Technical Methods: Transmission Network Analysis of India

1. Network Topology Construction

The transmission network graph \(G = (V, E)\) is constructed from OpenStreetMap (OSM) geospatial data, where vertices \(V\) represent electrical buses (substations, junction points) and edges \(E\) represent transmission lines and HVDC links. We restrict to the high-voltage (HV) and extra-high-voltage (EHV) system: \(V_\text{nom} \geq 132\) kV.

1.1 Bus Identification

Substation buses. OSM polygons and nodes tagged power=substation with voltage \(\geq\) 132,000 V. Polygon geometries are reduced to their centroid. These form the primary bus set \(V_\text{sub}\).

Junction buses. Line endpoints shared by two or more transmission lines and located >2 km from any substation bus.

Synthetic buses. Line endpoints that fall beyond the snap tolerance \(\delta\) from any existing bus, necessary to maintain network connectivity where OSM data has coordinate misalignment.

1.2 Endpoint Snapping & Bus Merging

Each line endpoint is assigned to its nearest bus using a \(k\)-d tree (scipy.spatial.cKDTree) with snap tolerance \(\delta = 1.0\) km. Buses within merging radius \(\rho = 0.5\) km are consolidated using a union-find data structure. Self-loops are removed.

1.3 Connected Component Pruning

The graph is decomposed into connected components using NetworkX. Components with \(|V_c| < 3\) buses are classified as stubs and removed. Generators attached to pruned buses are remapped to the nearest bus in the retained network. The largest connected component (7,452 buses) forms the main synchronous sub-network.

1.4 Line Length Computation

Physical line length is computed as the great-circle (haversine) distance, with a minimum floor of 1.0 km to prevent near-zero impedance:

where \(R = 6{,}371\) km is Earth's mean radius, and \((\phi, \lambda)\) are latitude and longitude in radians.

2. Electrical Parameter Assignment

2.1 Conductor Type Mapping

Each AC line is assigned a standard conductor type from the PyPSA/IEC line type database based on its voltage class, reflecting typical Indian transmission practice (CEA/PGCIL design standards):

2.2 Multi-Circuit Correction

When the OSM cables tag is available, the number of circuits is \(n_c = \max(1, \lfloor\text{cables}/3\rfloor)\). Line parameters are adjusted:

2.3 Thermal Rating Floor

OSM frequently lacks cable-count metadata, so we apply voltage-class-specific \(S_\text{nom}\) floors based on CEA/PGCIL typical values:

where \(S_\text{floor} = \{765\text{ kV}: 2400,\; 400\text{ kV}: 1040,\; 220\text{ kV}: 520,\; 132\text{ kV}: 310\}\) MW.

3. Generation and Demand Modeling

3.1 Generator Data

Plant-level generation capacity is sourced from Global Energy Monitor (GEM) power plant trackers, providing 5,710 individual facilities across 8 fuel types. Each generator is assigned to the nearest network bus via \(k\)-d tree spatial lookup. Total installed capacity: 471.5 GW.

3.2 State-Level Demand Allocation

Peak demand is specified at the state level from CEA Annual Report FY2024-25 (all-India peak: 249,856 MW). Each state's demand \(D_s\) is distributed across buses using voltage-weighted allocation:

Higher-voltage buses (400/765 kV) receive proportionally larger loads, reflecting the grid hierarchy. Total allocated demand: 247.0 GW.

4. Power Flow Computation

4.1 DC Power Flow Approximation

We use the DC (linearized) power flow model, standard for transmission planning. The full AC power flow equations for line \(ij\) are:

The DC approximation applies: (i) \(|V_i| \approx 1\) p.u., (ii) \(\sin\theta_{ij} \approx \theta_{ij}\), \(\cos\theta_{ij} \approx 1\), and (iii) \(G_{ij} \ll B_{ij}\). This yields:

Line power flow is determined by the voltage angle difference scaled by susceptance:

Power distributes through all parallel paths in inverse proportion to their reactance (Kirchhoff's Voltage Law). This is physically correct for a synchronous AC grid.

4.2 Merit-Order Economic Dispatch (SCED)

Generation dispatch is determined by a merit-order stack, dispatching generators in ascending order of marginal cost until total generation equals total demand.

Phase 1 (must-run): RE at peak-hour CFs, hydro at 70%, nuclear at 90%. Total: 111.6 GW.

Phase 2 (thermal): Remaining 135.4 GW filled in merit order: bioenergy (&rupee;2.0/kWh) → coal (&rupee;2.5) → gas (&rupee;4.5) → oil (&rupee;8.0).

4.3 Inter-Regional Power Transfer

The merit-order dispatch creates spatial mismatches between generation and load. Net transfer for state \(s\):

Key exporters: Rajasthan +14.2 GW, Chhattisgarh +9.7 GW, Odisha +6.8 GW. Key importers: Delhi −7.9 GW, Punjab −7.5 GW, Haryana −7.3 GW. These transfers drive flows through inter-regional 765/400 kV corridors.

4.4 Slack Bus Selection

The slack bus (\(\theta = 0\)) is placed at the thermal generator with the highest capacity × bus-degree score:

4.5 Line Loading

The loading ratio for each line:

Lines with \(\ell > 1.0\) are overloaded and would trip on overcurrent protection, require emergency rating (STE), or necessitate generation re-dispatch.

5. N-1 Contingency Analysis

5.1 Branch Outage Distribution Factors

N-1 security is assessed using the BODF matrix, derived from the PTDF matrix \(\mathbf{H} \in \mathbb{R}^{|E| \times |V|}\):

The BODF element \(D_{\ell k}\) gives the fraction of flow on outaged line \(k\) that redistributes to line \(\ell\):

5.2 Post-Contingency Flow

When line \(k\) trips, the post-contingency flow on line \(\ell\) is:

This avoids re-solving \(\mathbf{B}\boldsymbol{\theta}\) for each contingency, reducing cost from \(O(N_c \cdot |V|^3)\) to \(O(|E|^2 + N_c \cdot |E|)\).

5.3 Violation Screening

We screen the top 50 most-loaded lines. A violation is recorded when:

Infinite post-contingency flows (\(|D_{\ell k}| \to \infty\), indicating islanding) are excluded.

6. Transmission Expansion Planning

6.1 Spatial Clustering

The full network (7,746 buses) is reduced to \(k = 200\) clusters using weighted K-means. Sample weights are proportional to load + generation at each bus:

6.2 Line Aggregation

Lines connecting the same cluster pair are aggregated. Thermal ratings sum; impedances average:

6.3 LOPF Formulation

The expansion problem minimizes total system cost (dispatch + annualized investment):

Solved with HiGHS v1.13.1 via linopy v0.6.5. Corridors where optimal \(s_\text{nom}\) exceeds existing capacity are expansion candidates.

7. Computational Environment

Full pipeline completes in ~70 seconds on a single CPU core. Reproducible via python src/build_network.py && python src/analyze_network.py.

8. Assumptions, Limitations & Caveats

DC approximation. Ignores reactive power, voltage magnitude variations, \(I^2R\) losses, transformer taps, and phase-shifting transformers. Error typically <5% for EHV (\(\geq\)220 kV) lines with \(\theta_{ij} < 10°\).

Single snapshot. Peak-demand operating point only. Time-series with 8,760 hourly snapshots and storage dispatch would improve robustness.

OSM data completeness. Coverage is incomplete for rural 132 kV lines. voltage and cables tags are not always populated. Should be validated against CEA/CTU official maps.

Load allocation. Voltage-weighted distribution within states. Actual allocation depends on distribution substation locations and industrial/urban demand patterns not captured in OSM.

Generator siting. Plants snapped to nearest bus, which may not reflect the actual grid connection point.

Protection and stability. No transient, voltage, or frequency stability analysis. BODF-based N-1 captures steady-state thermal violations only.

Clustered expansion. 200-bus aggregation can mask line-level bottlenecks. Results should be disaggregated before informing investment decisions.

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