Optimization Models与chicken-and-egg problem求解咨询：电力系统发电成本预测中的循环依赖问题

Hey Eve, great question—this circular demand-cost dependency is such a common (and tricky) challenge in energy systems modeling, and you’re spot-on to connect it to lagged time series logic. Let’s walk through practical ways to tackle this in optimization frameworks, plus some resources to dive deeper.

1. Integrated Optimization with Endogenous Demand #

Instead of treating demand as a fixed, external assumption, make it an endogenous part of your model by linking it to the costs/prices your optimization produces. Here’s how to pull this off:

• Add a demand response function to your model constraints. For example, something like D = D_base - ε * P, where:
  • D is the realized demand (now a decision variable)
  • D_base is your baseline demand forecast
  • ε is the price elasticity of demand (a parameter you can calibrate from historical data)
  • P is the marginal generation cost (derived directly from your cost-minimization solver output)
• This turns your problem into an equilibrium model that solves for both optimal generation levels and the demand that balances with the resulting system costs—breaking the chicken-and-egg loop entirely. Many industry-standard tools like OSeMOSYS or PLEXOS use this approach for long-term forecasting.

2. Iterative Lagged Optimization Loops #

This is the direct parallel to the lagged variable idea you mentioned from time series. Think of it as a sequential feedback process:

• Step 1: Start with an initial demand forecast (e.g., D₀ based on historical trends or macroeconomic projections).
• Step 2: Run your cost-minimization optimization model using D₀ to get the resulting system cost/price P₀.
• Step 3: Update your demand forecast using a lagged feedback rule: D₁ = f(P₀, D₀). For example, you could use a historical relationship where a 10% increase in system cost leads to a 2% drop in demand.
• Step 4: Repeat steps 2-3 until the change in demand and price between consecutive iterations is below a small threshold (like 0.1%)—meaning the system has converged to a stable balance.
• This is super flexible and easy to implement with scripting tools (Python, R) that wrap your optimization solver, and it works well for both linear and non-linear demand relationships.

3. Dynamic Stochastic Optimization (DSO) for Uncertain Futures #

If you need to account for uncertainty (e.g., volatile fuel prices, unpredictable economic growth), dynamic stochastic optimization builds lagged feedback into a multi-stage decision framework:

• Define time stages (e.g., years or quarters) where each stage’s demand depends on the previous stage’s realized costs and prices.
• Use scenario trees to model uncertain drivers (like weather, policy changes) that affect both demand and generation costs.
• The model optimizes generation decisions across stages, accounting for how past cost outcomes shape future demand—and vice versa. This is especially useful for long-term strategic forecasting where the feedback loop unfolds over time.

Recommended Resources #

Books #

• Power System Economics: Designing Markets for Electricity by Daniel Kirschen et al. – This is a go-to for understanding equilibrium modeling of demand and generation costs, with deep dives into feedback loops in electricity markets.
• Energy System Modeling by Tom Brown et al. – Covers integrated optimization approaches, including how to embed demand response into cost-minimization models.

Articles #

• "Demand Response in Electricity Markets: An Overview" (IEEE Transactions on Power Systems) – Breaks down practical methods for modeling price-dependent demand in optimization frameworks.
• "Long-Term Electricity Demand Forecasting with Integrated Optimization Models" (Energy Policy) – Discusses iterative and integrated approaches specifically for handling demand-cost feedback in forecasting scenarios.

备注：内容来源于stack exchange，提问作者Eve Chanatasig