On Feasible Region of Droop-based Fast Frequency Response Controller Parameters of Wind Turbines

Droop-based fast frequency response(FFR)control of wind turbines can improve the frequency performance of power systems with high penetration of wind power.Explicitly formulating the feasible region of the droop-based FFR controller parameters can allow system operators to conveniently assess the feasibility of FFR controller parameter settings to comply with system frequency security,and efficiently tune and optimize FFR controller parameters to meet frequency security requirements.However,the feasible region of FFR controller parameters is inherently nonlinear and implicit because the power point tracking controllers of wind turbine would counteract the effect of FFR controllers.To address this issue,this letter proposes a linear feasible region formulation method,where frequency regulation characteristics of wind turbines,the dead band,and reserve limits of generators are all considered.The effectiveness of the proposed method and its application is demonstrated on a 10-machine power system.

An Analytical Method for Delineating Feasible Region for PV Integration Capacities in Net-zero Distribution Systems Considering Battery Energy Storage System Flexibility

To provide guidance for photovoltaic(PV)system integration in net-zero distribution systems(DSs),this paper proposes an analytical method for delineating the feasible region for PV integration capacities(PVICs),where the impact of battery energy storage system(BESS)flexibility is considered.First,we introduce distributionally robust chance constraints on network security and energy/carbon net-zero requirements,which form the upper and lower bounds of the feasible region.Then,the formulation and solution of the feasible region is proposed.The resulting analytical expression is a set of linear inequalities,illustrating that the feasible region is a polyhedron in a high-dimensional space.A procedure is designed to verify and adjust the feasible region,ensuring that it satisfies network loss constraints under alternating current(AC)power flow.Case studies on the 4-bus system,the IEEE 33-bus system,and the IEEE 123-bus system verify the effectiveness of the proposed method.It is demonstrated that the proposed method fully captures the spatio-temporal coupling relationship among PVs,loads,and BESSs,while also quantifying the impact of this relationship on the boundaries of the feasible region.

Hierarchical Dispatch Method for Integrated Heat and Power Systems Based on a Feasible Region of Boundary Variables

Fully utilizing the flexibility provided by a district heating system(DHS)can promote wind power accommodation for an electric power system(EPS).However,for privacy or communication reasons,existing power and heat dispatch methods are not suitable for practical application.In this paper,a general math formulation of the hierarchical dispatch method is proposed to coordinate EPS and DHS operators based on the feasible region of boundary variables(FRBV),and a method based on the simplicial approximation approach is proposed to obtain a conservative FRBV approximation of a DHS.A simulation based on a real 41-node DHS is constructed to determine the factors that may impact the boundaries of the FRBV,and then the performance of the simplicial approximation approach is displayed by visualizing the approximation process for the FRBV,and finally three dispatch methods are compared to show the advantages of the proposed hierarchical dispatch method.

Guaranteed feasible control allocation using model predictive control

This paper proposes a guaranteed feasible control allocation method based on the model predictive control. Feasible region is considered to guarantee the determination of the desired virtual control signal using the pseudo inverse methodology and is described as a set of constraints of an MPC problem. With linear models and the given constraints, feasible region defines a convex polyhedral in the virtual control space. In order to reduce the computational time, the polyhedral can be approximated by a few axis alig ned hypercubes. Employing the MPC with rectangular constraints substantially reduces the computational complexity .In two dimensions, the feasible region can be approximated by a few rectangles of the maximum area using numerical geometry techniques which are considered as the constraints of the MPC problem. Also, an active MPC is defined as the controller to minimize the cost function in the control horizon. Finally, several simulation examples are employed to illustrate the effectiveness of the proposed techniques.

Linear OPF-based Robust Dynamic Operating Envelopes with Uncertainties in Unbalanced Distribution Networks

Dynamic operating envelopes(DOEs),as key enablers to facilitate distributed energy resource(DER)integration,have attracted increasing attention in the past years.However,uncertainties,which may come from load forecasting errors or inaccurate network parameters,have been rarely discussed in DOE calculation,leading to compromised quality of the hosting capacity allocation strategy.This letter studies how to calculate DOEs that are immune to such uncertainties based on a linearised unbalanced three-phase optimal power flow(UTOPF)model.With uncertain parameters constrained by norm balls,formulations for calculating robust DOEs(RDOEs)are presented along with discussions on their tractability.Two cases,including a 2-bus illustrative network and a representative Australian network,are tested to demonstrate the effectiveness and efficiency of the proposed approach.

Exploiting Flexibility of Integrated Demand Response to Alleviate Power Flow Violation During Line Tripping Contingency

Multi-energy integrations provide great opportunities for economic and efficient resource utilization. In the meantime, power system operation requires enough flexible resources to deal with contingencies such as transmission line tripping. Besides economic benefits, this paper focuses on the security benefits that can be provided by multi-energy integrations. This paper first proposes an operation scheme to coordinate multiple energy production and local system consumption considering transmission networks. The integrated flexibility model, constructed by the feasible region of integrated demand response(IDR), is then formulated to aggregate and describe local flexibility. Combined with system security constraints, a multi-energy system operation model is formulated to schedule multiple energy production, transmission, and consumption. The effects of local system flexibility on alleviating power flow violations during N-1 line tripping contingencies are then analyzed through a multi-energy system case. The results show that local system flexibility can not only reduce the system operation costs, but also reduce the probability of power flow congestion or violations by approximately 68.8% during N-1 line tripping contingencies.

Distributed Robust Energy and Reserve Dispatch for Coordinated Transmission and Active Distribution Systems

The increasing penetration of renewable energy sources introduces higher requirements for the operation flexibility of transmission system(TS) and connected active distribution systems(DSs). This paper presents an efficient distributed framework for the TS and DSs to work cooperatively yet independently. In addition to conventional power interaction, upward and downward reserve capacities are exchanged to form the feasible access regions at the boundaries that apply to different system operation situations. A distributed robust energy and reserve dispatch approach is proposed under this framework. The approach utilizes the supply-and demand-side resources in different systems to handle various uncertainties and improve overall efficiency and reliability. In particular, integrated as aggregated virtual energy storage(AVES) devices, air-conditioning loads are incorporated into the optimal dispatch. In addition, a reserve model with charging/discharging-state elasticity is developed for AVESs to enhance system flexibility and provide additional reserve support. Different cases are compared to verify the effectiveness and superiority of the proposed approach.

Effects of Hard Limits on Bifurcation,Chaos and Stability

An SMIB model in the power systems, especially that concering the effects of hard limits on bifurcations, chaos and stability is studied. Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits. It has been proved that hard limits can affect system stability. We find that (1) hard limits can change unstable equilibrium into stable one; (2) hard limits can change stability of limit cycles induced by Hopf bifurcation; (3) persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle; (4) Hopf bifurcation occurs before SN bifurcation, so the system collapse can be controlled before Hopf bifurcation occurs. We also find that suitable limiting values of hard limits can enlarge the feasibility region. These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation, bifurcation diagram, trajectories, Lyapunov exponent, Floquet multipliers, dimension of attractor and so on.