Part of: Fault Analysis in Power Systems

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Thevenin Equivalent, Fault Level and Source Strength

Introduction

In Why Faults Matter in Power Systems, we introduced faults as abnormal operating conditions that create low-impedance paths within a power system. We saw that these events can produce currents many times greater than normal operating currents, placing significant thermal and mechanical stress on electrical equipment. We also discussed why fault studies are an essential part of power-system planning, equipment selection, and protection-system design.

An important question naturally follows.

How can engineers analyse faults in very large interconnected power systems without analysing every component individually?

Modern transmission networks consist of hundreds or even thousands of interconnected elements. Attempting to analyse every generator, transformer, transmission line, cable, and load each time a fault occurs would quickly become impractical.

The solution is to simplify the network while preserving the electrical behaviour observed from the fault location. This idea forms the foundation of practical fault analysis and is based on the concept of the Thevenin equivalent.

Motivation

Consider a fault occurring at a large transmission substation.

Although the fault may appear to occur at a single point on the network, it can be supplied by numerous electrical sources. Nearby generators contribute current directly, while more distant generators contribute through transmission lines and transformers. Parallel transmission corridors, neighbouring substations, and interconnected utility networks may also supply the fault.

A realistic transmission network may contain:

• Multiple synchronous generators
• Renewable generation connected through several substations
• Numerous transformers operating at different voltage levels
• Parallel transmission lines
• Distribution systems connected through zone substations
• Interconnections with neighbouring networks

Each of these elements influences the current available at the fault location.

If an engineer attempted to calculate the contribution from every individual component for every possible fault location, the analysis would become unnecessarily complicated. Even relatively small networks contain many parallel current paths, making manual calculations difficult and increasing the likelihood of errors.

Power-system engineers therefore seek a representation that captures the electrical behaviour of the surrounding network without requiring every component to be considered individually.

The Need for Simplification

An important observation makes this simplification possible.

When a fault occurs at a particular location, the fault does not "know" the detailed arrangement of generators, transformers, and transmission lines elsewhere in the network.

Instead, the fault responds only to the electrical behaviour presented by the network at the point where it occurs.

In other words, the fault effectively looks back into the network.

Everything beyond the fault location influences the fault only through the voltage available at that point and the impedance between the electrical sources and the fault.

Whether that impedance is created by one transmission line or many interconnected network elements does not matter to the fault itself. Only the combined electrical effect influences the resulting current.

This perspective allows engineers to replace a complicated network with a much simpler equivalent while preserving the behaviour observed from the fault location.

Rather than analysing every component individually, the engineer focuses on what the fault "sees."

This simplification dramatically reduces the complexity of practical fault calculations while preserving the information required for engineering analysis.

Thevenin Equivalent

The method used to simplify the surrounding network is known as the Thevenin equivalent.

Instead of representing every generator, transformer, transmission line, and interconnected network explicitly, the entire system behind the fault location is replaced by two quantities:

• The Thevenin equivalent voltage, denoted by $V_{th}$
• The Thevenin equivalent impedance, denoted by $Z_{th}$

Conceptually, the surrounding network is reduced to a single ideal voltage source connected in series with a single equivalent impedance.

Complex Network

 G1 ----\
          \
 G2 ------ T1 ------\
                      \
 Grid -------- T2 -----+------ Fault
                      /
 Wind Farm ----------/

↓

Thevenin Equivalent

 V_th
  │
 [ Z_th ]
  │
 Fault

This simplified representation does not imply that the physical network has changed.

The generators, transformers, transmission lines, and other equipment remain exactly as they were.

Only the mathematical representation used for analysis has changed.

The important property of the Thevenin equivalent is that, when viewed from the fault location, it produces the same electrical behaviour as the original network.

From the perspective of the fault, the detailed arrangement of the surrounding system has been replaced by an equivalent voltage source and an equivalent impedance that respond in exactly the same way.

This allows engineers to focus on the quantities that directly influence fault behaviour without becoming distracted by unnecessary network detail.

Viewing the Network from the Fault Location

The concept of "looking into the network" is one of the most useful ways to interpret the Thevenin equivalent.

Imagine standing at the fault location and observing the electrical system behind you.

The fault does not distinguish between individual generators, transformers, or transmission lines. Instead, it experiences the combined effect of everything connected to the network.

This viewpoint naturally leads to the equivalent representation.

Original Network

Generators
      │
Transformers
      │
Transmission Network
      │
────────────── Fault Location

↓

Viewed from the Fault

Equivalent Source

      V_th
        │
      Z_th
        │
────────────── Fault Location

Regardless of how complicated the original network may be, the quantities presented to the fault can often be represented by this much simpler model.

This simplification is one of the reasons fault studies remain practical even for very large interconnected power systems.

Large interconnected power systems contain many generators, transformers, transmission lines, and other network elements that all contribute to fault behaviour. Analysing every individual component for every fault location would quickly become impractical.

The Thevenin equivalent provides an elegant solution by replacing the surrounding network with an equivalent voltage source, $V_{th}$, and an equivalent impedance, $Z_{th}$. Although the mathematical representation is simplified, the electrical behaviour observed from the fault location remains unchanged.

Once the network has been simplified into a Thevenin equivalent, calculating fault current becomes straightforward.

Fault Current

From the perspective of the fault, these quantities contain all the information required to determine the current supplied by the network.

Before introducing the equation, it is useful to consider the physical behaviour of the system.

The equivalent voltage represents the electrical driving force available at the fault location. The equivalent impedance represents the combined opposition presented by generators, transformers, transmission lines, and other network elements between the electrical sources and the fault.

If the network impedance is reduced, the fault encounters less opposition and a larger current flows.

Conversely, if the network impedance increases, the current supplied to the fault decreases.

This relationship follows the same principle encountered throughout circuit analysis: higher impedance limits current, while lower impedance allows more current to flow.

Once the network has been represented by its Thevenin equivalent, the fault current can be estimated using

$$I_f = \frac{V_{th}}{Z_{th}}$$

where

• $I_f$ is the fault current,
• $V_{th}$ is the Thevenin equivalent voltage, and
• $Z_{th}$ is the Thevenin equivalent impedance.

Although practical fault studies often require more detailed models, this relationship captures the fundamental dependence of fault current on the available voltage and the impedance between the source and the fault.

Engineering Insight: The equation above illustrates the fundamental physical relationship between voltage, impedance, and fault current. Practical fault studies may use phase quantities, per-unit values, and more detailed network models, but the underlying principle remains the same: the fault current is governed by the equivalent voltage and impedance seen from the fault location.

A useful way to interpret this equation is:

Lower Z_th

↓

Less opposition to current

↓

Higher I_f

Likewise,

Higher Z_th

↓

Greater opposition to current

↓

Lower I_f

This simple relationship explains why identical faults can produce very different fault currents at different locations within the same network.

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Worked Example 1

Consider the simplified network below.

Generator

    │

Transformer

    │

Fault

Suppose the fault occurs on the high-voltage side of the transformer. Assume that the Thevenin equivalent seen from the fault location is

• $V_{th}=132~\text{kV}$ (line-to-line)
• $Z_{th}=5~\Omega$ For a three-phase fault, the fault current is approximated by

$$I_f = \frac{V_{LL}}{\sqrt{3}\,Z_{th}}$$

Substituting the values,

$$\frac{132,000} {\sqrt{3}\times5}$$ $$15,242\ \text{A}$$

or approximately

$$15.2~\text{kA}$$

Interpretation

The calculation shows that the surrounding network is capable of supplying approximately 15.2 kA to the fault.

Notice that the calculation required only the equivalent voltage and equivalent impedance.

The individual generator characteristics, transformer leakage impedance, and transmission-line impedances have already been incorporated into the Thevenin equivalent.

This illustrates one of the principal advantages of network reduction. Once the equivalent has been obtained, the fault calculation becomes straightforward.

Fault Level

Fault current indicates the magnitude of current supplied during a fault.

Another commonly used quantity is the fault level, which expresses the fault in terms of apparent power.

Fault level is commonly expressed as apparent power (MVA), while fault current is commonly expressed in kA. Both quantities describe the same fault from different perspectives.

For a three-phase fault,

$$S_{fault} = \sqrt{3}\,V_{LL}\,I_f$$

where

• $S_{fault}$ is the fault level,
• $V_{LL}$ is the line-to-line voltage, and
• $I_f$ is the fault current. Using the previous example,

$$S_{fault} = \sqrt{3}\times132\times15.2$$ $$S_{fault} \approx 3480~\text{MVA}$$

This value represents the apparent power associated with the fault at that location.

The relationship between impedance, fault current, and fault level can be summarised as

Lower Impedance

↓

Higher Fault Current

↓

Higher Fault Level

Similarly,

Higher Impedance

↓

Lower Fault Current

↓

Lower Fault Level

Fault current and fault level therefore describe the same physical behaviour from different perspectives.

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Engineering Interpretation

Fault level provides an indication of the network's ability to supply current during fault conditions.

A higher fault level means that larger currents can be delivered to a fault. Equipment installed at that location—including circuit breakers, switchgear, busbars, current transformers, and other primary equipment—must therefore be capable of withstanding higher electrical and mechanical stresses.

Conversely, a lower fault level indicates that the available fault current is smaller. Although this may reduce the stress imposed on equipment, it also influences many other aspects of power-system behaviour that will be explored later in this series.

For this reason, utilities frequently specify fault levels for substations and connection points in addition to reporting fault current values.

Fault level tells engineers how strongly the network can supply a fault. Although fault current and fault level are closely related, engineers often prefer fault level when comparing different locations within a network because it provides a voltage-independent measure of the apparent power that can be delivered during a fault.

This naturally leads to the next question:

What does a high or low fault level actually tell us about the electrical strength of the power system?

Source Strength

Source strength is a qualitative description of how effectively the surrounding network can supply current to a fault.

Although it is influenced by many aspects of the power system, the underlying concept follows directly from the Thevenin equivalent introduced earlier.

A network with a small Thevenin equivalent impedance presents relatively little opposition to current flow. Consequently, a fault at that location can draw a comparatively large current.

Conversely, a network with a large Thevenin equivalent impedance limits the current supplied to the fault.

This relationship can be summarised as

Strong Source

↓

Low Z_th

↓

High Fault Current

↓

High Fault Level

and

Weak Source

↓

High Z_th

↓

Low Fault Current

↓

Low Fault Level

The distinction is not determined by the physical size of the network or the number of generators alone. Rather, it reflects the electrical behaviour seen from the fault location.

A large interconnected system may appear electrically weak at one location if significant impedance exists between the fault and the available generation. Similarly, a relatively small network can appear electrically strong if the fault occurs close to major generation sources.

For this reason, source strength is always associated with a particular location within the network rather than with the entire power system.

Worked Example 2

The influence of source impedance can be illustrated by comparing two simplified networks operating at the same voltage.

Assume the fault occurs on a 132 kV network.

Case A – Strong Source

Equivalent Source

 V_th
  │
[ Z_th = 2 Ω ]
  │
 Fault

Using the three-phase fault relationship,

$$I_f = \frac{V_{LL}}{\sqrt{3} Z_{th}}$$ $$I_f=38.1 \text{kA}$$

The corresponding fault level is

$$S_{fault} = \sqrt{3}\times132\times38.1$$ $$S_{fault} \approx 8710~\text{MVA}$$

Case B – Weak Source

Now consider the same network voltage with a higher equivalent impedance.

Equivalent Source

 V_th
  │
[ Z_th = 8 Ω ]
  │
 Fault

The fault current becomes

$$I_f=9.53\ \text{kA}$$

The corresponding fault level is

$$S_{fault} = \sqrt{3}\times132\times9.53$$ $$S_{fault} \approx 2180~\text{MVA}$$

Interpretation

Both examples represent faults occurring on a 132 kV network.

The only quantity that changed was the Thevenin equivalent impedance.

Increasing the impedance from 2 Ω to 8 Ω reduced the available fault current by approximately a factor of four. The fault level decreased by a similar proportion.

This illustrates an important engineering principle.

The electrical strength of the network, as observed from the fault location, depends primarily on the equivalent impedance presented to the fault.

Lower impedance allows the surrounding network to supply larger currents.

Higher impedance limits the current available during the disturbance.

Engineering Insight: Source strength is not an independent property of the network. It is simply another way of describing the electrical behaviour represented by the Thevenin equivalent impedance. A lower equivalent impedance results in a stronger source, while a higher equivalent impedance results in a weaker source.

Practical Engineering Meaning

Fault studies are performed for much more than calculating a single current value.

They provide information that influences many aspects of power-system design and operation.

Typical engineering questions include:

• Can the circuit breaker safely interrupt the maximum fault current?
• Are busbars, transformers, and cables adequately rated for the expected fault duty?
• Will protection systems detect and isolate faults as intended?
• How will a proposed generator or transmission project affect the fault levels throughout the network?

Answers to these questions determine equipment ratings, protection-system design, and network planning decisions.

Fault studies are also a routine component of generator and battery energy storage system grid-connection assessments. Network operators evaluate how new installations influence fault levels at nearby substations and whether existing equipment remains suitable for the revised operating conditions.

In modern power systems, increasing amounts of inverter-based generation have changed the way faults are supplied. Networks with relatively low fault levels are often described as electrically weaker systems.

The reasons for this behaviour, and its implications for inverter-based resources, extend beyond the scope of this article and will be explored in a future GridAnalytica series.

Animation Placeholder

[Animation: Building the Thevenin Equivalent]

This animation is intended to reinforce the physical interpretation of the Thevenin equivalent by showing how a complex power system can be simplified without changing the electrical behaviour observed from the fault location.

Panel 1 – Complex Network

Display a simplified transmission network containing:

• Multiple generators
• Transformers
• Parallel transmission lines
• Interconnected substations
• A selected fault location

Highlight the various current paths that could contribute to the fault.

The objective is to illustrate that many network elements influence the fault current, making direct analysis increasingly difficult as network complexity grows.

↓

Panel 2 – Thevenin Equivalent

Gradually collapse the surrounding network into its equivalent representation.

Display:

      V_th
        │
      Z_th
        │
      Fault

Animate the transition so that the original network fades while the equivalent voltage source and equivalent impedance remain.

Emphasize that the network has not changed physically. Only its mathematical representation has changed.

↓

Panel 3 – Effect of Equivalent Impedance

Provide an interactive slider controlling the value of $Z_{th}$

As the slider moves:

• Decreasing $Z_{th}$ causes the displayed fault current to increase.
• Increasing $Z_{th}$ causes the displayed fault current to decrease.

Display the relationships dynamically:

Lower Z_th

↓

Higher I_f

↓

Higher S_fault

and

Higher Z_th

↓

Lower I_f

↓

Lower S_fault

The educational objective is to reinforce that the equivalent impedance is the principal quantity governing the current supplied by the network during a fault.

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Interactive Tool Placeholder

[Interactive Tool: Fault Level & Thevenin Equivalent Calculator]

A companion calculator will accompany this article to allow readers to explore the relationships developed throughout the discussion.

Planned Inputs

• System line-to-line voltage
• Thevenin equivalent impedance
• Unit selection (Ω or per-unit)

Planned Outputs

• Fault current, $I_f$
• Fault level, $S_{fault}$
• Equivalent impedance in alternate units
• Engineering interpretation of the calculated result

Comparison Mode

An optional comparison mode will allow users to evaluate two cases side by side by varying the equivalent impedance while maintaining the same system voltage.

This provides a simple way to compare networks with higher and lower fault levels and observe how the available fault current changes.

The calculator is intended to complement the concepts presented in this article rather than replace engineering judgement or detailed fault-study software.

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Conclusion

Practical fault analysis begins by recognising that a fault does not need to "understand" every generator, transformer, and transmission line within a power system.

Instead, the surrounding network can often be represented by a Thevenin equivalent consisting of an equivalent voltage source, $V_{th}$, and an equivalent impedance, $Z_{th}$. This simplification preserves the electrical behaviour observed from the fault location while making analysis significantly more manageable.

From this equivalent representation, the relationships developed throughout this article follow naturally:

Complex Network

↓

Thevenin Equivalent

↓

Fault Current

↓

Fault Level

↓

Source Strength

These concepts underpin many areas of power-system engineering, including equipment selection, protection studies, network planning, and generator connection assessments.

Note on Unbalanced Faults: This article focuses on balanced three-phase fault conditions, which represent the most severe fault scenario and govern equipment ratings. Single-phase and phase-to-phase faults create unbalanced conditions that require sequence-component analysis. For an introduction to how unbalanced systems are decomposed into balanced components, see Sequence Components in Power Systems and Symmetrical Components: Decomposing and Reconstructing Three-Phase Systems.

If the network can now be represented by a single equivalent voltage source and impedance, the next question is straightforward: how can this simplified model be used to calculate the current flowing during an actual fault? The next article answers this question by examining the balanced three-phase fault and applying the Thevenin equivalent in practice.

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Related Articles

• Why Faults Matter in Power Systems
• Symmetrical Components: Decomposing and Reconstructing Three-Phase Systems
• Sequence Components in Power Systems (Series)