A non-PMU-based WAN protection scheme for swing detection and stability enhancement in power systems

The legacy-applied techniques of power swing detection and out-of-step protection rely on measurements of electrical parameters. The most widely used parameter is the impedance, where its rate of change is directly proportional to the swing frequency according to [2]. The out-of-step and stable power swing conditions are discriminated further based on the monotonicity of the impedance change. Figure 1 shows the rate of change of impedance method.

In [3, 4], the blinder technique is introduced. The measured impedance in this technique is the load impedance under typical system operating conditions, and its locus is normally away from the distance relay protection characteristics. When a fault occurs, the measured impedance moves almost instantaneously from the load impedance point to the point that corresponds to the fault in the impedance plane. Under swing condition, the measured impedance on the impedance plane moves in a slow pace on the impedance plane. Figure 2 shows the blinder scheme.

The main drawback of the blinder technique is the fact that extensive offline stability simulations for various swing scenarios are necessary for setting the impedance blinders; in addition, it is not suitable to detect swings of increasing frequency slips. Moreover, it is a local swing detection, confined to the protection connection point, and this scheme is mainly used to discriminate the power swing from fault condition in distance relays. As a modification to the rate of change of impedance method, the rate of change of apparent resistance is introduced in [5]. For the purpose of out-of-step detection, the study domain and the electrical parameters used are changed. Nonetheless, this method offers no advantages over rate-of-change impedance-based approaches.

Another conventional out-of-step detection method is the swing center voltage (SCV) technique [6], and it computes voltage at a virtual center in the power system. When the angles between the two sources of a two-source equivalent system are 180 degrees apart, there is a location in the network with zero voltage. The voltage at this location at different angle values is defined as the SCV. The SCV method utilizes the voltage change rate at the swing center to decide whether out-of-step condition is valid or not [2‐7]. The main drawback of the SCV method is that it is applicable only on the two-machine system; therefore, their implementation in actual multi-machine power systems requires extensive network reduction. Moreover, the estimation of voltage at the virtual center is accurate only when the line impedance angle is 90 ͦ.

The authors of [8] proposed a coordination transformation scheme for swing detection using a two-machine equivalent system; however, several empirical thresholds are used for multi-machine power systems, which requires offline studies. The authors of [9] proposed the study of the trajectory on state plane to determine the critical clearing time and angle based on estimation of total energy. However, reducing the entire network to the equivalent two-area system is necessary for this method.

A non-conventional swing detection scheme called continuous impedance calculation is introduced in [10]. It entails tracking the trajectory of three modified loop impedances in the complex plane. The criteria of power swing are met when the change in all three-loop impedances fulfills continuity, monotony and smoothness. A major advantage of the continuous impedance calculation is the fact that no settings are required and therefore it does not require any stability studies involving complex simulations, while the limitation is the fact that it is a local swing detection, confined to the protection connection point. Besides, the scheme is not applied by all relay manufacturers.

In [11], an algorithm for power swing detection based on the rate of change of impedance angle is proposed. The algorithm defines an index for measuring the impedance angle and another index for the rate of impedance angle change (RIAC). The RIAC index is used to discriminate fault from power swing, while the impedance angle index is used to identify the out-of-step condition during the power swing. The algorithm is fast and can be implemented in industrial relays; however, it is still local detection like the above-mentioned schemes.

The authors of [12] proposed a scheme for power swing detection and distance relay blocking using the variance calculation of the current sampled data. In a way to reduce computations, burden in a digital relay is to perform them directly on the sampled data. The proposed algorithm calculated the variance of discrete data of the three phase currents by averaging the square of the predicted or observed distance from the expected value. Since the variance is a measure of how a series of data are spread around their mean value, it can be used as a distinguishing parameter of the disturbance whether it is a fault or a swing. The changes in the variance value during power swings are small, but during a fault, these changes are extensively large. Accordingly, a threshold is calculated to distinguish the power swing from the fault case. The main drawback of this method is that the threshold value required by the scheme must be obtained using variety of power swing types and variety of fault types. Also, it is a local swing detection, confined to the protection connection point; therefore, it is mainly used to discriminate the power swing from fault condition in distance relays. Moreover, the scheme needs to be proven by industrial relay manufacturers.

Intelligence-based methods for protection against out-of-step were also proposed [13‐20]. A scheme based on fuzzy logic was introduced in [13] for out-of-step detection. The inputs used in the fuzzy inference blocks comprise measurements such as pre-fault and post-fault currents, voltages and the generators angular speeds. However, the out-of-step detection effectiveness is only demonstrated for a two-machine power system.

The authors of [17] used fuzzy logic to identify out-of-step conditions by utilizing phasor measurements. However, when used on big multi-machine power systems, the main challenges are identifying adequate input variables, membership functions and creating appropriate "if–then" decision rules.

Artificial neural network (ANN)-based approach was introduced by the authors of [14, 15] for out-of-step protection. Nevertheless, this approach was verified for systems comprising up to three machines only. In [20], a new ANN approach using the group method of data handling (GMDH) was introduced. The GMDH approach is better performing and requires less training time compared with other conventional neural networks. The response time of this approach is good, yet it requires the distance protection function to operate during detection. Besides, in principle, substantial offline simulations are necessary for ANN based approaches to train and test the algorithm. In [21], equal area criteria (EAC) in P‐δ curve is applied to detect out-of-step condition. According to the EAC-based method, the initial power angle and the critical clearing angle (δ_cr) are calculated and the accelerating area under the P‐δ curve following a fault is compared with the decelerating area following the fault clearance to determine whether an out-of-step condition occurs. The EAC method's primary flaw is that multi-machine power systems cannot be directly applied to it. The EAC approach is applied right away to a multi-machine power system in [22‐25] without network reduction and is adjusted to work in the time domain. However, [22‐25] use numerical simulation of only few chosen case studies to illustrate the suggested algorithm in multi-machine systems. The authors of [26] introduce an extended EAC (EEAC) that can be used for out-of-step detection in multi-machine systems. However, it reduces the multi-machine system to an equivalent two-area system. So, in the EEAC method, network reduction is still crucial, leading to system-specific settings for out-of-step detection.

With the advent of phasor measurement units (PMUs), the protection system of power grid was able to utilize the information contained in wide area measurement system (WAMS) and hence novel out-of-step protection algorithms could be invented.

Lyapunov's method has been successfully used for stability investigations in power systems [27, 28]. PMU-based out-of-step detection that uses dynamic state estimation and Lyapunov functions was developed by the authors of [29]; however, the technique is only realized for the two-area equivalent system. In an attempt to achieve a stability region that is similar to Lyapunov's direct technique, Zubov developed a modified method using approximations. Studies of power systems stability have employed Zubov’s method; however, protection applications have not. In [30], Zubov’s approximate stability boundaries were used for out-of-step detection application. The detection method used a group of those Zubov’s stability boundaries in power angle–frequency (Δ–ω) plane. The proposed algorithm is based on real-time PMU measurements and can be readily implemented for multi-machine power systems without requiring extensive offline simulation studies/network reduction for out-of-step settings. Zubov’s boundaries are computed given the information of δ₀ and ω₀ information, which can be obtained from measurement units placed on the power grids. Continuous PMU data streaming is received during the disturbance and utilized to plot trajectories on δ‐ω plane. For out-of-step detection, the δ‐ω trajectory must pass through the outermost boundary [30].

Case studies are carried out with this scheme in SMIB and New England 10-machine 39-bus power systems and showed good results. The main drawback of this method is that the boundaries are predefined based on initial operating condition and are not updated in real time according to load changes.

Another wide area PMU-based scheme in wide area network power swing detection was introduced in [31]. A maximal Lyapunov exponent (MLE)-based model-free rotor angle stability assessment approach is proposed. In order to measure the stability of dynamic systems, Lyapunov exponents (LEs), which describe the separation rate of infinitesimally close trajectories, are considered strong indicators. The system is unstable if its maximal Lyapunov exponent (MLE) is positive, and vice versa. Model-free LE-based stability assessment techniques were adopted as they can reduce calculation complexity and avoid model errors; however, a time window must be identified for MLE monitoring purpose. For fast and accurate evaluation of stability, the window size is essential. The scheme relies on determining the severely disturbed generator pairs (SDGPs) as they are the main factor controlling system dynamics following significant disturbances. The SDGP's relative rotor speed and the separation between the rotor angle trajectories are closely related. MLE is estimated for SDGP rotor angle trajectory. Real-time measurements of the rotor speed and relative rotor angle are collected by PMUs.

When the MLE curve of an SDGP is estimated, the assessment of rotor angle stability depends on the pattern of that curve, either increasing or decreasing with time. The system is considered stable if all SDGPs are stable; otherwise, the system is unstable. The main drawback in this method is the fact that the scheme needs relatively long time for the MLE estimation process to be completed, which is not adequate for detection of fast swings.

The authors of [32] proposed a method for assessing rotor angle stability using WAMS data. The method identifies the generator pair that is most adversely impacted by a disturbance by evaluating rotor angle deviations. According to [33], a system of a group of generators becomes angle unstable when a pair of generators have an angle difference of 180° or more between them. In [32], relative rotor angle between each generator pair is defined as the angle between each pair of machines at any time instant after disturbance. Relative angle between the same pair of machines just before disturbance is also defined. The generator angles are estimated with respect to the slack bus generator. PMUs measurements and streaming are used for the estimation of the generators’ rotor angles. Most disturbed generator pair (MDGP) is identified from the two defined relative angles for each generator pair. Stability assessment is then applied on the identified most disturbed generator (MDG) using a predictive auto-regression (AR) approach to identify unstable fast swing if the predicted value crosses a threshold. For slow swing, the damping coefficient of the most dominant frequency obtained from Prony analysis is used in conjunction with the instantaneous rotor angle values to obtain a stability index. The results show improved performance compared to the MLE approach in [31] in detecting fast swings.

A more recent technique is to apply machine learning and big data obtained from PMU-based WAMS system in stability assessment. In [34], a scheme based on big data and core vector machine was introduced to realize real-time calculations on overwhelming datasets. However, multi-stage offline training procedure is essentially required which increases complexity and time consumption and renders the accuracy of such schemes subject to the availability of very large amount of data. In addition, the adversarial examples are serious challenge to the machine learning approach in general which requires to be mitigated. Adversarial examples are inputs to a neural network that result in an incorrect output from the network. In [35], a mitigation model was proposed for the vulnerability of machine learning-based power system stability assessment under adversarial examples. However, the machine learning approach still needs more advancements to match power systems requirements.

In summary, it could be said that all the existing methods used in power swing detection and stability assessment are either local methods built in an individual device or require long offline stability simulations like in conventional impedance-based methods or consume long time for data gathering and training like in AI-based and machine learning-based methods. Furthermore, for the existing WAMS-based stability assessment methods, the absolute value of the rotor angle of some selected generators on the grid is estimated using synchrophasors calculated by PMUs. Thus, an additional device other than the normally existing devices in the power plant has to be placed at each selected generator node on the grid. Also, these schemes require continuous transmission of the estimated rotor angle whether there is a swing or not, and this may increase statistically the vulnerability to noise and errors. In addition, the PMUs have to synchronize their measurements using a time reference like a GPS clock, which adds to the restrictions of the existing WAMS-based schemes. It is also worth to mention that the available WAMS-based mathematical algorithms to evaluate stability are not standardized, as there are diverse mathematical approaches adopted by researchers and hence are not applied—so far—in the industrial level.

In this paper, a new scheme for power swing detection in multi-machine power systems that uses packet switched network industrial protocols is proposed. It adopts the smart grid concept which calls for expanded use of digital information and controls technology to enhance the electric power grid’s reliability, security and efficiency. The scheme aims to overcome the above-mentioned restrictions in the current techniques, especially the WAMS-based ones. This is accomplished by introducing the concept of asynchronous estimation of the change in rotor angle instead of the synchronous estimation of absolute rotor angle using PMUs. This is certainly achievable in the scheme since it relies on estimating the change of each generator rotor angle with respect to its own initial value, not on the angle absolute value.

By asynchronous estimation, we mean that the voltage angle at any bus on the grid is measured by an intelligent electronic device (IED) independently and not synchronized to the measurements at other buses. The IED can be the existing protective relay that normally measures the bus voltage and hence can compute the phase angle and reflect its change on the pattern of data it transmits on the network. This approach will replace estimating the absolute value of each generator angle via a PMU synchronously with other PMUs connected to the selected grid buses and sending the estimated data continuously whether there is a change in the angle or not, as in the WAMS technique.

Thus, the data transmission in the proposed scheme will be restricted to the power swing period and hence will reduce the traffic on the communication network and consequently vulnerability to errors. Last, the proposed scheme presents an approach to standardize the process of grid stability assessment by applying international industrial communication standards instead of applying diverse schemes involving various mathematical methods.

The rest of this paper is divided into three sections. Section 2 introduces the proposed scheme. Section 2.1 presents the basic operation principle. Section 2.2 introduces the concept of estimating the change in rotor angle in terms of change in the generator bus angle. Section 2.3 demonstrates the process of phase angle estimation as implemented in numerical relays. Section 2.4 illustrates the concept of transmission of phase angle change information in a coded form on the network when the angle exceeds predefined limits. Section 2.5 illustrates the concept of measuring a perturbation in a system using the GOOSE protocol. Section 4 shows the simulation results for fast unstable and stable swing cases, which proves the fast detection capability of the proposed scheme. Finally, the conclusion is presented in Sect. 4.

Following the major smart grid concept of increased employment of digital information and controls technology to improve the power grid reliability, the proposed scheme is developed.

For a cluster of interconnected generators in the grid as shown in Fig. 3, it is essential that each generator bus is connected to an IED that computes the bus voltage magnitude and angle. This normally existing IED will be used in the case of power swing to compute the angle change of the generator node suffering swing and transmit it in a coded or keyed form on a wide area network to one central detecting device (or more if needed). Since all modern IEDs can communicate using IEC 61850 standard and almost all power grids possess fiber optic cables that enable very high-speed data communications, the power grid data network can be used to transmit specific protocol data packets, indicating the swing rate in direct proportionality to the rate of change of the measured bus voltage angle.

The central detection node of that cluster (with IED 1 in Fig. 3) will receive the multicast protocol messages and detect the swing severity at the sending generator node based on a certain algorithm. It can react accordingly to each point suffering swing with the appropriate action through the same protocol. Thanks to the very high speed of the data network multicast protocol, the central detection IED can receive the messages from all nodes simultaneously without the need of synchronizing the measurements at all nodes like the PMU synchrophasor technique.

The most important contributions of the proposed scheme are:

It is an approach to standardize the process of grid stability assessment by using standard industrial network protocols instead of using diverse mathematical algorithms.

The traditional approach in evaluating rotor angle stability in most of wide area detection schemes was to estimate the absolute value of the rotor angle of some selected generators on the grid using synchrophasors calculated by PMUs. The computed phase of the synchrophasor of each selected generator is then transmitted continuously to a central processing device to be compared synchronously to the corresponding phase of other generators on the grid, and hence the grid stability is evaluated. In this section, it will be proven that the rate of change of the rotor angle of each selected individual generator could be used to evaluate stability when computed simultaneously with that of other generators. The simultaneous computation does not require synchronized measurements, it will be rather done via real-time high-speed network communications.

In this section, we will show mathematically that the rate of change of the rotor angle can be determined in terms of the rate of change of the generator bus voltage angle.

Assuming a varying frequency with time such as in the case of accelerating machine rotor, the instantaneous phase difference between the varying frequency voltage signal and the constant frequency voltage signal is:where ΔФ_i is the instantaneous phase shift from the constant frequency signal and Δω is the angular frequency change in rad/s.

Differentiating both sides of (1) yields:

Equation (2) reveals that the rate of change of the phase shift equals the instantaneous frequency deviation. It can then be concluded that when the angular frequency deviation becomes zero, the equation becomes:

Equation (3) implies that the phase shift becomes a constant value with time when the voltage signal frequency reverts to its nominal value. This condition holds when the generator rotor reverts to its nominal speed and hence indicates the onset of oscillations.

At steady state, the generator’s rotor is rotating with the nominal synchronous speed ω₀ and the rotor angle δ is constant. However, when a disturbance occurs to the system like a fault or a sudden load rejection, the rotor accelerates and δ increases with time. As a result of this acceleration, the instantaneous phase angle of the generator bus voltage increases also with time. In a similar argument, after the fault clearance or load restoration, the rotor decelerates (while δ is still increasing) till the rotor speed reaches ω₀ and then δ starts to decrease. In the latter case, the instantaneous phase angle of the generator bus voltage also follows δ in its behavior.

It can be shown that the instantaneous change in rotor angle from the nominal angle δ₀ is given by [28]:

From Eqs. (2) and (4), it can be seen that the rate of change in the instantaneous phase of the generator bus voltage is the same rate of change in the rotor angle:

Therefore, the estimated change in the phase angle of the generator bus voltage can be used to indicate the change in the rotor angle and hence the status of the generator from rotor angle stability perspective.

Instead of using PMUs in the electrical grids to compute the voltage phase angle, in the proposed approach, the inherent function of the phase angle estimation of phasors in any numerical IED will be exploited. The sampling process to extract the phasors is typical in both PMUs and other IEDs like numerical relays; however, the sampling in numerical relays is not synchronized to a time reference as it is the case in the PMUs.

In this section, we will start with the concept of numerical extraction of the phase angle of voltage phasors to reach a mathematical expression for the change in voltage angle as frequency deviates from its nominal value during power swing.

Mostly, all numerical relays as well as PMUs adopt the discrete Fourier transform to extract the phasor of the measured voltage signal.

In the modern numerical protection relays involving digital signal processing, the computations are performed in the discrete-time domain.

Discrete signal is created by taking samples of a given continuous signal at specific instants of time.

The finite length sequence x[n] now exists for a total number of samples N. The truncation of the signal into a limited number of samples x[n] yields the DFT whose general formulation is given by:where n is the sample number and k is the harmonic frequency order.

Evaluating X(k) at the fundamental frequency f₀ (corresponding to k = 1 in Eq. (14)) gives X(1), where the phase angle of which is given by: where Im(X(1)) and Re(X(1)) are the imaginary and real parts of the complex expression X(1), respectively. The expression in Eq. (10) gives the phase angle of the fundamental frequency with respect to an internal time reference in the IED. It is important to mention here that the time reference from which the angle is measured is not the cosine signal with the nominal system frequency synchronized to the universal coordinated time (UTC) reference as in the case of PMU synchrophasor technique. It is rather an internal time reference in the IED related to the start of sampling process, which is not of significant importance to know since the proposed approach relies on the change in the angle not on the absolute angle value. Assuming the initial phase angle value with respect to the internal time reference is θ, then the phase angle value computed every sinusoidal cycle with respect to that time reference is always θ if the signal frequency remains at its nominal value. During the acceleration or deceleration of the generator’s rotor, the frequency will continuously drift from its nominal value and the phase angle relative to the time reference will keep changing from θ and the voltage waveform will not be a pure sinusoid. Since the DFT samples the voltage waveform at integer multiples of the nominal or fundamental frequency (in our case, the integer is equal to one), the phasor extraction will not be at the true waveform fundamental frequency and the leakage phenomenon will occur. Leakage is defined as the phenomenon where the energy of the signal spectrum decreases at fundamental and spills over to the higher harmonics. Nevertheless, when the frequency drift is small enough relative to the fundamental frequency value, the leakage will be minimal. If we assume that ΔФ_i(t) defined in Eq. (1) for a slowly continuous varying frequency sinusoid is measured periodically at t₀ ms intervals, then it can be proven that these measured phase values are approximately equal to the phase values of the fundamental component computed by the DFT for that waveform at the same t₀ ms intervals [36]. This could be expressed as:where θ is the initial phase angle and nt₀ is multiple integer of the sinusoidal cycle time t₀. We can recall from Eq. (7) that the discrete phase angle relative to the IED internal time reference and computed at the fundamental frequency by DFT every sinusoidal cycle is calculated as:where X(1) is evaluated at θ + nt₀ intervals. Therefore, the change in discrete angle with time can be used to indicate the change in the generator bus voltage angle and consequently the change in rotor angle δ. Thus, the change in \(\Delta \emptyset_{{d\_{\text{fund}},t = \theta + nt_{0} }}\) can be used for the angle stability assessment. For simplicity, \(\Delta \emptyset_{{d\_{\text{fund}},{ }t = \theta + nt_{0} }}\) will be referred to as ΔФ_d in this context. Now, Eq. (5) can be rewritten as:where ΔФ_d is the discrete fundamental phase angle estimated every t₀ interval.

In principle, the phase angle of the generator bus voltage is computed by the measuring IED or PMU every cycle. In contrary to PMU-based wide area detection schemes, this approach does not necessitate synchronizing all phase measurements over the entire grid and send these measurements by the PMUs continuously in digital streams whether there is a swing or not. It would rather rely on measuring the angle asynchronously by each measuring IED and then transmitting a coded form (or network keyed packets) of the phase angle change asynchronously using a high-speed packet switched network protocol. The transmission will not be continuous, and it shall start only when the phase angle increases beyond a predefined limit. To achieve this, a convenient protocol should be selected. A multicast network protocol would be the best choice here in order to ensure the delivery of multi-source information at any desired destination node simultaneously within a very short transmission time.

The instantaneous phase ΔФ_i(t) will be compared to predefined angle boundaries (from β₁ to β_n) as shown in Fig. 4, and the comparison result will be mapped to Boolean variables. However, due to the numerical nature of the IED, it is not able to compute the continuous phase angle ΔФ_i(t) and it will compute instead the discrete ΔФ_d using the DFT. Let k₁ through k_n denote Boolean variables of some dataset D, D = {k₁, k₂, …., k_n}. To realize the mapping to Boolean variables, the following conditions shall apply:

where β_n is the farthest phase boundary corresponding to some phase value below 180 degrees. The Boolean variables will then be transmitted sequentially in packets using the multicast protocol. To have an insight on the transmitted packets content, the acceleration cycle of power swing will be considered as an example. As the rotor accelerates, ΔΦ_d will keep increasing; thus, the k Boolean variables will be incrementing from 0 to 1 sequentially. Then, the expected pattern of the Boolean sequence streams transmitted on the network will be as follows:where m is some integer less than n.

The transmitted Boolean sequences during acceleration can be expressed in matrix form as:

The stream m above exhibits the peak of the monotonic change of the variable ∆δ with time during the acceleration cycle of power swing. The successive increment of the values of Boolean variables can also be noticed from one stream to the stream following it as shown in the diagonal of the matrix of Fig. 5.

In this section, we will demonstrate how the sought protocol to fulfill the requirements of the approach introduced in the above section is very close to the Generic Object Oriented Substation Event (GOOSE) protocol or its successor Routable GOOSE (R-GOOSE). Yet, the handling of both of them needs to be manipulated to accommodate the dynamics of the electrical grid and its phase angle variations. The following subsection provides a brief introduction of the GOOSE protocol operation.

The simulator used in this part is IEC 61850 Xelas Energy Management. The simulator will be used to emulate a real IED measurement device. The Wireshark network analyzer will be used for the packets display and analysis. The Substation Configuration Language (SCL) file (refer to Appendix 1) imported in the simulator is a typical file of a P442 distance protection relay manufactured by GE.

The SCL file defines the basic IEC 61850 parameters such as the logical device, logical nodes and data objects of the protection and measurements functions of the physical device. It defines also the communication service blocks such as report control blocks and GOOSE control blocks where the dataset of the Boolean variables used in this scheme is located.

The distance protection function is usually used in the generator protection to detect power swing and hence enables the generator protection to discriminate between actual fault and swing. In addition, it discriminates between stable and unstable swing based on the classical impedance measurement method as mentioned in the introduction of this paper. Nevertheless, the power swing function in the simulated relay will not be used and the estimated voltage phasor angle will be used instead to implement the proposed scheme. Figure 10 shows the setup deployed in the simulation.

The SCL file is imported to Xelas simulator on two PCs as shown in Fig. 10. The below data attribute of the relay IEC 61850 model is used as the generation bus voltage angle:

Appendix 1 helps the reader to recognize the simulator view and the structure of an IEC 61850 data object

The data attribute mentioned above, which represents ΔФ_d of the generator bus voltage, is increased using the simulator in a continuous manner similar to the case of fast unstable swing.

The mapping is accomplished by entering Eqs. (11) through (13) with n = 4 as preconditions in the simulator for 30-degree-angle steps from 0 to 120 degrees. The angle is changed at a rate of 30 degrees every 20 ms approximately. As a result, the Boolean variables from k₁ to k₄ change from 0 to 1 successively. This will invoke the transmission of four GOOSE packets successively from the measuring device IED 1.

The Wireshark capture in Fig. 11 shows the four GOOSE packets numbered from 8 through 11 published by the measuring IED and the packet 12 which is the response from the detecting IED (IED 2 according to Fig. 10) after detecting the fast swing. The content of packet 8 is displayed in the bottom pane of Fig. 11.

Figure 12 shows graphical representation of the five consecutive packets with time. The GOOSE packets are shown as pulses, where the pulse is dark shaded when the corresponding k variable is equal to one and it is not shaded when the k variable is equal to zero.

This simulation represents a hypothetical case of a very fast unstable swing and hence demonstrates the capability of the proposed scheme to detect the worst real fast swings which are certainly slower that this hypothetical case. The Boolean sequence content of the four packets is depicted in Fig. 12. The k Boolean sequences are (1000), (1100), (1110) and (1111), corresponding to the angle changes of 30, 60, 90 and 120 degrees, respectively.

Therefore, the Boolean sequences increment consecutively without replica or retransmission packet between them, indicating monotonic fast swing. The remote detecting device IED 2 responds to the successive change of the Boolean variables and hence to monotonic rotor angle increase by packet 12 as shown in Fig. 11. Thus, this packet indicates unstable swing detection. According to [40], 120 degrees is the critical angle shift defined as the criteria to decide the instability condition. However, this is a conservative limit and it can be further increased for more precise assessment of stability. This will be realized in Sect. 3.2 of simulation and results.

It is observed from the timestamps of the recorded packets in Fig. 12 that the detection packet 12 takes place after the packet corresponding to the critical angle change (packet 11) by 5 ms approximately. The content of packet 12 is displayed in Fig. 13.

It is worth to note here that the 5-ms time interval is the average processing time of the scheme based on real packet network, obtained after conducting many simulations. Hence, it can be considered as the scheme average response time to monotonic change over any IEC 61850-based network. It is also independent on the number of phase boundary levels (β₁ to β_n) or critical angle. The network behavior of the stable oscillating swing case is also simulated in this work in Sect. 3.2.

The results of a simulated disturbance in the IEEE 10-machine 39-bus system obtained as per [32] for both stable and unstable cases are used to test the response of the proposed scheme. New England 39-bus system is a 60 Hz, 10-generator system with slack generator G2 at bus 31. Figure 14 depicts the IEEE 39-bus system. According to [32], a stable disturbance is simulated by creating a three-phase-ground fault at bus 2 at 1 s. Then, the fault is cleared by tripping the line 2–3 at the time instant 11.33 s. Figure 15a shows the relative angle of the most disturbed generator pair (MDGP) according to [32], which can be considered—in a reasonable approximation—as the worst-case phase deviation for a disturbed generator relative to the grid in the proposed scheme. The angle values of the shown simulation curve in Fig. 15a are entered to MATLAB. Six β boundaries are taken uniformly spaced by 30 degrees with corresponding six k variables.

The simulated GOOSE train as published by the measuring IED corresponding to the angle variations is shown as rectangular pulses. The dark part of each pulse corresponds to the Boolean variables with True or One values.

It can be obviously seen from Fig. 15 that the positive and negative peaks exhibit silent periods without new GOOSE transmission. These silent periods are interrupted by one or more replica (or retransmission) packet shown as a dashed pulse in the figure, the shaded part of which corresponds to the Boolean variables with True or One values. The GOOSE retransmission time is taken as three sinusoidal cycles (50 ms). It can also be noticed that each peak is indicated by a replica or a retransmission packet followed by a packet with decremented or incremented Boolean sequence relative to that of the retransmission.

It can be seen from Fig. 15 that there is one retransmission packet at 1.35 s before the angle reaches 150 degrees with Boolean sequence (111100), which indicates that the phase change rate starts to decrease and therefore the Boolean content of the subsequent packets shall be investigated. The packet next to the first retransmission shows an incremented Boolean sequence of (111110); however, this packet is followed by two retransmission packets at 1.433 s and 1.5 s, and then, the packet at 1.6 s shows a decremented sequence of (111100), which indicates the first positive peak in the oscillatory pattern. Similarly, there is a subsequent negative peak indicated by retransmission packet at 1.88 s with Boolean sequence (110000) followed by a packet at 1.96 s with decremented Boolean sequence (100000). It should be noted here that the mapping rules in the positive β angle ranges mentioned in Eqs. (11) through (13) are symmetrical to the mapping rules in the negative β angle ranges. Thus, for the range of phase angle between 0 and − 30 degrees, the k₁ variable is set equal to 1 and for angle between − 30 and − 60, k₂ is set equal to 1. Thus, the Boolean contents of the packets published at 1.82, 1.88 and 1.96 s reveal negative angle values where the angle at 1.96 is greater than that at 1.88 s. The second positive peak is indicated by the retransmission packet at 2.08 s with sequence (000000) followed by a packet at 2.15 s with an incremented sequence (100000). It is to be noted here also that at 2.15 s the angle goes below zero and the mapping rules imply that k₁ becomes one after being zero at 2.08; thus, the sequence (100000) actually reveals that the angle value becomes negative after the positive value attained at this peak.

From the above argument, it can be concluded that there are two positive peaks with a negative peak in between. The Boolean sequence corresponding to the first positive peak contains larger number of ones than that of the second positive peak. This indicates a stable swing according to Case (3) shown in Fig. 9 in Sect. 2.5, Accordingly, the decision of stable swing will be declared shortly by the detecting IED after the packet published by the measuring IED at 2.15 s is received. This declaration period is calculated from a simulation of a similar swing with the same oscillatory behavior using the simulation setup shown in Fig. 14 using Xelas IEC 61850 tool. In this simulation, the data attribute ΔФ_d,

EWL03_P442Measurements/SecFouMMXU1.PhV.MX.phsA.cVal.ang.f defined in Sect. 3.1, is set to follow a similar angle behavior shown in Fig. 15a. The detecting IED subscribes to the published GOOSE packets and detects the oscillatory stable swing accordingly.

Figure 16 shows the Wireshark capture obtained from the simulation of the oscillatory stable case. We will focus the capture on the induced packets around the second positive peak of the angle curve. The false value of the variable k₁ in packet 36 is retransmitted in packet 37, and then, k₁ turns to true in packet 38. This corresponds to the retransmission of the sequence (000000) and then its transition to sequence (100000) as typically shown in Fig. 15b. This indicates the second positive peak. Packet 38 in Fig. 16 corresponds to the packet at t = 2.15 s in Fig. 15. Packet 39 in Fig. 16 sent by the detecting IED indicates the detection of stability. As it can be seen, the difference in timestamp between packets 38 and 39 in Fig. 16 is 4 ms; therefore, it can be deduced that the stability declaration time would be at 2.154 s.

The unstable case is simulated according to [32] by increasing the fault clearing time to 1.331 s instead of 1.33. G1 is the most disturbed generator in this case. It is observed that the angle grows until it is out of step (passing 180 degrees indicates instability). Figure 17 depicts the unstable case.

It can be seen from Fig. 17 that there is an inrush of GOOSE frames starting from a phase angle change value of 60 degrees till 150 degrees without ceasing (without retransmission or replica packet), which indicates that most likely the angle will not recover before 180-degree limit and the generator will lose synchronism.

According to the second simulation part in Sect. 3.2, the instability is declared 5 ms later to the packet corresponding to the critical rotor angle change. This packet appears at 1.35 s and corresponds to a critical change of angle equal to 150 degrees. Thus, the instability is declared at 1.355 s. The value of 150 degrees is chosen here as the critical angle shift rather than the 120-degree limit defined in [40] to allow for more precise monitoring of rotor angle before final judgment of instability; meanwhile, there is still enough time to take a control action.

Comparing this with the results of [32], the prediction of rotor angle instability based on auto-regression (AR) scheme is declared at 1.333 s. However, according to MLE, the instability is declared at 1.6 s, although the generator has already been unstable since the time instant 1.467 s. Therefore, the MLE method failed to predict the instability condition before its actual occurrence, while both the proposed scheme and the AR technique of [32] succeed to predict the instability before its occurrence by 112 and 134 ms, respectively.

In summary, we have conducted several simulations in this section to prove the effectiveness of the scheme. First, the concept of induced GOOSE packets in response to changes in rotor phase angle is demonstrated. Then, a real IEC 61850 network has been constructed, where the induced packets are used to identify instability. The average measured detection time is found to be 5 ms in the fast monotonic swing case and 4 ms in the oscillatory stable case. Finally, the scheme was used to detect the swing of the affected generators due to a simulated disturbance in the IEEE 39-bus system. The results show that the scheme can discriminate between both stable and unstable swings; in addition, it predicts the fast unstable swing of the affected generator ahead of its occurrence by 112 ms approximately.

Since the proposed scheme proves an efficient way for stability assessment while using existing IEDs only without adding PMUs, it can lend itself to actually implemented WAM systems. As an example of the existing WAMS systems that has been studied to be upgraded to be a real wide area monitoring, protection and control (WAMPAC) system is that of the Croatian 400 and 220 kV network. The system described in [42] proposes using voltage angle difference between two buses (ΔФ) to establish a criterion for stability assessment. The criterion to initiate out-of-step protection (OOS) tripping has been set as ΔФ ≥ 20 degrees. ΔФ is measured as the phase angle between two network sections, where each section is provided with a PMU connected to one of its buses. In this regard, the scheme we propose in this paper can be deployed in the proposed WAMPAC system of [42] to replace the PMU function of computing the bus voltage angle with the same function inherent in one of the already existing protection relays. This relay can be that the connected to the section bus or to the transmission line connected to it, such as the distance protection relay or the line differential relay. Only One relay on either side shall be used to compute its bus voltage angle and transmit the induced GOOSE packets in direct proportionality to the rate of change of the angle in the case of swing in the way described above. Since the system used in [42] is modeled by a two-source equivalent model, the change in the measured bus angle here can be essentially referred to the other section bus. One detector device shall be located in the Control Center to detect the induced GOOSE packets and apply the criterion of successive increment of GOOSE sequence without retransmission in between as described in Sect. 3.2 to detect unstable swing. This detector function can be either integrated in the WAMPAC system or provided as standalone device capable pf communication with the WAMPC.

In addition to saving the costs of PMUs and avoiding complexity of processing, the time performance of the proposed non-PMU-based approach can be much better than that of the PMU-based one. The total processing time of the unstable or OOS swing using the non-PMU-based scheme is about 5 ms compared with the reported values in [42] of about 20-ms transmission delay in addition to processing delay less than 100 ms.