator, investigate the inner control loops related to the transitions between voltage control and MPPT operation for

this kind of DC microgrid, and propose a new control strategy. The proposed controller takes into consideration the

transition between the maximum available power of the PV panels and the voltage control regulation that is necessary to

maintain the DC voltage bus at the rated value, for an islanded DC microgrid without an energy storage system. The

design of the controller also focuses on the fact that the PV generators must work not only at their MPP, but also below

this point when necessary, according to the load demand. Associated with the PV generator, there is a quadratic boost

converter with the high voltage gain required to provide the necessary voltage variation. A study of the behaviour of this

isolated network under several conditions, such as transitions, perturbations , and different types of loads, is also

presented. The performance of the proposed control strategy is verified through several simulation and experimental tests.

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II. TRANSITION FROM VOLTAGE CONTROL MODE TO MPPT FOR PV

GENERATORS IN ISOLATED DC MICROGRIDS

Although many studies have been carried out on isolated DC microgrids supplied by PV generators, these have

typically assumed that storage systems are used to support the isolated microgrid, in order to mitigate the voltage

variations and load demand. In this context, the transition from voltage control to MPPT operation and vice versa is not

usually very problematic since the storage systems can provide support for the dynamic changes in the isolated DC

microgrid. Nevertheless, for several reasons, there are some cases in which DC microgrids do not have support from

storage systems, and the transition between the two modes of operation then becomes critical. In practice, storage

systems are usually very expensive [56], meaning that some applications may not be able to use them. Other

circumstances are associated with malfunction or end-of-life of the storage systems [57, 58]. Cases in which a DC

microgrid needs to operate without support from storage systems include:

Small installations in remote locations in which the loads are minimal, such as pumps, and other small loads

like lighting and small appliances ;

Houses with PV generators when in islanded mode. Under these conditions, instead of simply disconnecting

the PV generator, it could still operate if the generated power is sufficient to supply the load. Even in a

situation where the required load power is higher than the generated power, the PV system could continue to

operate by using a load shedding system [59, 60]. In this case, an overload may exist for a moment without

disconnecting the PV generator. Although a temporary overload may exist, the system will react by

disconnecting some non-critical loads, meaning that there will be a decrease in the associated load demand

to a level that can be stably supported by PV generation during operation in this emergency mode;

Other isolated small DC microgrids without storage systems but with support from a load shedding system

[60] for non-critical loads;

Installations operating in islanded mode but in a situation where the storage system suffers a malfunction or

is in the end-of-life stage [57, 58].

Regarding this application two different situations may arise in which an islanded DC microgrid is used without an

energy storage system. The first is where the DC microgrid is supplied by one, while the second one is supplied by

multiple PV generators. When multiple PV generators are used, an element of primary control is always required, i.e., a

mechanism for load power sharing within the microgrid [50]; this is not the case with a single PV generator, since the

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load is supplied by a unique power source. However, in both situations, inner control loops are always required for the

transition between voltage control operation and MPPT operation since each power source must be able to switch

between these two modes.

Although this type of system can be useful in several situations, as described above, some limitations may affect its

optimum use. These arise in the case where the load power is higher than the maximum available generated power. Under

these conditions, the system can only work in the context of an isolated DC microgrid if there is a load shedding system

that can maintain the total power load below the maximum power generated (although this could be higher in the

transient mode until some non-critical loads are disconnected). Another problem associated with this condition is the use

of electronically controlled loads with no limit on the converter input current. In this situation, the converter may fail, and

consequently the stability of the DC microgrid will be affected. Hence, these loads should be equipped with this type of

protection (which they normally have).

To ensure the operation of an isolated DC microgrid without support from storage systems, the PV generators must

include a controller that will allow them to operate in MPPT or voltage control mode. Several works have explored both

modes of operation, although in most cases applications have been related to PV generators connected in grid mode, and

the switch between the two modes of operation has been simply achieved by changing the setpoint reference [46]. There

have been few studies of transition mode control from voltage regulation to MPPT operation for PV generators in isolated

DC microgrids without storage systems, and some of the solutions that have been presented can be adapted to DC

microgrids without storage systems , despite having been developed in the context of a generator with a storage system.

For example, the authors of [61, 62] proposed methods for the two modes of operation (MPPT and voltage control). In

these approaches, the transition is established by a reference signal sent from a supervisory controller to switch between

the modes. Other studies of these two operation modes have also been presented in [63, 64]. However, some transition

problems remain, since a specific controller is required to ensure a smooth transition. Other strategies in which this aspect

of the MPPT or voltage control were considered under independent deployment of PV and the battery were also proposed

in [65, 66]. However, a solution to control the transition between the two operating modes is also required instead of an

independent integration which could affect the desired performance. A different study in which both modes were

integrated was proposed in [67]; a controller method was presented that unified MPPT and DC bus voltage regulation by

using the same control configuration. In this way, the need for an additional controller reconfiguration during the

transition between different operating modes was avoided. However, this control method has a weakness in the result of

the dP/dV calculation when there is no voltage variation producing an error in the denominator. The method proposed

here is similar to that presented in [67], since it considers the integration between the voltage regulator and MPPT

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operation, and there is an interconnection between them in order to provide a smooth transition over the two modes of

operation. The proposed method is also fully decentralised and does not rely on a communication system. The weakness

due to the dP/dV calculation is also avoided. Another aspect of the proposed approach is that it can easily be implemented

in DC-DC converters with high voltage gain, which are usually required for this kind of application. Table 1 presents a

comparison between the proposed approach and those presented in the studies described above.

Table 1 - Comparison between the proposed approach and those presented in the literature.

Proposed solutions

Integration of voltage

control and MPPT mode

Communication required

Bypass storage required

The solution can produce

errors in the control

calculations

[61] [62] No Yes No No

[63] [64] No No Yes No

[65] [66] No No No No

[67] Yes No No Yes

Proposed method Yes No No No

III. POWER ARCHITECTURE OF THE ISOLATED DC MICROGRID

The work presented in this study considers an isolated microgrid supplied by a single PV generator (see Fig. 1). The

DC microgrid supplies a set of DC loads that typically change throughout the day. The available PV power also changes

over the course of the day. Due to the variability in the load and power generation, the PV generator must be controlled to

ensure that the generated power is equal to the absorbed power at the rated DC voltage.

DC

DC

DC

Load 1

DC

Load N

PV Panel

DC Bus

Fig. 1: Conceptual design of the isolated DC microgrid.

Since single PV modules generally have low output DC voltages, it is usually necessary to use a DC-DC boost

converter with a high voltage gain in order to be able to supply loads of around 400V. As mentioned above, one of the

most well-known power converters with this characteristic is the quadratic boost converter [21-27]. Thus, the scheme

8

proposed in this paper uses a quadratic boost converter to demonstrate the validity of the developed control strategy.

Fig. 2 shows the proposed converter topology for a PV module supplying an isolated DC microgrid.

TVPH

D2

L2

VCo

D1 i0

DC BusPV Panel

D3L1

C1 CoVC1

iL1 iL2iD1

iD2

iD3

iT

Fig. 2: DC-DC quadratic boost converter for PV panels supplying an isolated DC microgrid.

Based on the assumption of ideal semiconductors and reactive components, the static input-output voltage gain of the

quadratic boost DC-DC converter is a function of the square of the duty cycle (), ϵ ]0,1[, as shown in the following

expression [21]:

PHCo VV

21

1

(1)

To obtain a dynamic model of the quadratic boost DC-DC converter, we consider a binary variable that is related to

the ON-OFF state of the controlled power semiconductor (T). This variable can be expressed as:

OFFisTif

ONisTif

0

1 (2)

The control variable has a value of one when T is ON and zero when T is OFF (Eq. 2). The following state-space

dynamic equations (3) are derived based on the assumption of an ideal and conservative quadratic boost circuit (where

the output power equals the input power) using , and considering continuous conduction mode (CCM) for the converter:

oo

Lo

Co

CoCL

LLC

PHCL

iC

iCdt

dV

VL

VLdt

di

iC

iCdt

dV

VL

VLdt

di

11

11

11

11

2

11

1

2

21

11

1

11

1

1

(3)

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These equations relate the dynamics of the DC-DC power converter to the control variable and will be used to

develop the proposed controllers.

IV. CONTROLLER DESIGN

To ensure the stability and fast regulation of a microgrid DC bus supplied by a PV DC-DC boost converter, a

closed-loop control is the best approach. The converter shown in Fig. 2 only has the capability to directly control the

switching state of the single switch using the control variable . To operate the PV module, either in MPP or in voltage

control mode, it is straightforward to control the quadratic boost input current to track a given input current reference

value. In order to guide the DC output voltage (V control) to its rated value, we exploit the fact that the dynamics of the

DC output voltage is much slower than the dynamics of the input current, and the DC voltage controller is designed as an

external loop that enforces slow variation in the reference value of the input current. The full control structure with the

controllers connected in cascade is shown in Fig. 3; this structure consists of an outer voltage controller that defines the

reference value for an inner current controller.

Voltage

Controller

VCo_ref

VCo

iL1_ref

iL1

Current

Controller

Power

ConverteriL1

VCo

Fig. 3: Cascade structure of the voltage and current controllers used to control the quadratic converter.

To control the input current of the quadratic boost converter (the inner loop controller), a nonlinear current controller is

used. In accordance with the state space model of the DC-DC converter presented in Eq. (3), we verify that the input

current has a strong relative degree of one [68] (as the first-time derivative of the input current contains the control

variable ). Based on the strong relative degree of the variable , and considering the feedback error as the state variable,

the sliding surface ensuring the robustness of the closed loop system [69] is given by:

111 LrefLi iieL

(4)

Since the converter is a discrete system with a reduced number of states and a limited switching frequency, the input

current will show some ripple, meaning that the difference between the reference refLi 1 and the input current 1Li values

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will not be zero at every time instant. This ripple causes a difference or error 1Li

e that is within a certain range 1Li /2,

as shown in Eq. (5):

2, 1

1111

Liiii

ie

LLLL

(5)

The convergence of the system for a reference value is assured by the following stability condition [62]:

01

1 dt

dee Li

L (6)

To meet the condition in Eq. (4), a hysteresis comparator with width 2 can be used to control the control variable .

From Eqs. (3) and (6), the state of the controlled power switch is:

00

10

1111

1111

1

1

dt

diiiie

dt

diiiie

LLLrefLi

LLLrefLi

L

L

(7)

Regarding the development and design of the outer loop voltage controller, the dynamics of the converter output is

given in the last expression in Eq. (3) and is dependent on the iL2 current (the control input). Based on the assumption of

an ideal converter, the relationship between the diode current average value ID3 and the input current IL1 can be expressed

as shown in Eq. (8). Given the fourth-order dynamics of the quadratic boost and considering the order reduction of the IL1

current controller, the internal dynamics of ID3 and IL1 can be approximated by a first order transfer function with a time

constant Td. This approximation is made based on an ideal (and therefore conservative) converter and allows us to obtain

Eq. (8), where KG is the steady-state quadratic current gain of the converter which relates the output diode D3 current and

the input inductor current. However, the variation in the input current is not instantaneous, and is a function of the small-

time constants associated with the inductors and the capacitor. Since these time constants are very small compared to the

output voltage dynamics, we can use a single time constant Td that is the sum of all of the smaller time constants. In this

way, the dynamics of the current ID3 in diode D3 can be represented as (1

1sTd

). The relationship between the diode

current ID3 and the input current IL1 is then as shown in Eq. (9):

113 LGLCo

PHD IKI

v

vI (8)

13 1L

d

GD I

sT

KI

(9)

11

The relationship between the output voltage, the output average current IO and the diode current average value ID3 is

given by:

oDCo IIsVsCo

3

)(

(10)

Using Eqs. (9) and (10), the transfer function for the converter output voltage for a given input current can be written

as shown in Eq. (11).

o

o

L

do

Go i

sCI

ssTC

Kv

112

(11)

In Eq. (11), the control input is the current IL1. However, an unknown load current io appears as an input disturbance

in the output integrator. Hence, to avoid steady-state errors in the DC output voltage, a compensator with integral

action, called the proportional integral (PI) compensator, is used. This compensator has a zero at - Tz and a pole at origin

with integral gain at KI = 1/Tp (Eq. 12). The proportional gain is then KP = Tz/Tp (Eq. 12). Fig. 4 shows a block diagram

of the output voltage closed loop controller.

p

zP

pI

T

TK

TK and

1

(12)

VCo_ref

i0

KI

KPsCo

1

s

1

1sT

K

d

G

Fig. 4: Block diagram of the power converter output voltage controller.

From Eq. (12) and the block diagram in Fig. 4, we obtain the final transfer function of the system in the closed loop as:

opd

G

opd

zG

d

o

od

dGLG

opd

z

refC

C

CTT

Ks

CTT

TKs

Ts

sICT

sTsKsIK

CTT

sT

sV

sV

o

o

23 1

111

(13)

To calculate the parameters of the PI compensator, the symmetrical optimum criterion will be used, since the

parameters will not appear as a function of the load [70, 71]. The open loop transfer function, including the PI

compensator, has three poles: two at the origin and a third at −1/Td, where Td is the sum of the relatively small delays due

to the nonlinear internal dynamics of the quadratic converter associated with the C1 L2 components. The PI zero cannot be

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used to compensate for the −1/Td equivalent pole, since the resulting system, with two poles at the origin plus neglected

dynamics, would be unstable. To maximise the phase margin M, we use the fact that the angle criteria gives the

frequency ωd of the maximum M, zdd TT/1 , which is the frequency of the geometric mean of the equivalent pole

1/Td and the PI compensator zero 1/TZ. The parameter a, which represents the symmetrical distance between 1/TZ and

ωd and between 1/Td and ωd, is then calculated to obtain a design value for M, as MMa sin1/sin1 . For a

design value of M ≈ 36.9º, we obtain a symmetrical optimum value of a = 2. For a = 2, we also have the best disturbance

rejection behaviour, although the damping factor ζ = (a−1)/2 is on the low side (ζ =0.5). For a value of M of around

53.1º, a = 3, the damping factor is ζ =1 and the disturbance rejection decreases (the value of a is usually between two and

four). The parameter a is also useful to write the terms of the closed loop characteristic third-order polynomial in Eq. (13)

in the form bk2 = abk-1bk+1, where bk are the polynomial terms (b3s

3+b2 s

2+ b1 s+ b0, b0=1). By writing the criteria for b1 (

20

2

1 babb ) and for b2 (31

2

2 babb ), two equations are obtained that can be solved to give the PI gains:

Gd

o

p

ZP

Gd

o

Z

IKaT

C

T

TKand

KTa

C

TK

23

1 (14)

In DC microgrids, the reference value of the DC bus is fixed. However, since the microgrid is supplied by the PV

quadratic boost, the PI controller should be joining to the MPPT controller. In fact, there are several issues that must be

considered, as follows:

• To maintain the stability of the grid voltage, the power available from the PV generator must be equal to or higher

than the load power. This means that in normal mode, the PV generator should feed the load with a power that is

lower than the available MPP. Alternatively, for fast and stable regulation during transient load changes, the PV

converter often needs to work at the MPP. Hence, the PI compensator cannot operate independently, otherwise

operation at the MPP would be at risk;

• The PI controller gives the reference value for the current controller, which should not be higher than the MPP of

the PV generator. However, saturation at the output of the controller does not ensure the fulfilment of this

condition, since the available MPP is a function of several factors such as the irradiance and temperature (the

MPP can only be obtained using one MPPT algorithm);

• To overcome these issues, the PI controller should be combined with the MPPT controller. However, when the

two controllers are combined, the iL1ref current must be selected from only one of them (Fig. 5). This means that

the PI integral, if not conditioned, will undergo windup and saturate, creating a rough transition when the PI is

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re-selected to give the value of iL1ref. This creates disturbances and may cause large signal instabilities. Hence,

when the system MPPT algorithm is in use, the PI controller should be driven in such a way as to track the value

of MPPT iL1ref, to avoid transient oscillations when re-selected.

Based on the above considerations, the MPPT and the PI controller should be combined in an interactive way, as

illustrated in Fig. 5. This system includes a switch to perform the transition between the PI controller and the MPPT. The

figure also shows the interaction of the iL1ref current between PI controller and the MPPT algorithm (since the output of

the PI controller forms one of the inputs to the MPPT).

The transition between the two controllers is a function of the DC voltage bus: if this voltage is near the reference

value, then the converter will be controlled by the PI controller, but if it drops below a defined threshold value CoV , the

reference switch will select the MPPT controller. The selection of one of the two controllers can be expressed as in

Eq. (15).

CoorefoMPPT

CoorefoI

PCoCorefrefL

VVVi

VVVs

KKVV

i

_

_1

when

when (15)

where iMPPT is the current established by the MPPT algorithm and VCo is the lower margin for operation of the PI

controller.

Vo_ref

KI

KP

s

1

MPPT

Current

Controller

Vo

VPV

IPV

IL1_ref

IL1_ref

Fig. 5: Block diagram of the combined voltage and MPPT controllers.

The proposed MPPT algorithm is based on the P&O principle [72], but also includes the iL1ref current as shown in the

flowchart in Fig. 6. In the MPPT mode, the algorithm computes the current reference value for the converter current

controller. However, as mentioned above, this algorithm cannot work independently when the system is controlled by the

PI controller. In the PI controller mode (voltage control mode), the MPPT algorithm provides the same reference current

as that given by the PI controller. This will ensure a soft transition when the global controller changes from the PI mode

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to the MPPT mode. The MPPT will therefore have an extra input, which is the current reference given by the PI

controller (Figs. 5 and 6).

A further problem arises in relation to the PI controller in the MPPT mode. To avoid instabilities , the MPPT algorithm

should also interact with the PI controller in the MPPT mode. When the reference switch (Eq. 15) changes to the MPPT

mode, the PI ceases to control the output voltage, and the integrator will undergo windup. Then, when the reference

switch (Eq. 15) returns to the PI mode, there will be a sudden change in the reference current. This can lead to significant

oscillations, and even to large signal instabilities. To overcome this problem, we propose a new global control system, as

shown in Fig. 7, in which an anti-windup system is added to the PI controller and is connected between the two

controllers. If the system is in the PI mode, then the difference between those controllers is zero, since the MPPT gives

the same value as the PI controller. In this way, the anti-windup block is deactivated in this mode. If the controller

switches to the MPPT mode, the anti-windup block will ensure that the PI controller converges to the same value of the

MPPT, despite the disturbance in the proportional gain.

The anti-windup gain kW is given in Eq. (16), where the parameter KP is defined as in Eq. (12).

PW

KK

1 (16)

This global control scheme allows for a smooth and stable transition between the MPPT and the voltage controller (and

vice versa), and also improves the response time to disturbances due to load changes in the DC micro-grid.

15

Start

Measure

IPV(i) and VPV(i)

Calculate Power

PPV(i) = IPV(i) x VPV(i)

V = VPV(i) - VPV(i-1)

P = PPV(i) - PPV(i-1)

P = 0

P > 0

Yes

No

V > 0 V < 0

IL1_ref (i):= IL1_ref (i-1)- Istep IL1_ref (i):= IL1_ref (i-1)+ Istep

Yes

Yes

No

No

Yes No

Return

From PV

Measure

IL1_ref

From Current

ControllerMPPT

Mode

Yes

No

IL1_ref (i):=IL1_ref

Return

Fig. 6: Proposed MPPT algorithm.

Vo_ref

KI

KP

s

1

MPPT

Vo

Kw

Current

Controller

VPV

IPV

IL1_ref

IL1_ref

Fig. 7: Proposed global control system.

V. SIMULATION TESTS

The behaviour of the system using the proposed controllers was tested via several simulations, which were carried out

using MATLAB/Simulink software. Models from the Simscape-Power System toolbox were used for the power converter

and loads. The control strategy, MPPT algorithm and PV module were implemented using blocks from the classical

MATLAB/Simulink library. The PV model was based on the single-diode model [73], and the time step used in the

16

simulations was 1 s. The DC microgrid configuration shown in Fig. 1 was used in the simulation tests . The PV panel

was connected to the DC-DC quadratic boost converter (Fig. 2) supplying the microgrid DC bus, and the loads were

connected and disconnected from the DC bus. The parameters of the quadratic boost converter are given in Table 2. A

rated or reference voltage of 400 V was set for the DC bus. The PV panel contained two strings in parallel, each of which

had two modules connected in series. The characteristics of each PV module (based on a multicrystal KYOCERA

KD325GX PV module) are summarised in Table 3. The perturbation step size (Istep) used in the MPPT algorithm was

0.001. For the PI controller parameters, we used the values of KI = 1.78 and KP = 0.07, which were obtained from

Eq. (14).

Table 2 - Parameters of the quadratic boost converter

Switching frequency 12 kHz

Inductance of input inductor L1 1 mH

Inductance of input inductor L2 2.2 mH

Capacitance of input capacitor C1 150 F

Capacitance of output capacitor Co 150 F

Table 3 - Characteristics of the KYOCERA KD325GX PV panel

Electrical performance under STC

Maximum power 325 W

Maximum power voltage (VMPP) 40.3 V

Maximum power current (IMPP) 8.07 A

Open circuit voltage (VOC) 49.7 V

Short circuit current (ISC) 8.69 A

The first test was carried out with an initial load with an equivalent resistance of 310 . At t = 1 s, an additional

resistance load of 650 was suddenly connected, and at t = 1.5 s, this load was disconnected. The dynamic response of

the system can be seen in Fig. 8a, which shows the transient waveform of the DC voltage bus. The results show that after

each connection/disconnection of the load (disturbance), the microgrid recovered to the rated DC value of 400 V. The

voltage in the intermediate capacitor appears to remain stable (Fig. 8b). The current from the PV panels can be seen in

Fig. 8c. As expected, there is an increase in the current with an increase in the load. In this case, the required current is

lower than the maximum power current of the PV panels (IMPP), and the controller does not shift to the MPPT mode.

The power generated by the PV panels can be seen in Fig. 8d, which shows the tracking of the required load power.

17

a)

b)

c)

d)

Fig. 8: Simulation results for the proposed controller with a change in the load from 310 to 210 (310 // 650 and return to

310 (a) DC bus voltage; (b) intermediate capacitor voltage in the converter; (c) current of the PV array; d) power generated by the

PV array.

18

A second simulation test was performed in which the sudden connection of a load required the system to shift from the

PI mode to the MPPT mode and back again. In this test, the initial load was equivalent to a resistance of 310 and at

t = 1 s an additional load of 300 was abruptly connected. The dynamic response of the DC microgrid is illustrated in

Figs. 9a and 9b, which show the transient waveforms for the DC bus voltage and the generated PV power, respectively.

The results show that the controller reacts by compensating the disturbance and maintaining the output voltage at the

reference value. However, it should be noted that in this situation, the control system shifts from the PI mode to the

MPPT mode under the transient conditions . After connection of the 300 load, the output voltage decreases to a value

that requires a current higher than the IMPP current to quickly track the output reference voltage. The controller therefore

shifts to the MPPT mode to ensure the maximum possible power. This is shown in Fig. 9b, where it can be seen that after

connection of the load, the generated PV power increases to the MPP, and the controller is then in the MPPT mode.

a)

b)

Fig. 9: Simulation results for the proposed controller with a change in the load from 310 to 152 (310 // 300 (a) DC bus voltage; (b) power generated by the PV array.

A further simulation test was also performed in which a load was suddenly connected that required a higher power

than the maximum available from the PV panels. In this test, the initial load had an equivalent resistance of 310 , and at

19

t =1 s, an additional load of 180 was connected. This extra load was then suddenly disconnected at t = 1.5 s, and at the

same time, another 300 load was connected. The response of the system in terms of the output voltage, intermediate

converter capacitor voltage and PV power generated is shown in Figs. 10a–c. It can be seen that when the second load is

connected, the maximum PV power generated is insufficient to ensure that the output voltage recovers to the reference

value. The control system therefore shifts to the MPPT mode to deliver the MPP, which is insufficient to increase the DC

voltage bus to the required value. Thus, a steady-state error appears as the PV generator cannot operate above its

maximum. However, after disconnection of the second load at t = 1.5 s, the controller returns to the PI mode and the DC

voltage bus recovers to the reference value (Fig. 10a). The intermediate capacitor voltage is shown in Fig. 10b, and it can

be observed that it remains stable even in this situation. Notice that the ripple in the generated power is not the same,

since it is a function of the ripple in the current imposed by the converter and controller. The controller ensures that the

current is within the hysteretic reference band. This hysteresis defines the limits of the maximum switching frequency of

the power switch of the converter. However, due to the characteristics of the PV panels, a positive variation in their

current causes a negative variation in the voltage through, thus the power ripple will be attenuated. Hence, if the system is

in MPPT mode and near the vertical zone of the V-I characteristic of the solar cell, this means that variations in the

current in that point will cause high variations the voltage (lower PV power ripple). However, if the current from the PV

panel is reduced (since the load does not require all of the generated power from the PV system) then it will be near the

horizontal zone of the V-I characteristic of the solar cell, in which variations of the current in this new point will imply

lower variations of the voltage (higher PV power ripple).

a)

20

b)

c)

Fig. 10: Simulation results for the proposed controller with a change in load from 310 to 114 (310 //180 and then to 152

(310 // 300 a) DC bus voltage; (b) intermediate converter capacitor voltage; (c) power generated by the PV array.

Similar tests were also performed with electronically controlled loads. These loads show different behaviour from

classical linear loads (resistors), since the design ensures that a certain power is supplied to the load as required. Hence, if

the supplied voltage is reduced, the input current increases , and vice versa. This may affect the behaviour of the controller

during the transition between the two modes of operation. To assess this behaviour, an initial test was performed using an

electronically controlled load of 520 W. At t = 1 s, an additional electronically controlled load of 245 W was suddenly

connected, and at t = 1.5 s, this additional load was disconnected again. The dynamic response of the system can be seen

in Fig. 11a, which shows the transient waveform of the DC bus voltage. The results show that after each load is

connected/disconnected (creating a disturbance), the microgrid recovers to the rated DC value of 400 V, thus

demonstrating the stability of the system even under this type of load. Although the power for these loads was similar to

that for the linear loads, it can be seen that due to their characteristics, a shift is required from the PI mode to MPPT

mode and back again, as shown in Fig. 11.

21

a)

b)

Fig. 11: Simulation results for the proposed controller for a change in the electronically controlled loads from 520 W to 765 W and

back to 520 W (a) DC bus voltage; (b) power generated by the PV array.

In the next simulation test, an electronically controlled load was suddenly connected that required a higher power from

the PV generator. In this situation, the problem of instability may arise when the generated power is lower than the load

power. In this case, if there is no limitation on the input current of the electronically controlled load, the current will

continuously increase, and the bus voltage will collapse to 0 V. However, these loads usually impose a limitation on the

input current, typically with the aim of protecting the equipment. We therefore imposed a current limitation of 20%

above the nominal value in this test. An initial load of 400 W was applied; at t = 1 s, an extra load of 900 W was

introduced, and the total load was finally reduced to 930 W at t = 1.5 s. The response of the system with regard to the

output voltage and PV power generated is shown in Figs. 12a and 12b. It can be seen from these figures that when the

second load is connected, the maximum PV power generated is not sufficient to ensure that the output voltage recovers to

the reference value. The control system therefore shifts to the MPPT mode to deliver the MPP, which is insufficient to

increase the DC bus voltage to the required value. However, after the load is reduced at t = 1.5 s, the controller returns to

the PI mode and the DC voltage bus recovers to the reference value. We can therefore conclude that even in this situation

the system maintains its stability.

22

a)

b)

Fig. 12: Simulation results for the proposed controller for a change in the electronically controlled load from 400 W to 1300 W and

then to 930 Wa) DC bus voltage; (b) power generated by the PV array.

The next test involved a PV generator with a battery system, where the mode of operation of the PV interface was

based mainly on the SoC of the battery. Initially, the battery controlled the bus voltage, but at t = 0.9 s it reached a state of

full charge, and the bus voltage began to be controlled by the PV generator. Connected to the bus there is an

electronically controlled load with 600 W of power was connected to the bus , meaning that the load power was below the

maximum available PV power. The response of the system in terms of the output voltage and PV power generated is

shown in Figs. 13a and 13b. Initially, the PV generator is in MPPT operation, with the excess energy being transferred to

the storage system. However, when the battery is fully charged, the PV generator changes to voltage control, and the

generated power is reduced. At t = 1.6 s, an additional electronically controlled load is connected, giving a total load of

1500 W. Since this power is higher than the maximum available from the PV generator, there is a change from voltage

control to MPPT mode, and the battery starts to discharge its energy to supply the load. The power generated by the PV

system reverts to the maximum capability (Fig. 13 b).

23

a)

b)

Fig. 13: Simulation results for the proposed controller for a PV + battery system a) DC bus voltage; (b) power generated by the PV

array.

VI. EXPERIMENTAL TESTS

To validate the simulation cases studied in the previous section, several additional experimental tests were performed.

The parameters used for the experimental DC-DC converter are given in Table 2. A PV simulator was used for the PV

panels that consisted of a remotely controllable EA Elektro-Automatik EA-PS 8160-60 DC power supply, which was

controlled by a DS1104 R&D controller board (with a sampling time of 1 s) into which the characteristics of the PV

panel were programmed using four modules (Table 3). The perturbation step size (Istep) used in the MPPT algorithm was

0.001. The experimental tests were similar to those in the simulations.

In the first test, an initial load with a resistance of about 310 was considered. An additional load of 650 was

suddenly connected followed by disconnection after 500 ms. The results of this experiment can be seen in Figs 14a–d.

Fig. 14a shows the response of the DC bus voltage to the variation in load, and it can be seen that after each disturbance

the controller compensates for the disturbances and returns to the steady state. In this situation it also recovers the rated

value of the DC voltage. The rejection is fast enough to minimise the effect of the disturbances. The intermediate

capacitor voltage is shown in Fig. 14b, and it can be observed that it remains stable even in this situation. Fig. 14c shows

that the PV current changes to a higher value almost instantly after the connection of the load , to track the DC reference

24

voltage. After disconnection of the load, the PV current returns to the initial value. Fig. 14d shows the generated PV

power. The power extracted from the PV panels is not fixed and tracks the required load power; the PV panels do not

achieve their MPP even in the transient state, and the control system does not shift to the MPPT mode. These

experimental results are very similar to the simulation results.

a)

b)

25

c)

d)

Fig. 14: Experimental results for the proposed controller for a change in load from 310 to 210 (310 // 650 and return to

310 (a) DC bus voltage (100 V/div); (b) intermediate converter capacitor voltage (100 V/div); (c) PV array current (3A/div); (d)

power generated by the PV array (200 W/div).

A second experiment was then performed with the same initial load (310 A second load (of nearly 300 )was

then connected in order to cause the controller to shift from the PI mode to the MPPT mode. The dynamic response of the

system in this test is illustrated in Figs. 15a and 15b, which show the transient waveforms of the DC bus voltage and the

generated PV power. Figs. 15a shows that after connection of the 300 load, the DC bus voltage falls with the

disturbance, but that the controller quickly reacts to the disturbance, ensuring the return of the DC voltage to its reference

value. To do this, the controller increases the power of the PV array to a higher value after the 300 load is connected.

The increase is limited to the MPP of the PV array (Fig. 15 b) and is achieved through a shift in the controller from the

voltage PI to the MPPT control mode.

26

a)

b)

Fig. 15: Experimental results for the proposed controller for a change in load from 310 to 152 (310 // 300) (a) DC voltage

bus (100 V/div); (b) power generated by the PV array (200 W/div).

In the next experimental test, a load was suddenly connected that required a higher power than the maximum available

from the PV panels. The initial load had an equivalent resistance of 310 and an extra load of 180 was connected at

t = 1 s and disconnected after 500 ms, while another 300 load was connected at the same time. The response of the

system in terms of the output voltage, intermediate converter capacitor voltage, PV array current and generated PV power

is shown in Figs. 16a–d. From an analysis of these figures, we can verify that when the second load is connected, the

maximum PV power generated is insufficient to ensure that the output voltage recovers to the reference value. The

control system therefore shifts to the MPPT mode to deliver the MPP, which is also insufficient to increase the DC bus

voltage to the required value. However, after disconnection of the second load at t = 1.5 s, the controller returns to the PI

mode and the DC voltage bus recovers to the reference value. The voltage in the intermediate capacitor remains stable

(Fig. 16b).

27

a)

b)

c)

Fig. 16: Experimental results for the proposed controller for a change in load from 400 to 124 400 // 180 and then to

171 400 // 300 (a) DC bus voltage (100 V/div); (b) intermediate converter capacitor voltage (100 V/div); (c) power

generated by the PV array (200 W/div).

28

VII. CONCLUSIONS

This work has proposed a new control system for a PV generator supplying energy to an islanded DC microgrid. The

quadratic boost DC-DC converter used to interface the PV generator provides the necessary high voltage gain that is

typically needed in these applications. The controller was designed with a particular focus on the transition from the

MPPT mode to the PI voltage control mode and vice versa, and the importance of this critical aspect was highlighted in

the text. The proposed MPPT plus PI voltage controller has a cascaded structure consisting of an inner input current

controller and outer output voltage controller. A PI controller was proposed for control of the output voltage, while a

MPPT algorithm was devised to achieve the MPP. Our MPPT plus PI voltage controller undergoes smooth transitions

between the PI controller and the MPPT algorithm, due to the interactivity when computing the reference current in both

modes. It must be mentioned that this work presents a different approach regarding the ones that addressed the transition

from the maximum power point to DC bus voltage regulation of PV generators. In this case the problem of DC bus

voltage control in a DC microgrid exclusively supplied by a PV generator was solved. In this context, it was also

investigated the inner control loops related to the transitions between voltage control and MPPT operation for this kind of

DC microgrid, and propose a new control strategy. The proposed control system was verified and tested through several

simulation studies. These simulations were confirmed through the use of a laboratory setup, which gave experimental

results that demonstrated the good performance and behaviour of the proposed control system, without instabilities

between the PI (voltage control) and MPPT modes. We were able to test the system under several conditions, by

changing the loads and analysing the system as the PV generator shifted from voltage control mode to MPPT and back

again. Transients in the output voltage were kept below ±10%, while the response times were around 10 ms. In the results

obtained for linear and electronically controlled loads, there was a small degradation in the system response due to the

different behaviour of the electronic load, which is usually designed to ensure the required power to the load. This can be

problematic when the power from the PV generator is insufficient to supply the load. However, since electronic loads are

typically designed with a limitation on the input current for their protection, we showed that under these conditions, the

system maintains the stability of the DC voltage.

ACKNOWLEDGMENT

This work was supported by national funds through FCT – Fundação para a Ciência e a Tecnologia, under project

UIDB/50021/2020 and UIDB/00066/2020.

29

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