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Assessment of Load Characteristics in Short-Circuit Studies of

Distribution Substations

Nguyen Thi Thanh Thuy*

Electrical Faculty, Thai Nguyen University of Technology, Thai Nguyen, Viet Nam

*Corresponding Author: thuyhtd@tnut.edu.vn

DOI: https://dx.doi.org/10.51244/IJRSI.2025.1210000335

Received: 08 November 2025; Accepted: 15 November 2025; Published: 22 November 2025

ABSTRACT

This paper evaluates the influence of electrical loads on the distribution of currents under both normal and fault

operating conditions in distribution substations. Static and dynamic loads are modeled using equivalent

impedance components, where dynamic loads are represented by the Conventional Load Model, Exponential

Load Model, Polynomial Load Model, and Comprehensive Load Model. The Newton-Raphson method is

applied for power flow analysis to determine current distribution under normal operating states. In addition, the

IEC short-circuit calculation method is adopted to analyze fault current distribution in the entire system under

short-circuit conditions. A five-bus test system, in which the load can switch between static and composite

(static + dynamic), is proposed to investigate current distribution under different operating conditions.

Simulations are performed in ETAP for both normal and fault modes, considering static loads and composite

loads. The results highlight current distribution across the system, clarifying the ability of dynamic loads to

contribute to fault currents during short-circuit conditions, unlike static loads. The contributions of this study

provide insights for designers and operators in understanding how electrical load characteristics affect the

performance of protection devices in distribution substations.

Index Terms: Composed Load, Electrical Load Model, Static Load, Motor Load, Newton-Rahpson method,

Short-Circuit Calculation.

INTRODUCTION

Electrical loads in distribution substations are diverse and vary depending on multiple factors, including

technological advancements and consumption patterns. Each type of load possesses unique characteristics that

influence the calculation of aggregated loads and the selection of protective devices. The contribution of loads

to the current in different operating modes of the substation depends on both load types and operating states,

and thus requires detailed evaluation.

Electrical loads in distribution substations are highly diverse and evolve in line with the development of

production technologies as well as the consumption characteristics of different categories of equipment [1], [2].

Each type of load exhibits distinct characteristics that directly affect the calculation of aggregated loads and the

selection of appropriate protective devices [3]. In power systems, loads are commonly categorized into Static

Loads (SL) and Dynamic Loads (DL). Static loads include electrical equipment without rotating elements, such

as lighting systems, electronic devices, and resistive appliances [4]. In contrast, dynamic loads are devices

driven by electric motors, such as pumps, fans, or compressors, which, due to their mechanical inertia, can

continue to supply energy for a short duration even after being disconnected from the power source [5], [6].

This characteristic allows dynamic loads to act as potential sources contributing to fault currents and thus must

be taken into account in short-circuit analysis and protection system design [7]–[9].

In practical operation, loads in distribution substations often exist as Composed Loads (CL), i.e., a combination

of static and dynamic loads. The proportion between these two components determines the electrical

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characteristics at each bus, thereby affecting the selection of conductors, switching devices, and protection

strategies [10], [11]. Recent studies have also indicated that the development of distributed generation and

renewable energy sources has increased the demand for improved load models to more accurately reflect the

operational behavior of modern distribution networks [12]–[14]. Furthermore, experimental results

demonstrate the need to consider the ZIP characteristics (Z–Impedance, I–Current, P–Power) when modeling

residential, commercial, and industrial loads [15].

Under normal operating conditions, loads determine the power and current levels that equipment must

withstand over long durations, thereby influencing the lifetime and reliability of the system [16]. In fault

conditions—particularly single-line-to-ground and three-phase short circuits—the current often far exceeds the

rated value and may cause severe damage to conductive elements if not properly protected [2], [7]. Moreover,

recent research shows that the participation of dynamic loads and renewable energy sources can significantly

alter fault current distribution, necessitating adjustments in short-circuit analysis and relay protection design

[8], [9], [12], [17], [18]. This is critical because the contribution of fault currents from dynamic loads can

directly affect the breaking capability of circuit breakers, the operating conditions of relays, and the thermal

endurance of conductors in distribution substations [13], [14], [19]–[21].

Based on the above analysis, this paper focuses on evaluating the impact of loads on current distribution in

distribution substations. Section II presents the modeling methods of electrical loads, including static and

dynamic loads. Section III introduces analytical methods for network operation under both normal and short-

circuit conditions. Section IV presents simulation results, highlighting the differences between Static Loads

(SL) and Composed Loads (CL). Finally, Section V concludes with key findings derived from this study.

LOAD MODELING

A. Static Load Model

A static load is defined by its active power (P), reactive power (Q), apparent power (S), and power factor

(cosφ). The mathematical relationships of these parameters are expressed as follows [4]:

S P Q

(1)

cos





(2)

where: P, Q, S are active power, reactive power, apparent power; cos is power factor.

Static loads typically consist of devices with constant or slowly varying currents, such as lighting equipment,

electric heaters, or electronic devices. Their power consumption is nearly independent of sudden voltage

changes, and thus, they rarely pose issues related to transient behavior or stability in the system.

B. Dynamic Load Models

Dynamic loads, particularly induction motors, represent the majority of industrial and commercial loads. Their

operating characteristics differ significantly from static loads because they involve rotating mechanical

components and inertia [5], [6]. When subject to voltage disturbances or during start-up, these loads exhibit

non-linear behavior that strongly affects system stability. To analyze them accurately, different mathematical

models are employed:

1) Conventional Load Model

The conventional representation assumes that the dynamic load can be modeled as a constant impedance at the

fundamental frequency. This approach is widely applied in short-circuit studies because it allows motors to be

represented as equivalent sources contributing to fault currents [4], [25].

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Exponential Load Model [7-9], [25]:

 

P PU K f  

(3)

 

Q Q U K f  

(4)

where:

, Q

: reference active and reactive power at nominal voltage U

;

P, Q are active power, reactive power at voltage U and frequency difference f;





;

f is current frequency of the system;

is norminal frequency of the system;

The parameters a and b represent the exponential indices that characterize the load behavior. Specifically, a

value of 0 corresponds to a Constant Power load, a value of 1 corresponds to a Constant Current load, and a

value of 2 corresponds to a Constant Impedance load. These indices are widely used in load modeling to

capture the nonlinear dependence of power consumption on bus voltage;

=(0÷3) is the frequency-dependence coefficient of the active power component with respect to frequency

deviation;

=(-2÷0) is the frequency-dependence coefficient of the reactive power component with respect to frequency

deviation;

Polynomial Load Model [25]:

 

0 1 2 3

P P pU p U p K f    

(5)

 

0 1 2 3

Q Q qU q U q K f    

(6)

where: p

, q

, p

, q

, p

, q

denote the power components corresponding to Constant Impedance, Constant

Current, and Constant Power characteristics, respectively. Each portion of the load is defined by these

constants.

Comprehensive Load Model:

The Comprehensive model of the Lumped Load uses the following equations to determine the real and reactive

power components of the load [10], [11], [25]:

 

0 EX 1 EX 2POLY P P

P P P P P  

(7)

where:

1 2 3POLY

P pU p U p  

 

EX 1 4 1

P pf

P p U K f  

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 

EX 2 5 2

P pf

P p U K f  

The formulation of the reactive load component follows an analogous structure, with reactive power

compensation modeled explicitly. The comprehensive load model integrates both polynomial and exponential

terms, parameterized by the constants p

, q

, p

, q

, p

, q

, p

, q

, p

, q

. These parameters describe the

contributions of constant impedance, constant current, constant power, and exponential elements within the

load.

The coefficients K

pf1

, K

pf2

correspond to the active power equations, typically varying in the range of 0 to 3.0.

Similarly, the coefficients K

qf1

, K

qf2

pertain to the reactive power equations, with typical values ranging from –

2.0 to 0.

In addition, short-circuit contribution levels are specified separately, in accordance with the IEC methodology,

and are categorized as outlined in Table [2], [7], [25]

TABLE I. SHORT-CIRCUIT CONTRIBUTION

Short-Circuit Contribution

Speed

High

Large

High RPM

Medium

Intermittent RPM

Low

Small

Low RPM

The lumped motor model includes parameters for grounding configuration, connection type, and rating. The

grounding connection can be specified by selecting among the available options, with Wye and Delta being the

supported types. The motor’s short-circuit reactance-to-resistance ratio X

, commonly referred to as the X/R

ratio, is also defined; if the Typical option is chosen, a standard representative value is automatically applied.

In addition, the transient time constant T'

, expressed in seconds, is considered, which is particularly relevant

for calculations performed under the IEC 61363 methodology





(8)

where: R

is rotor resistance.

METHOD FOR POWER ANALYSIS UNDER NORMAL OPERATING CONDITIONS

AND SHORT-CIRCUIT SCENARIOS

A. Power analysis under normal operating conditions

Mathematical model of medium voltage transmission lines is described in Fig. 1 [22-25].

Bus i Bus j

= R

+jX

Fig. 1 Mathematical model of cable in low voltage systems

Where: R

() is resistance and X

() is reactance of the transmission line connecting bus i and bus j.

Mathematical model of two-winding transformer is described in Fig. 2.

Bus i

Bus j

a. Power transformer

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Bus i

Bus j

= R

+jX

b. Equivalent circuit

Fig. 2 Mathematical model of two-winding transformer

Where: R

() is resistance and X

() is reactance of the transformer; K

is voltage ratio between bus i and

bus j of ideal transformer (without power loss). In Fig. 2b, voltage value of bus i is higher than voltage value of

bus j, so bus i is called HV bus and bus j is called LV bus.

A general distribution system include (N+1) buses, where N buses are normal buses and a bus is ground. Any

branch in the system can be classified to the standard line or transformer branch. These branches can be

defined by a general standard branch as depicted in Fig. 3 [22-25].

Bus i

Bus j

a. Bus i connecting to the ideal transformer directly

Bus i

Bus j

b. Bus i connecting to the ideal transformer indirectly through an impedance

Fig. 3 Diagram of general standard branch

In Fig. 3a and Fig. 3b, the current source

(from generations) is injects to bus i. If the branch describes a

transformer, voltage ratio can be calculated forward to bus i that is



. If the branch describes a

transmission line, voltage ratio is

K 

Applying Kirchhoff 1, current balancing equation at bus i can be determined by (9) [7].:

ij i









(9)

Using I’

, equation (1) can be converted to equation (10):

ij ij i

K I J









(10)

Using Ohm's law for i'j branch, equation (3) can be converted to equation (11) [7]:

ii k ij j i

Y U Y U J









(11)

where:

is individual admittance of bus i and

is interactive admittance of branch ij.

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can be determined by equation (12) and (13):















(12)



(13)

Working the same with Fig. 7b,

can be defined by equation (14):









(14)

In general case study, bus i can be connected to m buses directly through ideal transformers and k buses

indirectly through ideal transformers.

can be determined by equation (15) [22-25]:

ij ij

j i j i









(15)

Current balancing equations for whole system can be described in system of equations (16).

11 1 12 2 1 1

21 1 22 2 2 2

1 1 2 2

...

.............................................

...

N N NN N N

Y U Y U Y U J



   



   







   



(16)

From system of equations (16), matrix admittance can be derived as (17):

11 12 1

21 22 2

...

... ... ... ...

...

N N NN

Y Y Y











(17)

Almost buses in distribution systems are PQ buses (load buses). Capacitors can be implemented at these buses

and considered as reactive generators. In these systems, Newton-Raphson method is often used to determine

power flows and voltage buses.

To determine operating parameters for N-bus grid by using Newton-Raphson method, system of power

balancing equations at bus i can be defined by (18) and (19) [7]:

cos cos( )

i ii ii i j ij i j ij Li i

U y U U y P P

   





     



( 8)

sin sin( ) ( )

i ii ii i i ij i j ij Li Ci i

U y UU y Q Q Q

   





       



( 9)

where:

1, ; ;

i i i ij ij ij

i N U U Y y



    

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and Q

are active and reactive load power at the bus i; Q

are active and reactive power of the capacitor

bank at the bus i.

From solutions at the k

step including

()k



and

()k

, values of

()k

P

and

()k

Q

can be calculated. Moreover,

values of

()k





and

()k

U

at the k

step can be calculated by using reversed Jacobian matrix as described in

equation (20):

( ) ( )





   





   



   

   

(20)

where: J is Jacobian matrix.

Jacobian matrix at the i

step:









Solutions at the next step can be determined by equation (14) [20-21]:

( 1) ( ) ( )

k k k

i i i

k k k

i i i

U U U

  



     





     



     

     

(21)

This process will be stopped if both values of P

and Q

are smaller than allowable value



[7-9]. Fig. 4

describes the Newton-Raphson method to analyze a distribution system.

Start

Enter initial parameters: rated voltage; transmission lines;

transformers; electric loads at buses; bus types; acceptable

deviation of caculation; active and reactive power of generations

Calculate impedance matric (Y)

P

(k)

<  and

Q

(k)

< 

Calculate Jacobian and

reservered Jacobian matrices

Assign intial values of U

(0) and



(0), i=(1÷N)

Calculate P

(k)

and Q

(k)

Calculate U

(k)

and 

(k)

Power-flow

analysis results

Stop

k:=k+1

Fig. 4. Newton-Raphson algorithm to analyze whole grid

The Newton–Raphson method is characterized by quadratic convergence, enabling significantly faster

convergence compared to alternative load flow techniques. Its convergence process is guided by well-defined

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criteria that control the permissible mismatches in real and reactive power at each bus, thereby allowing direct

specification of the desired solution accuracy. In practical applications, the convergence tolerance is typically

set to 0.001 MW for active power and 0.001 MVAr for reactive power.

Despite its efficiency, the method is sensitive to the choice of initial bus voltage values. To enhance numerical

stability and reliability, careful initialization is recommended. In ETAP, several Gauss–Seidel iterations are

performed prior to executing the Newton–Raphson load flow, ensuring a consistent and well-conditioned set of

initial bus voltages.

B. Method for power analysis under fault conditions in accordance with IEC standard

IEC 60909 and related standards categorize short-circuit currents based on their magnitudes (maximum and

minimum) as well as their distance from the generator (near and far). Maximum short-circuit currents are used

to determine equipment rating requirements, while minimum short-circuit currents are critical for setting

protective devices. The classification into near-to-generator and far-from-generator faults dictates whether the

decay of the AC component should be explicitly considered in the calculation.

The three-phase short-circuit current (I”

) is evaluated using the following expression [22–25]:

(1)



(22)

Two-phase short-circuit current (I”

) is calculated using the following formula:

(1) (2) (1)

cU cU

Z Z Z

  



(23)

Two-phase-to-ground short-circuit current (I”

kE2E

) is calculated using the following formula [22-25]:







( ) ( )

kE E

(24)

Single-phase-to-ground short-circuit current (I”

) is calculated using the following formula [22-25]:

(1) (0)





(25)

where: Z

is the equivalent impedance at the fault location; U

is the normial grid voltage; Z

(1)

, Z

(2)

và Z

(0)

are

the positive-sequence, negative-sequence, and zero-sequence impedances, respectively, from the source to the

fault location.

Voltage factor c: This is the factor used to adjust the value of the equivalent voltage source for minimum and

maximum current calculations according to the following table.

TABLE II. VOLTAGE FACTOR (±5% VOLTAGE TOLERANCE)

Nominal Voltage U

For Maximum Short-Circuit

Current Calculation (c

max

)

For Minimum Short-Circuit

Calculation (c

min

)

Others < 1000 V

1.05

0.95

Medium voltage: > 1 kV to 230 kV

1.10

1.00

High voltage: > 230 kV

1.10

1.00

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TABLE III. VOLTAGE FACTOR (±10% VOLTAGE TOLERANCE)

Nominal Voltage U

For Maximum Short-Circuit

Current Calculation (c

max

)

For Minimum Short-Circuit

Calculation (c

min

)

Others < 1000 V

1.10

0.90

Medium voltage: > 1 kV to 230 kV

1.10

1.00

High voltage: > 230 kV

1.10

1.00

SIMULATION

A. Simulation parameters

Consider the power system network of a distribution substation with five buses, as illustrated in Fig. 5,

hereafter referred to as the E-5bus system.

Source

2 3

Load3

Load5

Load4

Load2

Fig. 5. Diagram of E-5bus

Parameters of transmission lines in Table IV, power source in Table V, transformers in Table VI, electric load

at bused using exponential model in Table VII.

TABLE IV. PARAMETERS OF TRANSMISSION LINES

Name

Sectional area of a conductor (mm

)

Insulation

Length (m)

Number of conductors/phase

Bus B2 - Bus B3

400

XLPE

100

Bus B3 - Bus B4

240

XLPE

Bus B3 - Bus B5

XLPE

TABLE V. PARAMETERS OF SOURCE

Type

Parameters

Power system

Rated voltage: 22 kV; Short-circuit power: 300 MVA; Reactance/Resistance: 10

TABLE VI. TRANSFORMERS

Location

Parameters

Voltage ratio: 22/0.4 kV; Rated power: 4 MVA; Impedance: Z=8.35%; Reactance/Resistance=13

TABLE VII. PARAMETERS OF ELECTRIC LOAD AT BUSES

Name

Static load and conventional load

Composed load (Exponential model)

Power (kVA)

Power factor

Ratio

(kW)

(kVAr)

Load B2

250

0.9

50%

230

100

0.1

Load B3

180

0.9

50%

162

0.1

Load B4

400

0.9

50%

230

100

0.2

Load B5

250

0.9

50%

360

175

0.15

0.1

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B. Simulation results

The Newton–Raphson method and ETAP software are employed to simulate the E-5bus network using the

parameters provided in the above table. The simulation results for the operating condition with all static loads

are presented in Fig. 6, while the aggregated load modeled with the conventional approach is illustrated in Fig.

7. The results of three-phase and single-phase short-circuit faults at location F1 are shown in Fig. 8 for the

static load case and in Fig. 9 for the dynamic load case.

Fig. 6 Current distribution under normal operating conditions when all loads are static, based on the

Conventional Model

Fig. 7 Current distribution under normal operating conditions with mixed loads, based on the Conventional

Model

a. Three-phase short circuit

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b. Single-phase-to-ground short circuit

Fig. 8 Current distribution under fault condition at bus B3 when all loads are static, based on the Conventional

Model.

The simulation results of three-phase and single-phase short-circuit faults at fault location F1 are presented in

Fig. 9.

a. Three-phase short circuit

b. Single-phase-to-ground short circuit

Fig. 9 Current distribution under fault condition at bus B3 with mixed loads, based on the Conventional Model

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The simulation results of three-phase and single-phase short-circuit faults at fault location F2 are shown in Fig.

10 for static loads and Fig. 11 for dynamic loads.

a. Three-phase short circuit

b. Single-phase-to-ground short circuit

Fig. 10 Current distribution under fault condition at bus B4 when all loads are static, based on the Conventional

Model

a. Three-phase short circuit

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b. Single-phase-to-ground short circuit

Fig. 11 Current distribution under fault condition at bus B4 with mixed loads, based on the Conventional

Model

From the above simulation results, the current distribution across the entire network under normal operating

conditions, for both static and aggregated loads, is illustrated in Fig. 12.

2 3

Load3

Load5

Load4

Load2

load2

load3

load5

Source

Fig. 12 Current distribution under normal operating conditions, based on the Conventional Model

For a short-circuit fault at F1, the current distribution in the network is shown in Fig. 13a for static loads and in

Fig. 13b for aggregated loads.

Load3

Load5

Load4

Load2

Source

a. Loads including all static components

Load3

Load5

Load4

Load2

F23

F24

Source

b. Load including dynamic components

Fig. 13 Current distribution in the substation under a fault at F1, based on the Conventional Model

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For a short-circuit fault at F2, the current distribution in the network is shown in Fig. 14a for static loads and in

Fig. 14b for aggregated loads.

2 3

Load3

Load5

Load4

Load2

Source

a. Loads including all static components

2 3

Load3

Load5

Load4

Load2

F34

F23

Source

F35

b. Load including dynamic components

Fig. 14 Current distribution in the substation under a fault at F2, based on the Conventional Model

The simulation results of current distribution considering the Exponential Load Model under a short-circuit

fault at F1 are illustrated in Fig. 15.

a. Normal operating conditions

b. Three-phase short circuit

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c. Single-phase-to-ground short circuit

Fig. 5 Current distribution in the substation under a fault at F1 based on the Exponential Load Model

The above figures demonstrate that the overall current distribution in the network remains unchanged

regardless of whether the load is static or dynamic. In the case of static loads under fault conditions, the load

does not contribute any current to the fault location, irrespective of the fault position within the network. By

contrast, when dynamic loads are considered under the Conventional Model, the loads contribute current to the

fault location, regardless of whether the fault occurs at the sending or receiving end of the feeder. The

magnitude of the fault current contribution depends on the proportion of motor load: the larger the motor share,

the greater the contribution. Under fault conditions with motor participation, the motors behave as internal

sources, injecting fault current into the fault point. However, under the Exponential Load Model, dynamic

loads do not contribute any current to the fault location, and the other load models yield similar results.

CONCLUSIONS

The contribution of this paper is the assessment of the impact of static and dynamic loads on the distribution of

short-circuit currents in distribution substations. These load types are modeled through various approaches,

including the Static Load Model, Conventional Load Model, Exponential Load Model, Polynomial Load

Model, and Comprehensive Load Model. The Newton–Raphson method is applied for load flow analysis under

normal operating conditions, while the IEC short-circuit calculation methodology is employed to determine

operating parameters under fault conditions. All system components are modeled and analyzed in ETAP

software.

The simulation results indicate that the current distribution and bus voltage parameters under normal operating

conditions are not affected by the type of load. This implies that the steady-state operation of the substation,

which corresponds to its long-term performance, remains independent of load characteristics. Under fault

conditions, however, motor loads influence fault current contributions when represented by the Conventional

Load Model, in which the load behaves as an additional current source at the fault location. In contrast, when

the Exponential, Polynomial, or Comprehensive Load Models are used, the load does not contribute to fault

current under any fault scenario. In such cases, dynamic loads behave equivalently to static loads with respect

to short-circuit current contribution.

The findings of this study can be applied to the design and operation of distribution substations. Designers and

operators must carefully select appropriate load models and account for the extent of load contribution to short-

circuit currents in order to properly coordinate protection systems and evaluate fault current magnitudes. Future

work will further investigate the design and operation of protective relaying systems, explicitly considering the

contribution of load current during fault conditions.

INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025

Page 3900

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ACKNOWLEDGMENTS

This study is completely supported by Thai Nguyen University of Technology, Thai Nguyen University, Viet

Nam.

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