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Optimal Scheduling of an Isolated Microgrid with Battery Storage Considering Load and Renewable Generation Uncertainties
Yang Li, Zhen Yang, Guoqing Li, Dongbo Zhao, Wei Tian
TL;DR
The paper addresses isolated-MG scheduling under uncertain load and renewable generation, where spinning reserves and main-grid support are limited. It proposes a chance-constrained model using ESS reserves and DST to transform the problem into MILP. On the modified ORNL DECC lab MG system, the approach outperforms HIA with more stable results and substantially less computation.
Problem
Isolated MG scheduling must manage uncertain load and renewable generation, while prior work gives limited attention to ESS-provided reserves and faces difficult chance-constraint transformations.
Method
The paper combines chance-constrained scheduling, ESS spinning reserves, and DST-based deterministic transformation into a MILP solved with CPLEX.
Results
The proposed approach achieves lower operation cost, shorter computation time, and more stable optimization results than HIA in the reported MG scheduling comparison.
Takeaways & Limitations
Proper confidence levels can balance isolated-MG reliability and economy while ESS participates in spinning-reserve provision.
Abstract
from arXiv · showhide
By modeling the uncertainty of spinning reserves provided by energy storage with probabilistic constraints, a new optimal scheduling mode is proposed for minimizing the operating costs of an isolated microgrid (MG) by using chance-constrained programming. The model is transformed into a readily solvable mixed integer linear programming (MILP) formulation in GAMS via a proposed discretized step transformation (DST) approach and finally solved by applying the CPLEX solver. By properly setting the confidence levels of the spinning reserve probability constraints, the MG operation can be achieved a trade-off between reliability and economy. The test results on the modified ORNL DECC lab MG test system reveal that the proposal significantly exceeds the commonly used hybrid intelligent algorithm with much better and more stable optimization results and significantly reduced calculation times.
I. INTRODUCTION
Isolated microgrids must schedule generation, storage, and loads despite uncertain renewable output and demand, while maintaining reliability without main-grid support. The paper proposes chance-constrained scheduling that uses ESS spinning reserves and DST to obtain a solvable MILP formulation.
- Isolated MG scheduling is vulnerable to uncertain load and renewable generation, making operation reliability and supply security difficult to guarantee.
- Existing approaches include MPC, robust programming, stochastic programming, and CCP, but each faces formulation, conservatism, distribution, or transformation challenges.Robust programming hedges against worst-case realizations, while stochastic programming requires known or estimable probability distributions.
- DST discretizes continuous random variables into probabilistic sequences and combines them through sequence operations to handle multiple uncertainties.This approach avoids requiring the inverse CDF when transforming chance constraints into deterministic equivalents.
- The proposed model uses ESS alongside microturbines to provide spinning reserves and represents reserve uncertainty with probabilistic constraints.The reserve probability constraints allow confidence levels to mediate reliability and economy.
- Tests on the modified ORNL DECC lab MG system report more stable optimization results and significantly reduced computation compared with HIA.The proposed approach also obtains lower operation cost and shorter computation time than HIA in the reported comparison.
- Wind uncertainty is modeled through wind-speed distributions and the relationship between wind speed and turbine power output.The passages identify the Weibull distribution for wind speeds and cut-in, rated, and cut-out operating points for turbine output.
B. Probabilistic PV Model
The probabilistic PV model represents solar irradiance with a Beta distribution and relates irradiance to photovoltaic output. PV output depends on irradiance, temperature, module characteristics, and conversion parameters.
- PV output depends on solar irradiance, ambient temperature, and the characteristics of the PV module.
- Solar irradiance for each hour is modeled with a Beta distribution defined over the interval (0, 1).The distribution uses shape factors and the Gamma function in its probability density formulation.
- The PV-output relationship uses solar irradiance, maximum-power-point tracking, radiation area, conversion efficiency, and solar incident angle.
- Because PV output is linear with solar irradiance, the output is generally modeled with a Beta distribution.The passage distinguishes PV output from its maximum value through the normalized output formulation.
C. Probabilistic Load Injection Model
The load model represents load fluctuations with a normal distribution and defines equivalent load as demand minus joint wind and photovoltaic output. Discretized probabilistic sequences support subsequent uncertainty operations.
- Load fluctuations are modeled with a normal distribution described by the load active-power mean and standard deviation.
- Equivalent load is defined as load power minus the joint power output of wind turbines and photovoltaics.This combines load and renewable-generation uncertainty into one power quantity.
- Continuous random variables are discretized into probabilistic sequences using a given discrete step and their respective probability density functions.
- Sequence operations generate new probabilistic sequences through mutual operations on discretized sequences.The supplied passage introduces sequence operations as the basis for combining uncertain quantities.
- Addition-type convolution and subtraction-type convolution are defined for operating on two discrete sequences.
B. Sequence Description of Intermittent DG Outputs
The model describes intermittent-generation, load, storage, and reserve behavior for isolated microgrid scheduling. It combines deterministic operating constraints with probabilistic reserve requirements to balance power adequacy, reliability, and cost.
- Objective Function: The microgrid objective includes fuel costs, spinning-reserve costs, and battery charge-discharge costs.
- Constraint Conditions: The scheduling model includes a power-balance constraint and controllable loads to avoid renewable oversupply.
- Constraint Conditions: Microturbine outputs are bounded by minimum and maximum limits when the units are committed.
- ESS Constraints: Battery energy evolves from charging and discharging while respecting efficiency, rate, capacity, and cycle-end constraints.The scheduling cycle is set to 24h, and the ending stored energy equals the initial stored energy.
- Spinning Reserve Constraints: In isolated microgrids, spinning reserves from microturbines and energy storage compensate for fluctuating equivalent-load power relative to its expected value.
- Spinning Reserve Constraints: Reserve requirements are modeled probabilistically because extreme low-renewable cases require costly capacity despite having very low occurrence probability.
V. SOLUTION METHODOLOGY
The methodology converts the proposed microgrid scheduling model into a mixed integer linear programming formulation using discretized step transformation, then solves it with CPLEX in GAMS.
- The proposed model is converted into a mixed integer linear programming formulation using DST and solved by a CPLEX solver in GAMS.
A. Model Conversion
The conversion method discretizes uncertain power distributions into probabilistic sequences, combines them through sequence operations, and replaces chance constraints with deterministic MILP-compatible constraints. This avoids directly determining a complex inverse cumulative distribution function.
- Probabilistic Sequence of Equivalent Load Power: Equivalent-load power sequences are calculated by subtraction-type convolution from load and renewable probabilistic sequences.
- Sequence operations discretize random-variable distributions because inverse-transform determination is difficult for the complex probability-density functions and may yield multiple solutions.
- Wind and photovoltaic uncertainties are assumed independent, and their joint output sequence is obtained through addition-type convolution.
- Probabilistic Sequence of Equivalent Load Power: A discretized step q maps each equivalent-load power level u_eq q to a corresponding probability in the probabilistic sequence.
- Deterministic Transformation of Chance Constraints: A binary variable W_e,t indicates whether the available reserve meets the reserve requirement for a possible equivalent-load output.
- Deterministic Transformation of Chance Constraints: The chance constraint requires the reserve condition to hold with confidence level α across possible equivalent-load outputs.
- Deterministic Transformation of Chance Constraints: Replacing the original chance constraint with the derived deterministic relations transforms the CCP-based model into a readily solvable MILP formulation.
B. Solving Process
The proposed DST solution process models microgrid uncertainties, transforms chance constraints into deterministic equivalents, and produces a MILP solved in GAMS with CPLEX.
- The process first models microgrid uncertainties and formulates the optimal scheduling problem using chance-constrained programming.
- WT, PV, and load outputs are discretized into probabilistic sequences, then combined into an equivalent-load sequence through sequence operations.
- The DST transforms chance constraints into deterministic equivalents and obtains a mixed integer linear programming formulation.
- The transformed model is defined in GAMS and solved using CPLEX’s branch-and-bound algorithm.
- If termination criteria are not met, the process updates the confidence level and load before repeating the solution steps; otherwise, it outputs the optimal scheduling scheme.
VI. CASE STUDY
The case study evaluates the proposed approach on a modified ORNL DECC lab microgrid test system using a specified PC simulation platform.
- The proposed approach is tested on a modified Oak Ridge National Laboratory Distributed Energy Control and Communication lab microgrid test system.
- Simulations use a PC with two 2.4 GHz Intel Core dual-core CPUs and 6 GB RAM.
A. Introduction of the Test system
The test system contains wind, photovoltaic, microturbine, and battery resources, with stated generation, storage, efficiency, load, and charge-discharge parameters.
- The modified system comprises a wind-turbine unit, photovoltaic panel, three microturbine units, and a battery pack.
- The battery’s maximum charge and discharge powers are both 40 kW, with state-of-charge limits of 32 and 160 kWh.
- The battery charge and discharge efficiencies are both 0.9, with charge and discharge prices of $0.3/kWh and $0.5/kWh, respectively.
B. Analysis and Discussion
The experiments examine confidence levels, ESS costs and parameters, spinning-reserve allocation, load fluctuations, and DST step size, revealing trade-offs among cost, reliability, accuracy, and computation time.
- Effect of ESS Charge-discharge Costs: When charge price exceeds discharge price, the system absorbs more ESS power for regulation and load-fluctuation stabilization.
- Spinning Reserves under Different Confidence Levels: A 90% confidence level requires 35–40 kW of reserve during joint WT-PV operation, while WT-only operation requires more reserve capacity.
- Spinning Reserves under Different Confidence Levels: Increasing confidence levels requires more spinning reserve capacity and raises operating costs, creating a reliability–economy trade-off.
- Spinning Reserves under Different Confidence Levels: ESS reserve provision generally exceeds MT provision because ESS has lower costs and faster response, with MTs used when ESS dump energy is insufficient.
- Influence of ESS Parameters: At fixed confidence levels, operation costs decrease monotonically as ESS charge-discharge power and energy-storage capacity increase.
- Impact of Load Fluctuations: At fixed confidence levels, higher load fluctuations increase operation costs because more spinning reserves are needed to maintain supply-demand balance.
- Influence of Discrete Steps: DST step sizes below 3 kW reduce optimization sensitivity but sharply increase computation time, whereas sizes above 4 kW produce large optimal-result gaps; 3–4 kW is appropriate here.
C. Comparison with Hybrid Intelligent Algorithm
The proposed approach is compared with HIA on the isolated MG scheduling model, showing lower operation costs and much shorter computation times. Its computational advantage persists as confidence levels increase, while HIA time rises substantially.
- The proposed approach yields lower operation costs than HIA for the proposed isolated MG scheduling model.
- As confidence levels increase, HIA computation time rises dramatically, whereas the proposed approach remains basically unchanged across the studied cases.The comparison uses α=95% and discrete step size q=2.5 kW, with HIA results averaged over 20 runs.
- Testing on the modified ORNL DECC lab MG system reports more stable solutions and significantly reduced computation compared with HIA.
- Future work targets multi-timescale scheduling by integrating day-ahead and real-time scheduling sub-models.