Distributed algorithms are increasingly being used to solve the economic dispatch problem of integrated energy systems (IESs) because of their high flexibility and strong robustness, but those algorithms also bring more risk of cyber-attacks in IESs. To solve this problem, this article investigates the distributed robust economic dispatch problem of IESs under cyber-attacks. First, as the first line of defense against attacks, a privacy-preserving protocol is designed for covering up some vital information used for economic dispatch of IESs. On this basis, a distributed robust economic dispatch strategy is presented to achieve the energy management of IESs in the presence of misbehaving units, which consists of a neighbor-observe-based detection process and a reputation-based isolation process. The proposed strategy is implemented in a fully distributed fashion and possesses strong robustness against various colluding and noncolluding attacks. In addition, the strategy can not only ensure the reliability of information transmission among energy units, but also solve the problem of incorrect measurement of distributed local load data caused by cyber-attacks. Finally, the effectiveness of the proposed strategy is illustrated by simulation cases on a 39-bus 32-node power–heat IES.

Recently, the converters controlled by droop controller with phase-locked loop (PLL) were observed in islanded ac microgrids. However, only state-space-based approach was applied to investigate the stability of this converter in the previous works. Compared with state-space-based approach, characteristic equation approach has plenty of advantages, such as convenient stability margin analysis (Phase Margin, Gain Margin, and so on) and simply stability criterion (Routh Criterion). Thus, a novel small-signal modeling approach based on characteristic equation for converter-dominated ac microgrids is proposed to assess the system low-frequency stability in this paper. Firstly, considering zero-order holder (ZOH) and time delay, the smallsignal characteristic equation of this converter is presented by Padé approximation and dynamic phasor model. Furthermore, the implementation and parameter design of the converters are studied under the practical considerations. Compared with the existing characteristic equation methods, the proposed approach can be verified that the performance is significantly improved. Eventually, simulations and experimental results are presented, indicating that the proposed approach can assess the system lowfrequency stability conveniently and accurately.

This paper investigates the economic dispatch problem of microgrids in a distributed fashion. To address this issue, a delay-free-based distributed algorithm is presented to optimally assign the whole energy demand among local generation units with the objective of minimizing the agminated operation cost. By implementing the proposed algorithm, each component can find its own optimal operations by only requiring local computation and communication. As a result, it enhances the system robustness, flexibility, privacy, etc. More importantly, the time-varying delays model is considered and embedded into the design of our distributed algorithm, such that the components can employ the delays information to achieve the collaborative operation, which are more general and applicable for practical power systems. In addition, we have proved that the proposed algorithm can converge to the global optimal point under some sufficient conditions. Finally, several simulations are provided to demonstrate the correctness and effectiveness of the proposed algorithm.

For the integrated energy system (IES) formed by a cluster of energy hubs (EHs), the outputs of EHs and system parameters, which greatly influence the security performance, should be properly adjusted. In this article, an event-triggered distributed hybrid control scheme is proposed to achieve security and economic operation for the IES. First, the EH output control is designed based on the features of energy networks as well as the containment and consensus algorithms. According to the control of outputs, the electricity and heat load power can be accurately shared without knowing the network parameters. Second, the pressure is bounded within an acceptable range, and the frequency is reverted to the reference value by implementing the proposed control method. Third, an event-triggered communication strategy is employed to design the corresponding protocols, resulting in reduced communication cost. Finally, the control of devices based on the equal incremental principle is proposed to achieve the minimal economic cost for each EH with considering energy prices. The results of numerical case studies are presented to validate the performance of the proposed control method.

Although the low-frequency/harmonic oscillation of grid-tied inverters under weak grids has been widely researched, the classical impedance-based approach focuses more on the identification of stable operating points and the stability margin of return-ratio matrix. Furthermore, it cannot provide stability regions of system parameters. Therefore, this paper proposes a line impedance cooperative stability region identification method. Firstly, the output impedance matrix and the input admittance matrix are respectively built in d-q axis. Secondly, a novel stability forbidden region is proposed. It is less conservative than the forbidden region criteria in existing literatures. Based on the stability forbidden region, the stability operation region is established via mirror, translation and rotation mappings. It is less conservative compared with the norm-based stability criteria. The solving of stability operation region is first transformed into the eigenvalue identification problem in this paper. Furthermore, the detailed line impedance cooperative stability region is solved by guardian map theory. It can provide guidance for system planning and stabilization method researches with simplified computational process. Finally, the simulation and experimental results show that the proposed line impedance cooperative stability region identification method is more effective and less conservative.

The droop control is an advantageous approach for stand-alone supply systems consisting of multiple batteries, allowing among various inverters without intercommunication. The droop coefficients of batteries always vary with their state-of-charge (SoC) and charge/discharge mode, resulting in small-signal instability. Nevertheless, the existing impedance-based approaches can only assess the droop coefficients stability point, but not the stability region. Therefore, this article proposes a droop coefficients stability region analysis approach. First, the charge/discharge SoC-based droop controlled battery, the P&Q controlled distributed generator and the constant power load are separately discussed. Meanwhile, the state matrix and return-ratio matrix are established, respectively. Furthermore, the novel forbidden region criterion based on the return-ratio matrix is constructed, which reduces conservatism compared with norm-based impedance criteria and partial forbidden region criteria. Such a forbidden region criterion is first switched to the Hurwitz identification problem regarding the equivalent return-ratio matrix. Combined the state matrix and the equivalent return-ratio matrix, the generalized incidence matrix is constructed to simultaneously identify subsystem stability and interactive stability. Based on the generalized incidence matrix, an adaptive step search strategy is proposed to obtain the droop coefficients coordinated stability region. Finally, the simulation and experimental results illustrate the validity of the proposed method.