There is a vast amount of techniques available in the literature for the study of SSO in electric power systems [73]-[84]. Depending upon the applications and requirements the most common techniques adopted are:
2.7. Subsynchronous Oscillation Analysis Methods
2.7.1 Screening Studies
The increased interest from the power systems equipment suppliers and system operators in the light of new SSO events paved the way for the developments in SSO screening studies as reported in [30, 81, 85]. The recent advancements in this direction can be summarised under the three categories:
2.7.1.1 Eigenvalue Analysis:
Eigenvalue analysis or modal analysis is identified as one of the most matured and detailed scree- ning technique for SSO identification [81, 85]. It is based on the mathematical representation of electrical network, generators and power electronic devices of interest in a common linearise system of differential equations [27, 85]. Eigenvalue analysis can be used to predict the system state behaviours under small-disturbances and are suitable for SSR, SSCI and SSTI analysis. Moreover, the detailed information on the system performance beyond the normal frequency scanning can be achieved for each modes of oscillation [27, 85]. Another key advantage of this method is that it can be combined with well known linear control schemes and can be used to design SSO damping methods [85, 86]. However, this method is computationally intensive and complex, which requires detailed mechanical and electrical system representation, with a separate linear model required for each network configuration [83, 85].
2.7.1.2 Frequency Scan/Harmonic Impedance Analysis:
Frequency scan analysis introduced in late 1970’s is used to determine the network impedance as a function of frequency viewed from behind the generator equivalent impedance [87]. Furt- hermore, it can be used to determine the approximate electrical resonance frequency and can be also used to recognise those sections in the system that is not influenced by SSR [27, 87]. The technique is a common tool in industry for SSR, SSCI and SSTI screening of a large system during the design stages [27, 47, 79]. Resonance points and damping of the system can be deduced from frequency scans to asses the possibility of SSO’s [27, 47, 79]. The main limitations of this technique is associated with the representation of the power electronic devices in the network and do not take into account system contingencies and transient events [47, 85] .
2.7.1.3 Unit Interaction Factor Analysis:
The influence of HVDC converter control on the torsional oscillations and damping of a genera- tor under study can be quantified by the Unit Interaction Factor (UIF) which was developed by Electric Power Reserch Institute (EPRI), US [88]. It is widely used as a screening level indicator for SSTI identification, so as to determine the level of risk [27, 88]. In general, UIF can be defined as: U I F =MV AHV DC MV AGi .[1 − SCGi SCT OT ]2 (2.1)
where MV AHV DC, MV AGi, are the rating of the HVDC and generator under study; SCGi, SCT OT
are the system short-circuit capacity at the HVDC bus with generator under study in-service and without service [27, 88]. A UIF value of less than 0.1, indicates less possibility of interactions and is recommended. The UIF is performed with different AC network configurations and contingencies so as to evaluate the SSTI condition when the system configuration changes [27, 88]. As this is routinely carried out before HVDC installations, once SSO risk is identified (UIF>0.1), a detailed Electromagnetic Transient (EMT) analysis is required for further evaluation and control design [27].
2.7.2 Damping Torque/Perturbation Analysis
A damping torque analysis can be used to determine the contribution made by the power systems towards the electrical damping of the generator unit of interest [27, 89]. It is a useful tool for SSR, SSCI and SSTI analysis which received much interest due to the simple representation of the mechanical characteristics [90]. This analysis can be carried out only with electrical representation of power system components in an EMT type simulation with a non-linear representation and detailed control system of associated power electronic device [27, 89]. This avoids the limitations associated with eigenvalue screening method. The damping torque analysis is carried out by perturbing the generator speed and correspondingly calculating the electric torque of the generator unit of interest [89, 90]. Further, this torque response is used to calculate the electric damping for all the subsynchronous frequency range by varying the perturbation signal frequency from zero to the fundamental value [89, 90]. To generalise, the real
2.7. Subsynchronous Oscillation Analysis Methods
part of the network transfer function (or network equivalent impedance) between speed change and the electrical torque indicates the electrical damping factor. If the resultant damping torque is negative the torsional oscillation is unstable [89, 90]. However, this method is computationally intensive and time-consuming.
2.7.3 Electromagnetic Transient Analysis
To overcome the modelling challenges associated with SSO screening techniques, detailed time-domain analysis in an EMT type digital software platform or real-time simulator is a proven alternative [26, 90]. The key advantage of th kind of solver is the identification of SSR- TA phenomenon instigated by a large system disturbance [90, 85]. Detailed models of both mechanical and electrical systems can be simulated for a large transient case and can also test corrective actions [26, 27]. Off-line simulation becomes handy when the overall system response needs to be simulated in response to an SSO event and to analyse the performance of necessary control actions and protection settings [26, 27]. Moreover, this approach is essential to analyse multiple network configurations and system topologies. Real-time simulation on the other hand, shows the closest realistic dynamic performance of a power system and is widely used by utilities and suppliers [6, 91, 92]. Moreover, they form the basic building block for hardware-in-the loop (HiL) analysis for system stability studies such as SSO [6].
2.7.4 Hardware-in-the-loop Experiments
To take a further step in the SSO analysis and control design HiL experiments can be conducted. The HiL simulations can be performed as a complementary test for off-line and real-time simulations, which can be considered as a final stage before implementing the device or solution in real-systems. Moreover, the HiL allows the tests to be performed in a safe and controlled environment without risking the real power system equipments and can represent the natural characteristics such as uncertainties, interferences, noises and practical limits of the real-system [6]. Research advancements in this direction have been recently reported in the literature. This include different options to replicate the dynamics of multi-mass enabled synchronous generators, HVDC and series-compensated AC lines [93, 94, 95]. However, a full scale series- compensated AC/DC grid representation with detailed power system models is still missing
from the literature.