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Method for distributed generation anti-islanding protection based on singular value decomposition and linear discrimination analysis
Electric Power Systems Research 130 (2016) 124–131
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Method for distributed generation anti-islanding protection based on singular value decomposition and linear discrimination analysis G. Marchesan ∗ , M.R. Muraro, G. Cardoso Jr, L. Mariotto, C.D.L. da Silva Federal University of Santa Maria, Brazil
a r t i c l e
i n f o
Article history: Received 8 June 2015 Received in revised form 23 July 2015 Accepted 28 August 2015 Keywords: Anti-islanding protection Frequency oscillation Distributed generation Passive protection
a b s t r a c t Anti-islanding protection is one of the most important requirements for the connection of distributed generators in power systems. This paper proposes an algorithm to detect unintentional islanding in power systems with distributed generation. It is based on the singular value decomposition and linear discrimination analysis to differentiate frequency oscillations in synchronous generators caused by islanding from those caused by non-islanding events. The algorithm requires a very low number of mathematical operations, which is suitable for relay purposes. This is possible because most of the operations are in the training process and are made off-line. The performance of the proposed algorithm is evaluated for different scenarios and load conditions in IEEE 34 Node Test Feeder. The algorithm is able to detect islanding with active power mismatch of 1.6% of DG nominal power. The pattern recognition also prevents undue tripping, ensuring great robustness for the method. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The distributed generation (DG) unintentional islanding can cause life-threatening, power quality deterioration, due to poor voltage and frequency regulation, and damage to system equipment and its loads. For these reasons, the islanded operation of distribution systems is normally not allowed and the anti-islanding protection is necessary for the connection of DGs to distribution networks. According to IEEE Std 1547 [1] islanding detection must occur up to 2 s after the island formation. To avoid said problems, many power utilities request reclosers with transferred trip in the DG connection point. Other utilities request dedicated feeders with transfer trip. Although these communication-based methods are more effective than local techniques, they can suffer with communication problems and its implementation implies very high costs. The local methods were proposed as alternatives to methods based on communication and they can be divided into three categories: Active, hybrid and passive methods. The active methods inject small signals in the distribution system or force the DG to an abnormal situation, whilst the connection to the system keeps it under normal conditions. In general these methods have a small non detection zone (NDZ); however,
∗ Corresponding author. Tel.: +55 5599072819. E-mail address: [email protected] (G. Marchesan). http://dx.doi.org/10.1016/j.epsr.2015.08.025 0378-7796/© 2015 Elsevier B.V. All rights reserved.
the disturbances inserted in the distribution system may cause power quality deterioration [2,3]. If the distribution system has multiple generators connected very close to others with similar techniques, they might cause interference into each other and impair the performance of these techniques. In [4] the performances of active frequency drifty methods are evaluated for multi inverter system. The non-detection zone increases when the inverters try to drift the frequency in opposite directions. In [5] an alternative solution for the interference problem has been proposed for inverter based generations. The method injects a high frequency signal in a master inverter and this signal is used in all other slave inverters for island detection. The slaves operate in a cancelation mode avoiding interference between inverters. Other solution for multi-DG was proposed in [6]. The method aims to estimate overall transient stiffness to distinguish prior- and postislanding. Each DG perturbs the system at different frequency, thus avoiding the interference inter DG; however, these perturbations can also cause power quality deterioration. An average absolute frequency deviation value based active islanding detection technique is proposed in [7]. The method has zero NDZ, detects stable island formation without forcing the island to lose its stable operation, and has a detection time up to 100 ms, however, the tolerance to short circuits is not evaluated yet. Due to lower cost of passive methods, it is common the use of anti-islanding schemes using protection functions such as the rate of change of frequency (ROCOF) [8], which is one of the
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
fastest passive protection algorithms used in relays for islanding detection. Other techniques such as under/over-frequency, under/over-voltage [9], and vector-surge [8] are also used, although these techniques are effective for islanding conditions with large power imbalance, passive methods may fail or spend too much time detecting low power imbalance. In addition, events like short circuits and switching of large blocks of load can cause islanding erroneous islanding detection. In [10], an Island detection method for inverter connected generators based on a dynamic estimator is proposed, which measures the current amplitude and phase. Aiming to get the best sides of active and passive methods, the hybrid methods often use a passive method that identifies a transient condition and the DG starts to cause a disturbance to destabilize parameters in case of islanding. Hybrid techniques also have been proposed [11]. The technique changes GD active power only when it cannot differentiate clearly islanding from other events, thus making the islanding detection easier. In [12], the method uses a ROCOF relay to decide when the DG frequency set is changed. The main problem with hybrid methods is they still depend on passive method threshold. A passive technique based on decision tree was proposed in [13], but it uses a very large set of parameters which hinders its implementation. Wavelet has also been used in an intelligent technique proposed in [14,15]. The wavelets extract voltage and current features and use a decision tree to identify the islanding. The method proposed by [14] uses a very large data set for training, which is a hard work considering that the method should be retrained at each topology change. In [16], a wavelet design for island detection is proposed. The algorithm is simpler than [14,15] and has lower computational effort using only the voltage and six wavelet coefficients. Techniques based on synchronous machine oscillation frequency estimation are proposed by [17,18]. The methods respectively use windows of 350 ms and 500 ms for estimating damping and oscillation frequency estimation, which demand too much time for islanding detection purposes. The method proposed in [17] aims to estimate the signal parameters using a TLS-ESPRIT algorithm. The method needs to minimize a cost function which demands a relatively high processing time. In [18], a different solution for estimating damping and frequency of oscillation is proposed using Tufts–Kumaresan method. The method of [18] is not recursive, requiring much less computational effort; however, given its large window, the island detection time is more than 600 ms. Although it may be less than the 2 s required by IEEE standard 1547 [1] this island detection time may be greater than recloser time. In general, utilities use auto reclosing times around 500 ms, which can result in out of synchronism reclosing. In this paper, a faster algorithm using smaller windows than previous methods is proposed. As well as [17,18], the proposed methodology uses the oscillation frequency to characterize islanding. However, the proposed methods do not use the value of the oscillation frequency, but the shape of the electrical frequency. In other words, the adopted strategy is to use the well-known information that during islanding the frequency behaves like an exponential or a low-frequency oscillation due to the governor effect. During events where the DG is connected to the system, like short circuits and load switching, the frequency oscillates at the damped natural frequency. The frequency is decomposed using singular value decomposition (SVD), and its components are analyzed with linear discrimination analysis (LDA) using the generalized Rayleigh quotient. The main contribution of proposed technique is an improvement in speed when compared with [17,18]. This was possible since the approach uses a pattern recognition technique with a small window, providing a faster detection.
125
In the following sections, the mathematical fundamentals regarding synchronous machine model, SVD, LDA, and the proposed algorithm are presented, along with the simulations results. 2. Synchronous machine models On a synchronous machine operating in steady state, the relative position between rotor and resulting magnetic field remain almost constant. When a sudden disturbance occurs, the angle between them oscillates dynamically according to the swing equation given by (1). dı 2H d2 ı +D = Pm − Pe ω0 dt 2 dt
(1)
where ı is the relative rotor angle, t is the time, H is the generator inertia constant, D is the damping coefficient, ω0 is the DG synchronous speed, and Pm and Pe are mechanical input and electric power output of the DG, respectively. 2.1. Frequency variation during non-islanding events When a small disturbance occurs in the electrical system, the DG oscillates and returns to its original state after some time. The electrical power injected by DG in the distribution system can be written as Pe = Pmax sin ı
(2)
A small perturbation ı in ı, from the initial operating position ı0 can be represented by ı = ı0 + ı
(3)
Due to this perturbation, the swing equation (1) can be linearized and rewritten as 2H d2 ı dı +D + Ps ı = 0 ω0 dt 2 dt
(4)
Ps is known as the synchronizing power coefficient and is defined by the equation Ps = Pmax cos ı0
(5)
Solving the differential equation shown in (4), [19] shows that the frequency deviation from nominal synchronous speed is given by (6). ω =
dı ωn ı(0) −ς ωt n sin ωt = − e d dt 1 − ς2
where ωd = ωn
ς=
D 2
ωn =
1 − ς2
(6)
(7)
ω0 2HPs
(8)
ω0 Ps 2H
(9)
From (6), one can see that the frequency is given by a damped sinusoidal waveform. 2.2. Frequency variation during islanding events During an islanding event, the DG loses connection with the main system and, therefore, the synchronizing coefficient is 0. In this way, (4) can be rewritten as (10). dı 2H d2 ı = P +D ω0 dt 2 dt
(10)
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G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
B - Island
Frequency
Frequency
A - Non-Island
Time
Time
Fig. 1. Frequency behavior in: (A) non-island events; (B) island events.
P is the power variation due to the islanding; in other words, the transmitting power in the electrical system split point. In this case, P is assumed as constant during the islanding. P is assumed positive when the electrical power in the split point is flowing from the main system to DG. Since the rotor angle is synchronized with the stator magnetic field before islanding, the two initial conditions for (10) are ı(0) = 0 and dı(0) = 0. Solving (10), the equation for electrical dt frequency deviation is obtained. ω =
P dı = (1 − e−ω0 Dt/2H ) D dt
(11)
Comparing (6) to (11), it can be observed that the frequency of the DG behaves differently. During DG parallel operation with the system, the frequency tends to oscillate at the damped natural frequency, ωd , as shown in Fig. 1A. Disregarding the voltage controllers, governors, and the load dynamic during islanding, which may change due to voltage and frequency variation, the frequency does not oscillate during an islanding, but it is given by an exponential response, as shown in Fig. 1B. 3. The singular value decomposition Singular value decomposition (SVD) is factorization of a matrix in to constitutive components. It is widely used in common applications such as least square fitting data and pseudo-inverse calculation. In electric power systems it was employed in some fields such as in [20,21]. In this paper, the SVD is used for pattern recognition [22] and identifying islanding amongst other events involving distributed generation. The SVD decomposes an m by n matrix A in a unitary matrix V n × n, a diagonal matrix m × n, and a unitary matrix U m × m, as shown in (12). A = U˙V ∗
(12)
The symbol * stands for the conjugate transpose. The diagonal matrix is composed of non-negative singular values i , where 1 ≤ 2 ≤ 3 · · · ≤ r , r = min (m, n)
(13)
∗ T
∗
∗
A A = (U˙V ) (U˙V ) = V ˙U U˙V 2
T
A A = V˙ V
∗
∗
(14) (15)
and AAT = (U˙V ∗ )(U˙V ∗ ) = U˙V ∗ V ˙U ∗ T
T
2
AA = U˙ U
∗
(16) (17)
Multiplying (15) and (17) on the right by V and U, respectively, two eigen value problems can be obtained. AT AV = V ˙ T
AA V = U˙
2 2
f =
fr − fr fr+1 − fr . . . fr+m−1 − fr T
(18) (19)
(20)
Matrix A can be rewritten as given in (21)
A = fni (1)
...
fni (N)
fi (1)
...
fi (N)
(21)
fni is the frequency deviation in non-islanding events, fi is the frequency deviation during islanding events, and N is the total number of events of each case. In this paper, training set A is defined by the simulation of 24 cases. The non-islanding set is composed of 12 short circuits and load switching in several system positions. The islanding set is composed of 12 islanding with several levels of power mismatches. The algorithm should be trained for each system; however, the number of simulations necessary are low. The tests show the algorithm performance does not improve significantly for more than 24 cases involving different power mismatches and disturbances situations such as short circuits and load switching. Applying the singular value decomposition in A, each column of U can be seen as one base of A, and V* can be seen in a geometric point of view as a scaling and rotation of base U to reconstruct matrix A. In the next section, V* will be called E. According to (13), the first singular values are the most significant; therefore, U can be limited to its firsts columns, and E to its firsts rows. In the calculations below, only the first 20 columns of U and the first 20 rows of E are being considered. 4. Linear discrimination analysis Given the definition shown in (22) E = ˙V ∗
(22)
Analyzing the construction of matrix A in (21), it can be deduced that the first N columns of E represent non-islanding events (Eni ), and the last N columns represent islanding events (Ei ), as shown in (23)
E = Eni (1)
Considering T stands for the transpose matrix, we have T
In this way, V and U are determined by the eigen vectors of AT A and AAT , respectively, and is determined by the square root of its eigen values. The values of i are always non-negative; in this way, the sign of U and V must be checked in order to ensure their self-consistency. As seen in the previous section, frequency during an islanding is clearly different from other events that may happen during a connected situation. For the constitution of the training set, the frequency is analyzed half cycle (8.333 ms) after the instant when the absolute value of frequency deviation of 60 Hz exceeds the threshold of 0.05 Hz. In this way, as expressed in (20), f is a vector which contains the absolute value of frequency deviation, where r is the instant where the threshold is exceeded and m is the window size, equal to 10 cycles of 60 Hz (166.667 ms).
···
Eni (N)
Ei (1)
···
Ei (N)
(23)
This paper proposes the use of statistics about E in order to characterize whether one event is an Islanding or not. The linear discrimination analysis was used with this goal. The LDA was proposed in [23] in the taxonomy context [22]. The main idea of LDA is to take a high dimensional problem and transform it into a lower dimensional, with a transform W. Considering this, W should project E in such a way that maximizes the distances inter-class of the E data, and minimizes the distance intra-class of E data. To achieve this, a criterion known as generalized Rayleigh quotient was used (24). W = argmax W
W T SB W W T SW W
(24)
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
127
SW is the within class scatter matrix and SB is the between class scatter matrix given by SB = (i − ni )(i − ni )T N
SW =
(25)
T
(Eni (j) − ni )(Eni (j) − ni ) +
j=1
N
(Ei (j) − i )(Ei (j) − i )
T
j=1
(26) ni and i are the mean values of E vectors according to 1 Eni (j) N N
ni =
(27)
j=1
1 Ei (j) N N
i =
(28)
j=1
The solution of the generalized Rayleigh quotient is given by the eigen value problem SB W = SW W
(29)
W is given by the eigen vector with associated eigen value that has the largest value. Being W is a unitary vector, the projection of E over W is given by (30) and (31). Pi = W T Ei
(30)
Pni = W T Eni
(31)
If the mean value of Pi is greater than Pni , the threshold is given by min (Pi ) + max (Pni ) Th = 2
min (−Pi ) + max (−Pi ) 2
(32)
(33)
5. The algorithm The definition of W transform and the threshold presented in previous section are made offline. In this section, the algorithm that produces the DG trip signal is presented and discussed. See flowchart presented in Fig. 2. The frequency is continually monitored, and is identified when the frequency deviation from 60 Hz exceeds the threshold of 0.05 Hz. If the frequency deviation exceeds the threshold, the vector containing synchronous machine frequency measurements f, should be projected in the bases of the training set. Taking f and multiplying by U−1 gives the coefficient C (34), which is equivalent to E obtained in the training set. Since U is a unitary, the transpose can be used instead of the inverse. C = U T f
(34)
Applying the transform W over C, P can be obtained (35). P = WT C
waits a time equivalent to three cycles of 60 Hz, i.e., Th2 is 384 for a sampling frequency of 7680 Hz. 6. Tests and results
Otherwise, W should be multiplied by −1 and the threshold is given by Th =
Fig. 2. Proposed island detection algorithm.
(35)
If P is greater than Th, an islanding event is characterized and a timer counter Z starts; otherwise, it is a non-islanding event. When Z reaches the threshold Th2, the trip signal is sent to disconnect the DG. The temporization given by Th2 is important to avoid an unwanted trip due to an misclassified event. A greater delay increases the robustness of the method, but also the detection time. In the studies carried out in this paper, the algorithm
To evaluate the performance of the proposed method, it has been used on the IEEE 34 node distribution test system, presented in Fig. 3 [24]. A synchronous generator is connected through a transformer to bus 854. The transformer data are given in Table 1. The diesel generator controls the power factor to 0.98 inductive its data are presented in Table 2, and DG voltage and frequency regulators are given in [25]. The excitation system model used in [25] is a static excitation equivalent to IEEE type ST2 Model [26], and the governor was the same used in [27]. A 0.2 MVA load with 0.92 inductive power factor is connected directly to the DG node. The proposed method is compared with one of the best-known islanding detection methods, the rate of change of frequency (ROCOF). The rate of change of frequency was calculated at each frequency sample by Eq. (36) df = (fr − fr−1 )fsampling dt
(36)
fsampling is the sampling frequency. When ROCOF exceeds the threshold, a time counter starts. This temporization is important Table 1 Transformer data. Parameter
Value
854-Point of common coupling Three phase transformer Rated power Nominal frequency Rated voltage Connection Vector group Positive sequence reactance (X1) Positive sequence resistance (R1) Zero sequence short circuit impedance Zero sequence short circuit resistance
3.0 MVA 60 Hz 24.9/2.4 kV D/yn Phase shift 1 × 30◦ 0.059371 p.u. 0.008667 p.u. 0.06 p.u. 0.0087 p.u.
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G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131 Table 3 Rate of change of frequency methods configuration.
df/dt (Hz/s) Delay (s) Voltage constraint (p.u)
Fig. 3. IEEE 34 Node Test Feeder [24].
because of the high sensitivity of ROCOF protection, and helps to avoid unwanted Trips for short time transients in the distribution system, especially short circuits. The method was adjusted to four typical settings, shown in Table 3. ROCOF4 operates if voltage
Table 2 Generator parameters. Parameter
Value
Parameter
Value
Reference machine
Not flag
1.56 p.u.
Mode of local voltage controller Dispatch – voltage
Voltage
Direct axis reactance (Xd ) Quad. axis reactance (Xq ) Direct axis transient reactance (Xd ) Direct axis subtransient reactance (Xd ) Quadrature axis subtransient reactance (Xq ) Direct axis short-circuit transient time-constant (Td ) Direct axis short-circuit subtransient time-constant (Td ) Quadrature axis short-circuit subtransient time-constant (Tq ) Main flux saturation – Sg10 Main flux saturation – Sg12
0.26 p.u.
1.0 p.u.
Nominal apparent power
3.125 MVA
Nominal voltage
2.4 kV
Power factor
0.8
Connection
yn
Inertia time constant (rated to Sgn) H
1.071 s
Leakage reactance
8.8%
Rotor type
Salient pole
1.06 p.u.
0.15 p.u.
0.15 p.u.
3.7 s
0.05 s
0.05 s
0.17 p.u. 0.60 p.u.
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
0.500 0.150 –
1.500 0.050 –
2.500 0.050 –
0.500 0.150 0.8
remains greater than 0.8 p.u. ROCOF 1, 2 and 3 do not use any voltage restriction. Two load conditions for the IEEE 34-bus distribution system were considered, 100% and 50%. The loads shown in the test system represent load condition 100%, whereas load condition 50% is obtained by reducing them accordingly. Several islanding conditions were tested and are shown in Table 4, which presents the line switched, the load condition, the DG generated power, the active and reactive switching interrupted power, and the protections tripping time. It is possible to see that the proposed method did not fail in any of the simulated cases. All algorithms based on rate of change of frequency failed twice due to very low transmitted active power on the switching point. The proposed technique island detection time is generally around 220 ms, slightly greater than ROCOF 1. Table 5 shows the methods’ performance during a single-phase to ground short circuit sustained in the system for 350 ms. After this time the fault line is disconnected, thus causing the DG islanding. Table 5 shows the short circuited bus and the fault resistance. The islanding detection time is the difference between the protection trip times and 350 ms; in this way, negative times represent protection trips before DG islanding, i.e., they represent failed trips. The proposed method did not fail in any simulated case presented in this table. ROCOF 1 failed once and had some detection times greater than 500 ms. ROCOF 2 failed in almost all cases, presenting negative islanding detection times. ROCOF 3 failed seven times. It detected the islanding during the short circuit in four times and did not trip during real islanding in three cases. Table 6 shows the algorithms’ performance for temporary phase to ground short circuit. The fault remains during 350 ms and disappears spontaneously without any switching. The proposed algorithm as well as ROCOF 1 and ROCOF 4 worked well in all simulated cases. ROCOF 2 and ROCOF 3 failed in 12 and 3 cases, respectively. Table 7 presents the tests of load switching, caused by the opening lines. The ROCOF 2 failed in case 5 identifying an islanding erroneously. The proposed method and ROCOF methods worked well in all tests. Fig. 4 presents the time detection for islanding caused by switching in bus 802. In Fig. 4A the power is changed in such a way that the interrupted reactive power remains 0 and active power changes from 0.016 to 0.36 p.u. regarding DG nominal power. The interrupted power is changed by a load introduced in bus 802. One can see the proposed method is able to detect the small active power mismatch, 0.016 p.u. In Fig. 4B the active power mismatch is set to 0 and the reactive power is changed. The methods based on ROCOF did not identify the island for any of the tested cases. However, the proposed methodology was able to detect islanding with reactive power mismatch up to 0.12 p.u. Although the proposed method may be slower than ROCOF for large active power mismatch, it is much more efficient for small values, detecting islanding were other methods were not able to do. Also, as shown in Fig. 4A, the proposed method can be faster than ROCOF 1 and ROCOF 4 for small power mismatches. Due to frequency pattern recognition, the proposed method avoids the nuisance tripping that would happen in other frequency based relays such as ROCOF and Under/Over frequency. This is an advantage since, for instance, in case of a big generation trip
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
129
Table 4 Performance of islanding detection methods during islanding events. Operating characteristic of the system
Islanding detection time (s)
Opened line
Load (%)
PG (MW)
POP (MW)
QOP (MVAr)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
800–802 830–854 800–802 830–854 800–802 830–854 800–802 830–854
100 100 50 50 100 100 50 50
2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0
−0.38 −0.75 −1.32 −1.61 1.12 0.72 0.05 −0.13
−0.11 −0.18 −0.67 −0.71 0.13 0.04 −0.31 −0.49
0.221 0.221 0.221 0.221 0.220 0.218 0.248 0.396
0.150 0.150 0.150 0.150 0.150 0.150 Not det. Not det.
0.050 0.050 0.050 0.050 0.050 0.050 Not det. Not det.
0.050 0.050 0.050 0.050 0.050 0.050 Not det. Not det.
0.150 0.150 0.150 0.150 0.150 0.150 Not det. Not det.
Table 5 Performance of islanding detection methods during phase to ground short-circuits, sustained for 350 ms, and followed by islanding. Operating characteristic of the system
Islanding detection time (s)
Short circuit bus
Opened line
Z fault ( )
Load (%)
PG (MW)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
802 802 816 816 830 830 802 802 816 816 830 830 802 802 816 816 830 830 802 802 816 816 830 830
802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854
0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60
100 100 100 100 100 100 50 50 50 50 50 50 100 100 100 100 100 100 50 50 50 50 50 50
2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.350 0.205 0.327 0.213 0.389 0.232 0.194 0.202 0.220 0.219 0.220 0.219 0.219 0.220 0.219 0.220 0.219 0.220 0.192 0.197 0.211 0.194 0.217 0.194
0.150 0.150 0.189 0.150 0.208 0.150 0.401 Not det. 0.490 0.540 0.490 0.527 0.128 0.150 0.150 0.150 0.150 0.150 0.123 0.150 0.150 0.150 0.150 0.150
−0.223 −0.230 0.323 −0.230 0.440 −0.230 −0.223 −0.230 0.050 −0.230 0.050 −0.230 −0.227 −0.229 0.050 −0.230 0.050 −0.230 −0.300 −0.230 −0.223 −0.231 0.050 −0.231
0.307 0.050 0.578 Not det. Not det. Not det. 0.050 0.050 0.050 0.050 0.050 0.050 −0.219 0.050 0.050 0.050 0.050 0.050 −0.221 0.050 0.050 −0.223 0.050 −0.222
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Table 6 Performance of islanding detection methods during temporary phase to ground short circuit, 350 ms. Operating characteristic of the system
Islanding detection time (s)
Short circuit bus
Z fault
Load (%)
PG (MW)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
830 830 852 852 842 842 830 830 852 852 842 842 830 830 852 852 842 842 830 830 852 852 842 842
0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60
100 100 100 100 100 100 50 50 50 50 50 50 100 100 100 100 100 100 50 50 50 50 50 50
2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0 2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Not det. 0.120 Not det. 0.124 Not det. 0.125 Not det. 0.120 Not det. 0.123 Not det. 0.124 Not det. 0.120 Not det. 0.124 Not det. 0.125 Not det. 0.119 Not det. 0.122 Not det. 0.123
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. 0.128 Not det. Not det. Not det. Not det.
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
130
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
Fig. 4. (A) Anti island methods time detection and NDZ for active power variation. (B) Anti island methods time detection and NDZ for reactive power variation.
Table 7 Load switching tests.
References
Operating characteristic of the system Case
Opened line
Load (%)
PG (MW)
POP (MW)
QOP (MVAr)
1 2 3 4 5 6 7 8
854–852 834–842 854–852 834–842 854–852 834–842 854–852 834–842
100 100 50 50 100 100 50 50
2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0
1.511 0.565 0.754 0.285 1.507 0.563 0.75 0.284
0.107 −0.376 −0.381 −0.593 0.112 −0.374 −0.375 −0.558
in a large DG penetration scenario, the DG may help the system in the recovering process. However, a large perturbation on the generation or transmission system may cause frequency variations similar to those present in case of islanding, producing a undesirable tripping. Therefore, the Standard IEEE 1547 [1] allows the system operator to specify the frequency setting and time delay for underfrequency trips down to 57 Hz. In these cases, the settings of the proposed method should take this recommendation in to account.
7. Conclusion This paper proposes a technique for islanding detection based on singular value decomposition and linear discrimination analysis. During islanding, the synchronous generator oscillates at very slow frequency due to governors’ actions or the frequency growth exponentially when the governors are unable to correct it. However, while connected to the main grid, the DG oscillates at a higher frequency. The method uses a pattern recognition methodology that detects the frequency signature during islanding and sends a trip signal to the synchronous generator switcher. It uses smaller windows than those used by methods that seek to estimate the frequency of oscillation and damping coefficient, providing faster tripping. Several simulations were performed on different scenarios with islanding and non-islanding events, and the proposed methodology proved to be more sensitive than ROCOF islanding protection. The proposed algorithm is able to detect islanding with power mismatches smaller than 1.6% and does not trip for the vast majority of non-islanding events. In short, the main advantages brought by the proposed algorithm over other methods are robustness for load switching and short circuits, small NDZ, and fast tripping.
[1] IEEE standard for interconnecting distributed resources with electric power systems. IEEE Std 1547-2003 vol. no. (2003) 1, 28, doi:10.1109/ IEEESTD.2003.94285. [2] D. Velasco, C. Trujillo, G. Garcera, E. Figueres, An active anti-islanding method based on phase-PLL perturbation, IEEE Trans. Power Electron. 26 (4) (2011) 1056–1066. [3] Jae-Hyung Kim, Jun-Gu Kim, Young-Hyok Ji, Yong-Chae Jung, Chung-Yuen Won, An islanding detection method for a grid-connected system based on the Goertzel algorithm, IEEE Trans. Power Electron. 26 (4) (2011) 1049–1055. [4] L.A.C. Lopes, Yongzheng Zhang, Islanding detection assessment of multiinverter systems with active frequency drifting methods, IEEE Trans. Power Deliver. 23 (1) (2008) 480–486. [5] D. Reigosa, F. Briz, C. Blanco, P. Garcia, J. Manuel Guerrero, Active islanding detection for multiple parallel-connected inverter-based distributed generators using high-frequency signal injection, IEEE Trans. Power Electron. 29 (3) (2014) 1192–1199. [6] M. Al Hosani, Z. Qu, H.H. Zeineldin, A Transient stiffness measure for islanding detection of multi-DG systems, IEEE Trans. Power Deliver. 30 (2) (2015) 986–995. [7] P. Gupta, R.S. Bhatia, D.K. Jain, Average absolute frequency deviation value based active islanding detection technique, IEEE Trans. Smart Grid 6 (1) (2015) 26–35. [8] W. Freitas, Wilsun Xu, C.M. Affonso, Zhenyu Huang, Comparative analysis between ROCOF and vector surge relays for distributed generation applications, IEEE Trans. Power Deliver. 20 (2) (2005) 1315–1324. [9] IEEE Recommended Practice for Utility Interconnected Photovoltaic (PV) Systems: IEEE Standard 929-2000. [10] M. Al Hosani, Zhihua Qu, H.H. Zeineldin, Development of dynamic estimators for islanding detection of inverter-based DG, IEEE Trans. Power Deliver. 30 (1) (2015) 428–436. [11] P. Mahat, Zhe Chen, B. Bak-Jensen, A hybrid islanding detection technique using average rate of voltage change and real power shift, IEEE Trans. Power Deliver. 24 (2) (April 2009) 764–771. [12] M. Khodaparastan, H. Vahedi, F. Khazaeli, H. Oraee, A novel hybrid islanding detection method for inverter-based DGs using SFS and ROCOF, IEEE Trans. Power Deliver. 99 (2015) 1,1. [13] K. El-Arroudi, G. Joos, I. Kamwa, D.T. McGillis, Intelligent-based approach to islanding detection in distributed generation, IEEE Trans. Power Deliver. 22 (2) (2007) 828–835. [14] N.W.A. Lidula, A.D. Rajapakse, A pattern recognition approach for detecting power islands using transient signals – part I: design and implementation, IEEE Trans. Power Deliver. 25 (4) (2010) 3070–3077. [15] N.W.A. Lidula, A.D. Rajapakse, A pattern-recognition approach for detecting power islands using transient signals – part II: performance evaluation, IEEE Trans. Power Deliver. 27 (3) (2012) 1071–1080. [16] S. Alshareef, S. Talwar, W.G. Morsi, A new approach based on wavelet design and machine learning for islanding detection of distributed generation, IEEE Trans. Smart Grid 5 (4) (2014) 1575–1583. [17] H.H. Zeineldin, T.A. Galil, E.F.E. Saadany, M.M.A. Salam, Islanding detection of grid connected distributed generators using TLS ESPRIT, Int. J. Elect. Power Syst. Res. 77 (2006) 155–162. [18] M. Bakhshi, R. Noroozian, G.B. Gharehpetian, Anti-islanding scheme for synchronous DG units based on Tufts–Kumaresan signal estimation method, IEEE Trans. Power Deliver. 28 (4) (2013) 2185–2193. [19] Hadi Saadat, Power System Analysis, McGraw-Hill International, 1999. [20] M. Dehghani, B. Shayanfard, A.R. Khayatian, PMU ranking based on singular value decomposition of dynamic stability matrix, IEEE Trans. Power Syst. 28 (3) (2013) 2263–2270.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Method for distributed generation anti-islanding protection based on singular value decomposition and linear discrimination analysis G. Marchesan ∗ , M.R. Muraro, G. Cardoso Jr, L. Mariotto, C.D.L. da Silva Federal University of Santa Maria, Brazil
a r t i c l e
i n f o
Article history: Received 8 June 2015 Received in revised form 23 July 2015 Accepted 28 August 2015 Keywords: Anti-islanding protection Frequency oscillation Distributed generation Passive protection
a b s t r a c t Anti-islanding protection is one of the most important requirements for the connection of distributed generators in power systems. This paper proposes an algorithm to detect unintentional islanding in power systems with distributed generation. It is based on the singular value decomposition and linear discrimination analysis to differentiate frequency oscillations in synchronous generators caused by islanding from those caused by non-islanding events. The algorithm requires a very low number of mathematical operations, which is suitable for relay purposes. This is possible because most of the operations are in the training process and are made off-line. The performance of the proposed algorithm is evaluated for different scenarios and load conditions in IEEE 34 Node Test Feeder. The algorithm is able to detect islanding with active power mismatch of 1.6% of DG nominal power. The pattern recognition also prevents undue tripping, ensuring great robustness for the method. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The distributed generation (DG) unintentional islanding can cause life-threatening, power quality deterioration, due to poor voltage and frequency regulation, and damage to system equipment and its loads. For these reasons, the islanded operation of distribution systems is normally not allowed and the anti-islanding protection is necessary for the connection of DGs to distribution networks. According to IEEE Std 1547 [1] islanding detection must occur up to 2 s after the island formation. To avoid said problems, many power utilities request reclosers with transferred trip in the DG connection point. Other utilities request dedicated feeders with transfer trip. Although these communication-based methods are more effective than local techniques, they can suffer with communication problems and its implementation implies very high costs. The local methods were proposed as alternatives to methods based on communication and they can be divided into three categories: Active, hybrid and passive methods. The active methods inject small signals in the distribution system or force the DG to an abnormal situation, whilst the connection to the system keeps it under normal conditions. In general these methods have a small non detection zone (NDZ); however,
∗ Corresponding author. Tel.: +55 5599072819. E-mail address: [email protected] (G. Marchesan). http://dx.doi.org/10.1016/j.epsr.2015.08.025 0378-7796/© 2015 Elsevier B.V. All rights reserved.
the disturbances inserted in the distribution system may cause power quality deterioration [2,3]. If the distribution system has multiple generators connected very close to others with similar techniques, they might cause interference into each other and impair the performance of these techniques. In [4] the performances of active frequency drifty methods are evaluated for multi inverter system. The non-detection zone increases when the inverters try to drift the frequency in opposite directions. In [5] an alternative solution for the interference problem has been proposed for inverter based generations. The method injects a high frequency signal in a master inverter and this signal is used in all other slave inverters for island detection. The slaves operate in a cancelation mode avoiding interference between inverters. Other solution for multi-DG was proposed in [6]. The method aims to estimate overall transient stiffness to distinguish prior- and postislanding. Each DG perturbs the system at different frequency, thus avoiding the interference inter DG; however, these perturbations can also cause power quality deterioration. An average absolute frequency deviation value based active islanding detection technique is proposed in [7]. The method has zero NDZ, detects stable island formation without forcing the island to lose its stable operation, and has a detection time up to 100 ms, however, the tolerance to short circuits is not evaluated yet. Due to lower cost of passive methods, it is common the use of anti-islanding schemes using protection functions such as the rate of change of frequency (ROCOF) [8], which is one of the
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
fastest passive protection algorithms used in relays for islanding detection. Other techniques such as under/over-frequency, under/over-voltage [9], and vector-surge [8] are also used, although these techniques are effective for islanding conditions with large power imbalance, passive methods may fail or spend too much time detecting low power imbalance. In addition, events like short circuits and switching of large blocks of load can cause islanding erroneous islanding detection. In [10], an Island detection method for inverter connected generators based on a dynamic estimator is proposed, which measures the current amplitude and phase. Aiming to get the best sides of active and passive methods, the hybrid methods often use a passive method that identifies a transient condition and the DG starts to cause a disturbance to destabilize parameters in case of islanding. Hybrid techniques also have been proposed [11]. The technique changes GD active power only when it cannot differentiate clearly islanding from other events, thus making the islanding detection easier. In [12], the method uses a ROCOF relay to decide when the DG frequency set is changed. The main problem with hybrid methods is they still depend on passive method threshold. A passive technique based on decision tree was proposed in [13], but it uses a very large set of parameters which hinders its implementation. Wavelet has also been used in an intelligent technique proposed in [14,15]. The wavelets extract voltage and current features and use a decision tree to identify the islanding. The method proposed by [14] uses a very large data set for training, which is a hard work considering that the method should be retrained at each topology change. In [16], a wavelet design for island detection is proposed. The algorithm is simpler than [14,15] and has lower computational effort using only the voltage and six wavelet coefficients. Techniques based on synchronous machine oscillation frequency estimation are proposed by [17,18]. The methods respectively use windows of 350 ms and 500 ms for estimating damping and oscillation frequency estimation, which demand too much time for islanding detection purposes. The method proposed in [17] aims to estimate the signal parameters using a TLS-ESPRIT algorithm. The method needs to minimize a cost function which demands a relatively high processing time. In [18], a different solution for estimating damping and frequency of oscillation is proposed using Tufts–Kumaresan method. The method of [18] is not recursive, requiring much less computational effort; however, given its large window, the island detection time is more than 600 ms. Although it may be less than the 2 s required by IEEE standard 1547 [1] this island detection time may be greater than recloser time. In general, utilities use auto reclosing times around 500 ms, which can result in out of synchronism reclosing. In this paper, a faster algorithm using smaller windows than previous methods is proposed. As well as [17,18], the proposed methodology uses the oscillation frequency to characterize islanding. However, the proposed methods do not use the value of the oscillation frequency, but the shape of the electrical frequency. In other words, the adopted strategy is to use the well-known information that during islanding the frequency behaves like an exponential or a low-frequency oscillation due to the governor effect. During events where the DG is connected to the system, like short circuits and load switching, the frequency oscillates at the damped natural frequency. The frequency is decomposed using singular value decomposition (SVD), and its components are analyzed with linear discrimination analysis (LDA) using the generalized Rayleigh quotient. The main contribution of proposed technique is an improvement in speed when compared with [17,18]. This was possible since the approach uses a pattern recognition technique with a small window, providing a faster detection.
125
In the following sections, the mathematical fundamentals regarding synchronous machine model, SVD, LDA, and the proposed algorithm are presented, along with the simulations results. 2. Synchronous machine models On a synchronous machine operating in steady state, the relative position between rotor and resulting magnetic field remain almost constant. When a sudden disturbance occurs, the angle between them oscillates dynamically according to the swing equation given by (1). dı 2H d2 ı +D = Pm − Pe ω0 dt 2 dt
(1)
where ı is the relative rotor angle, t is the time, H is the generator inertia constant, D is the damping coefficient, ω0 is the DG synchronous speed, and Pm and Pe are mechanical input and electric power output of the DG, respectively. 2.1. Frequency variation during non-islanding events When a small disturbance occurs in the electrical system, the DG oscillates and returns to its original state after some time. The electrical power injected by DG in the distribution system can be written as Pe = Pmax sin ı
(2)
A small perturbation ı in ı, from the initial operating position ı0 can be represented by ı = ı0 + ı
(3)
Due to this perturbation, the swing equation (1) can be linearized and rewritten as 2H d2 ı dı +D + Ps ı = 0 ω0 dt 2 dt
(4)
Ps is known as the synchronizing power coefficient and is defined by the equation Ps = Pmax cos ı0
(5)
Solving the differential equation shown in (4), [19] shows that the frequency deviation from nominal synchronous speed is given by (6). ω =
dı ωn ı(0) −ς ωt n sin ωt = − e d dt 1 − ς2
where ωd = ωn
ς=
D 2
ωn =
1 − ς2
(6)
(7)
ω0 2HPs
(8)
ω0 Ps 2H
(9)
From (6), one can see that the frequency is given by a damped sinusoidal waveform. 2.2. Frequency variation during islanding events During an islanding event, the DG loses connection with the main system and, therefore, the synchronizing coefficient is 0. In this way, (4) can be rewritten as (10). dı 2H d2 ı = P +D ω0 dt 2 dt
(10)
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G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
B - Island
Frequency
Frequency
A - Non-Island
Time
Time
Fig. 1. Frequency behavior in: (A) non-island events; (B) island events.
P is the power variation due to the islanding; in other words, the transmitting power in the electrical system split point. In this case, P is assumed as constant during the islanding. P is assumed positive when the electrical power in the split point is flowing from the main system to DG. Since the rotor angle is synchronized with the stator magnetic field before islanding, the two initial conditions for (10) are ı(0) = 0 and dı(0) = 0. Solving (10), the equation for electrical dt frequency deviation is obtained. ω =
P dı = (1 − e−ω0 Dt/2H ) D dt
(11)
Comparing (6) to (11), it can be observed that the frequency of the DG behaves differently. During DG parallel operation with the system, the frequency tends to oscillate at the damped natural frequency, ωd , as shown in Fig. 1A. Disregarding the voltage controllers, governors, and the load dynamic during islanding, which may change due to voltage and frequency variation, the frequency does not oscillate during an islanding, but it is given by an exponential response, as shown in Fig. 1B. 3. The singular value decomposition Singular value decomposition (SVD) is factorization of a matrix in to constitutive components. It is widely used in common applications such as least square fitting data and pseudo-inverse calculation. In electric power systems it was employed in some fields such as in [20,21]. In this paper, the SVD is used for pattern recognition [22] and identifying islanding amongst other events involving distributed generation. The SVD decomposes an m by n matrix A in a unitary matrix V n × n, a diagonal matrix m × n, and a unitary matrix U m × m, as shown in (12). A = U˙V ∗
(12)
The symbol * stands for the conjugate transpose. The diagonal matrix is composed of non-negative singular values i , where 1 ≤ 2 ≤ 3 · · · ≤ r , r = min (m, n)
(13)
∗ T
∗
∗
A A = (U˙V ) (U˙V ) = V ˙U U˙V 2
T
A A = V˙ V
∗
∗
(14) (15)
and AAT = (U˙V ∗ )(U˙V ∗ ) = U˙V ∗ V ˙U ∗ T
T
2
AA = U˙ U
∗
(16) (17)
Multiplying (15) and (17) on the right by V and U, respectively, two eigen value problems can be obtained. AT AV = V ˙ T
AA V = U˙
2 2
f =
fr − fr fr+1 − fr . . . fr+m−1 − fr T
(18) (19)
(20)
Matrix A can be rewritten as given in (21)
A = fni (1)
...
fni (N)
fi (1)
...
fi (N)
(21)
fni is the frequency deviation in non-islanding events, fi is the frequency deviation during islanding events, and N is the total number of events of each case. In this paper, training set A is defined by the simulation of 24 cases. The non-islanding set is composed of 12 short circuits and load switching in several system positions. The islanding set is composed of 12 islanding with several levels of power mismatches. The algorithm should be trained for each system; however, the number of simulations necessary are low. The tests show the algorithm performance does not improve significantly for more than 24 cases involving different power mismatches and disturbances situations such as short circuits and load switching. Applying the singular value decomposition in A, each column of U can be seen as one base of A, and V* can be seen in a geometric point of view as a scaling and rotation of base U to reconstruct matrix A. In the next section, V* will be called E. According to (13), the first singular values are the most significant; therefore, U can be limited to its firsts columns, and E to its firsts rows. In the calculations below, only the first 20 columns of U and the first 20 rows of E are being considered. 4. Linear discrimination analysis Given the definition shown in (22) E = ˙V ∗
(22)
Analyzing the construction of matrix A in (21), it can be deduced that the first N columns of E represent non-islanding events (Eni ), and the last N columns represent islanding events (Ei ), as shown in (23)
E = Eni (1)
Considering T stands for the transpose matrix, we have T
In this way, V and U are determined by the eigen vectors of AT A and AAT , respectively, and is determined by the square root of its eigen values. The values of i are always non-negative; in this way, the sign of U and V must be checked in order to ensure their self-consistency. As seen in the previous section, frequency during an islanding is clearly different from other events that may happen during a connected situation. For the constitution of the training set, the frequency is analyzed half cycle (8.333 ms) after the instant when the absolute value of frequency deviation of 60 Hz exceeds the threshold of 0.05 Hz. In this way, as expressed in (20), f is a vector which contains the absolute value of frequency deviation, where r is the instant where the threshold is exceeded and m is the window size, equal to 10 cycles of 60 Hz (166.667 ms).
···
Eni (N)
Ei (1)
···
Ei (N)
(23)
This paper proposes the use of statistics about E in order to characterize whether one event is an Islanding or not. The linear discrimination analysis was used with this goal. The LDA was proposed in [23] in the taxonomy context [22]. The main idea of LDA is to take a high dimensional problem and transform it into a lower dimensional, with a transform W. Considering this, W should project E in such a way that maximizes the distances inter-class of the E data, and minimizes the distance intra-class of E data. To achieve this, a criterion known as generalized Rayleigh quotient was used (24). W = argmax W
W T SB W W T SW W
(24)
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
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SW is the within class scatter matrix and SB is the between class scatter matrix given by SB = (i − ni )(i − ni )T N
SW =
(25)
T
(Eni (j) − ni )(Eni (j) − ni ) +
j=1
N
(Ei (j) − i )(Ei (j) − i )
T
j=1
(26) ni and i are the mean values of E vectors according to 1 Eni (j) N N
ni =
(27)
j=1
1 Ei (j) N N
i =
(28)
j=1
The solution of the generalized Rayleigh quotient is given by the eigen value problem SB W = SW W
(29)
W is given by the eigen vector with associated eigen value that has the largest value. Being W is a unitary vector, the projection of E over W is given by (30) and (31). Pi = W T Ei
(30)
Pni = W T Eni
(31)
If the mean value of Pi is greater than Pni , the threshold is given by min (Pi ) + max (Pni ) Th = 2
min (−Pi ) + max (−Pi ) 2
(32)
(33)
5. The algorithm The definition of W transform and the threshold presented in previous section are made offline. In this section, the algorithm that produces the DG trip signal is presented and discussed. See flowchart presented in Fig. 2. The frequency is continually monitored, and is identified when the frequency deviation from 60 Hz exceeds the threshold of 0.05 Hz. If the frequency deviation exceeds the threshold, the vector containing synchronous machine frequency measurements f, should be projected in the bases of the training set. Taking f and multiplying by U−1 gives the coefficient C (34), which is equivalent to E obtained in the training set. Since U is a unitary, the transpose can be used instead of the inverse. C = U T f
(34)
Applying the transform W over C, P can be obtained (35). P = WT C
waits a time equivalent to three cycles of 60 Hz, i.e., Th2 is 384 for a sampling frequency of 7680 Hz. 6. Tests and results
Otherwise, W should be multiplied by −1 and the threshold is given by Th =
Fig. 2. Proposed island detection algorithm.
(35)
If P is greater than Th, an islanding event is characterized and a timer counter Z starts; otherwise, it is a non-islanding event. When Z reaches the threshold Th2, the trip signal is sent to disconnect the DG. The temporization given by Th2 is important to avoid an unwanted trip due to an misclassified event. A greater delay increases the robustness of the method, but also the detection time. In the studies carried out in this paper, the algorithm
To evaluate the performance of the proposed method, it has been used on the IEEE 34 node distribution test system, presented in Fig. 3 [24]. A synchronous generator is connected through a transformer to bus 854. The transformer data are given in Table 1. The diesel generator controls the power factor to 0.98 inductive its data are presented in Table 2, and DG voltage and frequency regulators are given in [25]. The excitation system model used in [25] is a static excitation equivalent to IEEE type ST2 Model [26], and the governor was the same used in [27]. A 0.2 MVA load with 0.92 inductive power factor is connected directly to the DG node. The proposed method is compared with one of the best-known islanding detection methods, the rate of change of frequency (ROCOF). The rate of change of frequency was calculated at each frequency sample by Eq. (36) df = (fr − fr−1 )fsampling dt
(36)
fsampling is the sampling frequency. When ROCOF exceeds the threshold, a time counter starts. This temporization is important Table 1 Transformer data. Parameter
Value
854-Point of common coupling Three phase transformer Rated power Nominal frequency Rated voltage Connection Vector group Positive sequence reactance (X1) Positive sequence resistance (R1) Zero sequence short circuit impedance Zero sequence short circuit resistance
3.0 MVA 60 Hz 24.9/2.4 kV D/yn Phase shift 1 × 30◦ 0.059371 p.u. 0.008667 p.u. 0.06 p.u. 0.0087 p.u.
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G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131 Table 3 Rate of change of frequency methods configuration.
df/dt (Hz/s) Delay (s) Voltage constraint (p.u)
Fig. 3. IEEE 34 Node Test Feeder [24].
because of the high sensitivity of ROCOF protection, and helps to avoid unwanted Trips for short time transients in the distribution system, especially short circuits. The method was adjusted to four typical settings, shown in Table 3. ROCOF4 operates if voltage
Table 2 Generator parameters. Parameter
Value
Parameter
Value
Reference machine
Not flag
1.56 p.u.
Mode of local voltage controller Dispatch – voltage
Voltage
Direct axis reactance (Xd ) Quad. axis reactance (Xq ) Direct axis transient reactance (Xd ) Direct axis subtransient reactance (Xd ) Quadrature axis subtransient reactance (Xq ) Direct axis short-circuit transient time-constant (Td ) Direct axis short-circuit subtransient time-constant (Td ) Quadrature axis short-circuit subtransient time-constant (Tq ) Main flux saturation – Sg10 Main flux saturation – Sg12
0.26 p.u.
1.0 p.u.
Nominal apparent power
3.125 MVA
Nominal voltage
2.4 kV
Power factor
0.8
Connection
yn
Inertia time constant (rated to Sgn) H
1.071 s
Leakage reactance
8.8%
Rotor type
Salient pole
1.06 p.u.
0.15 p.u.
0.15 p.u.
3.7 s
0.05 s
0.05 s
0.17 p.u. 0.60 p.u.
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
0.500 0.150 –
1.500 0.050 –
2.500 0.050 –
0.500 0.150 0.8
remains greater than 0.8 p.u. ROCOF 1, 2 and 3 do not use any voltage restriction. Two load conditions for the IEEE 34-bus distribution system were considered, 100% and 50%. The loads shown in the test system represent load condition 100%, whereas load condition 50% is obtained by reducing them accordingly. Several islanding conditions were tested and are shown in Table 4, which presents the line switched, the load condition, the DG generated power, the active and reactive switching interrupted power, and the protections tripping time. It is possible to see that the proposed method did not fail in any of the simulated cases. All algorithms based on rate of change of frequency failed twice due to very low transmitted active power on the switching point. The proposed technique island detection time is generally around 220 ms, slightly greater than ROCOF 1. Table 5 shows the methods’ performance during a single-phase to ground short circuit sustained in the system for 350 ms. After this time the fault line is disconnected, thus causing the DG islanding. Table 5 shows the short circuited bus and the fault resistance. The islanding detection time is the difference between the protection trip times and 350 ms; in this way, negative times represent protection trips before DG islanding, i.e., they represent failed trips. The proposed method did not fail in any simulated case presented in this table. ROCOF 1 failed once and had some detection times greater than 500 ms. ROCOF 2 failed in almost all cases, presenting negative islanding detection times. ROCOF 3 failed seven times. It detected the islanding during the short circuit in four times and did not trip during real islanding in three cases. Table 6 shows the algorithms’ performance for temporary phase to ground short circuit. The fault remains during 350 ms and disappears spontaneously without any switching. The proposed algorithm as well as ROCOF 1 and ROCOF 4 worked well in all simulated cases. ROCOF 2 and ROCOF 3 failed in 12 and 3 cases, respectively. Table 7 presents the tests of load switching, caused by the opening lines. The ROCOF 2 failed in case 5 identifying an islanding erroneously. The proposed method and ROCOF methods worked well in all tests. Fig. 4 presents the time detection for islanding caused by switching in bus 802. In Fig. 4A the power is changed in such a way that the interrupted reactive power remains 0 and active power changes from 0.016 to 0.36 p.u. regarding DG nominal power. The interrupted power is changed by a load introduced in bus 802. One can see the proposed method is able to detect the small active power mismatch, 0.016 p.u. In Fig. 4B the active power mismatch is set to 0 and the reactive power is changed. The methods based on ROCOF did not identify the island for any of the tested cases. However, the proposed methodology was able to detect islanding with reactive power mismatch up to 0.12 p.u. Although the proposed method may be slower than ROCOF for large active power mismatch, it is much more efficient for small values, detecting islanding were other methods were not able to do. Also, as shown in Fig. 4A, the proposed method can be faster than ROCOF 1 and ROCOF 4 for small power mismatches. Due to frequency pattern recognition, the proposed method avoids the nuisance tripping that would happen in other frequency based relays such as ROCOF and Under/Over frequency. This is an advantage since, for instance, in case of a big generation trip
G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
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Table 4 Performance of islanding detection methods during islanding events. Operating characteristic of the system
Islanding detection time (s)
Opened line
Load (%)
PG (MW)
POP (MW)
QOP (MVAr)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
800–802 830–854 800–802 830–854 800–802 830–854 800–802 830–854
100 100 50 50 100 100 50 50
2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0
−0.38 −0.75 −1.32 −1.61 1.12 0.72 0.05 −0.13
−0.11 −0.18 −0.67 −0.71 0.13 0.04 −0.31 −0.49
0.221 0.221 0.221 0.221 0.220 0.218 0.248 0.396
0.150 0.150 0.150 0.150 0.150 0.150 Not det. Not det.
0.050 0.050 0.050 0.050 0.050 0.050 Not det. Not det.
0.050 0.050 0.050 0.050 0.050 0.050 Not det. Not det.
0.150 0.150 0.150 0.150 0.150 0.150 Not det. Not det.
Table 5 Performance of islanding detection methods during phase to ground short-circuits, sustained for 350 ms, and followed by islanding. Operating characteristic of the system
Islanding detection time (s)
Short circuit bus
Opened line
Z fault ( )
Load (%)
PG (MW)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
802 802 816 816 830 830 802 802 816 816 830 830 802 802 816 816 830 830 802 802 816 816 830 830
802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854 802–806 802–806 816–824 816–824 830–854 830–854
0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60
100 100 100 100 100 100 50 50 50 50 50 50 100 100 100 100 100 100 50 50 50 50 50 50
2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.350 0.205 0.327 0.213 0.389 0.232 0.194 0.202 0.220 0.219 0.220 0.219 0.219 0.220 0.219 0.220 0.219 0.220 0.192 0.197 0.211 0.194 0.217 0.194
0.150 0.150 0.189 0.150 0.208 0.150 0.401 Not det. 0.490 0.540 0.490 0.527 0.128 0.150 0.150 0.150 0.150 0.150 0.123 0.150 0.150 0.150 0.150 0.150
−0.223 −0.230 0.323 −0.230 0.440 −0.230 −0.223 −0.230 0.050 −0.230 0.050 −0.230 −0.227 −0.229 0.050 −0.230 0.050 −0.230 −0.300 −0.230 −0.223 −0.231 0.050 −0.231
0.307 0.050 0.578 Not det. Not det. Not det. 0.050 0.050 0.050 0.050 0.050 0.050 −0.219 0.050 0.050 0.050 0.050 0.050 −0.221 0.050 0.050 −0.223 0.050 −0.222
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Table 6 Performance of islanding detection methods during temporary phase to ground short circuit, 350 ms. Operating characteristic of the system
Islanding detection time (s)
Short circuit bus
Z fault
Load (%)
PG (MW)
Proposed
ROCOF 1
ROCOF 2
ROCOF 3
ROCOF 4
830 830 852 852 842 842 830 830 852 852 842 842 830 830 852 852 842 842 830 830 852 852 842 842
0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60 0 60
100 100 100 100 100 100 50 50 50 50 50 50 100 100 100 100 100 100 50 50 50 50 50 50
2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0 2.5 2.5 2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
Not det. 0.120 Not det. 0.124 Not det. 0.125 Not det. 0.120 Not det. 0.123 Not det. 0.124 Not det. 0.120 Not det. 0.124 Not det. 0.125 Not det. 0.119 Not det. 0.122 Not det. 0.123
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. 0.128 Not det. Not det. Not det. Not det.
Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det. Not det.
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G. Marchesan et al. / Electric Power Systems Research 130 (2016) 124–131
Fig. 4. (A) Anti island methods time detection and NDZ for active power variation. (B) Anti island methods time detection and NDZ for reactive power variation.
Table 7 Load switching tests.
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Operating characteristic of the system Case
Opened line
Load (%)
PG (MW)
POP (MW)
QOP (MVAr)
1 2 3 4 5 6 7 8
854–852 834–842 854–852 834–842 854–852 834–842 854–852 834–842
100 100 50 50 100 100 50 50
2.5 2.5 2.5 2.5 1.0 1.0 1.0 1.0
1.511 0.565 0.754 0.285 1.507 0.563 0.75 0.284
0.107 −0.376 −0.381 −0.593 0.112 −0.374 −0.375 −0.558
in a large DG penetration scenario, the DG may help the system in the recovering process. However, a large perturbation on the generation or transmission system may cause frequency variations similar to those present in case of islanding, producing a undesirable tripping. Therefore, the Standard IEEE 1547 [1] allows the system operator to specify the frequency setting and time delay for underfrequency trips down to 57 Hz. In these cases, the settings of the proposed method should take this recommendation in to account.
7. Conclusion This paper proposes a technique for islanding detection based on singular value decomposition and linear discrimination analysis. During islanding, the synchronous generator oscillates at very slow frequency due to governors’ actions or the frequency growth exponentially when the governors are unable to correct it. However, while connected to the main grid, the DG oscillates at a higher frequency. The method uses a pattern recognition methodology that detects the frequency signature during islanding and sends a trip signal to the synchronous generator switcher. It uses smaller windows than those used by methods that seek to estimate the frequency of oscillation and damping coefficient, providing faster tripping. Several simulations were performed on different scenarios with islanding and non-islanding events, and the proposed methodology proved to be more sensitive than ROCOF islanding protection. The proposed algorithm is able to detect islanding with power mismatches smaller than 1.6% and does not trip for the vast majority of non-islanding events. In short, the main advantages brought by the proposed algorithm over other methods are robustness for load switching and short circuits, small NDZ, and fast tripping.
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