Validating the IEEE 9-Bus Case Against a Reference Solution

Good to see you again. In the last lesson, you used your solved IEEE 9-bus base case as the starting point for a manual N-1 line outage. That result is only as trustworthy as the intact case beneath it. This lesson closes the 9-bus module by performing a more formal external validation: comparing your PSS®E base case with a published WSCC/IEEE 9-bus reference and documenting whether any differences are material.

This is the same discipline required when you receive an SPP cluster model, a transmission-owner planning case, or an OEM test system: do not merely accept that it converges. Establish which reference you used, prove that the modeled inputs are comparable, compare the solved electrical state, and leave an auditable explanation for every meaningful discrepancy.

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Validation is not simply “my case converges”

A converged AC load flow solves the equations for the network you entered. Validation asks a different question:

Does the solved network represent the intended published system closely enough for the stated study purpose?

Two cases can both converge cleanly while differing in a transformer base, tap, line-charging entry, generator voltage schedule, load sign, reactive limit, or branch status. Those differences can change voltages, losses, reactive production, and contingency behavior.

For this exercise, use the public 9-bus PSS®E package hosted by Alroomi as the primary reference artifact. Treat the associated single-line values as visual checks, but treat the actual reference files and their documented contents as more authoritative than numbers visible in a diagram.

The published single-line diagram provides a quick visual check of the expected operating condition.

From the diagram, the following displayed values are useful checkpoints:

Quantity	Published displayed value
Bus 1 voltage	1.040 p.u.
Bus 2 voltage	1.025 p.u.
Bus 3 voltage	1.025 p.u.
Bus 4 voltage	1.025 p.u.
Bus 5 voltage	1.000 p.u.
Bus 6 voltage	1.012 p.u.
Bus 7 voltage	1.027 p.u.
Bus 8 voltage	1.017 p.u.
Bus 9 voltage	1.033 p.u.
Generator at Bus 1	about 72 MW, 28 Mvar
Generator at Bus 2	about 163 MW, 5 Mvar
Generator at Bus 3	about 85 MW, -11 Mvar
Loads at Buses 5, 6, and 8	125/50, 90/30, and 100/35 MW/Mvar

Because the diagram rounds values for display and may reflect a particular software implementation, do not expect it alone to prove an exact numerical match. The independent PSS®E case is the stronger comparison.

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First prove that the two cases mean the same thing

Before comparing solved results, compare the model definition. This is more important than the final voltage table. If two input models differ, their output differences are expected rather than diagnostic.

Open your intact solved case, not the N-1 case:

IEEE9_SOLVED_BASE_R01.sav

Then create a working copy of the downloaded reference case. Preserve both originals. If your installed PSS®E version converts the older reference case, save the converted version with a clear name such as:

REF_IEEE9_ALROOMI_CONVERTED_R01.sav

Do not silently overwrite the original file. A later reviewer needs to distinguish the downloaded artifact from a version-converted copy.

Create a reference manifest before changing or solving anything:

Validation study: IEEE 9-bus external reference comparison
Internal case: IEEE9_SOLVED_BASE_R01.sav
Reference source: Alroomi 9-Bus System PSS/E package
Reference archive/file name: [record]
Download date: [record]
PSS/E release used: [record]
System base MVA: [record]
Reference case conversion performed: [yes/no; describe]
Solution method and tolerance: [record]
Comparison date and analyst: [record]

Now compare the two cases in the following order.

1. Network identity and topology

Confirm that both cases contain:

• nine buses;
• three generators;
• three two-winding generator step-up transformers;
• six transmission lines;
• three loads;
• no unintended out-of-service element;
• no extra switched shunt, fixed shunt, series device, or load representation that you did not intend to add.

For the conventional 9-bus arrangement, the generator buses are connected through transformers to the 230 kV transmission network. The transmission mesh includes the six line paths among Buses 4 through 9. A topology mismatch is material by definition: do not attempt to compensate for it by adjusting output tolerances.

2. Bus and control definition

Check, bus by bus:

• bus number and nominal kV;
• swing, PV, and PQ bus classification;
• voltage schedules at the swing and PV buses;
• load MW and Mvar;
• generator MW dispatch;
• generator reactive-power limits;
• transformer tap positions and control status;
• line resistance, reactance, charging, and in-service status.

The comparison must include control assumptions, not only equipment values. For example, a generator held at 1.025 p.u. is not equivalent to a generator producing the same initial MW but allowed to regulate a different bus or operating against different reactive limits.

A practical input comparison table is:

Item	Your case	Reference case	Match?	If different, likely importance
System MVA base	[record]	[record]	[yes/no]	High
Swing bus and angle reference	[record]	[record]	[yes/no]	High
Bus 2 MW and voltage schedule	[record]	[record]	[yes/no]	High
Bus 3 MW and voltage schedule	[record]	[record]	[yes/no]	High
Loads at Buses 5, 6, 8	[record]	[record]	[yes/no]	High
Transformer impedances and taps	[record]	[record]	[yes/no]	High
Six line impedances and charging	[record]	[record]	[yes/no]	High
Generator reactive limits	[record]	[record]	[yes/no]	Medium to high
Ratings, areas, zones, owners	[record]	[record]	[yes/no]	Depends on use

Items such as areas, zones, and owners will not normally change an ordinary load-flow solution, but they matter for later contingency and reporting workflows. Keep them in the manifest even if they are not validation-critical today.

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Solve both cases under controlled conditions

Use the same full Newton-Raphson solution method, mismatch tolerance, and control settings for both cases. The reference case should first be solved without altering its model data. Your objective is to observe what it does as supplied.

For each case, record:

• convergence status;
• total MW load and Mvar load;
• total MW generation and Mvar generation;
• total MW losses;
• swing-generator MW and Mvar output;
• PV buses that converted to PQ because of reactive limits;
• transformer tap or shunt movements, if automatic control was enabled;
• largest final mismatch.

If the reference case does not converge under your PSS®E release, first investigate case conversion, missing model data, and solution settings. Do not modify its network parameters merely to obtain convergence. Instead, document the behavior and establish whether the provided solved state is compatible with your installed release.

For a solved case, active-power balance should be internally coherent:

$$P_{\mathrm{generation}}=P_{\mathrm{load}}+P_{\mathrm{loss}}$$

The slack machine makes up the residual balance. Therefore, a difference in slack MW can indicate a difference in total real-power losses, a dispatch difference, or both. It is an important clue, not automatically an error.

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Compare outputs with consistent conventions

Once input comparability is established and both cases solve, export bus and branch reports from each case into a spreadsheet or comparison workbook. Do not compare screen captures manually if you can avoid it; a structured table becomes reusable later for utility-case reproduction.

For a bus voltage magnitude, calculate:

$$\Delta V_i=V_{i,\mathrm{your}}-V_{i,\mathrm{reference}}$$

For voltage angle, first ensure both cases use the same angular reference. If needed, normalize every angle to its swing-bus angle:

$${\delta }_i^{\prime }={\delta }_i-{\delta }_{\mathrm{swing}}$$

Then calculate:

$$\Delta {\delta }_i={\delta }_{i,\mathrm{your}}^{\prime }-{\delta }_{i,\mathrm{reference}}^{\prime }$$

This normalization matters because an absolute shift in all bus angles does not change physical power flows. A mismatch in angle differences, however, can indicate a dispatch, impedance, transformer, or topology discrepancy.

Use a bus comparison table like this:

Bus	$V_{\mathrm{your}}$ p.u.	$V_{\mathrm{reference}}$ p.u.	$\Delta V$ p.u.	${\delta }_{\mathrm{your}}^{\prime }$ deg	${\delta }_{\mathrm{reference}}^{\prime }$ deg	$\Delta \delta$ deg	Status
1	[record]	[record]	[calculate]	0.0	0.0	0.0	[record]
2	[record]	[record]	[calculate]	[record]	[record]	[calculate]	[record]
3	[record]	[record]	[calculate]	[record]	[record]	[calculate]	[record]
4–9	[record]	[record]	[calculate]	[record]	[record]	[calculate]	[record]

For generators, compare scheduled and solved quantities separately:

Generator bus	Scheduled MW match?	Voltage schedule match?	Your solved Mvar	Reference solved Mvar	Difference	Reactive-limit status
1	[record]	[record]	[record]	[record]	[calculate]	[record]
2	[record]	[record]	[record]	[record]	[calculate]	[record]
3	[record]	[record]	[record]	[record]	[calculate]	[record]

For branches, align the orientation before comparing signed MW and Mvar. A reference report may label a line as 5–7 while your export may show the flow from 7–5. In that situation, the signed flows should be opposite; the apparent-power magnitudes and losses should agree.

$$S_{ij}=P_{ij}+j{Q}_{ij}$$ $$\left|S_{ij}\right|=\sqrt{P_{ij}^2+Q_{ij}^2}$$

Compare branch loss using the sum of terminal real-power flows after applying the same orientation convention:

$$P_{\mathrm{loss},ij}=P_{ij}+P_{ji}$$

A good branch comparison table includes both terminals when reactive-power behavior is relevant, especially for lines with charging and transformers with magnetizing assumptions.

Element	Your MW flow	Reference MW flow	Your Mvar flow	Reference Mvar flow	Your MW loss	Reference MW loss	Assessment
Transformer 1–4	[record]	[record]	[record]	[record]	[record]	[record]	[record]
Line 4–5	[record]	[record]	[record]	[record]	[record]	[record]	[record]
Line 4–6	[record]	[record]	[record]	[record]	[record]	[record]	[record]
Remaining elements	[record]	[record]	[record]	[record]	[record]	[record]	[record]

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Decide what counts as material before looking for explanations

For a public teaching reference with displayed values rounded to three decimal places and whole MW/Mvar, use pre-declared screening flags, not arbitrary after-the-fact tolerances:

Comparison	Suggested flag for this exercise	Interpretation
Bus-voltage difference	$\left	\Delta V\right
Normalized angle difference	$\left	\Delta \delta\right
Generator or branch real-power difference	$\left	\Delta P\right
Generator or branch reactive-power difference	$\left	\Delta Q\right
Total real-loss difference	$\left	\Delta P_{\mathrm{loss}}\right
Topology, bus type, base kV, schedule, or status mismatch	Any difference	Material input discrepancy

These are practical teaching thresholds, not ERCOT, SPP, WECC, NERC, or transmission-owner acceptance criteria. If the reference PSS®E file is confirmed to have identical inputs and can be solved in the same release, tighten the numerical threshold substantially. Near-identical machine-readable cases should agree to normal numerical precision.

A difference smaller than a screening threshold is not automatically irrelevant. Conversely, a difference larger than a threshold is not automatically a modeling error. It is a prompt to identify the cause.

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Use a published numerical table carefully

The following article contains an alternative published IEEE 9-bus numerical solution. It is useful as an example of why validation must begin with case identity rather than an assumption that every item called “IEEE 9-bus” represents the same benchmark.

Do not merge parameters from this article with the Alroomi PSS®E package. For example, the IIETA Newton-Raphson table displays a Bus 1 voltage of 1.030 p.u., whereas the published single-line reference shown earlier displays 1.040 p.u. Its Table 9 also reports a 4 MW Newton-Raphson maximum mismatch. Those facts may arise from a different model configuration, a solution/reporting convention, or other implementation details; they do not, by themselves, prove that either source is wrong.

The professional conclusion is narrower and more useful:

A numerical result can serve as a validation target only after its input data, operating condition, control assumptions, and convergence quality have been established.

For a production interconnection study, the utility-provided reference solved case and associated study assumptions would take precedence over a generic published test case.

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Diagnose discrepancies systematically

Investigate in an order that moves from high-impact structural causes toward smaller numerical details.

Observed discrepancy	First checks
Many voltages, angles, and flows differ	System base MVA, topology, bus types, load and generation dispatch
One generator Mvar differs strongly	Voltage schedule, remote regulation, reactive limits, PV-to-PQ conversion
Voltage differences concentrated near one generator transformer	Transformer impedance base, winding data, tap ratio, phase shift, control mode
Real-power flows differ but voltages are similar	Generator MW dispatch, load MW, branch resistance/reactance, slack treatment
Reactive flows and losses differ more than MW flows	Line charging, transformer magnetizing data, shunts, voltage schedules
Only one branch flow has opposite sign	From-bus/to-bus orientation, not necessarily an electrical mismatch
Reference and internal total generation differ	Total load, losses, fixed shunts, or an unintended in-service device
Reference case does not solve after version conversion	File conversion, incomplete extraction, incompatible settings, or unintended edits

When you identify a cause, do not overwrite history. Make a controlled correction in a new revision, for example:

IEEE9_SOLVED_BASE_R02_TAPCORRECTED.sav

Then rerun the complete validation comparison. Never revise only the one output cell that looked wrong; corrections to voltage control or transformer data can affect the entire AC solution.

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Write a concise validation note

Your final deliverable for this lesson is a short validation record. It should allow another engineer to reproduce both the comparison and the conclusion without reconstructing your decisions from memory.

Title: IEEE 9-Bus PSS/E Base-Case Validation Record

Purpose
Validate internal IEEE9_SOLVED_BASE_R[revision].sav against the
published Alroomi PSS/E reference package.

Reference identity
Source and download date: [record]
Archive and extracted reference file(s): [record]
PSS/E version used for comparison: [record]
Conversion or import notes: [record]

Input-data comparison
Topology/equipment count: [match / describe difference]
System base MVA: [match / describe difference]
Bus types and voltage schedules: [match / describe difference]
Load and generator MW/Mvar schedules: [match / describe difference]
Transformer and line parameters: [match / describe difference]
Control, tap, shunt, and Q-limit assumptions: [match / describe difference]

Solution comparison
Both cases converged: [yes/no]
Largest bus-voltage difference: [value] p.u. at Bus [number]
Largest normalized angle difference: [value] degrees at Bus [number]
Largest MW-flow difference: [value] MW on [element]
Largest Mvar-flow difference: [value] Mvar on [element]
Total MW-loss difference: [value] MW
PV buses at reactive limits: [record]

Material differences and disposition
1. [difference, cause, case revision or rationale]
2. [difference, cause, case revision or rationale]

Conclusion
[Validated for IEEE 9-bus power-flow and manual N-1 teaching use /
not validated; additional correction required.]

If the base-case validation exposes a material difference from the external reference, repeat the Bus 4–Bus 5 N-1 contingency from the previous lesson using the corrected and newly validated base revision. The contingency result belongs to the validated model version, not to an earlier approximate draft.

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Key takeaways

A valid PSS®E study case is more than a converged solution. It is a traceable model whose topology, inputs, controls, and solved behavior have been compared against an appropriate reference.

• Use a machine-readable published PSS®E case as the primary benchmark when available; use diagrams and rounded numerical tables as supporting checks.
• Compare input data before interpreting output differences.
• Solve the intact reference and internal cases using controlled, documented settings.
• Compare voltage magnitude, normalized angle, generator output, branch flow, and losses with consistent sign and orientation conventions.
• Declare screening thresholds before reviewing differences, while recognizing that topology and control-definition discrepancies are material regardless of numerical size.
• Document the source, software version, case revisions, differences, causes, and final suitability conclusion.

This completes the IEEE 9-bus PSS®E foundation. The next module moves from a compact teaching network to utility-scale solar, BESS, collector-system, GSU-transformer, and POI-control representations—the modeling boundary that will later support interconnection, MQT, and PSS®E–PSCAD comparison work.