Source-linked AI summary
Optimal scheduling of isolated microgrid with an electric vehicle battery swapping station in multi-stakeholder scenarios: a bi-level programming approach via real-time pricing
Yang Li, Zhen Yang, Guoqing Li, Yunfei Mu, Dongbo Zhao, Chen Chen, Bo Shen
TL;DR
The paper addresses IMG–BSS scheduling when the BSS is an independent stakeholder whose interests are not represented by prior centrally controlled schemes. It proposes a bi-level real-time-pricing model solved by JAYA-BBA, and reports reduced IMG cost and increased BSS profit.
Problem
Prior work on MG scheduling with BSSs is limited and generally controls BSS charge-discharge decisions without considering BSS interests.
Method
A bi-level model minimizes IMG net cost at the upper level and maximizes BSS profit at the lower level, with JAYA and BBA solved through alternating iterations.
Results
3.16% IMG net-cost reduction and 5.36% BSS-profit increase are reported after introducing real-time pricing in Case 2 versus Case 1.
Takeaways & Limitations
The proposed real-time pricing mechanism coordinates IMG and BSS economics in a reported win-win situation.
Takeaways & Limitations
The study uses day-ahead scheduling and simplified battery-life treatment, with future work targeting multi-timescale scheduling, cycle-life calculation, and uncertainty correlations.
Abstract
from arXiv · showhide
In order to coordinate the scheduling problem between an isolated microgrid (IMG) and electric vehicle battery swapping stations (BSSs) in multi-stakeholder scenarios, a new bi-level optimal scheduling model is proposed for promoting the participation of BSSs in regulating the IMG economic operation. In this model, the upper-level sub-problem is formulated to minimize the IMG net costs, while the lower-level aims to maximize the profits of the BSS under real-time pricing environments determined by demand responses in the upper-level decision. To solve the model, a hybrid algorithm, called JAYA-BBA, is put forward by combining a real/integer-coded JAYA algorithm and the branch and bound algorithm (BBA), in which the JAYA and BBA are respectively employed to address the upper- and lower- level sub-problems, and the bi-level model is eventually solved through alternate iterations between the two levels. The simulation results on a microgrid test system verify the effectiveness and superiority of the presented approach.
1. Introduction
Existing work has rarely addressed integrated IMG–BSS scheduling while accounting for the BSS as an independent stakeholder. This paper proposes a bi-level, demand-response-based real-time pricing model and solves it with JAYA-BBA.
- 1.1 Literature review: Only a few studies have examined scheduling an MG incorporating BSSs.
- 1.1 Literature review: Earlier models generally let the MG control center determine BSS charge-discharge decisions without considering BSS interests.
- 1.1 Literature review: A new bi-level day-ahead model coordinates IMG and BSS scheduling in a multi-stakeholder setting.
- 1.1 Literature review: The proposed pricing mechanism uses demand responses to reflect dynamic supply-demand relationships between the IMG and BSS.
- 1.1 Literature review: JAYA solves the IMG upper level, BBA solves the BSS lower level, and alternating iterations solve the overall bi-level model.
- 1.1 Literature review: Simulations on a modified ORNL DECC lab microgrid test system verify the approach's effectiveness and superiority.
2. The model of MG
The model represents uncertain renewable generation, load, and EV arrivals probabilistically, then uses an equivalent load and BSS operating assumptions to describe IMG conditions and BSS interactions.
- 2.1 Probabilistic WT Model: Wind speed is modeled with a Weibull distribution, with wind-site correlations considered in probabilistic system analysis.
- 2.2 Probabilistic PV Model: PV output is modeled from solar irradiance using a Beta distribution and a linear irradiance-to-output relationship.
- 2.3 Probabilistic load injection model: Load fluctuations are represented with a normal distribution using the load's mean and standard deviation.
- 2.4 Equivalent Load Model: Equivalent load equals load power minus the joint WT and PV output, incorporating source and load uncertainty into one quantity.
- 2.5 BSS operations: The BSS charges batteries from the IMG during low-priced periods and discharges to the IMG during high-price periods while providing reserve capacity.
- 2.6 Arrival time of EVs: EV arrivals at the BSS during each period are modeled with a Poisson distribution parameterized by the arrival rate.
3. Problem formulation
The formulation is bi-level: the upper level models IMG operation, while the lower level models BSS operation under real-time prices determined through upper-level demand responses.
- 3. Problem formulation: The upper-level sub-problem models IMG operation, and the lower-level sub-problem formulates BSS operation under upper-level-determined real-time pricing.
3.1 Real-time-pricing mechanism
The mechanism sets BSS–IMG electricity prices from dynamic supply-demand relationships and distinguishes energy trading from reserve provision. BSS charging and discharging feed back into upper-level pricing decisions.
- Pricing principles: Real-time prices depend on the system’s overall load level, defined as equivalent IMG load plus electricity traded with the BSS.Prices exceed the reference price when overall load is higher than equivalent load and fall below it otherwise.
- Pricing principles: When the BSS provides spinning reserve without electricity trading, the IMG pays it reserve-service fees.In this operating mode, the BSS neither buys nor sells electricity to the IMG.
- Pricing procedure: The mechanism first obtains equivalent load, then optimizes the BSS charge-discharge scheme, and finally determines real-time electricity prices.The BSS scheme is fed back to the upper level before pricing is calculated.
- Pricing formula: The real-time price is calculated relative to a constant reference price and the BSS–IMG exchange state.The referenced formulation uses the BSS operating state and equivalent-load quantities to determine the price.
- BSS operating state: The BSS–IMG traded quantity is positive during charging and negative during discharging, while a binary state variable distinguishes exchange from reserve provision.The state variable is one for charge-discharge operation and zero when the BSS provides reserve capacity.
3.2 Upper-level sub-problem
The upper-level sub-problem minimizes IMG net cost while coordinating generation, controllable load, BSS exchange, and reserve under uncertain renewable generation and load.
- Objective function: IMG net cost includes charge-discharge, spinning-reserve, microturbine fuel, startup, and BSS reserve-provision costs.The upper-level objective minimizes these cost components over the scheduling horizon.
- Objective function: The scheduling horizon contains T=24 hourly periods, with microturbine state and startup variables included in the objective.Microturbine consumption factors, reserve costs, startup costs, output power, and spinning reserve are represented in the formulation.
- Power balance: IMG power balance incorporates microturbine output, renewable generation, BSS charging or discharging, predicted equivalent load, and controllable-load output.BSS charging and discharging powers are treated collectively as exchanging powers.
- Operating constraints: Microturbine output must remain between its minimum and maximum allowable levels whenever the unit is operating.The corresponding inequality constrains each microturbine during every scheduling period.
- Reserve constraints: Spinning reserve from microturbines is bounded by unused generation capacity and compensates for deviations between fluctuating equivalent load and its expected value.The study requires reserve to address uncertainty from renewable sources, original load, and BSS swap demand.
- Reserve constraints: The reserve requirement is imposed probabilistically at a pre-given confidence level α and may include reserve supplied by the BSS.The constraint compares available reserve with renewable, load, and equivalent-load deviations.
3.3 Lower-level sub-problem
The lower-level sub-problem maximizes BSS profit while enforcing battery capacity, power, reserve, battery-count, operating-state, and cycle constraints.
- Objective function: BSS profit combines charge-discharge costs, swapping income, battery depreciation costs, and reserve income.The lower-level objective maximizes total profit across the scheduling horizon.
- Objective function: Battery depreciation is represented through a charge-discharge process coefficient and each battery’s rated capacity.Swap income depends on arriving EVs and the BSS swap price.
- Capacity dynamics: BSS capacity evolves from charging and discharging powers while accounting for separate charge and discharge efficiencies.The charge-discharge equation links available capacity in periods t and t+1.
- Capacity constraints: The BSS minimum capacity is assumed to equal 20% of total capacity, below which the BSS does not operate.Capacity is also constrained to remain within minimum and maximum limits throughout the scheduling cycle.
- Power constraints: BSS charging power is constrained using initial capacity, charge power, discharge power, and efficiency terms to keep capacity within its allowable range.The constraint is intended to preserve feasible capacity over the entire scheduling cycle.
- Reserve constraint: Reserve supplied by the BSS cannot exceed its available capacity after accounting for discharge efficiency.The reserve constraint applies during periods when the BSS provides reserve capacity to the IMG.
- Battery constraints: Battery-count constraints balance full, empty, charging, and discharging batteries while limiting active batteries to available BSS charge-discharge positions.Additional constraints bound battery capacity and the number of charge-discharge cycles.
- Battery constraints: The number of battery charge-discharge cycles is limited by a pre-given maximum over the complete IMG scheduling cycle.The limit addresses battery lifetime concerns associated with frequent cycling.
4. Solution methodology
The solution methodology combines probabilistic-sequence modeling with the JAYA-BBA hybrid algorithm for the NP-hard bi-level scheduling problem.
- JAYA-BBA algorithm: JAYA-BBA uses JAYA for the upper-level IMG scheduling problem and BBA for the lower-level BSS scheduling problem.The two levels are connected through real-time prices and BSS charge-discharge schemes, with alternate iterations solving the bi-level model.
- Uncertainty representation: Sequence operation theory represents random power-system variables as probabilistic sequences and derives new distributions through sequence operations.The method is based on sequence convolution and operations between discrete probability sequences.
- Uncertainty representation: Wind, photovoltaic, and load variables are discretized into probabilistic sequences for representing source- and load-side uncertainty.The wind-output sequence length is determined from maximum output and the discrete step size q.
- Uncertainty representation: Table 1 organizes wind-turbine output values by power levels and pairs them with corresponding probabilities.The table describes the wind outputs and their probabilistic sequence.
- Uncertainty representation: The probabilistic sequence of wind-turbine output is calculated from its probability density function.The formulation maps wind-output values to their associated sequence probabilities.
4.2 Treatment of chance constraints
The chance constraint is converted into a deterministic form by representing equivalent-load uncertainty with probabilistic sequences and a binary reserve-feasibility variable.
- The equivalent-load power is represented by a probabilistic sequence with discrete step size q and length N_e,t.
- A new 0-1 variable W is introduced to transform the chance constraint into deterministic form.
- W is set to 1 exactly when available spinning reserve meets the difference between equivalent-load power and its expected value.
- The probability associated with each possible equivalent-load value is taken from the probabilistic sequence, enabling simplification of the original chance constraint.
- The resulting deterministic constraint ensures that the required confidence level α is met across all possible equivalent-load outputs.
4.3 JAYA algorithm
JAYA updates candidate solutions toward the best and away from the worst, using a hybrid real/integer encoding for the scheduling variables.
- JAYA modifies each candidate by moving it toward the best solution while avoiding the worst solution.
- The update uses two random numbers for each variable, both drawn from the range [0, 1].
- A candidate update is accepted when it gives a better function value.
- Continuous variables include microturbine outputs and reserves, BSS reserve capacity, and traded electricity.
- Discrete variables include microturbine and BSS states, startup status, and BSS charge-discharge powers.
4.4 Branch and bound algorithm
The solution methodology combines branch-and-bound search for BSS scheduling with iterative IMG–BSS coordination and a joint objective for selecting the final scheme.
- 4.4 Branch and bound algorithm: BBA begins with a heuristic solution, records its objective as an upper bound, and searches partial solutions in a queue.
- 4.4 Branch and bound algorithm: The joint objective selects among bi-level scheduling schemes by combining IMG cost and BSS profit changes under joint optimization.
- 4.4 Branch and bound algorithm: The upper-level IMG model is solved after deterministic chance-constraint conversion and real-time price generation.
- 4.4 Branch and bound algorithm: The lower-level BSS model uses BBA to optimize charge-discharge scheduling under the current real-time price.
- 4.4 Branch and bound algorithm: The final scheme minimizes F_JO and outputs IMG and BSS schedules simultaneously.
5. Case study
The case study evaluates the proposed scheduling approach on a modified ORNL DECC microgrid with renewable generation, microturbines, load uncertainty, and an EV battery swapping station. Results compare independent and joint optimization, showing economic gains and smoother microturbine operation with real-time pricing.
- 5.1 Introduction of the test system: The test system contains a wind turbine, photovoltaic panel, three microturbines, and a BSS.
- 5.2.1 Outputs of DGs and load: The analysis uses expected distributed-generation and load outputs derived from probabilistic models as inputs for subsequent case studies.
- 5.2.2 Swap demand of EVs: EV swap demand is modeled as random and further increases the uncertainty faced by IMG operation.
- 5.3 Independent optimization analysis of IMG and BSS: The three strategies are IMG-independent optimization, joint optimization, and BSS-independent optimization, evaluated with a 2.5 kW step, 90% confidence level, and 10% load fluctuation.
- 5.3.1 Independent optimization analysis of IMG and BSS: Under joint optimization, real-time pricing allows BSS charging to offset IMG operating costs while increasing BSS profits relative to IMG-independent optimization.
- 5.4.1 Charge-discharge scheduling: MT3 produces more power than MT2 because its lower consumption coefficients support lower system operating cost.
- 5.4.1 Charge-discharge scheduling: In Case 2, microturbine outputs are smoother than in Case 1, particularly during 15:00-16:00 and 19:00-20:00.
- 5.6 Economic comparison: Compared with grid pricing, real-time pricing improves both stakeholders’ economics, reducing IMG net cost by 3.16% and increasing BSS profit by 5.36%.
6. Conclusion
The paper investigates bi-level day-ahead scheduling of an isolated microgrid with a battery swapping station using demand-response-based real-time pricing. Simulations on a modified ORNL DECC lab microgrid test system show improved BSS participation, economic benefits, and solution efficiency, while future work targets broader scheduling and modeling capabilities.
- The proposed bi-level model coordinates IMG and BSS scheduling through real-time pricing designed around dynamic supply-demand relationships.The upper and lower stakeholders are coordinated while preserving their distinct operational objectives.
- Simulation experiments on the modified ORNL DECC lab MG test system demonstrate that the model promotes BSS participation in regulating IMG economic operation.
- The JAYA-BBA approach is reported to provide better economic benefits and faster solution efficiency than the state-of-the-art HIA method.
- Future work will integrate day-ahead and real-time scheduling sub-models for multi-timescale scheduling.
- Future extensions include machine-learning prediction of EV arrivals, battery cycle-life calculation, improved modeling of load-DER uncertainty correlations, and micro integrated energy system applications.