Locating Sources of Sub-Synchronous Oscillations in Wind Farms Based on Instantaneous Energy Supply on Port and Bicoherence

The sub-synchronous oscillation (SSO) which occurred in direct-driven wind generators (DDWG) based wind farms became a research hotspot. The SSO excited the shaft torsional vibration of thermal generators and caused trip failures, leading to economic losses and stabilization problems. However, the existing phasor-based oscillation source locating methods cannot be applied to the SSO since the power system quasi-steady-state assumption was not satisfied in the SSO scenarios. Thus, a novel locating method for SSO sources was urgently required. To fill this gap, this paper proposed an improved method for locating nonlinear sub-synchronous oscillation sources based on Energy Supply on Port (ESP) and bicoherence. The ESP was calculated with the instantaneous values of measured voltages and currents at some predefined network interfaces, i.e., the ports. The tendency of the ESP indicated the transient energy injection from a certain subsystem into the rest of the network during a designated period, which can help figure out the oscillation source of the SSO. After oscillation source localization, the nonlinear index and its threshold were proposed by defining the bicoherence coefficient in consideration of the nonlinear oscillation characteristics. According to the power-quality standard and the comparison of the bicoherence with the threshold, the nonlinearity of the oscillation source was examined. The feasibility and effectiveness of the proposed method were proved in the case study which simulated the oscillation scene of the accident in Hami.


Introduction
With the development of wind power generation technologies, the conventional power system has gradually been transformed into a power system with high penetration of renewables.Recently, the subsynchronous oscillation (SSO) related to the wind farms based on direct-driven wind generators (DDWG) became a research hotspot after a new type of SSO event occurred in Hami, Xinjiang Uygur Autonomous Region of China [1].There were some significant differences between this event and the past SSO accidents.In the past, the damaged devices usually directly participated in the accidents, in other words, they were one of the origins of the accidents [2].However, in this event, the tripped generators did not take part in the oscillation at first.The torsional vibration was excited by an external source located in the northern Shanbei area [3].
It is well known that a forced oscillation can be restrained only by eliminating the oscillation source.According to [4] and [5], one of the main causes of the sub-synchronous current was the improper configuration of the grid-side controllers of the DDWGs.Since more and more DDWGs and other devices with similar structures of voltage source converters, such as photovoltaics or flexible HVDCs, will be installed in the grid, similar accidents are inescapable.Therefore, an online oscillation source locating technique is urgently needed to form an effective generator-tripping strategy and prevent equipment from being damaged in this kind of SSO event.
To suppress the oscillation, locating the sources of oscillation is an important measure [6].Correspondingly, in [7], a lot of methods for oscillation source location are surveyed and categorized, and the most notable is the energy-based method (EBM) [8], which tracks the system-wide energy flow to locate the oscillation sources.The advantages of EBM include (i) comparing with the location methods based on damping torque analysis or mode shape estimation, the EBM is adapted to locate the forced oscillations as well as the poorly damped oscillations [7]; (ii) the EBM is convenient for the voltage or current measurement in the wide-area networks [8].With the rapid development of the phasor measurement unit (PMU), the EBM has been successfully used in oscillation monitoring in actual power systems [9].Thus, this paper focuses on the EBM.Moreover, the existing oscillation source locating methods are mainly developed for low frequency oscillation (LFO).[10] proposed an oscillation source localization method, which was applied to LFO based on Energy Supply on Port (ESP).By calculating the ESP of each node with the help of online measurement, the position of the oscillating source can be quickly determined.To locate the oscillation source, [11] applied both the cut set energy scheme and the torque decomposition scheme to analyze the data obtained from the wide-area measurement system (WAMS).[12] presented a technique that considered multi-dimensional characteristics to differentiate the LFO type.[13] suggested a technique to locate the disturbance source of LFO, which took into account the absence of critical node data.However, these researchers fail to adapt to the circumstance of locating the oscillating source of SSO, which has a faster dynamic response.
This paper proposes an oscillation source locating and nonlinear detection technique based on the instantaneous ESP and higher order statistics, which can promptly figure out the nonlinear oscillation source of the SSO.It uses only online measurements and provides information about the wind farm or even the wind generators that are producing sub-synchronous energy.This information helps the operators eliminate the oscillation in the early stage to prevent worse accidents like trip failures or shaft fractures.The abbreviations in this paper are summarized in Table 1.

System Modeling
Hami, which is situated in the northwest of China, is quite distant from the major load centers.As a result, the electricity generated by wind farms in this area normally converges at a collecting substation before being transmitted to the grid through long transmission lines.In this paper, multiple identical DDWGs with a capacity of 1.5 MW constitute a wind farm.The model of DDWG and the topology of the grid-connected wind farm are shown in Figure 1, where 5 DDWGs firstly connect through their boost transformers and transmission lines forming a string.Eight strings are connected to the point of common coupling (PCC), then to the main grid through transmission lines.The electricity finally inflows Hami through parallel transmission lines from Shanbei and then is transmitted to the outer power network, which is considered an infinite bus in this paper.
As is shown in Figure 2, the wind farms in Hami present a radial hierarchy of "DDWG -Wind farm -Wind power collection station", which emphasizes the importance of a fast and accurate oscillation source location method.

Overall Framework
The overall framework of the proposed oscillation source locating and analyzing method is shown in Figure 3, which contains the following two steps.(1) Instantaneous-ESP-based oscillation source locating.Through defining the instantaneous ESP, a locating method for sub-synchronous oscillation sources is introduced.With this method, we can gradually locate the wind turbine which causes the oscillation.(2) Nonlinear detection.Through nonlinear detection, we can analyze whether this oscillation is caused by a nonlinear behavior in the control system.According to the results of nonlinear detection, we can further study the corresponding oscillation suppression strategies.In the following subsections, we respectively introduce the two steps in detail.
Figure 3.The overall framework of the proposed method.

Instantaneous-ESP-Based Oscillation Source Locating
The existing research is applied to the analysis of low frequency oscillation (0.2 Hz -2.5 Hz), so the calculation is based on phasor measurement, i.e., the electric quantities of RMS value.Because the frequency of SSO is higher (10 Hz -45 Hz), the quasi-steady-state assumption is no longer satisfied and the RMS value fails to describe the oscillation accurately.Therefore, it is necessary to use the instantaneous value acquired by measurement devices, such as the phasor measurement unit (PMU), data acquisition (DAQ) card and fault recorder, to capture the electromagnetic transient process.

Instantaneous-ESP-Based Oscillation Source Locating Nonlinear Detection
Step where i P is the active power outflow at node i, i Q is the reactive power outflow at node i, i U is the voltage amplitude at node i, i  is the voltage phase angle compared with the phase angle of the voltage- oriented vector of the network.In the energy function theory, the stability of a subsystem is determined by its cumulative energy that is affected by every ESP i .Hence, to assess the impact of the i-th input on the dynamic stability of the system, the corresponding ESP i would be a useful indicator.Considering Park transformation adopted in the control strategy of DDWGs, the electric quantities are redefined by using the instantaneous value in this paper as follows.
    where , di qi e e are the results of applying Park transformation on the three-phase voltage at node i, , are the results of applying Park transformation on the three-phase current at node i, and , i i e e   are the results of applying Clark transformation on the three-phase current at node i.The operating process of the oscillation source locating method is described as follows: Step 1: The system is chosen to be studied and the nodes are selected to be the boundary ports of subsystems.
Step 3: The nearest (in the opposite direction of power flow) nodes i connected are selected to the boundary node of the subsystem that has been confirmed to have the SSO source inside.
Step 4: ESP | with real-time measurement (with the nodes i selected in Step 3) is calculated.
Step 5: Based on the results, whether the SSO source in each designated subsystem connected is judged to the selected nodes: ESP |  indicates that the subsystem connected to node i injects transient energy into the network during 1 2 [ , ] t t , which contributes to the increase of energy storage and motivates or maintains the SSO.So, it can be determined that the SSO source exists in the subsystem.[ , ] t t , which contributes to the decrease of energy storage and inhibits the SSO.So, it can be determined that the SSO source does not exist in the subsystem.

(b)
Step 6: Steps 3 to 5 are repeated until the smallest subsystem that contains the SSO source is found.

Nonlinear Detection
In the view of timing signal analysis, the oscillatory current of DDWG conforms to the characteristic of stationary random process X (n) = A cos (Ω n + Φ), where A, Ω, and Φ are the independent random variables, and Φ conforms the uniform distribution ranging from 0 to 2π; hence, the mathematical expectation of X (n) is zero.Further, according to the principle of higher-order statistics, the third-order cumulant for the stationary random process X (n), which is understood as the skewness coefficient, can be expressed as and if X (n), X (n + τ 1 ), and X (n + τ 2 ) are independent, In (7), it is shown that the cumulant c 3 (τ 1 , τ 2 ) is an impulse function, and the Fourier transform of the impulse function is a constant, so the spectrum of the cumulant c 3 is flat.In addition, the cumulant also has a linear superposition property, i.e., if the random process X (n) and Y (n) are independent, then the cumulant Thus, if a signal X (n) composed by the sinusoidal fundamental and harmonic components satisfies the principle of linear superposition, the cumulant of the signal can be equal to the sum of the cumulant for each component, and according to Formula (7), the spectrum of the third-order cumulant for X (n) is flat.However, if there is a coupling between the harmonic components of X (n) so that the signal X(n) is nonlinear, it does not satisfy the superposition principle, and the resulting spectrum of the cumulant c 3(X) will be not flat.Hence, the nonlinearity hidden in the signal X (n) could be detected by the cumulant calculation.
Moreover, in practice, the spectrum of c 3(X) is usually defined as the bispectrum B X (ω 1 , ω 2 ), and the bispectrum can be normalized to an absolute scale in the range 0 through 1, which is called the bicoherence coefficient.The spectrum of the bicoherence coefficient and its magnitude is defined as where f 1 , f 2 , and (f 1 + f 2 ) are the frequencies for Fourier transformation; P X (ꞏ) represents the power spectrum.According to (9), the bicoherence spectrum could reflect a coupling phenomenon between the components at the frequencies f 1 and f 2 .The square of bic could be proved to represent the fraction of power generated by the nonlinear coupling between the components at f 1 and f 2 to the total power of the component at (f 1 + f 2 ).Thus, according to the property of cumulant calculation, the criterion of nonlinear detection for a random process X (n) can be described as follows: if the value of bic for X (n) is constant, the process X (n) is a linear one; otherwise, the situation is opposite.So, a nonlinear index μ for checking the flatness of bic could be defined as In (10), if μ > 0, the signal-generating process is nonlinear.
According to the power-quality standard [14], Table 2 reports the harmonic limitations for 35 kV networks, and the corresponding result of index μ is 0.0180 obtained by simulation; compared with the result from simulation, the threshold value has a sufficient margin.Based on the above analysis, the method to determine if the nonlinear oscillation occurs for DDWG is as follows: according to the result of oscillation source searching, the value of nonlinear index μ is calculated by measuring the output current of the DDWG at PCC.If the μ value for a DDWG is a bit high and more than the threshold, the oscillation associated with the DDWG is nonlinear.

Case Study
In this section, a test system that is similar to the actual grid in Hami will be simulated and studied to verify the method proposed in Section 3. The topology is simplified according to Section 2, as shown in Figure 4.
Due to the computational complexity of the simulation, all the wind farms are supposed to contain 10 DDWGs (2 strings, 5 DDWGs in a string) in this paper.As shown in Figure 5, to induce the SSO, DDWG 8 is chosen in the wind farm W 3 and configured the control parameters so that it has a pair of characteristic roots in the right half-plane and outputs sub-synchronous current.When the oscillation causes the current reference i dref to reach the hard limit of the PI in the d-axis outer control loop of voltage, it becomes a self-sustained oscillation.The oscillation can be observed at the generator terminal of the fault DDWG, as shown in Figure 6.An oscillation superimposed on the current at the fundamental frequency could be observed.After performing Park transformation, a sub-synchronous oscillation at 34 Hz could be noticed in Figure 6, which thus arouses oscillation at any node in the system.For example, as shown in Figure 7, the oscillation at node 9 is with a frequency of 34 Hz, which is the same at the terminal of the fault DDWG.To locate the oscillation source, a period is randomly ([2 s, 5 s] in this case) selected and ESPs are calculated as proposed in Section 3.  Firstly, ESPs are calculated at nodes 7, 8 and 10 by using the instantaneous value.The nodes 7, 8 and 10 are chosen prior to the others because they are the nearest nodes connected to the infinite bus in the opposite direction of power flow.As shown in Figure 8, the subsystem connected to node 10 has almost no contribution to the increase of energy storage of the whole system.Meanwhile, the ESP from node 7 finally inserts into the infinite bus through node 8. Noted that W1, W2, W3 and W4 are connected to node 7 directly or indirectly in the direction of power flow, the SSO source must exist among them.The search range narrows down to the red square frame in Figure 4.  Secondly, by calculating ESPs at nodes 3, 4 and 6, it can be concluded similarly that only the subsystem connected to node 3 injects energy into the network during [2s, 5s], which motivates the SSO.Therefore, the search range narrows down to the blue square frame in Figure 4, so the fault DDWG exists in the wind farm W3.
Thirdly, ESPs are calculated at the generator terminal of each DDWG inside W3 by using the instantaneous value.DDWG 8 is exactly the generator with the badly-configured parameters.The waveforms of ESP of the rest of the DDWGs inside W3 are almost the same, so DDWG 3 is picked randomly to compare with DDWG 8.In Figure 9, the ESP of DDWG 8 increases significantly while that of DDWG 3 decreases slightly.Therefore, the oscillation source locating technique can promptly figure out that DDWG 8 is the oscillation source of the SSO.
Finally, the nonlinear index μ in Formula ( 10) is calculated for DDWG 8. Figure 10 is the contour map of the bicoherence spectrum, which exhibits peaks, indicating nonlinearity.After calculation, the value of μ is 0.3727, which is much larger than the threshold of 0.10 derived in Subsection 3.3.Therefore, the nonlinear index indicates that the oscillation source has a nonlinear behavior, which is consistent with the configuration of the case.

Discussion
This paper proposes a novel method for locating SSO sources based on ESP and bicoherence, and the effectiveness of the method is verified according to the simulation results.In this section, the limitations, application conditions and future improvements of the proposed method are further discussed as follows.
First, the proposed method depends on advanced measurement technologies (e.g., the PMUs) and reliable communication systems.If there exists a measurement fault or communication fault in the power system, the SSO sources will not be located rapidly and accurately, which is a limitation of the method.
Second, since the ESP adopted in the proposed method is calculated according to the instantaneous values of the electrical quantities; thus, the proposed oscillation sources locating method can be applied to both LFO and SSO scenarios, which shows the generality of the method.
Third, considering the future improvements, since the SSO sources can be accurately located and the nonlinear cause of the SSO can be detected with the proposed approach, effective SSO suppression methods can be further investigated.Moreover, since the mechanism and corresponding analysis method of the nonlinear oscillations are different from those of linear oscillations, and the direct analysis of the SSO using a linearized method and adoption of the corresponding measures to suppress the oscillation are unacceptable, thus, the SSO nonlinear detection results can help analyze the mechanisms of the SSO, which is of vital significance for the power system security and stability.

Conclusion
With the occurrence of SSO accidents related to high penetration of renewables, this paper addressed the issue of locating SSO sources caused by wind farms based on DDWGs and identifying their nonlinearity.The conclusions were summarized as follows: (1) To capture the electromagnetic transient process in SSO accurately, the instantaneous energy supply on the port was defined, and an instantaneous-ESP-based oscillation source locating method was proposed, which could be applied to the determination of the smallest subsystem that contained an SSO source.(2) To identify the cause of the SSO, a nonlinear detection technique based on bicoherence analysis was proposed, which could show whether the SSO was derived from nonlinear behavior in hard limits.(3) The detailed steps for oscillation source localization and nonlinear detection in engineering were proposed.
In the case study, a simplified practical system imitating the oscillation scene in Hami was tested.The searching area was swiftly narrowed down to the fault DDWG after three rounds of calculation and then its nonlinearity was examined by comparison of the proposed nonlinear index with the threshold.The simulation results verified the effectiveness of the developed SSO source locating method and the nonlinear detection approach.

Figure 2
Figure 2 shows the topology of the power network studied in this paper.The voltage level inside the wind farm is 35 kV, while the lines in green and red represent transmission lines with the voltage level of 110 kV and 220 kV respectively.The electric power flows from Wind Power Collection Station 2 (connecting 8 wind farms) and Wind Power Collection Station 2 (connecting 7 wind farms) into Shanbei.Three other wind farms connect to Wind Power Collection Station 3 and send power to Shanbei as well.The electricity finally inflows Hami through parallel transmission lines from Shanbei and then is transmitted to the outer power network, which is considered an infinite bus in this paper.As is shown in Figure2, the wind farms in Hami present a radial hierarchy of "DDWG -Wind farm -Wind power collection station", which emphasizes the importance of a fast and accurate oscillation source location method.

Figure 1 .
Figure 1.Grid-connected wind farm model.Figure 2. Topology of the wind farms in Hami.

Figure 2 .
Figure 1.Grid-connected wind farm model.Figure 2. Topology of the wind farms in Hami.
indicates that the subsystem connected to node i extracts transient energy from the network during 1 2

Table 1
For the interconnected subsystems, the ESP i (t) at node i is defined as: 4

Table 2 .
Harmonic limitation and the threshold for nonlinear detection.