Abstract:
This article delves into the voltage regulation challenges faced by distribution networks integrated with high penetration levels of renewable energy sources, particularly focusing on the role of battery energy storage system (BESS). The paper firstly outlines the structure of a hybrid energy storage system integrated within an active distribution network. Subsequently, it discusses the theory of distributionally robust optimization models accounting for renewable energy uncertainties, introducing concepts such as photovoltaic (PV) uncertainty and Wasserstein uncertainty sets. Finally, a detailed analysis of a two-stage voltage regulation strategy for active distribution systems containing hybrid energy storage is presented, and its feasibility is validated through case simulations.
Keywords: Renewable energy generation, energy storage system, distribution network voltage regulation
1. Introduction
The increasing integration of renewable energy sources (RES), such as solar photovoltaic (PV) and wind turbines, into distribution networks has significantly impacted their operational characteristics. RES inherently exhibit intermittent and fluctuating output power, leading to voltage fluctuations and even violations that threaten the stable and reliable operation of the grid. To mitigate these issues, energy storage systems (ESS) have emerged as vital flexible resources, enabling the smoothing of RES output fluctuations and improving overall grid stability.
Energy storage systems can be categorized into single-type, hybrid, and multi-energy systems based on their configuration. Hybrid energy storage systems, which combine complementary storage technologies like batteries and supercapacitors, offer significant advantages in terms of energy density, power density, response time, and operating lifespan. These attributes enable them to effectively address voltage violations and improve the reliability, economic efficiency, and flexibility of the distribution network.
2. System Overview: Hybrid Energy Storage-Integrated Active Distribution Network
2.1 Basic System Architecture
The hybrid energy storage-integrated active distribution network (see Figure 1) comprises several key components:
- Distribution Network: Connected to the main grid through a step-down transformer, enabling power transactions.
- Distributed Photovoltaic Generation: Integrated via inverters at the point of common coupling (PCC), injecting variable power into the network while also offering reactive power support for voltage regulation.
- Hybrid Energy Storage System: A combination of batteries and supercapacitors, leveraging their complementary strengths in energy density, power density, and response time for multi-timescale coordinated dispatch.
2.2 Role of Hybrid Energy Storage System
The hybrid energy storage system is crucial in managing RES output fluctuations and ensuring voltage stability within the distribution network. Batteries, with their high energy density, are utilized for longer-timescale charging and discharging to smooth out significant RES power variations. Supercapacitors, known for their rapid response and high power density, are deployed for short-term adjustments to counteract sudden changes in RES output, enhancing system reliability and responsiveness.
3. Distributionally Robust Optimization Model Considering Renewable Energy Uncertainties
3.1 Photovoltaic Uncertainty and Wasserstein Uncertainty Set
PV output power is inherently uncertain, with significant deviations between predicted and actual values. Limited sample sizes and computational constraints further complicate the accurate estimation of its prediction error distribution. To address this, distributionally robust optimization (DRO) is adopted, leveraging Wasserstein uncertainty sets.
Wasserstein Uncertainty Set: This is a ball-shaped uncertainty set based on the Wasserstein probability distance, offering robust performance guarantees and computational tractability. It preserves as much prediction error information as possible while enhancing computational feasibility.
3.2 Two-Stage Distributionally Robust Optimization Model
Given the uncertainties in PV output, a two-stage distributionally robust optimization model (TSDRO) is proposed, balancing system robustness and economic efficiency. This model considers the complementary dispatch characteristics of the hybrid energy storage system across different timescales, facilitating day-ahead and intra-day joint scheduling.
The objective function of the TSDRO model encompasses operational costs and risk costs, with the latter tied to random variables. A key challenge lies in the “min-max” term within the risk cost component, which necessitates the introduction of auxiliary variables for equivalent transformation based on the constructed Wasserstein uncertainty set.
4. Voltage Regulation Strategy for Active Distribution Systems with Hybrid Energy Storage
4.1 Two-Stage Distributionally Robust Voltage Regulation Framework
The proposed two-stage framework addresses voltage violations arising from high RES integration by leveraging the hybrid energy storage system’s capabilities.
4.2 Day-Ahead and Intra-Day Robust Voltage Regulation Strategies
In this section, we elaborate on the two-stage distributionally robust voltage regulation strategies employed in the active distribution system with hybrid energy storage. The two stages are designed to cater to the diverse needs of voltage stability across different time scales, considering the uncertainties associated with renewable energy sources.
4.2.1 Day-Ahead Battery Energy Storage Optimization
The day-ahead stage focuses on the strategic allocation of battery energy storage to address voltage fluctuations anticipated based on photovoltaic (PV) power forecasts. A distributionally robust optimization model is formulated to minimize the overall operating cost and risk cost associated with the uncertainties in PV power output. Specifically, the model incorporates the construction of a Wasserstein uncertainty set, utilizing the limited samples available to approximate the true distribution of PV forecast errors.
The optimization objectives in this stage include maintaining node voltages within acceptable limits, maximizing renewable energy consumption, and minimizing battery degradation costs. Conditional Value at Risk (CVaR) is utilized to transform the opportunity constraints into convex and solvable forms, enabling the inclusion of voltage violation risks within the optimization framework.
By optimizing the charging and discharging schedules of battery energy storage systems and coordinating with PV curtailment and reactive power support from inverters, the day-ahead stage aims to provide a robust and cost-effective plan for voltage regulation.
4.2.2 Intra-Day Supercapacitor Optimization and Model Predictive Control
The intra-day stage further refines the voltage regulation strategies by leveraging the fast response capabilities of supercapacitors. The model predictive control (MPC) approach is employed to address the reduced but still significant uncertainties in PV power output at shorter time scales.
In this stage, the day-ahead battery storage schedules serve as constraints, while the MPC framework continuously updates the forecast errors within the prediction horizon. A rolling optimization model is formulated for supercapacitors, distributed PV systems, and power exchange with the main grid, aiming to optimize the actual dispatch outcomes in real-time.
The MPC framework operates in a receding horizon manner, optimizing the dispatch decisions over a fixed window of time. At each time step, the optimal decisions within the current window are implemented, and the window is shifted forward by one time interval before recalculating the optimization for the new window. This process ensures that the system can dynamically respond to unforeseen changes in PV output and load demands.
By integrating battery energy storage for long-term energy balancing and supercapacitors for short-term power balancing, the proposed two-stage distributionally robust voltage regulation strategy ensures voltage stability across diverse time scales and mitigates the impact of renewable energy uncertainties on the distribution network.
5. Case Study Analysis
5.1 Simulation Setup
To validate the effectiveness of the proposed two-stage distributionally robust voltage regulation strategy, a modified IEEE 37-bus test system is utilized. The system is augmented with distributed PV generation at 21 nodes, and real-world load and PV output data are employed to simulate the operation. The Wasserstein radii for day-ahead and intra-day PV forecast errors are set to 0.1 and 0.01, respectively, and a risk preference coefficient of p = 30 is adopted.
5.2 Day-Ahead Optimization Results
The battery energy storage schedules demonstrate a successful balance between charging during periods of excess PV generation and discharging during load peaks to alleviate voltage issues. The charging actions initiated at 9:00 AM effectively lower the voltages, while the discharging actions at 6:00 PM help to restore voltages, keeping them within the safe range of 0.95–1.02 p.u.
5.3 Intra-Day Optimization Results
The supercapacitors respond rapidly to instantaneous fluctuations in PV output, providing necessary support to maintain voltage stability. The inverter reactive power outputs are adjusted according to the location of PV installations, with more reactive power required at nodes further away from the point of common coupling. While some PV curtailment is necessary during peak generation hours, the overall renewable energy consumption is significantly improved compared to scenarios without energy storage.
6.Conclusion
This paper presents a two-stage distributionally robust voltage regulation strategy for active distribution systems incorporating hybrid energy storage. By leveraging the complementary characteristics of battery energy storage and supercapacitors, the proposed strategy effectively addresses voltage issues arising from high renewable energy penetration. The day-ahead optimization ensures a robust and cost-effective plan, while the intra-day MPC approach provides dynamic adjustment to unforeseen changes. The simulation results demonstrate the effectiveness of the proposed.