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International Journal of Energetica (IJECA)
https://www.ijeca.info/index.php/IJECA/index
ISSN: 2543-3717
Volume 1. Issue 1. 2016 Page 12-19

IJECA – ISSN: 2543-3717. December 2016

Modeling and Simulation of Energy Management Hybrid Sources System composed

of Solar-PV and Battery

M. Maamir
1
, A.Betka

1
, H. Aboub

1
LGEB Laboratory, Electrical Engineering Department, University of Biskra, Algeria,

2
LEB, university of Batna

Email: m.maamir39@ gmail.com

Abstract— This paper describes the modeling and control of a hybrid source consisting of PV generator (as
main source) along with a battery (as an auxiliary source) and a dc-load are connected through power

converters and a dc-link. The main objective of this paper is to design a power manager to control effectively the

power of the different sources. To test the effectiveness of the different control techniques involved, simulation

results are plotted and commented.

Keywords: Hybrid system, energy storage, PV generator, Power management, battery, fuzzy logic, batteries.

1. INTRODUCTION

Currently, most of the energy demand in the world is met by fossil and nuclear power plants. A small part is

drawn from renewable energy technologies such as wind, solar, fuel cell, biomass and geothermal energy [1].

Renewable energy sources are considered as alternative energy sources to conventional fossil fuel energy

sources due to the environmental pollution and global warming problems. The combination of all different kinds

of available renewable energy associated with available energy storage units produces an hybrid energy system

(HES) [2]. Therefore, in order to supply electric power to fluctuating loads with a hybrid system composed of

solar cell and electric energy-storage system is needed to compensate for the gap between the output from the

renewable energy sources and the load, in addition to the collaborative load sharing among those energies.

To control the power flow among the elements Consisting HES a suitable energy management system (EMS)

must be designed. The EMS is usually a central controller that drives all the elements. Thus, the complexity in

designing an EMS increases with the level of hybridization of the HES (the number of elements present in the

system).

Energy management of multi-power sources has already been studied recently, for example, Control,

robustness, stability, efficiency, and optimization of hybrid sources remain an essential area of research. Several

researchers have studied different topologies. G. Boukettaya [3] studied A dynamic power management strategy

of a grid connected hybrid generation system using wind, photovoltaic and Flywheel Energy Storage System in

residential applications. R. Souad [4] studied the development and the realization of an Intelligent Power Strip

for Energy Consumption Management in Hybrid Wind/Photovoltaic Systems. M. Mohammedi [5], studied

Passivity Based Control and Fuzzy Logic Estimation applied to DC Hybrid Power Source using Fuel Cell and

Super capacitor. Shiyas P.R [6] Fuzzy controlled Dual input DC/DC Converter for Solar-PV/Wind Hybrid

Energy System. M. Y. Ayad [7], studied Sliding Mode Control applied to Fuel Cell, Super capacitors and

batteries for Vehicle Hybridizations.

In this paper, a control strategy for the energy management of an hybrid renewable energy system is

presented. The system is composed of a photovoltaic solar array and batteries which are connected in a common

dc-link bus. The DC bus is connected in parallel with resistive charge. DC-DC power converters are introduced

to quietly perform the different control strategies proposed. Fig.1 is shown a synoptic scheme of the system. The
paper focuses on the design of a power supervisor able to decide, at each moment and according to the load

power demand, which source has to supply or absorb the energy and eventually define the ratio of using of

different sources in the same time [8]. The rest of the paper is organized as follows: In section2; an explicit

Madiha. Maamir et al

IJECA – ISSN: 2543-3717. December 2016 13

modeling of the different sub-systems are given. In section3, both the power management algorithm and the

proposed control techniques are properly detailed. In section 4, simulation results conducted with both various

load demand.

Fig1: System architecture

2. SYSTEM MODELING

2.1 PV Array Model

The equivalent circuit of the PV device can be represented as a current source in parallel with diode includes

a parallel resistor (Rsh) expressing a leakage current, and a series resistor (Rs) describing an internal

resistance [9] .The model is shown in Fig2.

Fig 2: equivalent circuit of Photovoltaic module.

Since Rsh is very high, the mathematical model which relates the output current to the output voltage is given by

the following expression [10]:

I = Icc − I0 [exp
V +R p I

V th
− 1] (1)

The adaption of Eq. (1) for different levels of solar insolation and temperature can be handled by the following

equations.

∆𝑇 = 𝑇 − Tref (2)

∆I = α
E

E ref
∆T + (

E ref
− 1)Iccref (3)

∆V = −β∆T − rs ∆I (4)

𝑉 = 𝑉𝑟𝑒𝑓 + ∆V (5)

I = Iref + ∆I (6)

2.2 Battery model:

In general a battery device can be viewed as a voltage source 𝐸𝑏𝑎𝑡 in series with an internal resistance 𝑟𝑏𝑎𝑡
as shown in fig 3. [8].

Madiha. Maamir et al

IJECA – ISSN: 2543-3717. December 2016 14

Fig 3: Dynamic model of lead-acid battery

The terminal voltage 𝑉𝑏𝑎𝑡 is given by:
𝑉𝑏𝑎𝑡 = 𝐸𝑏𝑎𝑡 − 𝑟𝑏𝑎𝑡 . 𝑖𝑏𝑎𝑡 (7)

As the internal voltage 𝐸𝑏𝑎𝑡 is assumed to be a function only of the state of charge (SOC) [11] [12], or the depth
of discharge (𝐷𝑂𝐷𝑏𝑎𝑡 ). Eq. (8) describes the used open voltage:

𝐸𝑏𝑎𝑡 = 𝑛(2.15 − 𝐷𝑂𝐷𝑏𝑎𝑡 . 2.15 − 2.00 (8)

In addition, SOCbat and 𝐷𝑂𝐷𝑏𝑎𝑡 are respectively estimated by [11]:

𝑆𝑂𝐶𝑏𝑎𝑡 =
𝐶𝑎𝑐𝑡𝑢𝑒𝑙𝑙𝑒

𝐶𝑡𝑜𝑡𝑎𝑙𝑒
= 𝑆𝑂𝐶𝑏 𝑖𝑛𝑡 +

100

𝐶𝑁
𝑖(𝑡)𝑑𝑡 (9)

𝐷𝑂𝐷𝑏𝑎𝑡 = 1 − 𝑆𝑂𝐶𝑏𝑎𝑡 (10)

2.3 Average state-space models of the static converters

- DC/DC boost converter model:

The dc-dc boost is modeled using an average state-space approach, given in eq (11) [12] to check the

effectiveness of the control techniques via continuous models:

𝑑𝑖𝐿

𝑑𝑡
𝑑𝑣𝑐

𝑑𝑡

=
0 −

1−𝛼𝑝𝑣

𝐿𝑝𝑣

1−𝛼𝑝𝑣

𝐶
−

𝑅𝐶

𝑖𝐿𝑝𝑣
𝑉𝑐

(11)

In order to maximize the energy extracted from the PV array, a fuzzy logic based MPPT strategy has been

applied because it has the advantages of robustness, and minimal requirement for accurate mathematical model

[13].

- Bidirectional DC/DC converter model

The bidirectional DC/DC converter is a current reversible DC/DC converter. It can work as a boost

converter when the current (of the bidirectional DC/DC converter inductance) flows from the super

capacitor (battery) to the DC bus. It works as buck converter when the current flows on the opposite

direction [14]. Thus, to achieve energy transfer in two directions, the buck and boost converters were

associated as shown in Fig 4.

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IJECA – ISSN: 2543-3717. December 2016 15

Fig 4: Structure of the bidirectional DC-DC converter

The average model of the converter in both power direction flow can be written as:

Lbat
d ibat

dt
= Vbat − 1 − αbat Vdc (12)

3. CONTROLLER FOR HYBRID SYSTEMS

In the present work, three operating modes are distinguished and smoothly permuted through the presented

power management system. Throughout the simulation the photovoltaic generator operates on MPPT:

- Mode1: the main source is the PV array and the battery, supply energy to the load.

- Mode2: power load is below to the maximum power point (MPPT), then the battery is charged.

- Mode3: This mode starts when the power of the PV array demand equal to the power demand, where the

Photovoltaic array supplies only the load demand.

To permit a global flow of the different source’s energy, the DC bus must be kept constant. A main voltage

loop with a Lyapounov controller generates the total current reference that should be taken from the dc-link bus.

In the EMS depicted in (Fig 5), a low-pass filter is introduced, which extracts the low frequency content of the

reference sent to the battery, and through the chosen constant time, the battery contributes mainly in steady state.

The rules are summarized in eq. (13) for battery.

Fig 5: Energy management system

𝐼𝑏𝑎𝑡𝑟𝑒𝑓

0, 𝑖𝑓

𝐼𝑑𝑐𝑟𝑒𝑓 < 0 𝑎𝑛𝑑𝑆𝑂𝐶𝑏𝑎𝑡 > 95%,

𝐼𝑑𝑐𝑟𝑒𝑓 > 0 𝑎𝑛𝑑𝑆𝑂𝐶𝑏𝑎𝑡 < 25%

𝐼𝑏𝑎𝑡 𝑟𝑒𝑓 , 𝑖𝑓

𝐼𝑑𝑐𝑟𝑒𝑓 <0 𝑎𝑛𝑑 𝑆𝑂𝐶𝑏𝑎𝑡 <95%,
𝐼𝑑𝑐𝑟𝑒𝑓 >0 𝑎𝑛𝑑 𝑆𝑂𝐶𝑏𝑎𝑡 >25 %,

(13)

- Battery current control loop

The design of the bidirectional DC-DC converter of the battery or SC is based on the direct lyapunov theory.

The controller adjusts the duty cycle by comparing the reference and the actual battery currents to operate the

converter in boost and buck mode [15].

Let the battery current error defined as :

e = Ibat − Ibat ref (14)

One can define a quadratic positive defined function related to the tracking error [16]:

V =
1

2
e2 (15)

The gradient function of the loss function V is derived as:

V = e e (16)
To ensure the error convergence to zero, Let’s choose the desired gradient function of the form:

V = −Ke2 (17)
By a proper adjustment of the constant K, the system dynamics are improved, and the battery current tracks its

reference in a finite time.

By equation (16) and (17), the closed loop error dynamic is derived as a stable first order equation:

e = −Ke (18)

The duty cycle is computed as:

𝛼𝑏𝑎𝑡 = 1 −
𝑉𝑒

𝑉𝑑𝑐
(19)

Madiha. Maamir et al

IJECA – ISSN: 2543-3717. December 2016 16

- PV current control loop

The PV panels are equipped with the maximum power point tracking controller to track the MPP

and extract maximum possible power from the panel [17].

In this study, fuzzy logic has been applied for tracking the MPP of PV systems because it has the advantages

of robustness, design simplicity, and minimal requirement for accurate mathematical model [18].

The fuzzy controller consists of three blocks: the fuzzification of input variables which is performed in

the first block, it allows the passage from the real domain to fuzzy domain. The second block is

devoted to inference rules, while the last block is the defuzzification for returning to the real domain.

This last operation uses the center of mass to determine the value of the output. Fig 6 shows the basic

structure of the used MPPT Fuzzy controller [18].

Fig 6: Block diagram of the fuzzy logic controller

4. SIMULATION RESULTS

The whole system has been implemented in the Malab-simulink using the system parameters shown in table1.

Table 1: Sources parameters

Fig 7 : Load demand and battery Power

0 5 10 15 20 25
-500

500

1000

1500

T(s)

P
o

w
e
r
s(

w
)

Pch

Ppv

Pbat

Photovoltaic generator

Vop=68.8v Iop=14.A Icc=15.3A Voc=86.v

Battery Vbat=48v Cn=200h n=24 cellule

Madiha. Maamir et al

IJECA – ISSN: 2543-3717. December 2016 17

Fig 8 : Load current

Fig 9 : battery current

Fig 10: State of charge

Fig 11: dc-link voltage

Fig 12: PVG Boost and battery bidirectional converters controls

0 5 10 15 20 25
0

T(s)

il
o

a
d

(
A

)

0 5 10 15 20 25
-8

-6

-4

-2

T(s)

ib
a

t(
A

)

0 5 10 15 20 25
0.65

0.7

0.75

0.8

0.85

0.9

T(s)

so
c
b

a
t

0 5 10 15 20 25
0

100

T(s)

V
d

c
(V

)

0 0.005 0.01
0

100

Vdcref

Vdc

0 5 10 15 20 25
0

0.2

0.4

0.6

0.8

T(s)

D
b

a
t
,

D
p

Dpv

Dbat

Madiha. Maamir et al

IJECA – ISSN: 2543-3717. December 2016 18

Fig 13: refrences currents battery

Fig 7 shows the powers transfer of the system, the PV generator and the battery provide the power to the load

(0 s - 9 s).To 9s at 17s, the PV generator suplyies energy to the load and charge the battery, when the power

load equals the power of the PV generator the battery current becomes zero (17s-25s).

In fig 10, increase battery state of charge correspond to a charge, and the decrease to a discharge.

The DC bus voltage tracks well the reference without overshoot and no state error (with a response time

of 0.00065s) (fig 11).

Fig 12 presents the network boost controller, the the battery bidirectional converter controller. 𝛼𝑝𝑣 and 𝛼𝑏𝑎𝑡 are

in the interval [0.5].

Fig 13 shows the battery current ibat. It tracks well the reference, this current becomes positive to

compensate for an increase in the load power demand that oppears between time (t= 0s and t=9s) resulting in

discharge of the battery, negative when the battery is charged (for example between t=9s and t=17s) and takes

zero values if the battery is completely Charged or discharged.

5. CONCLUSION

Energy management of multi-power sources has been proposed as a solution for a hybrid energy system

that uses renewable energy from solar cells and a storage with batteries, when the PV array is used as a source

of power supply to stand alone loads, it is necessary to use the MPPT to get the maximum power point from

the PV array and implemented with MATLAB/SIMULINK for simulation. The Energy management System

(EMS) is operated in suitable modes according to the conditions of PV panel and battery.The problem of the

DC Bus Voltage control is solved by using a direct lyapunov theory.

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