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Distributed Power Allocation Scheme with Prescribed Performance and Intermittent Dynamics for BESSs with Discharge Rate Constraints in Microgrids

Yalin Zhang, Zhongxin Liu, Fuyong Wang, Zengqiang Chen

arXiv:2609.19069v1eess.SY

TL;DR

Balancing SoC and sharing power across BESSs under dynamic loads calls for coordinated estimates of both states. The paper develops PPC-based distributed estimators with event- and self-triggered communication; simulations report improved consensus and tracking performance, alongside a triggering-frequency limitation for the self-triggered scheme.

  • Problem

    The paper addresses distributed estimation of power sharing and SoC balance under dynamic loads, states needed for allocation intended to maintain supply-demand balance and avoid premature BESS depletion.

    Source: §I · pp. 2–3

  • Method

    The authors design two PPC-based distributed estimators using intermittent communication, one event-triggered and one self-triggered, for power-sharing and SoC-balance states.

    Source: §I · p. 3

  • Results

    Simulations show improved consensus and dynamic-tracking performance over existing schemes; compared with, the proposed SoC-balance estimator performs less well but triggers less frequently.

    Source: B. Case 2. Comparison with Other Methods · p. 10, §VI · p. 11

  • Takeaways & Limitations

    The authors conclude that the estimators let each BESS-managing agent track power-sharing and SoC-balance states to help prevent premature exit among BESSs with the same relative SoC change rate.

    Source: §VI · p. 11

    The self-triggered scheme uses an upper bound on consensus error and consequently triggers more frequently; the authors also note PPC challenges with actuator saturation and disturbance.

    Source: §VI · p. 11

Abstract

from arXiv · show

The State-of-Charge (SoC) is an important parameter of a battery energy storage system (BESS), and its balance problem is also an issue worth studying in a multi-BESS network. Recently, some researchers have proposed a power allocation method, claiming that as long as the power sharing state and SoC balance state can be obtained in real-time, it can not only maintain supply and demand balance, but also ensure that any BESS will not exit early due to insufficient energy storage. Considering this, we are attempting to design {a distributed dynamic average tracking algorithm} based on multi-agent systems (MASs) with prescribed transient and steady state performance to estimate the power sharing and SoC balance states \textcolor{blue}{of} a BESSs network with dynamic load in a distributed manner. Two versions of the solution are designed here, where one is event triggered and the other is self triggered. These two schemes ensure the performance of the estimators under intermittent communication to varying degrees, \textcolor{blue}{respectively}. In each constructed estimation scheme, prescribed performance control (PPC) method is implemented to ensure the expected steady-state and dynamic performance, which is encapsulated in a performance function. Thus, it achieves almost zero error estimation of the fast time-varying {power} sharing and the SoC balance states. In addition, consensus and average tracking performance are decoupled, which provides convenience for \textcolor{blue}{parameters} tuning. Finally, to verify the results of \textcolor{blue}{the} theoretical analysis, some cases are studied and relevant simulations are performed on a 4 bus system.

I. Introduction

The paper motivates distributed BESS coordination by the need to balance SoC and power sharing under dynamic loads. It proposes PPC-based distributed estimators and intermittent communication schemes for that setting.

I. Introduction

  • SoC balancing can maximize battery-capacity utilization and often extend battery-pack lifespan, making power-flow allocation a cooperative-control concern.Source: §I · p. 2
  • Earlier distributed schemes studied SoC balance and power sharing mainly under constant loads, while dynamic-load approaches had coupled consensus and tracking performance and could require load knowledge.Source: §I · p. 2
  • The proposed contribution combines prescribed performance control with distributed dynamic average tracking and event- and self-triggered communication to estimate power-sharing and SoC-balance states.The authors also state that the scheme does not require prior knowledge of dynamic load and decouples consensus and tracking performance for gain selection.Source: §I · p. 3

II. Problem statement

  • The problem statement calls for two distributed estimators with predetermined dynamic and steady-state performance for a power-allocation scheme intended to ensure time-oriented SoC balance and supply-demand balance.Source: §II · p. 3

A. SoC of A BESS

  • A BESS's SoC variation is related to its output current and power, while its actual capacity decreases as its cycle count increases.Source: A. SoC of A BESS · p. 3

B. A Power Allocation Scheme for BESSs

This section motivates a power-allocation scheme based on a shared relative SoC change rate. Its distributed form uses estimates of average power and SoC to support coordinated depletion and supply-demand balance.

B. A Power Allocation Scheme for BESSs

  • Existing droop-controlled allocation schemes based on proportional power or marginal-cost consensus may cause circulation and battery-mode changes, or fail to achieve SoC balance.The passage links mode changes to capacity degradation and notes that charging and discharging certain batteries during balancing is not conducive to battery-life protection.Source: B. A Power Allocation Scheme for BESSs · pp. 3–4
  • For a resistive network, a unified SoC relative rate of change is stated to guarantee SoC balance while maintaining supply-demand balance.Source: B. A Power Allocation Scheme for BESSs · p. 4
  • The centralized allocation relies on real-time average power and SoC values; distributed dynamic average tracking is proposed to estimate those quantities.Source: B. A Power Allocation Scheme for BESSs · p. 4
  • The proposition states that the allocation can ensure time-oriented SoC balance and supply-demand balance when average load and SoC are well estimated.Source: B. A Power Allocation Scheme for BESSs · p. 4

C. Control Objectives

The control objectives specify accurate distributed estimates of power sharing and SoC balance despite dynamic loads and intermittent communication. The preliminaries introduce graph concepts and prescribed performance control used in the estimator design and analysis.

C. Control Objectives

  • The objectives target power-sharing and SoC-balance estimates with convergence rates no slower than predetermined values and steady-state errors within prescribed bounds.Source: C. Control Objectives · p. 4

III. Preliminaries

  • The section introduces graph theory, prescribed performance control, and dynamical-systems knowledge as foundations for estimator design and stability proofs.Source: §III · p. 4

A. Graph Theory

  • In a directed communication graph, an edge from agent i to agent j means i's information flows to and is usable by j; an undirected edge permits mutual use.Source: A. Graph Theory · pp. 4–5

B. PPC Method

  • Prescribed performance control uses a performance function to constrain error evolution and ensure convergence to a residual set at a predetermined minimum rate.Source: B. PPC Method · p. 5
  • The performance function is selected so the initial error lies inside its bound, keeping the scalar error within the prescribed region and supporting the steady-state performance.Source: B. PPC Method · p. 5

C. Dynamical Systems

This section introduces the dynamical-system concepts used to analyze the estimators and states the load assumption for the intermittent scheme.

C. Dynamical Systems

  • A maximal solution is one that cannot be extended to the right, and the stated regularity conditions ensure one exists over an initial time interval.The system function must be locally Lipschitz in the state, piecewise continuous, and locally integrable in time.Source: C. Dynamical Systems · p. 5
  • The section introduces two prescribed-performance estimators driven by intermittent dynamics to estimate power-sharing and SoC-balance states.The schemes are subsequently developed to achieve intermittent communication.Source: C. Dynamical Systems · p. 5
  • The intermittent estimator design assumes the total load is continuous, bounded, and has a first derivative.Source: C. Dynamical Systems · p. 5

A. Design of Estimators under Intermittent Dynamics

The event-triggered estimators use prescribed performance to estimate average load and SoC while constraining consensus errors. Their analysis establishes tracking properties and Zeno-free triggering, with asynchronous updates over directed links.

A. Design of Estimators under Intermittent Dynamics

  • The event-triggered scheme is asynchronous over directed links, and each BESS can transmit its SoC and power-sharing estimates at different times.Source: A. Design of Estimators under… · p. 6
  • Both estimators recover the average load or average SoC with prescribed consensus-error performance and avoid Zeno behavior.The power-sharing result is stated in Theorem 2 and the SoC result in Theorem 3.Source: A. Design of Estimators under… · pp. 6, 8
  • Power-sharing consensus errors remain within their prescribed performance bounds for all time, with the tracking error converging exponentially at rate λ.The steady-state performance condition is stated for kP_r > λ.Source: A. Design of Estimators under… · p. 7
  • The estimator analysis excludes Zeno behavior, so infinitely many triggers cannot occur within a finite time interval.Source: A. Design of Estimators under… · p. 7
  • The performance function parameters adjust dynamic and steady-state performance, while increasing kP_r can accelerate consensus and average-load tracking.The effect of kP on results depends on the load and communication-network configuration.Source: A. Design of Estimators under… · p. 7
  • Triggering parameters affect both communication frequency and estimator response, and their effects can depend on load dynamics.The impact of increasing c0 on triggering frequency requires trial and error because the trigger-interval bound depends on load and its derivative.Source: A. Design of Estimators under… · p. 8

B. A Self Triggering Mechanism for Intermittent Communication

The self-triggered mechanism schedules the next communication time using information available at the current trigger. It preserves the stated estimator performance but may become increasingly frequent over time.

B. A Self Triggering Mechanism for Intermittent Communication

  • The next trigger time depends only on information at the current trigger, avoiding continuous communication.The passage describes the mechanism as self-triggered, or time-triggered.Source: B. A Self Triggering Mechanism for… · p. 8
  • Under the self-triggered protocol, power-sharing and SoC-balance states are estimated with prescribed consensus performance, and Zeno behavior is excluded.Source: B. A Self Triggering Mechanism for… · p. 8
  • Although Zeno-free, the self-triggered scheme may trigger communication increasingly often as its admissible intervals shorten.The calculation of the bound used by the mechanism requires the specified network quantity.Source: B. A Self Triggering Mechanism for… · p. 8

V. Some Simulation Cases

The simulations comprise five cases testing event-triggered and self-triggered schemes, comparison with prior work, plug-and-play operation, and scalability.

V. Some Simulation Cases

  • Five simulation cases test event-triggered effectiveness, comparison with an existing scheme, plug-and-play operation, scalability, and self-triggered performance.Source: §V · p. 8
  • Case 1 tests the event-triggered scheme, while Case 2 compares it with the event-triggered scheme in.Source: §V · p. 8
  • Cases 3 and 4 test plug-and-play function and scalability, respectively, and Case 5 tests the self-triggered scheme.The described DC system has four sections, each containing a BESS and load.Source: §V · p. 8

A. Case 1. The Test on the Designed Scheme with the Event-triggering Mechanism (10)

Case 1 tests the event-triggered estimators and their effect on power allocation under changing communication and energy conditions. The estimates are useful overall but oscillate, while supply-demand balance is interrupted when available energy is insufficient.

A. Case 1. The Test on the Designed Scheme with the Event-triggering Mechanism (10)

B. Case 2. Comparison with Other Methods

Case 2 compares the proposed estimators with the scheme in. The proposed power-sharing estimator is more distributed, while the comparison reports limitations in the estimators’ tracking and supply-demand balance.

B. Case 2. Comparison with Other Methods

  • Unlike the scheme in, the proposed power-sharing estimator does not require a centralized method to obtain the network’s average load.The paper also states that its average-tracking and consensus performance can be tuned separately.Source: B. Case 2. Comparison with Other Methods · p. 10
  • Increasing λ and k is reported to accelerate convergence, while reducing ρ∞ improves control accuracy and increasing k_r improves average-tracking performance.Source: B. Case 2. Comparison with Other Methods · p. 10
  • The scheme in has poorer power-sharing tracking for rapidly changing loads, requiring faster triggering, and shows significant supply-demand deviations.Its SoC balance estimator performs better than the proposed estimator, but triggers more frequently.Source: Figure 9 · p. 9, B. Case 2. Comparison with Other Methods · p. 10

C. Case 3. The Test of Play-and-Plug

Case 3 tests play-and-plug behavior by disconnecting and restoring the part of the network containing BESS 1. The remaining agents continue estimating states and maintaining power allocation during the disconnection.

C. Case 3. The Test of Play-and-Plug

D. Case 4 The Test on Scalability of the Designed Algorithm

Case 4 tests the event-triggered algorithm with 12 BESSs. The simulations report state-estimation accuracy, bounded consensus error, maintained supply-demand balance, and simultaneous depletion.

D. Case 4 The Test on Scalability of the Designed Algorithm

  • With 12 BESSs, SoC balance estimates track the real-time average and consensus error stays within the preset value; power-sharing estimates show similar behavior.The authors conclude that the algorithm has a degree of scalability.Source: D. Case 4 The Test on Scalability of… · p. 10
  • The 12-BESS simulations also report that supply-demand balance is maintained and all BESS SoCs ultimately converge to zero simultaneously.Source: D. Case 4 The Test on Scalability of… · p. 10

E. Case 5. The Test with the Self-triggering Mechanism

The self-triggered scheme retains estimation and supply-demand performance in Case 5, with more frequent triggering as a trade-off. The conclusions emphasize performance decoupling and identify limits of the current triggering and PPC designs.

VI. Conclusions

  • The conclusions report that two distributed estimators let each BESS agent obtain current power-sharing and SoC-balance states, aiming to prevent premature exit when BESSs share a relative SoC change rate.The self-triggering simulation is conducted for Case 1 and its results are shown in Figs. 16–18.Source: E. Case 5. The Test with the… · p. 10, §VI · p. 11

E. Case 5. The Test with the Self-triggering Mechanism

  • In Case 5, power-sharing and SoC-balance errors remain almost zero and converge at least as fast as predefined; local oscillations disappear versus Case 1, but triggering becomes more frequent.Supply-demand balance remains well maintained, and all BESSs are almost simultaneously depleted.Source: Figure 16 · p. 11, Figure 17 · p. 11, Figure 18 · p. 11

VI. Conclusions

  • PPC decouples consensus from dynamic tracking performance, which the authors say makes gain selection easier.Source: §VI · p. 11
  • The event-triggered and self-triggered mechanisms are designed to save actuators and communication resources.Source: §VI · p. 11
  • The self-triggered design uses an upper bound on consensus error, increasing triggering frequency; the PPC approach may struggle with actuator saturation and disturbances.The authors identify a suitable observer and non-fragile PPC as directions for addressing these issues.Source: §VI · p. 11
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