A Fast Dynamic Internal Predictive Power Scheduling Approach for Power Management in Microgrids

1. Problem Statement

The paper addresses the challenge of optimizing power management in microgrids that integrate distributed renewable energy (Photovoltaic/PV), energy storage systems (ESS), and diverse prosumers (consumers who also produce energy).

Key challenges identified include:

• Computational Complexity: Traditional power scheduling models often use Mixed-Integer Non-Linear Programming (MINLP) due to the non-linear interactions between binary variables (e.g., charging vs. discharging states) and continuous power variables. Solving MINLP problems in real-time is computationally prohibitive.
• Static Objectives: Existing methods often rely on static cost functions that minimize expenses based solely on Time-of-Use (ToU) tariffs. This fails to account for specific operational goals, such as shifting power exchanges to specific time windows or managing peer-to-peer (P2P) trading dynamics.
• ESS Lifespan: Many short-term optimization strategies overlook the long-term degradation of Energy Storage Systems (ESS) caused by excessive charge-discharge cycles.
• Real-Time Feasibility: There is a need for a scheduling approach that can handle uncertainties and execute within the tight time constraints required for real-time microgrid control.

2. Methodology

The authors propose a Dynamic Internal Predictive Power Scheduling (DIPPS) approach. The methodology involves three main stages:

A. System Modeling

The microgrid is modeled with PV generation, ESS, and load. The power flow is governed by:

• Power Balance: Ensuring load demand is met by PV, ESS discharge, or grid purchase.
• Mutual Exclusivity: Binary variables ($b_V, b_G, b_C$) ensure that charging/discharging and buying/selling do not occur simultaneously to minimize conversion losses.
• State of Charge (SoC): The ESS SoC is constrained between 0.2 and 0.8 to prevent overcharging or deep discharge, with a requirement to return to a specific SoC (0.5) by the end of the scheduling horizon to ensure readiness for the next cycle.

B. Optimization Formulation (MINLP to MILP)

1. Initial Formulation (MINLP-PS): The problem is initially modeled as a Mixed-Integer Non-Linear Programming problem with Predictive Scheduling (PS). The non-linearity arises from the multiplication of binary decision variables and continuous power variables.
2. Linearization (McCormick's Relaxation): To reduce computational complexity, the authors apply McCormick's relaxation. This technique transforms the non-linear terms into linear constraints by introducing auxiliary variables (e.g., $z, y, w$).
3. Resulting Formulation (MILP-PS): The problem is converted into a Mixed-Integer Linear Programming (MILP) problem, which is significantly faster to solve.

C. Dynamic Objective Function

A key innovation is the introduction of a time-varying binary parameter ($b_S(t)$) into the objective function.

• Static Case: The objective minimizes cost based on ToU tariffs ($J_1$).
• Dynamic Case (DIPPS): The objective function is modified to $J_D = \text{Cost} - b_S(t) \times \text{Power Sold}$.
  • When $b_S(t) = 0$: The system optimizes for profit based on tariff rates.
  • When $b_S(t) = 1$: The system is forced to sell surplus power (from ESS or PV) to the grid regardless of the current tariff rate. This allows operators to shift power exchanges to specific time windows (e.g., for grid stability or specific P2P agreements).

3. Key Contributions

• Computational Efficiency: Successfully transformed a complex MINLP problem into a tractable MILP problem using McCormick's relaxation, enabling real-time implementation.
• Dynamic Control: Introduced a mechanism to dynamically control the timing of external power exchanges via a binary parameter, moving beyond simple cost minimization to include operational constraints and strategic scheduling.
• ESS Longevity: The predictive window approach limits ESS charge-discharge cycles to approximately one per day, theoretically extending battery lifespan.
• Scalability: The approach is designed to simulate heterogeneous microgrid communities with diverse generation and storage capacities.

4. Experimental Results

The approach was validated using real-world load data (UCI Energy Dataset) and PV data over a 24-hour period across three case studies:

• Case A (Static): Standard cost minimization. Power is sold during high tariff periods (13–19 hrs).
• Case B (Dynamic - Morning): The binary parameter forces power sales between 0–6 hours. The ESS discharges completely to meet this requirement.
• Case C (Dynamic - Evening): The binary parameter forces power sales between 18–24 hours.

Performance Metrics:

• Computation Time:
  • MINLP-PS: Average solve time of 38.27 seconds (with high variance and outliers up to 271s).
  • MILP-PS (DIPPS): Average solve time of 0.92 seconds.
  • Improvement: A 97.6% reduction in computational time, making real-time control feasible.
• Power Exchange: While the total power sold to the grid remained consistent across cases (~1,850 kW), the source and timing shifted. In dynamic cases, the ESS was utilized more aggressively to meet the forced time-window constraints.
• Window Length: A predictive window of at least 6 hours was found optimal. Shorter windows caused the solver to fail in meeting the final SoC constraints, while longer windows increased computation time without significant cost benefits.

5. Significance and Conclusion

The paper demonstrates that DIPPS is a viable solution for real-time microgrid management. By converting a non-linear problem into a linear one and introducing a dynamic control parameter, the authors achieved:

1. Real-Time Feasibility: Solving the optimization in under 1 second allows for integration into actual microgrid control systems.
2. Operational Flexibility: Grid operators can now dictate when power is exchanged with the external grid, not just how much, facilitating better grid stability and P2P trading strategies.
3. Sustainability: By limiting daily charge-discharge cycles, the approach supports the economic viability of microgrids by extending the lifespan of expensive battery storage systems.

This work bridges the gap between theoretical optimization and practical, real-time deployment in heterogeneous microgrid communities.