Attributed Property Graphs to Drive Grid Simulations

Concept Summary

This document defines a modeling strategy for forecasting and stress-testing U.S. electrical grid demand, capacity, congestion, and market outcomes using an attributed nonlinear graph. The core approach is to represent the grid, market structure, weather, fuel, assets, constraints, scenarios, and hedge exposures as a temporal property graph, then use graph analytics to identify relevant subgraphs, simplify model scope, and guide physics- and market-valid numerical solves. This approach enables LLM agentic workflows and MCP Tool Servers with structured queries and supports reproducible experiments with evidence chains.

The graph is not itself the power-flow or market-clearing solver. Instead, it is the system-of-record and dependency layer that organizes data, identifies high-impact regions of the network, supports scenario construction, and persists sensitivities. Numerical models such as DC power flow, AC power flow, OPF, SCED, unit commitment, and reduced-order approximations are then executed over full networks or graph-selected subgraphs. This allows an agentic workflow to ask structured questions such as: “Assuming all other things are equal, what is the sensitivity of Houston real-time prices to a 10% derate on a north-to-Houston import constraint during evening peak?”

The strategy is built around three linked graphs:

Physical graph — buses, lines, substations, transformers, generators, storage, loads, and topology.
Market dependency graph — settlement nodes, hubs, zones, constraints, fuel dependencies, bids, products, and hedge instruments.
Scenario and sensitivity graph — shocks, assumptions, solver runs, derivatives, elasticities, confidence, and validity regions.

Together, these graphs support the key hedge-fund question:

Where will the grid be short, when, by how much, and how will that scarcity propagate into price, congestion, volatility, basis, reserve scarcity, and tradable hedge exposure?

1. Strategic Objective

The objective is not merely to forecast electrical demand. Hedge funds and derivatives market participants need a model that translates physical and operational grid conditions into tradable market consequences.

The modeling stack would estimate:

Load by node, zone, hub, ISO, and time horizon.
Generation availability by fuel class, unit, zone, and operating state.
Renewable output, curtailment risk, and forecast error.
Transmission congestion and likely binding constraints.
Locational marginal price formation.
LMP decomposition into energy, congestion, losses, and scarcity components.
Reserve margin and scarcity pricing risk.
Fuel-linked marginal cost effects.
Basis risk between nodes, zones, and hubs.
FTR/CRR exposure and congestion hedge value.
Day-ahead versus real-time spread risk.
Scenario-conditioned P&L exposure.

The model should support both forecasting and counterfactual sensitivity analysis.

Example hedge-relevant questions:

Where will prices separate under a high-load weather scenario?
Which constraints are likely to bind if a specific generator or line is unavailable?
Which weather cells have the highest marginal impact on load, renewable output, congestion, or price?
How sensitive is a regional power price to a gas basis shock?
Which nodes are exposed to a particular fuel hub or pipeline constraint?
Which subgraphs can be approximated safely, and which require a full solve?
What is the change in hedge P&L under a targeted network shock?

2. Hedge-Fund and Market Analysis Requirements

2.1 Enabling Predictions

The goal is to combine scalar load forecasts with probabilistic views of how physical grid state and market structure interact.

Core prediction targets might include:

Category	Prediction Target	Trading Relevance
Demand	Load by bus, zone, hub, and ISO	Energy price level, scarcity risk, reserve margin
Supply	Available thermal generation	Marginal unit, fuel exposure, price stack
Renewables	Wind and solar production	Volatility, negative prices, curtailment, ramp risk
Storage	State of charge and dispatch behavior	Peak clipping, arbitrage, reserve provision
Transmission	Flow, derates, outage states	Congestion, basis spreads, FTR/CRR value
Market Constraints	Binding probability and shadow price	LMP separation and congestion rent
Fuel	Gas, coal, oil, and basis prices	Heat-rate economics and spark spread
Weather	Temperature, wind, irradiance, humidity	Load and renewable forecast error
Ancillary Services	Reserve scarcity and regulation needs	Price spikes and tail risk
Portfolio	Position-level P&L sensitivity	Hedge sizing, risk limits, scenario exposure

2.2 Time Horizons

Different decisions require different horizons.

Horizon	Use Case	Required Model Behavior
Real-time / intraday	RT price, congestion, virtual trade adjustment	Fast state update, current topology, outage ingestion
Day-ahead	DA bids, virtuals, next-day hedge	Weather/load forecast, unit availability, constraint forecast
Week-ahead	Gas/power positioning, risk limits	Weather ensembles, outage schedule, fuel basis
Seasonal	Capacity, heat/cold risk, storage value	Load distribution, reserve margin, outage risk
Long-term	Capacity market, infrastructure thesis	Demand growth, retirements, interconnection queues

2.3 Core Market Outputs

The model should produce market-native outputs, not just engineering quantities.

Output	Description
`LMP_energy`	System marginal energy component
`LMP_congestion`	Price component caused by binding transmission constraints
`LMP_loss`	Marginal loss component
`Reserve_price`	Ancillary or scarcity component
`Basis`	Price difference between node, zone, hub, or ISO reference
`Spread`	DA/RT, hub/node, gas/power, or inter-regional spread
`Constraint_shadow_price`	Marginal value of relaxing a binding constraint
`Congestion_rent`	Economic value created by constrained transmission
`Binding_probability`	Probability a constraint binds under a scenario distribution
`P&L_sensitivity`	Position-level exposure to modeled shocks

3. Attributed Nonlinear Graph Architecture

The proposed architecture uses a heterogeneous, temporal property graph as the organizing abstraction.

The graph contains:

Physical infrastructure.
Market settlement structure.
Asset behavior.
Weather dependencies.
Fuel dependencies.
Transmission constraints.
Historical and forecast time series.
Scenario definitions.
Solver outputs.
Sensitivity results.
Hedge exposures.

The graph is attributed because every node and edge carries quantitative and categorical state. It is nonlinear because the relationships between load, flows, voltage, dispatch, congestion, and price are not globally linear, even if some screening approximations use linearized models.

3.1 Three-Graph Design

The modeling strategy should explicitly separate three linked graphs.

3.1.1 Physical Graph

The physical graph represents grid topology and operating state.

Primary entities:

Buses.
Lines.
Transformers.
Substations.
Generators.
Renewable assets.
Batteries and storage.
Loads.
Interfaces.
Contingencies.

Primary purpose:

Power-flow modeling.
Constraint screening.
Contingency analysis.
Network reduction.
Physical validation.

3.1.2 Market Dependency Graph

The market dependency graph represents how physical state maps into price formation and tradable instruments.

Primary entities:

Settlement nodes.
Trading hubs.
Load zones.
Constraints.
Fuel hubs.
Bid curves.
Ancillary-service products.
FTR/CRR products.
Hedge portfolios.

Primary purpose:

LMP decomposition.
Basis analysis.
Hedge exposure mapping.
Fuel-to-power dependency tracing.
Market-product sensitivity.

3.1.3 Scenario and Sensitivity Graph

The scenario and sensitivity graph records structured model questions and their outputs.

Primary entities:

Shocks.
Assumptions.
Frozen variables.
Endogenous variables.
Solver runs.
Baseline states.
Counterfactual states.
Sensitivities.
Validity regions.
Confidence metrics.

Primary purpose:

Reproducible “what-if” analysis.
Agentic workflow orchestration.
Sensitivity persistence.
Model-governance and auditability.

4. Core Property Graph Components

4.1 Node Types

Node Type	Description	Representative Attributes
`Bus`	Electrical bus in the transmission network	voltage level, voltage magnitude, angle, zone, ISO, LMP, net injection
`Line`	Transmission line or branch	resistance, reactance, susceptance, thermal limit, flow, outage state
`Transformer`	Transformer between voltage levels	tap ratio, phase shift, rating, availability
`Substation`	Physical aggregation point	location, voltage levels, connected assets
`Generator`	Thermal or dispatchable generator	fuel type, capacity, heat rate, ramp rate, outage probability, bid curve
`RenewableAsset`	Wind or solar asset	nameplate capacity, forecast output, weather dependency, curtailment risk
`StorageAsset`	Battery or pumped storage	state of charge, charge rate, discharge rate, efficiency, strategy
`LoadZone`	Aggregated load area	forecast load, weather sensitivity, customer mix, demand response
`WeatherCell`	Weather station or gridded weather region	temperature, humidity, wind speed, irradiance, forecast error
`FuelHub`	Gas, coal, or other fuel pricing location	price, basis, pipeline constraint, volatility
`MarketNode`	Settlement node or pricing point	LMP, congestion component, loss component, hub mapping
`TradingHub`	Aggregate trading hub	hub price, volume, associated nodes
`Constraint`	Monitored transmission or operating constraint	flow limit, shadow price, binding probability
`Contingency`	N-1 or N-k outage condition	affected assets, probability, derate magnitude
`Scenario`	Composite state assumption	probability, timestamp, shock vector, weather/fuel/topology state
`Shock`	Counterfactual perturbation	variable, target, magnitude, units, timestamp
`Sensitivity`	Modeled response to a shock	derivative, elasticity, confidence, validity region
`ModelRun`	Executed calculation	solver tier, assumptions, baseline, result, convergence status
`PortfolioPosition`	Hedge or trading exposure	instrument, quantity, location, tenor, risk factor

4.2 Edge Types

Edge Type	From → To	Description
`CONNECTED_TO`	Bus → Bus	Electrical connectivity through line or transformer
`INJECTS_AT`	Generator → Bus	Generator injection point
`DRAWS_FROM`	LoadZone → Bus	Load allocation to physical grid
`LOCATED_IN`	Asset → Zone / ISO	Geographic or market containment
`WEATHER_DRIVES`	WeatherCell → LoadZone / RenewableAsset	Weather dependency for load or renewable output
`FUEL_SUPPLIES`	FuelHub → Generator	Fuel-price dependency
`CONSTRAINS`	Constraint → Line / Interface	Constraint monitors or limits asset flow
`SETTLES_AT`	Bus / Asset → MarketNode	Settlement relationship
`AGGREGATES_TO`	MarketNode → TradingHub	Hub composition
`PART_OF`	Bus / Asset → Community	Derived partition membership
`CONTINGENCY_AFFECTS`	Contingency → Line / Generator	Outage or derate impact
`CORRELATED_WITH`	Weather / Fuel / Market nodes → Same	Statistical dependency
`AFFECTS`	Shock → Asset / Variable	Scenario perturbation target
`PRODUCES`	Shock / ModelRun → Sensitivity	Output sensitivity relationship
`MEASURED_ON`	Sensitivity → MarketNode / Constraint / Position	Target of sensitivity calculation
`VALID_FOR`	Sensitivity → Subgraph / Scenario	Validity domain
`USES_MODEL`	Sensitivity → ModelRun	Provenance and solver reference

5. Key Variables to Model

5.1 Physical Network Variables

For each bus i:

Variable	Description
`V_i`	Voltage magnitude
`theta_i`	Voltage angle
`P_load_i`	Real power demand
`Q_load_i`	Reactive power demand
`P_gen_i`	Real power generation
`Q_gen_i`	Reactive power generation
`P_net_i`	Net real-power injection
`LMP_i`	Locational marginal price
`zone_i`	Market or operational zone
`iso_i`	ISO/RTO membership

For each branch or line (i,j):

Variable	Description
`r_ij`	Resistance
`x_ij`	Reactance
`b_ij`	Susceptance
`F_ij`	Real power flow
`S_ij`	Apparent power flow
`Fmax_ij`	Thermal or operational flow limit
`outage_state_ij`	Available, unavailable, or derated
`shadow_price_ij`	Constraint value if binding
`loading_pct_ij`	Flow as percentage of limit
`contingency_set_ij`	Relevant N-1 or N-k events

5.2 Supply-Side Variables

For each generator or dispatchable resource:

Variable	Description
`Pmin`	Minimum stable output
`Pmax`	Maximum available output
`ramp_up`	Maximum upward ramp rate
`ramp_down`	Maximum downward ramp rate
`heat_rate`	Fuel efficiency
`fuel_price`	Fuel cost from linked fuel hub
`variable_om`	Variable operating and maintenance cost
`startup_cost`	Cost to start unit
`no_load_cost`	Cost to keep unit online
`forced_outage_rate`	Probability or rate of forced outage
`planned_outage_state`	Scheduled maintenance state
`bid_curve`	Market offer curve
`emissions_cost`	Carbon or pollutant cost where applicable
`must_run_flag`	Reliability, nuclear, CHP, or regulatory must-run state

For renewable assets:

Variable	Description
`forecast_output`	Expected generation
`forecast_error_std`	Forecast uncertainty
`wind_speed`	Wind driver
`solar_irradiance`	Solar driver
`cloud_cover`	Solar attenuation driver
`curtailment_probability`	Risk of economic or reliability curtailment
`weather_cell_id`	Linked forecast region

5.3 Demand-Side Variables

For each load zone, market node, or bus-level load:

Variable	Description
`base_load`	Weather-normalized demand
`forecast_load`	Expected demand at horizon
`temperature_sensitivity`	Load response to temperature
`humidity_sensitivity`	Cooling-load response
`calendar_effect`	Hour, weekday, weekend, holiday, season
`industrial_load_factor`	Industrial demand exposure
`commercial_load_factor`	Commercial demand exposure
`residential_load_factor`	Residential demand exposure
`EV_load`	Electric-vehicle charging load
`DER_response`	Distributed energy resource response
`demand_response_probability`	Curtailment or flexible-load response
`forecast_error_std`	Demand forecast uncertainty

5.4 Fuel and Commodity Variables

Variable	Description
`gas_price`	Natural gas price at relevant hub
`gas_basis`	Difference between local and reference gas price
`pipeline_constraint_state`	Gas deliverability constraint
`coal_price`	Coal price where relevant
`oil_price`	Oil price where relevant for peakers or macro linkage
`emissions_price`	Carbon or environmental compliance price
`spark_spread`	Power price minus gas-implied generation cost
`dark_spread`	Power price minus coal-implied generation cost

5.5 Market Variables

Variable	Description
`LMP`	Locational marginal price
`LMP_energy`	Energy component of LMP
`LMP_congestion`	Congestion component of LMP
`LMP_loss`	Loss component of LMP
`reserve_price`	Ancillary or scarcity price
`constraint_shadow_price`	Marginal value of relaxing a constraint
`binding_constraint_id`	Constraint responsible for congestion
`binding_probability`	Probability of constraint binding
`hub_price`	Aggregated trading hub price
`node_to_hub_basis`	Node price minus hub price
`zone_to_hub_basis`	Zone price minus hub price
`DA_RT_spread`	Day-ahead minus real-time price spread
`FTR_value`	Financial transmission right value
`CRR_value`	Congestion revenue right value
`portfolio_PnL`	Portfolio-level profit and loss

5.6 Scenario Variables

Scenario Dimension	Examples
Weather	Heat dome, cold snap, wind drought, cloud cover, storm front
Fuel	Gas price spike, basis blowout, pipeline constraint, LNG pull
Supply	Generator outage, derate, ramp scarcity, planned maintenance
Transmission	Line outage, interface derate, transformer failure, congestion limit
Load	Industrial surge, demand response failure, EV charging spike
Market	Bid-curve shift, scarcity adder, reserve shortage, rule change
Portfolio	Position change, hedge ratio adjustment, basis exposure

6. Dynamic Values Computed Over Subgraphs

The property graph would enable dynamic computation over subgraphs. These values are not merely descriptive, but support screening features and control variables that determine which full or reduced model an agent might run for quick hypothesis testing as part of its research task.

6.1 Electrical and Market Subgraphs

Useful subgraph definitions include:

ISO/RTO region.
Load zone.
Trading hub neighborhood.
Generator-to-market-node influence neighborhood.
Constraint-centered neighborhood.
Weather-driven load pocket.
Fuel-hub-exposed generator set.
Congestion community.
Islanded or weakly connected region.
Portfolio-exposed subgraph.

6.2 Dynamic Subgraph Metrics

Metric	Interpretation
`net_load`	Load minus renewable generation within subgraph
`dispatchable_capacity`	Available controllable generation
`renewable_share`	Renewable output as percentage of load
`reserve_margin`	Available capacity above expected demand
`import_dependency`	Share of demand requiring imports from adjacent regions
`export_capacity`	Ability to export surplus generation
`constraint_pressure`	Flow proximity to monitored limits
`binding_probability`	Probability one or more constraints bind
`marginal_fuel_exposure`	Sensitivity of price to fuel hub movement
`weather_elasticity`	Load or renewable response to weather variables
`basis_volatility`	Expected node-to-hub or zone-to-hub volatility
`hedge_exposure`	Portfolio exposure to subgraph outcomes

6.3 Example Subgraph Stress Score

A market-relevant stress score may combine physical, weather, supply, and market attributes:

SubgraphStress = f(
  net_load,
  reserve_margin,
  import_dependency,
  renewable_forecast_error,
  outage_probability,
  constraint_pressure,
  historical_binding_frequency,
  fuel_price_volatility,
  basis_volatility
)

The stress score would prioritize which subgraphs and scenarios deserve more expensive analysis.

7. Graph Analytics and cuGraph Role

7.1 Role of Graph Analytics

Graph analytics are used to reduce model complexity, identify high-impact components, and construct valid candidate subgraphs for deeper analysis.

They are most useful for:

Partitioning the grid into coherent communities.
Identifying weakly coupled regions.
Detecting islanding or disconnection.
Ranking critical buses, lines, generators, and constraints.
Extracting k-hop neighborhoods around shocks.
Screening candidate binding constraints.
Identifying boundary edges for reduced-order models.
Supporting agentic retrieval of relevant model context.

7.2 Role of cuGraph

cuGraph and related GPU graph analytics are appropriate for large-scale screening, partitioning, and ranking over graph representations of the grid and market dependencies.

Use cuGraph-style analytics for:

Analytic	Purpose
Connected components	Identify islanding, disconnected regions, or separable topology
Weakly connected components	Identify directed dependency regions with weak coupling
Strongly connected components	Identify mutually reachable directed regions
Louvain / Leiden communities	Find coherent electrical or market communities
Spectral clustering	Reveal near-block-diagonal structure and weak interfaces
Betweenness centrality	Rank buses, lines, or interfaces mediating flows
PageRank / Katz centrality	Rank dependency influence in market or fuel graphs
Shortest path / k-hop traversal	Extract local neighborhoods around shocks
Minimum cut / bridge analysis	Identify vulnerable interfaces or separable regions
Triangle / motif analysis	Characterize redundancy versus radiality
Ego networks	Define localized sensitivity neighborhoods

7.3 What cuGraph Should Not Do

cuGraph would not replace the underlying solvers:

AC power flow.
DC power flow.
AC optimal power flow.
DC optimal power flow.
Security-constrained economic dispatch.
Security-constrained unit commitment.
Sparse Newton solvers.
Interior-point OPF solvers.
Stochastic optimization.

Instead, graph analytics layer answers:

Where should the expensive model run, what should it include, and what candidate constraints or sensitivities matter?

Then the numerical solver answers:

Given the model equations and constraints, what is the physically and economically valid state?

7.4 Complexity-Reduction Pattern

The intended pattern is:

Full temporal property graph
  -> graph analytics
  -> candidate communities and interfaces
  -> reduced subgraphs
  -> fast linear screening
  -> nonlinear or OPF validation
  -> persisted sensitivities

7.5 Weakly Coupled and Block-Diagonal Structure

Graph analytics can help identify regions where the grid or dependency graph approximates a block-diagonal structure.

This is useful because:

Weakly coupled regions can sometimes be solved locally with boundary conditions.
Spectral clustering can identify low-conductance cuts.
Communities can define candidate reduced-order models.
Interface edges can be modeled as boundary constraints.
Full-model validation can determine where approximation error is acceptable.

However, block structure in a graph or matrix is a model-reduction cue, not proof that independent subgraph solves are valid. Boundary conditions, loop flows, contingencies, and market coupling can invalidate a naive decomposition.

8. Full Models and Approximation Tiers

The system should use a tiered modeling stack.

8.1 Tier 0 — Property Graph State

Purpose:

Store topology, assets, time series, scenarios, assumptions, and results.
Resolve graph neighborhoods and dependencies.
Maintain provenance.

Outputs:

Candidate subgraphs.
Feature sets.
Scenario specifications.
Solver input packages.

8.2 Tier 1 — Fast Graph-Screened Approximation

Purpose:

Rank scenarios quickly.
Identify likely binding constraints.
Compute first-order sensitivities.
Filter out low-value model runs.

Representative methods:

DC power flow.
PTDF analysis.
LODF analysis.
Historical congestion models.
Reduced-order linear models.
Constraint-proximity screening.
Weather-to-load regression or machine-learned forecast models.

Outputs:

Candidate constraints.
Approximate flow changes.
Approximate congestion risk.
Approximate price/basis sensitivity.

8.3 Tier 2 — Nonlinear Local Solve

Purpose:

Validate high-value subgraph results with more physical realism.
Study localized stress under boundary assumptions.

Representative methods:

Local AC power flow.
Local AC-OPF.
Reduced network with boundary equivalents.
Equivalent injection models at cut edges.

Outputs:

Local voltage and flow feasibility.
Refined congestion assessment.
Validated subgraph sensitivity.

8.4 Tier 3 — Full-Market Solve

Purpose:

Produce ground-truth or highest-confidence estimates.
Validate approximation error.
Support final trading or hedge decisions.

Representative methods:

Full DC-OPF.
Full AC-OPF.
SCED.
SCUC.
Stochastic or robust optimization.
Scenario ensemble modeling.

Outputs:

Full-grid dispatch.
Full LMP surface.
Binding constraints and shadow prices.
Portfolio-level risk and P&L exposure.

9. Sparse Matrix and Nonlinear Solver View

9.1 Graph-to-Matrix Mapping

The property graph should be capable of materializing matrices used by power-flow, optimization, and graph-reduction models.

Matrix	Description
`A`	Adjacency matrix
`L`	Graph Laplacian
`L_norm`	Normalized Laplacian for spectral clustering
`Y_bus`	Complex admittance matrix
`B_bus`	Bus susceptance matrix
`B_branch`	Branch susceptance mapping
`PTDF`	Power transfer distribution factor matrix
`LODF`	Line outage distribution factor matrix
`J`	AC power-flow Jacobian
`KKT`	Optimal power-flow optimality system

9.2 Nonlinear Does Not Mean “No Linear Steps”

AC power flow and AC-OPF are nonlinear problems. However, practical nonlinear solvers usually perform sparse linear algebra inside each iteration.

The common pattern is:

Nonlinear physical or market problem
  -> iterative nonlinear solver
  -> sparse linearized system per iteration
  -> state update
  -> convergence check

Examples:

Newton-Raphson power flow solves Jacobian systems.
Interior-point OPF solves KKT systems.
Sequential quadratic programming solves linearized or quadratic subproblems.
Krylov methods may solve sparse linear systems inside larger nonlinear iterations.

The graph contributes by defining sparsity, locality, decomposition candidates, and dependency structure while the solver performs the numerical calculation.

10. Subgraph Approximation Strategy

10.1 Subgraph Construction

A candidate subgraph might be derived from both physical and market relevance.

Inputs:

Electrical topology.
Historical binding constraints.
Graph communities.
Settlement-node relationships.
Weather dependencies.
Fuel dependencies.
Portfolio exposures.

A subgraph may be centered on:

A constraint.
A generator.
A trading hub.
A load pocket.
A weather shock.
A fuel hub.
A high-centrality bus or interface.
A portfolio exposure.

10.2 Boundary Modeling

A subgraph approximation requires boundary treatment.

Boundary options include:

Fixed voltage magnitude and angle.
Fixed net injection.
Equivalent source or sink.
Thevenin equivalent.
PTDF-derived boundary response.
Historical import/export response.
Scenario-conditioned boundary curve.

Boundary assumptions must be persisted with the model run.

10.3 Validation Against Full Model

Should every reduced model should be compared against a full solve or higher-fidelity benchmark?

I imagine we might run periodic test cases and create lumped parameters to identify regimes when agents can be allowed make approximations with bounded errors (so they can perform rapid hypothesis testing).

Validation metrics:

Metric	Description
`flow_error`	Difference in branch flow prediction
`LMP_error`	Difference in nodal price prediction
`basis_error`	Difference in spread prediction
`binding_set_error`	Difference in predicted binding constraints
`shadow_price_error`	Difference in constraint marginal value
`PnL_error`	Difference in portfolio impact
`validity_region`	Scenario range where approximation remains acceptable

Approximation results could then be promoted only when they have stable error bounds for the target use case.

11. Sensitivity Modeling

Sensitivity modeling should be a first-class component of the system, not an ad hoc report.

11.1 Sensitivity Object

A sensitivity captures the response of a target variable to a structured perturbation.

Representative fields:

Field	Description
`shock_id`	Shock or perturbation being evaluated
`target_id`	Target node, constraint, market product, or portfolio position
`target_variable`	Variable being measured
`baseline_value`	Value before perturbation
`counterfactual_value`	Value after perturbation
`delta`	Absolute change
`derivative`	Local derivative or marginal response
`elasticity`	Percentage response to percentage shock
`model_tier`	Approximation or solver level used
`valid_region`	Conditions under which result is valid
`confidence`	Confidence score or uncertainty estimate
`timestamp`	Run time or scenario time

11.2 Common Sensitivities

Sensitivity	Meaning
`dLoad_i / dTemp_j`	Load response to weather
`dWindOutput_i / dWindSpeed_j`	Wind generation response
`dSolarOutput_i / dIrradiance_j`	Solar generation response
`dFlow_l / dInjection_i`	Flow response to bus injection
`dFlow_l / dOutage_k`	Flow response to outage
`dLMP_i / dLoad_j`	Price response to load
`dLMP_i / dFuelHub_k`	Price response to fuel price
`dBasis_ij / dConstraint_k`	Spread response to constraint
`dReservePrice / dAvailableCapacity`	Scarcity response to capacity
`dPnL / dScenario_s`	Portfolio response to scenario

11.3 “All Else Equal” Semantics

“All else being equal” must be encoded as an explicit assumption set.

A valid sensitivity query must specify:

Shock variable.
Shock magnitude.
Shock target.
Frozen variables.
Endogenous variables.
Model tier.
Time horizon.
Market context.
Validity assumptions.

Example:

shock:
  variable: fuel_price
  target: Waha
  magnitude: +20%

frozen:
  - topology
  - load_forecast
  - renewable_forecast
  - generator_outage_state
  - bids_except_fuel_adjusted_units

endogenous:
  - affected_generator_marginal_cost
  - dispatch
  - branch_flows
  - congestion
  - LMP
  - basis
  - portfolio_PnL

The model should reject or flag underspecified sensitivity requests.

12. Agentic Workflow for Market Sensitivity Questions

12.1 Agent Role

The agent should not directly reason over the grid in unconstrained free text. Its job is to compile natural-language questions into structured model specifications and queries on the property graph. This would be a tool call that executes or requests the correct modeling tier, runs a simulation, and returns a “governed” evidence-based explanation.

12.2 Agent Input

Example natural-language question:

Assuming all other things are equal, what is the sensitivity of Houston-area real-time prices to a 10% derate on a north-to-Houston import constraint during a high-load evening?

12.3 Compiled Model Specification

question_type: sensitivity
market: ERCOT
target:
  variable: real_time_lmp
  region: Houston
shock:
  type: transmission_derate
  magnitude: -10%
  asset_class: import_constraint
context:
  load_condition: high
  hour_type: evening_peak
assumptions:
  freeze:
    - fuel_prices
    - renewable_forecast
    - unit_availability
  endogenous:
    - dispatch
    - branch_flows
    - congestion_component
    - LMP
model_tiers:
  - graph_screening
  - DC_OPF
  - local_AC_power_flow_if_needed
outputs:
  - dLMP_dConstraintLimit
  - affected_nodes
  - binding_probability_change
  - basis_change
  - hedge_PnL_sensitivity

12.4 Execution Flow

1. Resolve market, region, and asset references from the property graph.
2. Extract relevant physical and market subgraphs.
3. Identify historical binding constraints and high-centrality interfaces.
4. Run graph analytics for community, centrality, cut, and neighborhood context.
5. Run fast PTDF/LODF or reduced-order screening.
6. Promote high-impact cases to DC-OPF, AC power flow, or OPF as required.
7. Compare counterfactual state to baseline state.
8. Persist sensitivity objects back into the graph.
9. Return result with assumptions, validity limits, confidence, and hedge impact.

12.5 Agent Output

The answer should include:

The interpreted question.
Shock and assumptions.
Relevant subgraph.
Solver tier used.
Main sensitivity result.
Affected constraints and market nodes.
Confidence and validity region.
Hedge exposure implication.
Recommendation for whether a higher-fidelity model is required.

13. Component-by-Component System Architecture

13.1 Data Ingestion Component

Purpose:

Ingest topology, asset, weather, fuel, market, outage, and portfolio data.

Data classes:

ISO/RTO topology.
Bus and branch models.
Generator metadata.
Load forecasts.
Weather observations and forecasts.
Renewable forecasts.
Fuel prices and basis.
Outages and derates.
Market prices and LMP components.
Constraint and shadow-price history.
Portfolio positions.

Key requirement:

Every ingested data point should be time-stamped, source-tagged, and versioned.

13.2 Temporal Property Graph Component

Purpose:

Maintain a unified graph of physical, market, and scenario state.

Responsibilities:

Entity resolution across grid, market, weather, and portfolio data.
Time-versioned state storage.
Dependency traversal.
Subgraph extraction.
Provenance tracking.
Scenario and sensitivity persistence.

13.3 Graph Analytics Component

Purpose:

Reduce complexity and identify where detailed modeling is warranted.

Responsibilities:

Community detection.
Centrality ranking.
Connected-component detection.
Cut and bridge analysis.
k-hop neighborhood extraction.
Constraint relevance screening.
Weak-coupling and block-structure analysis.

13.4 Forecasting Component

Purpose:

Generate baseline forecasts for load, renewables, fuel, outage risk, and market variables.

Responsibilities:

Load forecast by zone and bus allocation.
Weather-to-load modeling.
Wind and solar production modeling.
Fuel-price and basis scenario modeling.
Outage probability modeling.
Reserve-margin forecast.
Forecast uncertainty quantification.

13.5 Physical Solver Component

Purpose:

Compute physically valid flows and feasibility.

Responsibilities:

DC power flow.
AC power flow.
Contingency analysis.
Boundary-conditioned subgraph solves.
Full-network validation.

13.6 Market Solver Component

Purpose:

Translate physical state into dispatch, constraints, prices, and hedge-relevant market outputs.

Responsibilities:

Economic dispatch.
OPF.
SCED where available.
Unit commitment where necessary.
LMP decomposition.
Constraint shadow pricing.
DA/RT spread modeling.
Reserve scarcity modeling.

13.7 Scenario Engine

Purpose:

Define, execute, and compare baseline and counterfactual states.

Responsibilities:

Shock definition.
Assumption-set management.
Frozen/endogenous variable selection.
Scenario probability assignment.
Ensemble execution.
Baseline/counterfactual comparison.

13.8 Sensitivity Engine

Purpose:

Calculate local and scenario-conditioned sensitivities.

Responsibilities:

Derivative and elasticity estimation.
Finite-difference scenario comparisons.
PTDF/LODF-style first-order sensitivities.
Solver-based nonlinear sensitivities.
Confidence and validity-region assignment.
Portfolio P&L sensitivity calculation.

13.9 Agentic Query Component

Purpose:

Convert user questions into structured model actions.

Responsibilities:

Intent classification.
Entity resolution.
Assumption extraction.
Model-tier selection.
Execution orchestration.
Result explanation.
Escalation to higher-fidelity models when needed.

13.10 Governance and Audit Component

Purpose:

Make results reproducible, inspectable, and defensible.

Responsibilities:

Version all input data.
Persist assumptions.
Track solver tier and convergence.
Store baseline and counterfactual references.
Record confidence and validity domains.
Maintain lineage from question to result.

14. Example End-to-End Workflow

14.1 Natural-Language Request

What is the price sensitivity in ERCOT Houston if north-to-Houston transfer capability is reduced by 10% during evening peak, assuming fuel prices and unit outages are unchanged?

14.2 Structured Interpretation

question_type: sensitivity
market: ERCOT
region: Houston
time_context: evening_peak
shock:
  type: transmission_limit_derate
  target: north_to_houston_import_constraints
  magnitude: -10%
frozen:
  - fuel_prices
  - unit_outage_states
  - renewable_forecast
endogenous:
  - dispatch
  - flows
  - congestion
  - LMP
  - basis
outputs:
  - dLMP_dTransferLimit
  - dBasis_dTransferLimit
  - binding_probability_change
  - affected_market_nodes
  - portfolio_PnL_sensitivity

14.3 Graph Retrieval

The graph retrieves:

Houston-area market nodes.
Relevant import constraints.
Buses and lines associated with those constraints.
Historical binding frequency.
Weather/load conditions matching evening peak.
Generators serving the region.
Portfolio positions exposed to Houston basis.

14.4 Analytics and Screening

The graph analytics component computes:

Constraint-centered subgraph.
High-betweenness lines and buses.
Community membership.
Boundary interfaces.
Candidate binding constraints.
Historical shadow-price analogs.

14.5 Solver Execution

The solver stack runs:

Baseline dispatch and flow estimate.
Derated constraint counterfactual.
LMP and basis comparison.
Portfolio P&L impact.
Optional higher-fidelity validation if screening indicates material exposure.

14.6 Persisted Output

The system writes back:

Shock node.
ModelRun node.
Sensitivity nodes.
Updated constraint binding probabilities.
Portfolio P&L sensitivity.
Validity and confidence metadata.

15. Model Outputs for Hedge Decisions

The final system should produce outputs directly tied to hedge execution and risk management.

Output	Hedge Decision Supported
Node/hub LMP forecast	Long/short power exposure
Basis sensitivity	Node-to-hub or zone-to-hub hedge sizing
Constraint binding probability	FTR/CRR and congestion exposure
Fuel-price sensitivity	Gas-power spread and spark-spread trades
Weather sensitivity	Heat/cold and renewable volatility positioning
Reserve scarcity probability	Tail-risk and option-like exposure
DA/RT spread forecast	Virtual bidding and intraday adjustments
Portfolio P&L scenario	Risk limits and position sizing
Approximation confidence	Whether to trust reduced model or escalate

16. Design Principles

16.1 Separate State, Analytics, and Solvers

The graph stores state and dependencies. Graph analytics reduce complexity. Solvers calculate physically and economically valid outcomes.

16.2 Treat Sensitivities as Data Products

Sensitivities should be persisted, versioned, queried, compared, and audited like any other market data product.

16.3 Use Graph Analytics to Decide Where to Spend Compute

Do not run expensive full-network nonlinear models for every question. Use graph screening to prioritize the cases that matter.

16.4 Make Assumptions Explicit

Every “all else equal” question must specify frozen variables and endogenous variables.

16.5 Validate Reduced Models Against Full Models

Subgraph approximations are useful only when their error bounds are understood.

16.6 Maintain Temporal Versioning

Grid state, market prices, forecasts, topology, and sensitivities are time-dependent. The graph should support temporal snapshots and historical replay.

16.7 Design for Agentic Use, Not Agentic Guessing

The agent should compile questions into structured model specifications. It should not invent assumptions silently.

17. Conceptual Data Model

17.1 Physical Graph

(:Bus)-[:CONNECTED_TO]->(:Bus)
(:Line)-[:CONNECTS]->(:Bus)
(:Generator)-[:INJECTS_AT]->(:Bus)
(:LoadZone)-[:DRAWS_FROM]->(:Bus)
(:Transformer)-[:CONNECTS]->(:Bus)
(:Constraint)-[:CONSTRAINS]->(:Line)
(:Contingency)-[:CONTINGENCY_AFFECTS]->(:Line)

17.2 Market Dependency Graph

(:Bus)-[:SETTLES_AT]->(:MarketNode)
(:MarketNode)-[:AGGREGATES_TO]->(:TradingHub)
(:FuelHub)-[:FUEL_SUPPLIES]->(:Generator)
(:Constraint)-[:AFFECTS_PRICE_AT]->(:MarketNode)
(:PortfolioPosition)-[:EXPOSED_TO]->(:MarketNode)
(:PortfolioPosition)-[:EXPOSED_TO]->(:Constraint)
(:PortfolioPosition)-[:EXPOSED_TO]->(:FuelHub)

17.3 Scenario and Sensitivity Graph

(:Shock)-[:AFFECTS]->(:FuelHub)
(:Shock)-[:AFFECTS]->(:Line)
(:Shock)-[:AFFECTS]->(:Generator)
(:Shock)-[:AFFECTS]->(:WeatherCell)
(:Scenario)-[:INCLUDES]->(:Shock)
(:ModelRun)-[:USES_SCENARIO]->(:Scenario)
(:ModelRun)-[:USES_SUBGRAPH]->(:Subgraph)
(:ModelRun)-[:PRODUCES]->(:Sensitivity)
(:Sensitivity)-[:MEASURED_ON]->(:MarketNode)
(:Sensitivity)-[:VALID_FOR]->(:Subgraph)
(:Sensitivity)-[:IMPACTS]->(:PortfolioPosition)

18. Implementation-Agnostic Pipeline

The document intentionally avoids binding the architecture to a single programming language or database implementation. The system may use Rust, Python, C++, SQL engines, graph databases, GPU analytics, or distributed compute depending on production constraints.

The important architectural pattern is:

Raw data
  -> temporal property graph
  -> graph analytics and subgraph selection
  -> forecast and scenario construction
  -> fast screening models
  -> nonlinear or market-valid solver execution
  -> sensitivity and hedge-output persistence
  -> agentic query interface

19. Recommended Development Sequence

Phase 1 — Graph Schema and Data Foundation

Define canonical entities and edge types.
Load topology, market-node, generator, load-zone, weather, and fuel metadata.
Establish temporal versioning.
Implement entity resolution.

Phase 2 — Baseline Forecast and Market State

Add load, renewable, fuel, outage, and price forecasts.
Map weather cells to load zones and renewable assets.
Map generators to fuel hubs and market nodes.
Map buses and nodes to hubs and zones.

Phase 3 — Graph Analytics Layer

Compute connected components.
Compute centrality metrics.
Detect communities.
Identify weakly coupled subgraphs.
Extract constraint-centered and portfolio-centered neighborhoods.

Phase 4 — Screening Models

Implement fast flow and congestion approximations.
Compute PTDF/LODF-style sensitivity features.
Rank likely binding constraints.
Generate candidate market impacts.

Phase 5 — Higher-Fidelity Solvers

Add local and full-network power-flow validation.
Add OPF or market-clearing approximations.
Validate reduced models against full solves.

Phase 6 — Sensitivity and Agentic Workflow

Define sensitivity objects.
Implement structured scenario compilation.
Persist assumptions and validity regions.
Return hedge-relevant outputs through agent queries.

20. Core Takeaway

The graph should be used as the market-physics operating model: a temporal, attributed, queryable representation of how weather, fuel, demand, generation, transmission, constraints, prices, and hedge exposures interact.

Graph analytics, including cuGraph-style GPU analytics, should be used to identify critical subgraphs, simplify the model, and focus expensive numerical solvers on the portions of the network that matter. The actual market and grid state must still be validated with appropriate physical and economic models.

The final product is a hedge-focused decision engine that translates network state and counterfactual shocks into:

LMP changes.
Basis changes.
Congestion risk.
Reserve scarcity.
Fuel-linked price exposure.
Portfolio P&L sensitivity.
Confidence and validity bounds.

Each is enabled using an agentic workflow (e.g., LangGraph/LangChain) and an MCP tool server that calls the graph and simulation engine for iterative planning and execution.