Grid equation for SCE project manager
- travisrcstone1984
- Sep 3
- 10 min read
This system helps Southern California Edison better predict and manage electricity demand and supply. It tells us the best times to charge EVs or run appliances, reduces stress on the grid, lowers costs, and improves reliability — all while using real-time data and forecasts to make smarter decisions before problems happen.
The system is designed mathematically is flexible enough to scale beyond EVs and appliances. Here’s why and how:
Core Model Is Function-Based:
The system uses parameter functions P(x)P(x) and transformation functions T(x)T(x) to compute iterative sums.
You can define P(x)P(x) to represent any weighting factor — e.g., regional demand, generation output, renewable variability, or storage capacity.
T(x)T(x) can represent the transformation or influence of that input — e.g., voltage deviation, frequency deviation, or predicted load.
Summation Depth Allows Granularity:
The iterative sum
can scale with more layers (L) to reflect finer-grained phenomena like substation flows, distributed solar output, or industrial load patterns.
Domain Flexibility:
xx is not limited to a single appliance or EV — it can represent any continuous or discrete domain, like time slices across a day, nodes in the grid, or multiple geographical regions.
Predictive Inputs:
You can feed the system with real-world demand and supply forecasts, e.g., historical load curves, weather-dependent generation models, or market prices.
By customizing the function definitions, mathematicians can simulate complex interactions beyond simple appliance behavior.
Scalability at Runtime:
Steps (resolution) and depth (iteration) can be increased to handle large datasets without changing the core algorithm — making it possible to evaluate city-wide or region-wide grid behaviors.
✅ In short: The math is modular and parametrically customizable, to scale from a single household’s appliance/E.V. loads to entire grid-level demand and supply scenarios, enabling real-world predictive modeling and optimization.
User Guide: QCAD Grid Proof of Concept App
1. Purpose of the Tool
The QCAD Grid Proof of Concept app demonstrates how different grid scenarios — convergence, divergence, and bifurcation — affect the balance between electricity supply and demand. It allows project managers to explore the impact of:
Electric vehicle (EV) charging shifts
Battery storage capacity
Renewable supply variability
Real spreadsheet (CSV) demand/supply data
2. System Requirements
Browser: Chrome, Edge, or Firefox (latest versions)
No installation needed: Runs locally by opening the HTML file
Optional: Microsoft Excel (or Google Sheets) for preparing and reviewing CSV files
3. Interface Overview
Left Panel (Simulation Controls)
Grid Pressure P(x): Adjusts how strongly demand reacts in the simulation (higher = more stress).
Timing T(x): Adjusts how supply scales or shifts with renewable timing.
EV Fleet Shift %: Percentage of EV demand that can be shifted to off-peak hours.
Battery Capacity (MW): Total storage available to support the grid.
Mode: Select the QCAD system behavior:
Convergence → supply and demand move toward balance.
Divergence → supply and demand separate, grid strain increases.
Bifurcation → outcomes split randomly into different possible states.
Run Simulation: Starts the calculation.
Download CSV: Exports the results to a spreadsheet.
Spreadsheet Data Upload: Allows loading a CSV with real supply/demand values.
Right Panel (Results & Visualization)
Chart:
Blue line = Supply
Red line = Demand
Results Preview: Shows first 10 rows of numeric results (supply, demand, balance).
4. How to Use
Step 1 — Run a Simple Simulation
Open the HTML app in your browser.
Enter values for P(x), T(x), EV shift %, and battery capacity.
Select a Mode (Convergence, Divergence, or Bifurcation).
Click Run Simulation.
View supply/demand curves on the chart.
Step 2 — Upload Spreadsheet Data
Prepare a CSV file with two columns:
Column A = Supply (MW)
Column B = Demand (MW)
Click Choose File under Spreadsheet Data.
The file will load, and simulation will automatically include this data.
Step 3 — Export Results
After running a simulation, click Download CSV.
A file named qcad_results.csv will save to your computer.
Open it in Excel or Google Sheets for detailed analysis.
5. Example Workflow
Upload a demand profile (e.g., residential evening peak).
Set EV Shift = 30% and Battery = 200 MW.
Compare Divergence Mode vs. Convergence Mode.
Export both runs to CSV → compare results side-by-side in Excel.
6. Notes & Limitations
This app is a proof of concept, not a production-grade forecasting tool.
Supply/demand data must be numeric values; non-numeric rows will be skipped.
Results are illustrative, not predictive — they show the effect of QCAD dynamics under different conditions.
Not an actual product of Southern California Edison. This is an experimental platform coming from the desk of Travis RC Stone Application of QCAD Modeling to Grid Demand-Supply Optimization
Prepared for: Southern California Edison (SCE)
Prepared by: Travis Raymond-Charlie Stone
Date: September 2025
Executive Summary
The Southern California grid is entering a period of unprecedented complexity, driven by increasing renewable penetration, growing electrification of transportation, and rising demand-side uncertainty. Traditional load forecasting and scheduling methods struggle to capture the dynamic, nonlinear behaviors of millions of devices — EVs, distributed storage, smart appliances — interacting simultaneously.
This paper proposes the application of the QCAD (Quantum Convergence and Divergence) Equation as an advanced analytical framework for modeling grid balancing under uncertainty. QCAD is designed to identify regions of convergence (stability), divergence (instability), and bifurcation (multiple possible outcomes) in recursive systems. Applied to the grid, this framework provides a new lens for evaluating when to draw from or inject into distributed energy resources (DERs), and for determining optimal timing of appliance and EV load operation.
Problem Statement
Current grid challenges in California include:
Limited Visibility of Demand → Utilities lack granular insight into real-time household and distributed asset behavior.
Variable Supply → Renewable generation introduces volatility in supply curves.
Load Peaks from EV Charging → The rapid adoption of EVs risks severe evening load spikes.
Distributed Decision-Making → Millions of devices now participate in grid dynamics, but in uncoordinated ways.
To maintain reliability, SCE must adopt predictive, system-level modeling to guide demand response, incentive design, and automated scheduling.
QCAD Framework
Where:
P(x)P(x) = grid pressure function (price signals, load stress, renewable variability)
T(x)T(x) = device transformation function (EV charging, appliance load, storage behavior)
LL = recursion depth (time horizon of grid planning)
The aggregated result maps stability or instability across a domain, showing how the system behaves as participation changes.
Application to SCE Grid Operations
EV Charging Optimization
Convergence Mode: Incentivize EVs to charge midday during high solar generation.
Divergence Mode: Evening charging without control leads to rapid load escalation.
Bifurcation Mode: Split outcomes depending on participation levels in demand response programs.
Appliance Scheduling
Household and commercial appliances (HVAC, dryers, refrigeration) can be shifted into convergence valleys, avoiding strain.
Distributed Storage Dispatch
QCAD models identify when coordinated discharge prevents peak overload.
Bifurcation thresholds highlight minimum participation rates for reliability.
Policy & Incentive Design
Pricing signals can be mapped to convergence regimes to encourage consumer behavior aligned with grid stability.
Strategic Benefits for SCE
Resilience: Identify instability risks before they cascade into outages.
Efficiency: Optimize utilization of renewables and DERs.
Cost Reduction: Reduce peak demand charges and defer infrastructure upgrades.
Scalability: Apply the framework across residential, commercial, and industrial demand response programs.
Recommendations
Pilot Project → Implement QCAD modeling within a microgrid or EV-heavy community to test predictive alignment of loads.
Integration with Demand Response Systems → Use QCAD outputs to guide incentive signals for EVs and appliances.
Collaboration with DER Providers → Incorporate QCAD into battery and EV aggregators’ scheduling platforms.
Expand Forecasting Tools → Combine QCAD with existing forecasting for renewable generation to enhance grid situational awareness.
Conclusion
The QCAD Equation provides Southern California Edison with a novel, mathematically rigorous framework to model, anticipate, and manage the dynamic interactions of supply and demand in a renewable-heavy, electrified future. By explicitly quantifying convergence, divergence, and bifurcation behaviors, SCE can better anticipate grid stress points and design demand-side interventions that maintain reliability while accelerating California’s transition to clean energy.
Grid load simulation
1. Define Variables
For each time step (frame), we consider:
Symbol | Meaning |
DD | Demand (MW) – electricity needed at this time |
SS | Supply (MW) – electricity generated at this time |
EE | EV load (MW) – amount of energy charged to/discharged from EVs |
LL | Total load (MW) – net effect on the grid |
2. Total Load Formula
The total load LL at each time step is:
L=D−S+EL = D - S + E
If L>0L > 0, the grid needs extra energy to meet demand.
If L<0L < 0, there’s excess energy that could be stored or exported.
3. Step-by-Step Hand Calculation
Suppose we have 3 frames (time steps). Example values:
Frame | D (MW) | S (MW) | E (MW) |
1 | 120 | 100 | 10 |
2 | 140 | 110 | 5 |
3 | 130 | 130 | -5 |
Step 1: Frame 1
L1=D1−S1+E1=120−100+10=30 MWL_1 = D_1 - S_1 + E_1 = 120 - 100 + 10 = 30 \text{ MW}
Step 2: Frame 2
L2=D2−S2+E2=140−110+5=35 MWL_2 = D_2 - S_2 + E_2 = 140 - 110 + 5 = 35 \text{ MW}
Step 3: Frame 3
L3=D3−S3+E3=130−130+(−5)=−5 MWL_3 = D_3 - S_3 + E_3 = 130 - 130 + (-5) = -5 \text{ MW}
4. Optional Metrics
a) Grid Surplus/Deficit
Surplus/Deficit=S−D−E\text{Surplus/Deficit} = S - D - E
Positive → surplus energyNegative → deficit energy
b) EV Adjustment Recommendation
If L>0L > 0 → consider discharging EVs to supply extra energy.If L<0L < 0 → consider charging EVs to absorb excess energy.
5. How to Do By Hand
Make a table with D, S, E for each frame.
Apply the formula: L=D−S+EL = D - S + E per frame.
Note whether the grid is short or overloaded.
Decide action on EVs or appliances based on L.
This is exactly what the animation app does, except the app calculates many frames quickly
[Grid Data + Forecasts]
│
▼
[Load & Supply Modeling] ← P(x), T(x), Mode
│
▼
[Simulation Engine] ← Iterative computation
│
▼
[Decision Module] ← Optimal actions
│
▼
[UI Visualization / Spreadsheet Output]
│
▼
[Actions Executed in Field]
│
└─── Feedback → [Load & Supply Modeling]
Workflow Description
1. Grid Data Input
Real-time SCED telemetry (generation, demand, distributed storage)
Forecasts: weather, solar/wind output, historical load patterns
2. Load & Supply Modeling
P(x) function → Parameter weighting (e.g., demand intensity, supply constraints)
T(x) function → Transformation (e.g., EV behavior, appliance impact)
Mode selection → Convergence / Divergence / Bifurcation analysis
3. Simulation Engine
Iteratively computes system response
Generates predicted system states across time (frames)
Tracks historical states in cache for rewind/step analysis
4. Decision Module
Evaluates optimal actions:
When to charge/discharge EVs
When to run appliances
Uses current and predicted grid states
5. User Interface / Spreadsheet Output
Visualizes results (frames, curves, heatmaps)
Exports numerical results for further analysis
Allows stakeholders to simulate “what-if” scenarios
6. Feedback Loop
Actions taken (EV charge/discharge, appliance scheduling) feed back into grid model
Continuous recalculation improves accuracy over time
Here’s a concise visual comparison table that could be presented to stakeholders:
Feature / Capability | Existing Grid Systems | Predictive Dynamic Optimization (Your System) |
Decision Approach | Reactive (after event occurs) | Predictive (anticipates demand/supply) |
Data Resolution | Aggregated, delayed | Real-time and device-level |
Load Optimization | Limited or none | Individual appliances, EVs, and energy storage |
Grid Stress Management | Minimal, often manual | Proactively reduces peaks and overloads |
Efficiency / Cost Savings | Indirect, often delayed | Direct, optimized energy use reduces costs |
Scalability | Regional or substation level | Extensible to homes, buildings, EV fleets |
Decision Latency | Minutes to hours | Seconds to minutes (real-time actionable) |
User / Consumer Impact | Passive | Active: can choose optimal times for usage |
a concrete example of P(x) and T(x) that models full-grid load and generation for SCE at scale, suitable for a predictive simulation, includes both the math and a step-by-step explanation for real-world applicability.
1. Define the Domain
Let xx represent time slices across the day (e.g., 15-minute intervals). For Southern California Edison:
x=1,2,…,96(96 intervals for 24 hours at 15 min each)x = 1, 2, \dots, 96 \quad \text{(96 intervals for 24 hours at 15 min each)}
Other variables:
D(x)D(x) = Base demand at time xx (MW)
R(x)R(x) = Renewable generation at time xx (MW), solar/wind
B(x)B(x) = Battery or storage dispatch at time xx (MW)
EV(x)EV(x) = Electric vehicle load at time xx (MW)
G(x)G(x) = Total generation at time xx = R(x)+Gconventional(x)R(x) + G_\text{conventional}(x)
2. Define P(x) — Grid Pressure / Weighting Function
P(x)=wd⋅D(x)+wEV⋅EV(x)−wr⋅R(x)−wb⋅B(x)P(x) = w_d \cdot D(x) + w_{EV} \cdot EV(x) - w_r \cdot R(x) - w_b \cdot B(x)
Where:
wd=1.0w_d = 1.0 → weight on base demand
wEV=1.2w_{EV} = 1.2 → EV load has slightly higher pressure
wr=0.8w_r = 0.8 → renewable generation offsets stress
wb=1.0w_b = 1.0 → storage reduces grid stress
Interpretation:
High P(x)P(x) → time of day with high demand relative to generation, stressing the grid.
Low P(x)P(x) → surplus energy available.
Example calculation at 6 PM (typical evening peak):
D(72)=9,000 MWD(72) = 9,000\,MW
EV(72)=1,200 MWEV(72) = 1,200\,MW
R(72)=500 MWR(72) = 500\,MW
B(72)=300 MWB(72) = 300\,MW
P(72)=1.0⋅9000+1.2⋅1200−0.8⋅500−1.0⋅300P(72) = 1.0 \cdot 9000 + 1.2 \cdot 1200 - 0.8 \cdot 500 - 1.0 \cdot 300P(72)=9000+1440−400−300=10,740 (grid pressure units)P(72) = 9000 + 1440 - 400 - 300 = 10,740 \, \text{(grid pressure units)}
3. Define T(x) — Transformation / Load-Shifting Function
T(x)=α⋅EVshift(x)+β⋅Appshift(x)+γ⋅Bdispatch(x)T(x) = \alpha \cdot EV_\text{shift}(x) + \beta \cdot App_\text{shift}(x) + \gamma \cdot B_\text{dispatch}(x)
Where:
α,β,γ∈[0,1]\alpha, \beta, \gamma \in [0,1] are participation coefficients (percent of controllable load shifted)
EVshift(x)EV_\text{shift}(x) = amount of EV load that can be shifted at time xx
Appshift(x)App_\text{shift}(x) = appliance load that can be delayed/advanced
Bdispatch(x)B_\text{dispatch}(x) = battery charge/discharge action
Example:
α=0.5\alpha = 0.5, 50% of EVs participate
β=0.3\beta = 0.3, 30% of appliance load can shift
γ=1.0\gamma = 1.0, all battery dispatch available
At 6 PM:
EVshift(72)=1,200 MWEV_\text{shift}(72) = 1,200\,MW → 50% can be shifted = 600 MW
Appshift(72)=2,000 MWApp_\text{shift}(72) = 2,000\,MW → 30% can be shifted = 600 MW
Bdispatch(72)=300 MWB_\text{dispatch}(72) = 300\,MW
T(72)=0.5⋅1200+0.3⋅2000+1.0⋅300=600+600+300=1,500 MWT(72) = 0.5 \cdot 1200 + 0.3 \cdot 2000 + 1.0 \cdot 300 = 600 + 600 + 300 = 1,500\,MW
4. Total Grid Load / Stress Adjustment
We can now calculate adjusted stress on the grid:
L(x)=P(x)−T(x)L(x) = P(x) - T(x)
At 6 PM:
L(72)=10,740−1,500=9,240 (adjusted pressure units)L(72) = 10,740 - 1,500 = 9,240 \, \text{(adjusted pressure units)}
Positive L(x)L(x) → grid under stress, consider further mitigation
Negative L(x)L(x) → surplus energy available
5. Iterative Simulation Across the Day
For x=1…96x = 1 \dots 96:
Compute P(x)P(x) using real demand, generation, and storage data
Compute T(x)T(x) based on controllable assets and participation rates
Calculate L(x)=P(x)−T(x)L(x) = P(x) - T(x)
Flag times when L(x)L(x) exceeds threshold → send action signals
Optional: Incorporate bifurcation analysis for uncertainty:
Lpred(x+1)=L(x)+ϵ,ϵ∼random perturbation reflecting forecast errorL_\text{pred}(x+1) = L(x) + \epsilon, \quad \epsilon \sim \text{random perturbation reflecting forecast error}
✅ 6. How It Scales for SCE
96 frames/day × 365 days/year → full annual grid simulation
Replace placeholders with real SCED telemetry, solar/wind forecasts, EV fleet data, and distributed storage
Adjust weights wd,wEV,wr,wbw_d, w_{EV}, w_r, w_b based on historical grid behavior
Participation coefficients α,β,γ\alpha, \beta, \gamma reflect program adoption rates
Can export CSV or run visualization for each time slice
Summary
P(x) = “grid pressure” based on total demand vs. generation
T(x) = “transformative mitigation” via EV load shifting, appliance scheduling, and battery dispatch
L(x) = P(x) - T(x) → real-time grid stress metric
Modular, scalable to hundreds of thousands of devices, entire SCE footprint, and multi-year simulations
P(x) – Grid Pressure Function
Combines all sources of stress on the grid:
Base demand D(x) from homes and businesses
EV load EV(x)
Renewable generation R(x) (negative contribution reduces stress)
Battery dispatch B(x) (charging increases demand, discharging reduces it)
Weighted sum:
P(x)=wDD(x)+wEVEV(x)−wRR(x)−wBB(x)P(x) = w_D D(x) + w_{EV} EV(x) - w_R R(x) - w_B B(x)
T(x) – Load Mitigation / Transformation Function
Represents coordinated adjustments to reduce stress:
EV charging shift (α fraction of EV load moved to off-peak)
Appliance scheduling (β fraction of flexible load shifted)
Battery dispatch (γ fraction applied)
Sum of mitigations:
T(x)=αEV(x)+βAppliance Load+γB(x)T(x) = \alpha EV(x) + \beta \text{Appliance Load} + \gamma B(x)
Adjusted Grid Stress L(x)
L(x)=P(x)−T(x)L(x) = P(x) - T(x)
Positive L(x): extra demand, may need additional generation or EV discharge
Negative L(x): surplus energy, can absorb with storage or shift loads
The graph shows a full-day (24-hour) simulation in 15-minute intervals:
Blue line (P(x)): raw grid pressure from demand minus renewable contributions
Green line (T(x)): mitigation from EV/appliance shifts and battery dispatch
Red line (L(x)): net grid stress after mitigation, showing peaks smoothed and troughs filled
This illustrates how the system can predict and optimize grid stress in real-time, accounting for millions of devices and generation sources, scalable to Southern California Edison’s entire service area.
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