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Stochastic optimal scheduling of demand response-enabled microgrids with renewable generations: An analytical-heuristic approach
Yang Li, Kang Li, Zhen Yang, Yang Yu, Runnan Xu, Miaosen Yang
TL;DR
The paper addresses how isolated microgrids can coordinate demand response with uncertain PV and WT generation while balancing microgrid and user interests. It proposes a bi-level stochastic model solved by Jaya-IPM through real-time price and electricity-plan iteration, and reports improved economics, peak-load shaving, and computational efficiency against HIA and CPLEX.
Problem
The paper addresses limited prior coordination of demand response with multiple renewable-generation uncertainties from both microgrid and user perspectives.
Method
A bi-level stochastic model uses real-time pricing, with IPM solving the lower level, Jaya solving the upper level, and alternating iterations linking prices and user plans.
Results
The proposed method coordinates demand response and renewable uncertainty for peak-load shaving, while Jaya-IPM yields higher MG net revenue, lower user cost, and shorter calculation time than HIA and CPLEX.
Takeaways & Limitations
The approach provides a way to balance microgrid and user interests while mitigating renewable-generation uncertainty in isolated microgrid scheduling.
Takeaways & Limitations
The study does not consider ESS capacity losses or power-transmission losses and does not further examine participation and satisfaction across user types.
Abstract
from arXiv · showhide
In the context of transition towards cleaner and sustainable energy production, microgrids have become an effective way for tackling environmental pollution and energy crisis issues. With the increasing penetration of renewables, how to coordinate demand response and renewable generations is a critical and challenging issue in the field of microgrid scheduling. To this end, a bi-level scheduling model is put forward for isolated microgrids with consideration of multi-stakeholders in this paper, where the lower- and upper-level models respectively aim to the minimization of user cost and microgrid operational cost under real-time electricity pricing environments. In order to solve this model, this research combines Jaya algorithm and interior point method (IPM) to develop a hybrid analysis-heuristic solution method called Jaya-IPM, where the lower- and upper- levels are respectively addressed by the IPM and the Jaya, and the scheduling scheme is obtained via iterations between the two levels. After that, the real-time prices updated by the upper-level model and the electricity plans determined by the lower-level model will be alternately iterated between the upper- and lower- levels through the real-time pricing mechanism to obtain an optimal scheduling plan. The test results show that the proposed method can coordinate the uncertainty of renewable generations with demand response strategies, thereby achieving a balance between the interests of microgrid and users; and that by leveraging demand response, the flexibility of the load side can be fully exploited to achieve peak load shaving while maintaining the balance of supply and demand. In addition, the Jaya-IPM algorithm is proven to be superior to the traditional hybrid intelligent algorithm (HIA) and the CPLEX solver in terms of optimization results and calculation efficiency.
NOMENCLATURE
The nomenclature defines the paper’s microgrid, renewable-generation, demand-response, optimization, cost, storage, load, and scheduling symbols.
- MG and IMG denote microgrid and isolated microgrid, while RG and DR denote renewable generation and demand response.
- JAYA and IPM denote the Jaya algorithm and interior point method used in the solution approach.
- F1 represents microgrid cost, F2 represents user cost, and ωrt represents the real-time electricity price.
- The notation includes MT outputs, reserve, startup and state variables, together with ESS charge, discharge, capacity, voltage and efficiency quantities.
- Load notation distinguishes time-shiftable and non-time-shiftable power, movement amount, preset ratio, and discrete shifting step.
- Probabilistic sequences a, b, d and e represent PV, WT, load and equivalent-load outputs, respectively.
1. Introduction
The introduction motivates coordinating demand response with uncertain renewable generation in isolated microgrids and presents a multi-stakeholder bi-level stochastic approach. It positions the method against prior robust, stochastic, and demand-response scheduling studies.
- 1.1 Background: Renewable energy supports environmental objectives, decarbonization and operational flexibility, while isolated microgrids face renewable uncertainty without main-grid support.
- 1.1 Background: Coordinating demand response with uncertain renewable generations is identified as an important microgrid scheduling problem.
- 1.2 Literature review: Prior microgrid scheduling studies have used robust and stochastic programming to address renewable-generation uncertainties.
- 1.2 Literature review: Existing demand-response research has combined demand response with PV or WT uncertainty in separate scheduling studies.
- 1.3 Goals: The paper identifies limited prior work jointly treating multiple renewable uncertainties, demand response, and microgrid and user interests.
- 1.4 Contributions: The proposed contributions include a bi-level stochastic model, real-time pricing, sequence operation theory, and the Jaya-IPM solution approach.
2. The modeling of microgrid
The modeling framework represents uncertainty in solar irradiance, PV output, wind speed, WT output, load, and equivalent load. Equivalent load combines demand with renewable outputs to simplify stochastic scheduling.
- 2.2 Probabilistic model of photovoltaic: Solar irradiance is modeled with a Beta distribution using shape factors, maximum light intensity and actual light intensity.
- 2.2 Probabilistic model of photovoltaic: PV output is related linearly to solar irradiance, conversion efficiency and radiation area, so PV output also follows a Beta distribution.
- 2.3 Probabilistic model of wind turbine: Wind-speed uncertainty is modeled with a probability density function using shape factor, scale factor and actual wind speed.
- 2.3 Probabilistic model of wind turbine: WT power output is modeled as a function of wind speed using rated, cut-in and cut-off wind-speed parameters.
- 2.3 Probabilistic model of wind turbine: The probability density function of WT output is derived from the wind-speed model and WT power relationship.
- 2.4 Probabilistic model of load: Load fluctuations are represented with a normal distribution defined by load power, mean and standard deviation.
- 2.5 Equivalent load: Equivalent load is introduced to handle multiple random variables and is formulated as load power minus PV output plus WT output.PEL = PL − PPV + PWT.
3. Problem formulation
The problem formulation uses a bi-level model balancing microgrid and user interests under real-time pricing, with operational, balance, generation, storage and load-related constraints. The formulation includes microgrid costs, user costs, renewable uncertainty and storage feasibility requirements.
- 3. Problem formulation: The bi-level model minimizes user cost at the lower level and microgrid operational cost at the upper level, linked by real-time prices and user electricity plans.
- 3.1.1 Objective function: Microgrid operating cost includes ESS charging and discharging, micro-turbine operation, spinning reserves and startup costs.
- 3.1.1 Objective function: Micro-turbine cost terms use consumption coefficients, reserve and startup costs, state and startup variables, power output and spinning reserve.
- 3.1.2.1 System power balance constraint: System power balance must hold during scheduling and accounts for load shedding, predicted equivalent load and expected equivalent load.
- 3.1.2.2 Power constraint of micro-turbines: Micro-turbine output is bounded by minimum and maximum generation limits when units are in their operating states.
- 3.1.2.3 Constraints of energy storage systems: The ESS is modeled as a zinc-bromine flow battery because of its deeper discharge capacity, longer service life and lower use costs.
- 3.1.2.3 Constraints of energy storage systems: ESS state of charge evolves through charging and discharging efficiencies over each scheduling interval and must remain within capacity limits.
- 3.1.2.3 Constraints of energy storage systems: ESS constraints also limit charge and discharge power, reactive power, battery voltage, and equality between initial and remaining cycle energy.
0 Tend SOC SOC SOC (17)
The model represents renewable-generation uncertainty through spinning-reserve requirements, while demand response shifts flexible load under real-time prices. The pricing mechanism iterates user electricity plans and microgrid prices between the two optimization levels.
- Spinning reserve constraints: ESS and MT units jointly provide spinning reserves to compensate for discrepancies between equivalent load and expected renewable generation.The reserve formulation addresses supply-demand balance under renewable uncertainty.
- Spinning reserve constraints: Chance constraints balance reliability and economy by limiting reserve constraint-violation risks under rare extreme renewable-generation conditions.The paper notes that zero joint renewable output, such as no wind at night, would require costly reserves.
- Demand response model: User loads are divided into time-shiftable and non-shiftable categories, with the lower level minimizing electricity cost under real-time prices.The electricity-cost objective combines both load categories and the real-time price.
- Demand response model: Time-shiftable load preserves total equivalent-load energy, maintains a prescribed share of equivalent load, and remains within minimum and maximum power bounds.These constraints regulate load movement without changing total equivalent-load energy.
- Real-time pricing mechanism: The real-time pricing mechanism alternates lower-level load movement and upper-level price updates until the iterative process terminates.The initial price is the time-of-use price, and the resulting user plan is sent to the upper level.
4. Proposed solution methodology
The proposed methodology combines Jaya and IPM to solve the non-convex bi-level scheduling problem. It represents renewable and load uncertainty with discrete probability sequences derived from probability-density functions.
- Hybrid solution method: Jaya-IPM assigns IPM to the lower level and Jaya to the upper level, determining scheduling schemes through alternate iterations.The hybrid design combines analytic and heuristic methods to trade off solution speed and accuracy.
- Sequence operation theory: Sequence operation theory generates discrete probability sequences for PV, wind-turbine, and load power from discretized probability-density functions.PDF values are integrated over preset intervals, which become the probabilities of the corresponding output levels.
- Sequence operation theory: The PV-output probability sequence is formed by associating discretized PV-power intervals with their integrated probabilities.The resulting sequence provides a discrete representation of PV outputs for subsequent uncertainty calculations.
- Sequence operation theory: The method similarly constructs probabilistic sequences for wind-turbine output and load power before calculating their expected values.The expected values support the equivalent-load representation used in scheduling.
4.2 Handling of chance constraints
The chance-constraint treatment combines probabilistic sequences of renewable generation and load to represent equivalent-load uncertainty. It then converts the probabilistic reserve requirement into a deterministic equivalent using an auxiliary binary variable.
- Probabilistic equivalent load: PV and wind probabilistic sequences are combined through addition-type convolution to obtain the joint renewable-output sequence.The construction assumes PV output, wind output, and load power are independent.
- Probabilistic equivalent load: Subtraction-type convolution combines the joint renewable-output sequence with the load sequence to obtain the probabilistic sequence of equivalent load.The equivalent-load sequence captures uncertainty in the difference between load and renewable generation.
- Probabilistic equivalent load: The expected equivalent load is calculated by summing load-sequence values and subtracting PV and wind output contributions weighted by their probabilities.This calculation produces the expected value used in the scheduling formulation.
- Deterministic chance-constraint equivalent: An auxiliary binary variable is introduced to obtain a deterministic equivalent of the chance constraint.The transformation uses the probability associated with each possible equivalent-load level.
- Deterministic chance-constraint equivalent: The deterministic formulation requires reserve capacity to satisfy the target confidence level for all possible equivalent-load powers.The paper states that this formulation is equivalent to the original probabilistic reserve constraint.
4.3 Jaya algorithm
The Jaya algorithm updates candidate solutions toward the best solution and away from the worst solution without algorithm-specific control parameters. The implementation uses mixed real-integer coding for the scheduling variables.
- Jaya algorithm principle: Jaya moves each candidate toward the best solution and away from the worst solution during optimization.The update uses random factors for the best- and worst-solution directions.
- Jaya algorithm principle: A newly generated candidate is accepted when it produces a better solution.This acceptance rule governs the update process after candidate construction.
- Coding scheme: The implementation uses real-integer coding, with continuous variables for generation, reserve, equivalent-load, price, and storage decisions and discrete variables for unit states and start-up decisions.The initial population is randomly generated across the feasible domain.
4.4 Interior point method
The interior point method solves the lower-level linear programming subproblem by iteratively reducing the primal-dual gap until a near-optimal solution is obtained.
- IPM is selected for the lower-level subproblem because its linear programming structure suits the primal-dual method.
- The primal optimization variable x represents the power of the time-shiftable load, while y and z are dual-problem variables.
- The algorithm begins by choosing an initial feasible solution and calculating its dual gap.
- When the dual gap falls below ε=10^-5, the current solution is accepted as optimal or near-optimal; otherwise, the solution is updated iteratively.
4.5 Determination of the final scheme
The final scheduling scheme is selected by jointly evaluating microgrid and user interests across the iterative bi-level solution process.
- The joint optimization objective determines the final scheduling scheme from the solutions generated by the bi-level model.
- The objective combines differences between joint and independent operation for microgrid net operating cost and user cost.
- Joint operation accounts for both microgrid and user interests, whereas independent operation represents cases emphasizing one stakeholder objective.
- The scheme with the smallest joint objective is selected as the final scheme.
- The overall procedure alternates upper-level Jaya optimization and lower-level IPM optimization through updated prices and user electricity plans.
5. Case study
The case study evaluates the proposed scheduling approach on an isolated microgrid with renewable generation, storage, dispatchable units, and flexible loads. Results examine stakeholder costs, pricing, uncertainty, demand response, and computational performance.
- Test system: The test system contains three microturbines, one wind turbine, one photovoltaic panel, one energy storage system, and shiftable and non-shiftable loads.
- Simulation scenario: The simulation scenarios combine load power, renewable-generation outputs, and equivalent-load power for subsequent scheduling analysis.
- Economic cost analysis: The three strategies separately prioritize microgrid interests, jointly coordinate microgrid and user interests, or prioritize user interests.
- Economic cost analysis: Under the stated test settings, Strategy 2 reduces user electricity cost and increases microgrid net revenues relative to Strategies 1 and 3.
- Pricing and demand response: The real-time pricing mechanism produces a smoother final price curve than the initial real-time price and achieves peak-load shaving relative to time-of-use pricing.
- Uncertainty analysis: Higher confidence levels increase microgrid operating cost and reserve-related reliability while reducing economic performance, creating a reliability-economy trade-off.
- Demand response: Demand response shifts time-shiftable loads away from peak periods toward off-peak periods, supporting peak-load shaving and supply-demand balance.
- Comparison with other solution methods: Compared with HIA and CPLEX, Jaya-IPM raises microgrid net revenue by 10.9% and 11.9%, lowers user cost by 6.1% and 7.7%, and reduces calculation time by about 90% and 60%, respectively.
6. Conclusion
The proposed approach coordinates demand response with uncertain renewable generation, reducing peak demand while improving renewable utilization and balancing stakeholder interests. Jaya-IPM achieves favorable economic and computational results, although the study omits ESS capacity degradation, transmission losses, and differentiated user participation or satisfaction.
- Demand response and renewable generation coordination achieves peak load shaving in microgrid scheduling.Reduced peak-period demand lowers spinning reserves needed for renewable uncertainty, while increased off-peak demand consumes more renewable output.
- Jaya-IPM solves the proposed scheduling model accurately and quickly.The hybrid method combines the reported scheduling performance with improved computational efficiency relative to HIA and CPLEX.
- 10.9% and 11.9% higher MG net revenue are achieved than HIA and CPLEX, respectively.User cost is 6.1% and 7.7% lower, while calculation time decreases by about 90% and 60% compared with HIA and CPLEX.
- Coordinating demand response with uncertain renewable generations guides user participation and mitigates renewable-generation uncertainty effects.The authors connect these results with promoting low-carbon transition toward sustainable production.
- The study does not consider ESS capacity losses or power-supply transmission losses.It also does not further examine participation and satisfaction among different user types using demand response strategies.
- Future work could introduce game-theory-based demand response and privacy-preserving energy scheduling.The authors also propose extending the method to multi-objective energy management under uncertain renewable generation.