DIgSILENT PowerFactory: QV Curves, Continuation Power Flow and Python Automation

The previous five articles built the theoretical foundation: what voltage stability is, the two-bus model, PV curve derivation, the nose point and Jacobian singularity, and QV curves with the L-index. This article moves entirely into practice.

DIgSILENT PowerFactory is the industry-standard tool for voltage stability assessment. It implements three distinct methods natively: QV curve analysis, which gives the reactive power margin in Mvar at each bus; Continuation Power Flow (CPF), which traces the full PV nose curve without numerical divergence; and Modal / Eigenvalue analysis, which identifies which buses, generators, and branches drive instability. All three are covered below, with exact dialog settings and numerical results on the IEEE 39-bus New England test system, plus full Python code to automate the entire workflow.

1. Setting Up Your Network in PowerFactory

1.1 Minimum Requirements Before Running Voltage Stability

Before any voltage stability study makes sense, your base case load flow must converge cleanly. Check these settings in the ComLdf dialog:

1.2 Network Model Checklist

1.3 Study Case Organisation

Create a dedicated Study Case for each scenario. This keeps your base case intact and allows side-by-side comparison.

Project → Study Cases → right-click → New Study Case

Name examples:
  VS_Study_N0             ← base case, all elements in service
  VS_Study_N1_Line_L05    ← single line outage contingency
  VS_Study_N1_Gen_G02     ← generator loss contingency

Each study case stores its own ComLdf, ComVstab,
and ComCpf objects independently.

2. QV Curve Analysis — Step by Step

2.1 Conceptual Recap

A QV curve at bus k shows the reactive power Q that must be injected at bus k to maintain voltage V, while the rest of the network operates normally. The minimum of the curve is the collapse point for that bus.

A positive Qmargin means reactive reserve exists. Zero means the bus is at the collapse boundary. A negative Qmargin — possible in heavily stressed contingency cases — means the operating point is already on the unstable (lower) branch.

2.2 Running QV Curves in PowerFactory

Navigate to Calculation → Voltage Stability Analysis to open the ComVstab dialog.

2.3 Reading and Exporting Results

PowerFactory generates a Virtual Instrument Panel (VIP) with QV plots for each selected bus. The operating point is marked with a dot; the curve minimum is the collapse point. Export numerical results via Results → Output → Voltage Stability Results → File → Export → CSV.

3. Continuation Power Flow (CPF)

3.1 Why Standard Load Flow Fails Near the Nose

Standard Newton-Raphson solves g(x, λ) = 0 where x is the state vector and λ is the loading parameter. Near the nose of the PV curve the Jacobian J = ∂g/∂x becomes singular — N-R diverges before reaching the turning point, so you never observe maximum loadability.

Continuation Power Flow reformulates the problem by parameterising the solution path:

1. Predictor: take a tangent step from the current solution along the solution curve in (x, λ)-space
2. Corrector: solve a modified load flow with one extra equation that pins the step size — either arc-length parameterisation or fixing a specific state variable

The augmented system remains non-singular through the nose and onto the lower (unstable) branch.

3.2 CPF Setup — ComCpf Dialog

Navigate to Calculation → Continuation Load Flow.

3.3 Reading CPF Results

The key output is the critical loading factor λ_crit. The loading margin in MW:

4. Modal Analysis and Participation Factors

4.1 The Reduced Q-V Jacobian

QV curves and CPF tell you how much margin exists. Modal analysis tells you why — which components drive instability — and therefore where to invest in reactive compensation. The method examines the reduced Q-V Jacobian:

All eigenvalues positive → stable. Smallest eigenvalue (λ_min) → 0 at the collapse point. Negative eigenvalue → that mode is already unstable.

4.2 Running Modal Analysis in PowerFactory

In ComVstab, change Method to Modal Analysis. Set the number of eigenvalues to 5–10 smallest. Enable bus, branch, and generator participation factor output.

4.3 Reading and Using Participation Factors

For the critical mode (smallest λ), each bus has a participation factor p_k ∈ [0, 1]. High p_k means bus k strongly participates in the critical mode — it is a weak bus, and reactive compensation there has the largest impact on stability margin.

Practical workflow: rank buses by participation factor. For each of the top 3–5, add 50–100 Mvar of shunt compensation in a sensitivity study and re-run CPF. The bus showing the largest improvement in λ_crit per Mvar is the optimal compensation location.

5. Identifying Weak Buses — Combining All Three Methods

6. Worked Example: IEEE 39-Bus New England System

6.1 Network Description

The IEEE 39-bus (New England) test system is the most widely used benchmark for voltage stability studies — a simplified representation of the northeastern United States power system.

Selected Load Bus Data

6.2 Building the Network in PowerFactory

The most efficient workflow is to import a PSS/E RAW format file, available from the IEEE PES Test Case Archive or the University of Washington Power Systems Test Case Archive.

Step 1 — Create a new project
File → New → Project
  Name:             IEEE_39_Bus_VS_Study
  System frequency: 60 Hz
  Base voltage:     345 kV

Step 2 — Import PSS/E RAW data
File → Import → PSS/E RAW File
  Select: ieee39.raw

Step 3 — Verify converged base case
Calculation → Load Flow (ComLdf)
  Method: Newton-Raphson  |  Reactive limits: ON

Expected base case results (approximate):
  Bus 39 (slack):  V ≈ 1.030 pu,  δ = 0°
  Bus 8:           V ≈ 0.954 pu   ← one of the lowest
  Bus 4:           V ≈ 0.981 pu
  All voltages:    0.90–1.05 pu

6.3 QV Curve Results (N-0)

Running ComVstab (QV Curve method) on all 29 load buses, Q sweep from −400 to +400 Mvar in 5 Mvar steps, all generator Q-limits active.

6.4 CPF Results

Uniform load scaling, proportional generation redispatch, constant-power loads, adaptive arc-length parameterisation, initial step λ = 0.02 pu.

N-1 Contingency Comparison — Most Critical Lines

The Line 5-6 outage is the most critical single contingency — it reduces the loading margin from 2,133 MW to 1,170 MW, a reduction of 963 MW (45%). This line is the primary reactive power path from the generation-rich western area to the weak southeastern buses.

6.5 Modal Analysis Results (Base Case)

Bus Participation Factors — Critical Mode (λ₁ = 4.73)

Bus 8 and Bus 7 together account for 64.5% of the participation in the critical mode. A sensitivity study shows that 100 Mvar of shunt compensation at Bus 8 raises λ_crit from 1.341 to approximately 1.412, increasing the loading margin by roughly 446 MW.

6.6 Weak Bus Consolidation

7.8 Full End-to-End Script

import sys, time
import pandas as pd

PF_PATH = r"C:\Program Files\DIgSILENT\PowerFactory 2023 SP4\Python\3.10"
sys.path.insert(0, PF_PATH)
import powerfactory as pf

def main():
    app = pf.GetApplicationExt()
    if not app: raise RuntimeError("Cannot connect")
    app.Show()
    app.ActivateProject("IEEE_39_Bus_VS_Study")

    # 1. Base load flow
    assert run_load_flow(app) == 0, "Load flow did not converge!"

    # 2. QV analysis
    load_buses = ["Bus 3", "Bus 4", "Bus 7", "Bus 8", "Bus 15",
                  "Bus 16", "Bus 20", "Bus 21", "Bus 24", "Bus 27"]
    qv = run_qv_analysis(app, load_buses)

    # 3. CPF
    base = run_cpf(app)
    traj = extract_cpf_trajectory(app, ["Bus 8", "Bus 7", "Bus 4", "Bus 15"])
    plot_pv_curves(traj, "PV Curves - IEEE 39-Bus (N-0)", "pv_curves_N0.png")

    # 4. N-1 sweep
    t0 = time.time()
    cont_df, _ = run_n1_contingency_sweep(app)
    print(f"Done in {time.time()-t0:.0f} s")

    # 5. Print summary
    print(f"Loading margin: {base['mw_margin']:.0f} MW  (lambda={base['lambda_crit']:.3f})")
    for bus, d in sorted(qv.items(), key=lambda x: x[1]["Q_margin"] or 9999)[:5]:
        print(f"  {bus:10s}  {d['Q_margin']:6.1f} Mvar")

    # 6. Export
    export_to_excel(qv, cont_df, base, "VS_Study_39Bus_Results.xlsx")

if __name__ == "__main__":
    main()

8. Interpreting Results and Margin Calculations

8.1 Reactive Power Margin

From QV curves, equation (1) gives Qmargin in Mvar for each load bus. Typical planning thresholds:

• N-0: Qmargin ≥ 0 Mvar (absolute minimum), ≥ 50 Mvar (planning standard)
• N-1: Qmargin ≥ 0 Mvar after worst credible single contingency

8.2 Voltage Margin

From CPF results, the voltage distance to collapse at each monitored bus:

A common criterion is ΔV ≥ 0.05–0.08 pu at all 220 kV and above buses.

8.3 Loading Margin

From equation (2), for the IEEE 39-bus system:

9. Common Pitfalls and How to Avoid Them

9.1 Generator Q-Limits Left at Default (±9999 Mvar)

If Qmax is left at 9999 Mvar — the PowerFactory default when machine data is not entered — generators supply unlimited reactive power and voltage collapse will never occur in simulation. Always enter realistic Qmin and Qmax from the machine datasheet or capability curve before running any VS study.

9.2 Wrong Load Type in CPF

Constant impedance loads become smaller as voltage drops (P ∝ V²), reducing reactive stress and giving optimistic results. For planning studies, always use constant power loads unless you have measured load characteristics for the specific system.

9.3 OLTC Behaviour During CPF

9.4 CPF Step Size Too Large

A large initial λ step can jump over the nose point entirely, causing PowerFactory to report “no nose found”. Use adaptive step size and set the initial step to ≤ 0.02 pu for stressed or radial networks.

9.5 Not Saving to an ElmRes Object

PowerFactory discards intermediate CPF results (the V vs. λ trajectory) after execution if no results object is assigned. The final λ_crit is stored in ComCpf but the full curves are gone. Always assign an ElmRes object in the Output tab before running.

9.6 Python API Attribute Names Vary by Version

API attribute strings such as "c:Qmargin", "m:u", "c:lambdacrit" can change between major versions. If GetAttribute() returns None, verify the name using the PowerFactory Variable Monitor or the Result Variable browser in the GUI.

9.7 Running CPF Without a Converged Load Flow

CPF is a predictor-corrector continuation of the load flow starting from a converged base point. If ComLdf has not been executed first — or if it failed — ComCpf fails immediately. Always call ldf.Execute() and verify the return code equals 0 before calling cpf.Execute().