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Joint Planning of Distributed Generations and Energy Storage in Active Distribution Networks: A Bi-Level Programming Approach
Yang Li, Bo Feng, Bin Wang, Shuchao Sun
TL;DR
The paper addresses joint planning of distributed generation and energy storage under renewable-output uncertainty in active distribution networks. It proposes a bi-level model with an IBPSO-based solution, reporting reduced planning deviation and improved voltage profile and operational economy on the PG & E 69-bus system.
Problem
Renewable-output uncertainty complicates separate planning of distributed generation and energy storage, motivating a coordinated approach for active distribution networks.
Method
A bi-level programming model jointly optimizes DG and storage location and capacity at the upper level and storage operation at the lower level, solved using chaos-optimization-based IBPSO.
Results
The proposed approach reduces planning deviation caused by DG-output uncertainty and improves distribution-system voltage profile and operational economy.
Takeaways & Limitations
Joint DG-storage planning coordinates investment decisions with storage operation, supporting more stable and economically favorable distribution-network planning.
Takeaways & Limitations
The study models renewable-generation uncertainty with specified probability distributions and identifies deep-generative scenario modeling as a more realistic future direction; island operation is also left for future study.
Abstract
from arXiv · showhide
In order to improve the penetration of renewable energy resources for distribution networks, a joint planning model of distributed generations (DGs) and energy storage is proposed for an active distribution network by using a bi-level programming approach in this paper. In this model, the upper-level aims to seek the optimal location and capacity of DGs and energy storage, while the lower-level optimizes the operation of energy storage devices. To solve this model, an improved binary particle swarm optimization (IBPSO) algorithm based on chaos optimization is developed, and the optimal joint planning is achieved through alternating iterations between the two levels. The simulation results on the PG & E 69-bus distribution system demonstrate that the presented approach manages to reduce the planning deviation caused by the uncertainties of DG outputs and remarkably improve the voltage profile and operational economy of distribution systems.
1. INTRODUCTION
The paper motivates jointly planning distributed generation and energy storage to manage DG uncertainty while improving active distribution network performance. It positions bi-level planning as a way to coordinate investment decisions with storage operation.
- DG integration can bring economic and environmental benefits but creates operational challenges such as power flow reversal.
- Unreasonable DG locations or capacities may increase line losses, cause voltage deviations, and reduce distribution-system economic efficiency.
- DG output uncertainty makes traditional planning prone to considerable planning errors, motivating explicit uncertainty modeling.
- Planning DGs before storage prevents the two resources from cooperating and constraining one another to achieve maximum economic benefits.
- The proposed contribution plans DGs and storage simultaneously and uses bi-level programming to connect their locations and capacities with storage operation.
particle swarm optimization algorithm
The paper organizes its presentation from uncertainty modeling through joint planning and solution procedures to case studies and conclusions.
- Section 2 presents uncertainty modeling for distributed-generation outputs.
- Section 3 describes the joint planning model, while Section 4 details the model solution process.
- Section 5 evaluates the approach on the PG & E 69-bus distribution system before Section 6 gives the conclusions.
2. UNCERTAINTY MODELING of DGs
The paper models wind and photovoltaic uncertainty probabilistically, converts continuous distributions into sequences, and derives hourly expected DG outputs for planning.
- 2.1 Probabilistic WT Model: Wind-speed uncertainty is modeled with a Weibull distribution whose shape and scale factors characterize its probability density.
- 2.2 Probabilistic PV Model: PV output depends on solar irradiance, ambient temperature, and PV-module characteristics, with irradiance represented using a Beta distribution.
- 2.2 Probabilistic PV Model: PV output is linear with solar irradiance and is calculated from irradiance, maximum-power-point tracking, radiation area, conversion efficiency, and incident angle.
- 2.3 Sequence Operation Theory: Sequence operation theory discretizes continuous random variables into probabilistic sequences and combines them through addition-type and subtraction-type convolution operations.
- 2.3.2 Sequence Description of Intermittent DG Outputs: Using a 24-hour planning interval and representative seasonal hours, the method obtains hourly expected outputs for wind turbines and photovoltaic generation.
3. Joint planning model
The proposed bi-level model jointly plans DGs and energy storage while coordinating investment decisions with intraday storage operation. The upper level minimizes annual cost, and the lower level optimizes seasonal daily storage scheduling under distribution-network constraints.
- 3.1 Bi-level programming theory: Upper- and lower-level models exchange installation decisions and optimized operating cost through hierarchical feedback.The upper level passes x to the lower level, which returns its optimal objective value v.
- 3.3 Lower-level model: The lower level uses upper-level installation decisions to optimize intraday energy-storage charging and discharging for annual fluctuating operation cost.Scheduling is performed across representative days for four seasons.
- 3.2 Upper-level model: The upper level optimizes DG and energy-storage locations and capacities to minimize annual cost.Annual cost includes equipment investment, operation and maintenance, and grid power-purchase costs.
- 3.2 Upper-level model: The annual objective combines investment, operation and maintenance, and power-purchase costs, with storage operation affecting losses and grid purchases.Storage charging and discharging are priced through time-of-use electricity costs.
- 3.3 Lower-level model: The lower-level network model uses forward-backward sweep power flow for a radial ADN with bidirectional power flow.Voltage and branch-current limits are included as technical constraints.
4 Model solution
The paper solves the bi-level planning problem with an improved binary particle swarm optimization algorithm enhanced by chaos optimization. The algorithm monitors population diversity and alternates upper- and lower-level optimization until termination.
- 4 Model solution: IBPSO solves the upper- and lower-level models while transmitting global planning and operation solutions between levels.Alternating iterations ultimately produce the DG allocation.
- 4.1 Binary particle swarm optimization algorithm: Original BPSO represents particle positions with binary values, while velocities encode the probability of each bit taking value 0 or 1.A sigmoid transfer function converts real-valued velocities into probabilities for position updates.
- 4.2 Proposed IBPSO algorithm: The proposed dynamic monitoring mechanism detects premature convergence using population fitness variance and activates chaos optimization to maintain population diversity.Optimization variables are mapped into chaotic variables when premature convergence occurs.
- 4.2 Proposed IBPSO algorithm: A Tent map is selected as the chaos map, with random perturbations applied when periodic or fixed points occur.The perturbations re-enter the chaotic state.
- 4.3 Solving process: The solution process passes upper-level DG and storage positions and capacities to lower-level scheduling, returns operating cost, updates particles, and checks termination.The lower level evaluates four-season, 24-hour operation before the upper-level objective and constraints are recalculated.
5 Case studies
The case studies evaluate the bi-level joint planning model on the PG & E 69-bus system under four DG and storage scenarios. Results indicate economic, operational, voltage, and algorithmic benefits, while the study identifies scope boundaries for storage capacity and uncertainty modeling.
- Parameter settings: The PG & E 69-bus system has a 12.66 kV voltage level, 3715 kW total active load, and 2300 kVar total reactive load.The IBPSO setup uses 50 particles and 100 maximum iterations.
- Scenario design: The four scenarios compare a traditional network with joint WT, PV, and storage planning, joint WT and storage planning, and joint PV and storage planning.DG capacity is limited to 30% of total load and storage capacity to 10%.
- Economic comparison: Scenario 1 has the highest total cost, indicating that DG planning considering time-of-use electricity prices improves economic benefit.Scenario 3 has the largest DG capacity, smallest storage capacity, and least cost; Scenario 4 has the highest cost among the renewable-generation configurations.
- Economic comparison: Wind turbines provide stronger economic benefits than photovoltaic units because of lower investment and operating costs and longer effective working time.Photovoltaic units require more energy storage capacity because they operate only during periods of light.
- Intraday operation: Storage charges or remains idle from 0:00–17:00 and discharges from 18:00–23:00, matching low- and high-electricity-price periods.Distributed generation lowers active network losses during the common wind and photovoltaic output period.
- Algorithm and model comparison: IBPSO achieves lower total cost than Tabu search and BPSO and reduces calculation duration by 6~10%, while the bi-level model outperforms the centralized version in each cost component and total cost.The joint planning model also improves voltage relative to separate DG planning, and storage operation alleviates DG-induced fluctuation while supporting peak shaving and network-loss reduction.