System Electromechanical Oscillations Research Articles

Time Integration-Based IGD Methods for Eigen-Analysis of Large Delayed Cyber-Physical Power System

Two spectral discretization methods based on linear multistep and implicit Runge-Kutta discretization of infinitesimal generator (IGD-LMS/IRK) are presented in this paper for eigen-analysis of large delayed cyber-physical power system (DCPPS) with large time delays. First, the whole delay interval is partitioned into several sub-intervals by time delays in the system. The piecewise partitioning allows the avoidance of interpolations in evaluating system states at the delay points. Second, two time integration methods, i.e., LMS and IRK, are utilized to discretize infinitesimal generator on each sub-interval, resulting in highly structured and sparse discretization matrices. Third, IGD-LMS/IRK are efficiently implemented to compute the system's electromechanical oscillation modes. The shift-invert preconditioning technique is used and the sparsity in augmented system state matrices is exploited to guarantee the efficiency and scalability of IGD-LMS/IRK in dealing with large DCPPS. Numerical results on the two-area four-machine test system and a real-life large transmission grid validate the improved efficiency and accuracy of the proposed methods in analyzing DCPPS with large time delays.

Parameter Preserving Model Order Reduction of Large Sparse Small-Signal Electromechanical Stability Power System Models

This paper proposes a method for the model order reduction (MOR) of large scale power system models that produces reduced order models (ROM) which preserve the access to selected parameters exactly like the original full order model (FOM). The preserved parameters are related to decentralized power system devices, including, but not limited to, power system stabilizers that are used for the damping control of system electromechanical oscillations. The problem formulation of this parametric MOR (PMOR) is described, as well as the implementation details regarding efficiency and flexibility. Test results are described for large practical power system models used in small-signal electromechanical stability studies. The ROM produced sufficiently accurate responses following parameters changes, when equivalently compared to the original FOM results. The proposed method allows preserving specified nonlinearities in chosen devices of the parameterized ROMs. It can also be applied to the reduction of differential algebraic equation models related to other areas of engineering.

Modifying the control design of DFIG‐based wind turbines in order to inhibit power system oscillations

Providing additional damping for system electromechanical oscillations through doubly fed induction generator (DFIG)-based wind turbines is investigated in this study. In this regard, first an objective function is developed to tune the DFIG control gains, aim to maximise the wind farm (WF) contribution to system oscillation damping, but it is shown that it causes a decrease in the damping of DFIG stator mode. In other words, with the current DFIG control design, it is not possible to improve both the small signal stability of the power system and the dynamic stability of WF together. Afterwards, two high-pass filters are suggested to be employed in the control design of DFIG. It is shown that with the modified control design, it is possible to improve the system oscillation without spoiling the dynamic stability of the WF itself. Eigenvalue analysis is performed to validate the effectiveness of the modified control design.

Sparse and Resilient Hierarchical Direct Load Control for Primary Frequency Response Improvement and Inter-Area Oscillations Damping

The aim of this paper is to define and develop an optimal hierarchical demand-side power-system primary-frequency control structure in order to provide a reliable complement to generator inertia and governor response while improving inter-area oscillation damping. This resilient optimal load control strategy utilizes both wide-area and local signals to guarantee that the system remains stable in the case of communication failures. In the device layer, we deal with demand-response and frequency regulation by minimizing the total disutility of consumers subject to power balance and frequency regulation over the network. In the supervisory layer, we handle the power system's electromechanical oscillations using an linear-quadratic regulator (LQR)-based state feedback scheme with sparsity promotion to achieve the necessary tradeoff between complexity and performance. Since the wide-area feedback loops are built on top of an existing decentralized load control strategy, this design approach creates a decentralized/hierarchical demand-side load-control structure with significant advantages in terms of reliability and operational flexibility. Our study clearly shows by simulation that a demand-side hierarchical load-control strategy has a significant potential for improving the dynamic performance of power systems, even when implemented with a limited number of measurement units and controlling less than $1\%$ of the total base load.

Impact of Dynamic Interactions Introduced by the DFIGs on Power System Electromechanical Oscillation Modes

This paper derives the index of dynamic interactions (IDI), which is the sensitivity of a power system electromechanical oscillation mode (EOM) of concern to the dynamic interactions introduced by a grid-connected double-fed induction generator (DFIG). Based on the IDI, analysis is carried out with the following generally-applicable conclusions obtained: 1) Impact of dynamic interactions introduced by the DFIG increases when wind power penetration increases; 2) as long as the frequency response of an equivalent single DFIG model approximately matches the frequency response of a wind farm around the frequency of electromechanical oscillations of concern, this equivalent dynamic model of single DFIG can be used to represent the wind farm to examine the impact of wind farm on EOMs. Furthermore, an indicator of DFIG control (IDC) is derived for comparing the impact of terminal voltage control and reactive power control implemented by the DFIG. Main merit of the IDC is the computational simplicity without need to know dynamic model of the DFIG to indicate that either the terminal voltage control or the reactive power control is more beneficial to power system stability. An example multi-machine power system with grid-connected DFIGs is presented to demonstrate and validate the analysis and conclusions made in the paper.

PLL-Induced Modal Resonance of Grid-Connected PMSGs With the Power System Electromechanical Oscillation Modes

This study investigates the impact of a grid-connected permanent magnet synchronous generator (PMSG) for wind power generation on the power system electromechanical oscillation modes (EOMs) caused by a phase-locked loop (PLL). A closed-loop interconnected model of a power system with the PMSG is established, where the PLL and rest of the power system are modeled as two separate open-loop interconnected subsystems. Analysis based on the established model indicates that, when an open-loop PLL oscillation mode (POM) is close to an open-loop EOM of concern on the complex plane, the dynamic interactions between the PMSG and the power system may become strong. It is very likely that the modal resonance due to the closeness of the open-loop POM and EOM may degrade the small-signal stability of the power system. In this paper, case studies of an example power system with PMSGs are presented. It is demonstrated that open-loop modal resonance occurs when power system operating conditions change and the PLL parameters are tuned. Strong dynamic interactions between the PMSGs and power system are caused by the open-loop modal resonance, resulting in considerable damping degradation of the low-frequency electromechanical oscillations.

Power System Electromechanical Oscillation Modes as Affected by Dynamic Interactions From Grid-Connected PMSGs for Wind Power Generation

Dynamic interactions between a grid-connected permanent magnet synchronous generator (PMSG) and power system are normally weak. This paper reports a special condition of modal resonance, under which the grid-connected PMSG may dynamically interact with power system strongly to affect power system electromechanical oscillation modes (EOMs). The special condition of modal resonance reported in this paper is that an open-loop converter oscillation mode (COM) of PMSG is close to an open-loop EOM of a power system on the complex plane. Damping torque analysis is carried out to explain why strong dynamic interactions between PMSG and power system may occur under the condition of modal resonance. Results of theoretical analysis in this paper indicate that occurrence of modal resonance may possibly cause the damping of either closed-loop COM or EOM to decrease such that power system small-signal angular stability is affected negatively by grid connection of PMSG. Responsible COMs for modal resonance are found to be related with active/reactive power control systems of a grid-side converter of PMSG. In the paper, an example multimachine power system with PMSGs is presented to demonstrate and validate analysis and conclusions made.

Formulation and Characterization of Power System Electromechanical Oscillations

When generators of a power system are subject to a large disturbance, their electromechanical oscillations (EOs) are essentially nonlinear as observed from their rotor angle waveforms due to the nonlinear power network. However, traditional modal analysis has not given enough considerations to nonlinearities in EOs. This paper analytically formulates the accurate oscillation frequency (OF) of an EO mode addressing nonlinearities. It is revealed that when the system model and condition are fixed, the OF of any EO mode is energy-dependent as a function of the oscillation amplitude (OA). That is characterized by a new tool named Frequency-Amplitude (F-A) curve regarding each mode, from which the frequency decreases from the natural frequency toward zero when the amplitude grows to a critical threshold. The paper proves that an F-A curve is actually a projection of the system trajectory between the stable equilibrium and the stability boundary onto the OF-OA plane regarding one mode. Based on the concept of F-A curve, a stability index is defined and estimated from measurements for online angle stability analysis. The proposed methodology is presented in detail using an SMIB system and then demonstrated on the IEEE 9-bus system and WECC 179-bus system having multiple EO modes.

A Method to Examine the Impact of Grid Connection of the DFIGs on Power System Electromechanical Oscillation Modes

Grid connection of a DFIG for power generation changes the power system load flow and introduces dynamic interactions with the synchronous generators (SGs). A method is proposed in this paper for the separate examination of the impact of those two affecting factors, the change of load flow and dynamic interaction brought about by the DFIG, on the electromechanical oscillation modes of a power system. The method is developed on the establishment of a “closed-loop control system” type of state space model of the power system where the DFIG is treated as the feedback controller. The established model unambiguously indicates that the impact of the DFIG can be examined separately: (1) With the DFIG being modelled as a constant power injection into the system, the impact of the load flow change brought about by the DFIG on the oscillation modes is determined; (2) The impact of the dynamic interactions introduced by the DFIG is estimated by calculating the contribution of the damping torque from the DFIG with its full dynamics being considered. Thus a more detailed examination on and deeper insight into the impact of grid connection of the DFIGs on power system small-signal angular stability is obtained by using the proposed method.

Improvements for electromechanical oscillation mode estimation via subspace identification methods

Two improvements of power system electromechanical oscillation estimation via subspace identification are proposed in this paper. Singular value-based criteria are introduced not only to improve the computation efficiency for determining the model order of the estimated system but also to improve the accuracy of the estimates. A mode matching method based on the characteristics of accurate mode shape estimates is proposed to ensure the correctness of the estimates. Numerical results from three different scale power systems illustrate the feasibility of the proposed methods.

Power Systems Oscillations Damping with Regard the Finite Speed of Propagation the Electromechanical Waves

Damping of the power system electromechanical oscillations with magnitude-phase excitation controller (MPH-EC), which is responsive to the deviations of the magnitude and phase of the terminal voltage phasor, and taking into account the finite speed of propagation the electromechanical waves, caused perturbation the power balance are considered in this paper. The structure of an integrated excitation control system of synchronous machines (IECS SM) using a remote phasor measurement units (PMU’s) to identify the cross-sections (tie lines) of electromechanical oscillations and putting into operation the function of power system stabilizer, installed on the revealed cross-sections of electromechanical oscillations has been proposed. A significant advantage of the proposed method and technology of damping the low-frequency electromechanical oscillations in the power system is its selectivity in relation to the main modes, with the lowest damping ratio, making the greatest contribution to the development of the power system instability, due to the action of the optimal number of MPH-EC located taking into account the given grid topology.

Trajectory-Based Supplementary Damping Control for Power System Electromechanical Oscillations

This paper considers a trajectory-based approach to determine control signals superimposed to those of existing controllers so as to enhance the damping of electromechanical oscillations. This approach is framed as a discrete-time, multi-step optimization problem which can be solved by model-based and/or by learning-based methods. This paper proposes to apply a model-free tree-based batch mode reinforcement learning (RL) algorithm to perform such a supplementary damping control based only on information collected from observed trajectories of the power system. This RL-based supplementary damping control scheme is first implemented on a single generator and then several possibilities are investigated for extending it to multiple generators. Simulations are carried out on a 16-generator medium-size power system model, where also possible benefits of combining this RL-based control with model predictive control (MPC) are assessed.

Optimal tunning of type-2 fuzzy logic power system stabilizer based on differential evolution algorithm

In this paper, a type-2 fuzzy logic power system stabilizer with differential evolution algorithm is proposed. As an extension of type-1 fuzzy logic theory, type-2 fuzzy logic theory can effectively improve the control performance by uncertainty of membership function especially when we have to confront with less expert knowledge or unpredicted external disturbances. The corresponding parameters and rule base of type-2 fuzzy logic power system stabilizer are optimally tuned by using differential evolution algorithm for multi-machine power system. Through simulation under different operational conditions, the results demonstrate the effectiveness of the proposed approach for damping the power system electromechanical oscillations.

Characteristics extraction and controllability evaluation based on dynamic response of electro-mechanical oscillation

The system identification theory based on SSI(Stochastic Subspace Identification) algorithm is researched,a method of electro-mechanical oscillation characteristics identification based on SSI is designed for power system and a method of participation factor calculation based on response is proposed, by which the quantitative evaluation of system controllability is realized. The proposed method is applied to calculate the dynamic angular frequency response of each generator in a system and the system electro-mechanical oscillation characteristics can be globally analyzed to effectively avoid the defect of traditional low-frequency oscillation analysis with insufficient information based on single signal. Simulative results of IEEE 39-bus system show its high identification accuracy and calculation efficiency.

Coordinative Optimal Design for PSS and Auxiliary Damping Controller on SVC under Multi-Operating Conditions

Based on power system stabilizer (PSS) and the damping controller of flexible AC transmission system (FACTS),a problem of optimal design is researched by the example of static var compensator (SVC). Minimum damp ratio of system electromechanical oscillation modes eigenvalue in the weak damping operation condition is selected as the object function. Parameters of damping controllers are optimized by the algorithm which is combined by genetic algorithm (GA) and back propagation (BP) neural network based on adaboost (Ada-BP). Simulation shows the optimized damping controllers can restrain the low frequency oscillation in multi-operating conditions of system. The algorithm provides an effective solution for optimization calculations which calls the complicated calculations.

Power System Oscillation Modes Identifications: Guidelines for Applying TLS-ESPRIT Method

Abstract Fast measurements of power system quantities available through wide-area measurement systems enables direct observations for power system electromechanical oscillations. But the raw observations data need to be processed to obtain the quantitative measures required to make any inference regarding the power system state. A detailed discussion is presented for the theory behind the general problem of oscillatory mode indentification. This paper presents some results on oscillation mode identification applied to a wide-area frequency measurements system. Guidelines for selection of parametes for obtaining most reliable results from the applied method are provided. Finally, some results on real measurements are presented with our inference on them.

Interaction of the dynamics of doubly fed wind generators with power system electromechanical oscillations

The interaction of the dynamics of doubly fed wind generators with the electromechanical mode of nearby synchronous generators (SGs) can affect the small signal stability of power systems with high penetration levels of wind power. In this study, a novel approach is developed to investigate these interactions and their impact on the damping of power system oscillations. In this approach it is not necessary to model the dynamic behaviour of system SGs and only the frequencies of system oscillations are important. This approach is based on the sensitivity of SGs electromechanical eigenvalue with respect to variations in the Jacobian matrix of power system. By applying this approach to a test system, two of the wind farm (WF) modes are identified to have interaction with the SG electromechanical mode, one has detrimental and the other has beneficial impact, which decrease the damping of system electromechanical oscillation altogether. By using the modal analysis technique, the WF controller gains are retuned to shift the detrimental and beneficial interacting modes away and towards the frequency of system oscillation, respectively. It is shown that this results in the improvement of system oscillation damping whereas the dynamic performance of WF remains satisfactory.

The impact of wind farms with doubly fed induction generators on power system electromechanical oscillations

Introduction of large amounts of new wind generation can affect the small signal stability of power systems with three mechanisms: displacing synchronous generators (SGs); reducing SGs power generation; and the dynamics of wind farms (WFs) interacting with the electromechanical mode of SGs. In this paper a novel approach is developed to investigate the impact of the latter mechanism on existing power systems oscillations. In this approach, the dynamic behavior of grid connected WFs is studied independent of the dynamic behavior of system SGs. This approach helps to identify the conditions in which the dynamics of WFs may interact with the electromechanical mode of SGs. Also it helps to foresee the impact of these probable interactions on the frequency and damping of system oscillations. By using this approach in a test system, it was shown that under some circumstances these dynamic interactions considerably decrease the damping of system oscillations but they barely change the frequency of system oscillations. The frequency of system oscillation and the operating point of WF are the two major parameters determine the severity of the decrease in oscillation damping. Comparison of the SG electromechanical eigenvalues calculated before and after the introduction of the WF in the test system, confirmed the prospects of the proposed approach.

Mode selective damping of power system electromechanical oscillations for large power systems using supplementary remote signals

This paper presents the design of local decentralized power system stabilizer (PSS) controllers, using selected suitable remote signals as supplementary inputs, for a separate better damping of specific inter-area modes, for large-scale power systems. System identification technique is used for deriving lower order state-space models suitable for control design. The lower-order model is identified by probing the network in open loop with low-energy pulses or random signals. The identification technique is then applied to signal responses, generated by time-domain simulations of the large-scale model, to obtain reduced-order model. Lower-order equivalent models, thus obtained, are used to design each local PSS controller separately for each of the inter-area modes of interest. The PSS controller uses only those local and remote input signals in which the assigned single inter-area mode is most observable and is located at a generator which is most effective in controlling that mode. The PSS controller, designed for a particular single inter-area mode, also works mainly in a frequency band given by the natural frequency of the assigned mode. The locations of the local PSS controllers are obtained based on the amplitude gains of the frequency responses of the best-suited measurement to the inputs of all generators in the interconnected system. For the selection of suitable local and supplementary remote input signals, the features or measurements from the whole system are pre-selected first by engineering judgment and then using a clustering feature selection technique. Final selection of local and remote input signals is based on the degree of observability of the considered single mode in them. To provide robust behavior, H∞ control theory together with an algebraic Riccati equation approach has been applied to design the controllers. The effectiveness of the resulting PSS controllers is demonstrated through digital simulation studies conducted on a sixteen-machine, three-area test power system.

Mode Selective Damping of Power System Electromechanical Oscillations Considering Time Delay Uncertainty in Supplementary Remote Signals

AbstractThis paper presents the design of H∞-based local decentralized power system stabilizer (PSS) controllers for large-scale power systems, using selected suitable remote signals from the whole system as supplementary inputs, for a separate better damping of specific inter-area modes, considering uncertainty in time delay. System identification technique is used for deriving lower order state-space models suitable for control design. The PSS controller uses only those local and remote input signals in which the assigned single inter-area mode is most observable and is located at a generator which is most effective in controlling that mode. The PSS controller, designed for a particular single inter-area mode, also works mainly in a frequency band given by the natural frequency of the assigned mode. The effectiveness of the resulting PSS controllers is demonstrated through digital simulation studies conducted on a sixteen-machine, three-area test power system.