Analysis of the Influence of PV Integration on an Unbalanced Grid

Voltage Deviation

A. ABAYOMI, AGHA F. NNACHI

Department of Electrical Engineering,

Tshwane University of Technology, eMalahleni,

SOUTH AFRICA

Abstract: - With the increasing utilization of renewable energy sources (RES) to mitigate climate pollution

from fossil fuel-based energy production, it is imperative to investigate the influence of integrated Photovoltaic

(PV) generation on distribution grid voltage levels and power losses. Voltage stability in dispersed systems

with high PV penetration is a major challenge due to solar power dynamic generation. Voltage stability is an

important parameter for measuring the level of penetration of PV systems on distribution grids in terms of load

capacity. As a result, this study provides analytical voltage stability, which is achieved using a 4.16 kV voltage

level on a modified IEEE 13 bus radial distribution system. The network was modeled, simulated, and analyzed

based on a snapshot power flow solution. Four simulation scenarios were tested for PV penetration levels on

the grid. The collected outcomes demonstrated that the system voltage profile and losses remained within the

voltage limit established by international standards with PV penetration. As a result, PV penetration levels

greater than 40% of the loading capacity resulted in voltage increases that exceeded the prescribed limits,

reverse power flow, and an increase in grid power loss.

Key-Words: - PV generation, losses, PV placement, low-voltage grid, deviation, modeling, InCond MPPT

algorithm, dynamic gravity search algorithm, voltage drop, reverse power flow.

Received: April 11, 2024. Revised: August 17, 2024. Accepted: September 17, 2024. Published: October 24, 2024.

1 Introduction

The low-voltage distribution system has undergone

an immense rise in the integration of renewable

energy sources (RES), driven by global demand for

sustainable and clean energy alternatives. Solar

photovoltaic (PV) and wind power generation

systems are two of the most common RES

technologies, as shown in Figure 1, [1]. PV system

penetration into the distribution grid is increasing

year after year, particularly in densely populated

urban regions, where consumers are driven to

environmentally benign energy options and lower

installation costs. However, as the number of PV

generators connected to the distribution network

grows, maintaining voltage levels within acceptable

limits becomes more difficult due to the grid's

original architecture, which failed to account for

bidirectional power flows. This is because these PV

generators are dependent on fluctuating weather

conditions, [2]. It can be integrated into both

transmission and distribution networks, including

medium- medium and small-scale small-distributed

generation systems, [3], [4]. Large-scale Large PV

generators, typically three-phase and ranging from

an output of 1 to 10 MW, are connected to the

power grid through interconnection via connection

transformers connected in parallel. These systems

are either directly integrated directly into the

transmission network or connected to dedicated

special distribution substation feeders equipped

with voltage and overcurrent protection. Medium-

scale Medium-sized PV units, systems with

capacities outputs between 10 and 1000 kW and are

usually installed in commercial buildings. With the

exception of the transformer's rated power, larger

units with hundreds of kW are configured similarly

to large PV systems, [5], [6]. The 10 kW maximum

output small photovoltaic generator is integrated

into the home of the energy consumer and is

typically single-phase. The most popular type

requires no connection transformer at this

installation level, [7]. The power grid's PV system

penetration was found to be highest in the

distribution system, [8]. Small-scale generating and

industrial customers will continue to integrate PV

into the grid system as a result of government

incentives and falling PV panel costs, as PV

penetration is believed to provide technical and

environmental benefits, [9], [10]. However, high

PV penetration levels may have an impact on the

distribution system, resulting in voltage unbalance,

voltage rise, and reverse power flow, all of which

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contribute to higher power loss [11], [12]. This

negative impact has an effect on grid operation and

control since the low-voltage distribution system is

not designed to accept external power sources such

as PV devices.

Fig. 1: Public use of renewable energy worldwide,

[1]

As PV integration on the distribution network

increases, the technical influence needs to be

examined and determined. This study investigates

the impact of PV system integration on a

distribution network using an adapted IEEE 13 bus

test system with domestic and industrial feeders

and real-time time series analysis of solar

irradiance data, [13], [14]. The integration level is

adjusted to adequately reflect the effects of PV

integrated into the distribution network.

2 Description of Modelled System

Figure 2 depicts the layout of a 10 kW PV system

simulated for this study, including all electrical

power components and the DC-DC boost converter,

which increases the PV voltage at maximum power

from 273 Vdc to 500 Vdc. The Incremental

Conductance (InCond) MPPT algorithm improves

duty cycle switching performance. The MPPT is

designed to automatically alter the duty cycle to

create the voltage required to track maximum

power.

Fig. 2: The basic configuration of the modeled

system

A three-phase three-level voltage source

inverter (VSI) is connected to the DC-DC

converter, which converts the connection voltage of

500 Vdc to 250 Vac. It maintains the system's

power factor (PF) at unity. The VSI control system

has two feedback loops: an inner loop controls grid

currents Id and Iq (active and reactive components),

while an outer loop regulates DC link voltage to

±250V. Equations (1) and (2) explain the voltage

equations of a grid-tied inverter in the synchronous

reference frame, with L as the filter inductance and

R as the filter resistance, [15].

where: Vq and Vd are the voltage output of the

inverter, Iq and Id are the inverter currents,  is

the angular frequency of the grid, and eq and ed

are the grid voltages.

When solar radiation decreases due to cloud

movement, the power generated by the PV system

follows the Figure 3(a) pattern. In a 10 kW PV

system, solar radiation drops from 1000 W/m2 to

152 W/m2 at 36°C ambient temperature within 20

seconds of cloud shadow, which reduces the system

output from 1700 watts to 139 watts, [16]. Figure

3(b) shows an increase in power after cloud

movement, [17]. Most PV systems installed in

residential areas operate at a power factor of unity

for maximum active power generation; Therefore,

in terms of active power, an increase in the PV

power capacity corresponds to a decrease in load,

[18].

Fig. 3(a): Solar irradiation impact on PV power

drop

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Fig. 3(b): Solar irradiation impact on PV power rise

As solar radiation intensifies, as shown in

Figure 3(b), the voltage rises because of the

integration of PV systems into the network, which

reduces line current and voltage drops along the

distribution lines. For significant PV penetration in

an unbalanced distribution network, this effect must

be thoroughly analyzed. Such impacts may require

distribution system operators (DSOs) to implement

protective measures to mitigate voltage surges

caused by large spikes. While these scenarios are

all possible within a distribution network, this study

focuses specifically on the widespread adoption of

PV systems and the associated challenge of voltage

increases they induce.

Grid-integrated PV was simulated using the

IEEE 13 bus distribution network. A schematic

system diagram can be seen in Figure 4. Buses 632,

633, 634, 671, 692, and 675 are examples of three-

phase overhead lines; 645, 646, and 684 are

examples of two-phase buses; and 611 and 652 are

examples of single-phase buses. With 2.102 MVar

and 3.466 MW of distribution loads between

industrial and domestic electric power consumers,

the distribution system is fairly loaded for a 4.16

kV bus. Along with distributed loads connected in

star and delta configurations with constant current

and impedance, the network is made up of

overhead wires, parallel capacitors, and a grounded

delta-star transformer. In line with most modern

distribution systems, buses 633 and 634 are linked

to a 4point 16 kV/480 V step-down transformer.

[19], [20] All buses have a voltage of 4.16 kV, with

the exception of bus 634, which has 480 V.

Fig. 4: Schematic of the adapted system

The magnitude of the loads dictated the

location of load categories to the busbars, with each

bus assigned a certain load category (i.e. residential

or commercial). The distribution network's

electrical restrictions were analyzed using power

flow results, which took into consideration the

current across the lines while keeping the voltage

within the permitted range (0.95-1.05 p.u), [21].

The iterative equation was used in the power flow

analysis to compute the network's power losses,

voltage, voltage angles, and active and reactive

power.

3 Test System Analysis Approach

Equations (1) through (5) were used to select and

design a polycrystalline PV module that would

satisfy the needs of the various scenarios in this

study. The effects of PV penetration on an

unbalanced distribution network were investigated

using a MATLAB/Simulink model of an adapted

IEEE-13 bus test system. The model file was

updated with the network parameters, and the

system's baseline results were contrasted with

varying PV penetration levels. Grid-integrated PV

penetration levels of thirty, forty, and fifty percent

of the total load were subsequently put into practice

after first creating and testing the model base

scenario without PV [22]. Next, the effects of

various penetration levels were looked at. The

voltage curve and power losses are examined using

the snapshot power flow analysis method [23],

[24].

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3.1 PV Module Model

A single diode circuit was utilized to evaluate the

parameters of a single PV cell and compute the

output current in Equation (3) [25], [26].

dph III 

(3)

where; Iph = photocurrent, Id = diode current, that is

proportionate to the saturation current.

Equations (4) and (5) show that a PV cell's

output current is proportional to temperature and

solar irradiance.

iSCph G

TKII )( 

(4)

Where: Iph = photocurrent; ISC = short-circuit

current; Ki = temperature co-efficient of the cell ISC;



T = change in cell temperature (K); G = irradiance

(kW/m2); GO = nominal irradiance (kW/m2).

The impact of temperature on the saturation

current (Io) of the PV cell is expressed in equation

(5) [27], [28].







































rsOTTnK

qxE

II 11

exp

(5)

The current-voltage characteristic (I-V) can

then be described quantitatively, as illustrated in

Equation (6).

Oph I

AKT

III 

























1exp

(6)

where: Iph = photocurrent; I0 = reverse saturation

current of the diode; q = electron charge; A = diode

ideality constant, K = Boltzmann constant, and Id =

Shockley diode current, [1].

Equation (7) represents the real version of a

solar module modified to accommodate the

serial/parallel configuration of the PV modules,

[29], [30].

 

spvpv

sph

Oph R

RIV

III 



























 1exp

(7)

where: I = load current; Iph = photocurrent; I0 =

saturation current; V = output voltage; Rs = series

resistance; Rsh = shunt resistance Vt = thermal

voltage.

3.2 PV Location Scenario

For the best tuning of the D-STATCOM PI

controller, the dynamic gravity search algorithm

(DGSA) is used, which is based on mass

interactions and Newton's laws and ensures errors

in a finite time span due to its fast convergence

functions. Performance is determined by

considering the location of the masses that

constitute the population in this algorithm. The four

characteristics of a mass are its location, its inertial

mass, its active mass due to gravity, and its passive

mass. Although the mass's position implied a

solution, its gravity and inertial masses were related

to the fitness function. Gravity forces all of these

particles to move toward each other according to

Newton's laws. This effect causes heavier masses,

which correspond to good solutions, to move

slower than lighter masses, which correspond to

bad solutions. After the recorded iteration, the

global solution and overall fitness of the problem

are determined by the optimal fitness and position

of the corresponding agent in the search space. The

exploitation step of the algorithm in the system is

modeled and shown in Figure 4.

The system was simulated with a single PV

array of the required size to provide different

penetration levels after obtaining a realistic load

profile, [31]. As shown in Figure 5, the PV system

was installed on bus 611 to assess its effect on the

system.

Fig. 5: Illustration of the model in one line

3.3 The Penetration Level of the PV

The maximum output of the PV system divided by

the maximum grid consumption - i.e. the total

installed loads - defines the PV penetration in this

study. In other words, twenty percent of PV

integration results in 28 kW power generation at

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STC when the maximum grid intake on Phase A of

Bus 632 is 150 kW, [32], [33]. The system is

believed to produce the most solar energy possible.

𝑆𝑃𝑉 𝑝𝑒𝑛𝑒𝑡𝑟𝑎𝑡𝑖𝑜𝑛(%)

=𝐴𝑟𝑟𝑎𝑦 𝑚𝑎𝑥. 𝑝𝑜𝑤𝑒𝑟

𝐺𝑟𝑖𝑑 𝑚𝑎𝑥. 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛

(8)

A simple iterative power flow analysis was run

on each distribution system unit to ascertain the

voltage profile, angle, real and imaginary power,

and power losses of the test system.

4 Simulation Result

This section discusses the results of various

simulation scenarios. Table 1 contains the basic

power flow results for the voltage curve and the

total active and reactive power with losses, without

PV integration into the grid. Normally, the voltage

level in the distribution system decreases relative to

the main bus of the system due to a voltage drop in

the network. Figure 6 shows the voltage diagram

for the system without PV integration; The voltage

level remains within an acceptable range (0.95 pu

to 1.05 pu). The lowest voltage on the network is

reported to be 0.9701 on bus 611, and a significant

voltage drop is observed on the buses further

downstream. Figure 7 provides a detailed

examination of the various scenarios in phase A of

the network.

Table 1. Base Case power flow results

The minimal voltage rises between thirty and

forty percent penetration depth, from 0.9599 pu to

0.9793 pu, with a maximal voltage peak of 1.0499

pu, which is under the permitted voltage limit. At

fifty percent integration, the voltage rises above the

limit, increasing from 1.0499 pu to 1.07621 pu,

because power consumer loads are sensitive to

voltage swings, this breach may cause damage to

them. The grid current also shifts, resulting in a

reverse flow of electricity.

Fig. 6: Voltage magnitude of the base scenario

Fig. 7: Different integration scenarios profile on

Phase A

Figure 7, Figure 8 and Figure 9 depict the

system voltage fluctuation based on a comparative

analysis of the results obtained at different PV

integration depth on bus 611 in the network.

There was a noticeable voltage drop on the

busbar of the grid source prior to the PV generator

being installed. The PV system's installation has

improved all bus voltages and raised the minimal

voltage magnitude from 0.9607 pu to 1.0108

mitigating the trend in Phase A.

On the C phase, the maximum voltage

magnitude on bus 632 exceeded the 1.05 pu limit at

the fifty percent integration level, indicating that

the system voltage stability cannot be maintained at

the permissible limit above the forty percent

integration level.

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Table 2. Overview of System Analysis Findings

Table 2 shows that system losses were

drastically reduced with PV integration compared

to the results without system integration. Power

losses decreased significantly at thirty percent and

forty percent PV integration depth, but began to

increase at fifty percent penetration, indicating that

the grid's PV penetration is limited to fifty percent

penetration. This leads to a reverse power flow,

which increases power losses in the network.

Fig. 8: Different integration scenarios profile on

Phase B

Fig. 9: Different integration scenarios profile on

Phase C

5 Conclusion

The influence of integrating PV systems on low

voltage distribution systems voltage magnitude and

losses in an imbalanced distribution system was

studied utilizing an adapted 13 bus test system with

a nominal voltage of 4.16 kV/480 V. Four

simulated scenarios were considered: the base case

study and three different integration levels of the

PV system on the grid. The system model and

simulation results depict that the PV connection

reduces voltage dips on the test system's buses,

improves the network voltage profile, and

significantly reduces system power losses

comparatively to the results obtained without the

PV. The highest voltage was determined to be

1.0559 p.u in the base case, which improved to

1.0472 p.u with grid-integrated PV. Similarly, with

forty percent PV integration, power losses improve

from 315.73 kVar to 278.98 kVar. It has been noted

that a forty percent PV integration depth is most

acceptable for maintaining a reasonable voltage

level and reducing reverse power flow, as a higher

integration of the solar system increases power

losses on the grid. To avoid power losses, the level

of PV integration on the distribution grid should

not be too high.

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