The sub-synchronous control interaction (SSCI) has frequently occurred in the direct-drive permanent magnetic synchronous generators (PMSGs) based wind farm integrated to the weak AC network. The system strength, i.e. short-circuit ratio (SCR) has been believed as the critical factor so far. However, the impedance–frequency characteristics of the practical network exhibit a strong resonance that might have impacts on the SSCI as well. In this study, considering the network resonance, the eigenvalue- and impedance-based analyses are conducted to study the SSCI phenomenon in the grid-connected PMSG system. The impacts on SSCI from system strength, network resonance and network-resonant frequency are investigated firstly. Then, the parameter limits of PMSG control for the stable region are calculated to discuss the effects of network resonance on the parameter design. The results show that the network resonance plays a critical role in the SSO mode. When the network resonance is considered in the PMSG system, the SSO would arise more easily, and the stable region of the control parameter will be reduced. Meanwhile, the frequency of the SSO mode matches well with the network resonance frequency in dq frame. The analytical results are all verified by simulation.

Recently, emerging sub-synchronous oscillation (SSO) issues caused by the interaction between power electronic converters and weak AC grids have provoked serious stability concerns. Impedance-based modelling approaches have been widely employed for stability analysis of such interactions. In this study, a sequence-domain frequency-coupled impedance model (FCIM) and the corresponding stability criterion are proposed. First, a fast identification method of the FCIM is proposed, in which the impedance-frequency curves of the FCIMs at multiple frequencies are measured, followed by identification of their transfer function models. Next, the proposed method is applied to model a practical system, where a SSO event once occurred due to the interactions between direct-drive wind turbines and a weak AC grid. The individual FCIMs of wind turbine generators, steam turbine generators and static var generator in this system are derived. After that, an aggregated FCIM is formed by combining the FCIMs without extra coordinate transformation. Then, the aggregated FCIM-based stability analysis is carried out to investigate the interaction between the wind farms and weak AC grids. In the end, the results of FCIM-based stability analysis are verified by time-domain simulations.

The demand response, providing the reserve service, becomes more and more important in the wind-power-integrated power systems. This study proposes a two-stage stochastic unit commitment model with the air conditioning (AC) aggregators providing the reserve service. A classification compensation scheme is proposed to promote AC users to provide more reserve capacity, which quantifies the users' comfort and their contribution to the system. Besides, a new AC scheduling method with adaptive response capacity (ARC) is proposed to help system operators to determine reasonable reserve capacity with smaller total cost. In addition, the inactive constraints identification is utilised to improve computational performance. Finally, the effectiveness of the proposed method is tested on the modified IEEE 118-bus system with 50 AC aggregators. The simulation results show that the proposed classification compensation scheme and the ARC method can promote more AC response capacity and save the total and reserve costs. The price game between the AC aggregators and the thermal units have a great impact on the decision results. The inactive constraints identification can save the total time by about 70%.

The offshore all-DC wind farm with increasing capacity will bring problems such as the weakening of grid frequency stability and the increase of equivalent grid impedance. To overcome this, a coordinated control strategy for the offshore all-DC wind farm is proposed here with two salient features: better performance under weak grid condition and real-time frequency support from the wind farm. The control strategy consists of three parts: the inertia synchronising control of the receiving-end converter, the constant ratio control of the DC transformer and the frequency response of the wind farm. With the proposed strategy, the all-DC wind farm operates like a synchronous generator to the onshore grid, which provides fast frequency support when the onshore grid frequency changes. The effectiveness of the proposed method is validated in power systems computer aided design (PSCAD)/electromagnetic transients including DC (EMTDC) using a typical IEEE 9 bus system.