Optimal wind farm energy and reserve scheduling incorporating wake interactions

This paper proposes a novel two-stage stochastic programming framework that integrates FLORIS-based wake modeling and wake steering to optimize wind farm energy and reserve scheduling, demonstrating significant revenue gains and reduced imbalance penalties compared to conventional methods that neglect wake interactions.

The Gist

The Big Picture: The Wind Farm as a Team of Runners

Imagine a wind farm not as a collection of isolated machines, but as a relay team of runners sprinting down a track.

In the old way of doing things (the "Power Curve" method), the coach told each runner, "Run as fast as you can, individually!" The coach didn't care that the runner in front was kicking up a massive cloud of dust (a wake) that made it harder for the runners behind them to breathe and run fast.

Because the coach ignored the dust cloud, he told the team, "You will all run at top speed!" He sold tickets to the public promising a record-breaking time. But when the race started, the runners behind got choked on the dust, slowed down, and the team finished much slower than promised. The coach had to pay a huge fine for lying about the time.

This paper proposes a new strategy: A "Smart Coach" who understands the dust clouds. This coach knows that if the front runner slows down slightly and turns sideways (a technique called Wake Steering), they can blow the dust cloud away from the runners behind. This allows the whole team to run faster together, even if the front runner is slightly slower.

The Problem: The "Dust Cloud" (Wake Effects)

When a wind turbine spins, it steals energy from the wind. The wind coming out the back is slower and more turbulent. This is called a wake.

• The Old Mistake: Most wind farm operators pretend the wind is perfectly clean everywhere. They use a simple chart (a "Power Curve") to guess how much electricity they will make. They assume every turbine gets full, fresh wind.
• The Reality: The turbines in the back get "dirty," slow wind. They produce less power.
• The Consequence: When wind farms sell electricity to the grid, they promise a certain amount. If they guess too high (because they ignored the dust clouds), they fail to deliver. In the UK electricity market, this results in heavy fines (imbalance penalties).

The Solution: The "Smart Coach" Strategy

The authors created a new computer model that acts like a smart coach. It does three main things:

1. Seeing the Invisible (Wake-Aware Modeling)

Instead of guessing, the model uses advanced physics (simulated by software called FLORIS) to see exactly how the wind flows between turbines. It calculates exactly how much "dust" (wake) the front turbines are creating and how much it slows down the back ones.

• Analogy: Instead of guessing the runners' speed, the coach has a drone flying overhead to measure the exact wind speed at every runner's face.

2. The Magic Trick (Wake Steering)

This is the most exciting part. The model suggests that the front turbines should turn slightly sideways (yaw).

• How it works: If a front turbine turns 20 degrees, it stops blocking the wind directly behind it. It pushes the "dust cloud" to the side, letting the fresh wind flow to the turbines behind.
• The Trade-off: The front turbine loses a tiny bit of power by turning, but the back turbines gain a lot more power because they finally get fresh air. The total team power goes up.
• Analogy: It's like a runner in a race turning slightly to the side to let the person behind them get a better draft, even if it costs the front runner a tiny bit of speed.

3. Playing the Market Game (Scheduling)

The model doesn't just look at the wind; it looks at the price tags.

• It decides: "Should we sell this extra power as regular electricity? Or should we save it to sell as an emergency backup (Reserve) if the grid needs it?"
• It calculates the best mix to make the most money while avoiding fines.

The Results: Who Won the Race?

The authors tested this on a real wind farm (the London Array) and compared three strategies:

1. The "Optimist" (Power Curve): Ignores the dust.
   • Result: Promised too much power. Got fined heavily. Lost money.
2. The "Realist" (Baseline): Knows about the dust but doesn't try to fix it.
   • Result: Made a decent amount of money, but left some potential cash on the table.
3. The "Smart Coach" (Proposed Method): Knows about the dust AND uses Wake Steering to fix it.
   • Result: Made 1-2% more money than the Realist.
   • Bonus: Compared to the Optimist, the Smart Coach avoided massive fines and actually made 3% more real money than the Optimist thought they would.

Why This Matters

• For the Planet: As we move away from fossil fuels, we need wind to be reliable. If wind farms are constantly fined for not delivering, it hurts the economy of green energy.
• For the Grid: The electricity grid needs stability. By understanding how turbines interact, we can get more power out of the same number of machines without building new ones.
• For the Wallet: It turns out that being a "team player" (turning slightly to help neighbors) is more profitable than being a "selfish individual" (running straight ahead and blocking everyone else).

In a Nutshell

This paper teaches us that wind farms are teams, not individuals. By using smart computer models to see how turbines block each other's wind, and by having the front turbines turn slightly to help the back ones, we can generate more electricity, avoid expensive fines, and make more profit. It's a small turn of the head that leads to a big win for the whole team.

Technical Summary

1. Problem Statement

As wind energy penetration increases globally, Wind Power Producers (WPPs) are increasingly required to participate in both day-ahead (DA) energy markets and ancillary service markets (specifically Frequency Restoration Reserve, FRR) to ensure grid stability. However, current scheduling models face two critical limitations:

• Neglect of Wake Effects: Conventional bidding strategies often rely on manufacturer power curves ("Power Curve" approach) which assume uniform inflow. This ignores wake interactions between turbines, leading to an overestimation of available power.
• Lack of Active Wake Management: While some models account for wake losses ("Baseline" approach), they typically do not employ active control strategies like wake steering (yaw misalignment) to mitigate these losses.
• Consequences: Overestimation leads to significant imbalance penalties in real-time markets, reducing actual revenue. Conversely, failing to utilize wake steering leaves potential revenue on the table.

The paper addresses the research gap between aerodynamic wake modeling and market-oriented decision-making, proposing a framework that explicitly integrates wake physics into the bidding strategy for energy and reserve markets.

2. Methodology

The authors propose a two-stage stochastic programming framework designed to optimize the joint scheduling of energy and reserve bids for a wind farm.

A. Wake Modeling & Simulation

• Tool: The study utilizes FLORIS (a Python-based wind farm simulation library) to model wake interactions.
• Model: The Cumulative Curl model is used to calculate velocity deficits and wake deflection.
• Control Strategy: Wake Steering is implemented, where upstream turbines are intentionally yawed to deflect their wakes away from downstream turbines, thereby increasing total farm output.
• Scenarios: Uncertainty in wind speed, wind direction, and FRR duration is handled through scenario generation and reduction:
  • Wind speed is modeled using a Normal distribution (representing forecast error).
  • Wind direction is modeled using a von Mises distribution (circular normal).
  • Scenarios are clustered using the K-medoids algorithm to reduce computational load while maintaining statistical accuracy (15 representative scenarios were selected).

B. Optimization Framework

The problem is formulated as a quadratic program solved via the IPOPT solver in Pyomo.

• Objective: Maximize the WPP's expected daily profit ($\Pi_d$) while minimizing imbalance costs.
• Decision Variables:
  • First Stage (Day-ahead): Bids for Energy ($P_e$), Upward Mandatory Frequency Response (MFR), and Upward Fast Reserve (FR).
  • Second Stage (Real-time): Redispatch adjustments ($\Delta P$) based on realized scenarios.
• Revenue Components:
  • Energy sales, MFR holding payments, FR availability fees, and FR utilization payments.
  • Penalties: Squared imbalance costs for deviations in energy and FR, penalizing the WPP for failing to meet commitments.
• Approaches Compared:
  1. Power Curve: Ignores wake effects (Optimistic/Upper limit).
  2. Baseline: Includes wake effects but no active steering (Conservative/Lower limit).
  3. WRC (Wake Redirection Control): Includes wake effects + active yaw optimization.
     • WRC1: Allocates extra power from steering to both energy and reserves.
     • WRC2: Allocates extra power exclusively to reserves (to avoid over-committing energy if steering is risky).

3. Key Contributions

1. Wake-Aware Power Estimation: The study moves beyond simple power curves by integrating state-of-the-art engineering wake models directly into the market bidding optimization, providing a more realistic estimate of available capacity.
2. Active Wake Management for Markets: It demonstrates how wake steering can be integrated into a profit-maximizing market framework, showing that active control can recover lost power and increase revenue.
3. Extended Market Scope: Unlike previous studies focusing primarily on primary frequency control (FCR), this work expands the analysis to secondary control (FRR/FR), addressing the specific timescale challenges (minutes) of wake propagation relative to reserve activation.
4. Quantitative Economic Impact: The paper provides a rigorous comparison of three methodologies, quantifying the revenue losses of ignoring wake effects and the gains of active management.

4. Case Study & Results

The methodology was tested on the London Array (630 MW offshore wind farm) participating in the Great Britain (GB) electricity markets. Simulations were run for two specific days in April 2015.

Key Findings:

• Overestimation by Power Curve: The traditional "Power Curve" method overestimated production by 12–13% compared to the wake-aware "Baseline" method.
• Revenue Loss: Due to the overestimation, the Power Curve approach incurred significant imbalance penalties. Consequently, its actual realized revenue was 3% lower than the Baseline approach, despite submitting higher bids.
• Benefit of Wake Steering: The proposed WRC (Wake Steering) approach yielded an additional 1–2% increase in income compared to the Baseline approach. This gain comes from both increased total energy production and better optimization of reserve bids.
• Bidding Behavior:
  • When energy prices were low (<£35/MWh) or wind conditions were highly variable, the model shifted bids toward the reserve (FR) market to maximize expected profit and minimize imbalance risk.
  • Wake steering allowed the farm to offer more competitive bids in both markets by increasing the available headroom.
• Response Time: Simulations confirmed that wake steering effects propagate to downstream turbines within 2–5 minutes, which is compatible with the activation timescales of secondary frequency reserves (FRR).

5. Significance and Implications

• Economic Viability: The study proves that neglecting wake effects in market participation is financially detrimental. Accurate wake modeling is essential to avoid imbalance penalties that can erode profits.
• Operational Strategy: Wake steering is not just an aerodynamic optimization but a viable market strategy. It allows WPPs to extract more value from existing assets without new hardware.
• Grid Stability: By improving the accuracy of wind power forecasts and enabling active participation in reserve markets, this approach supports the integration of higher shares of renewable energy into the grid.
• Future Outlook: The paper highlights that while current steady-state models are sufficient for day-ahead planning, future work must address the structural fatigue costs of continuous yawing and the use of dynamic wake models for real-time control.

In conclusion, the paper establishes that integrating wake physics and active control strategies into stochastic market optimization is critical for maximizing the profitability and reliability of wind farms in modern electricity markets.