Islanding detection is essential for secure and reliable operation of microgrids. Considering the relationship between the power generation and the load in microgrids, frequency may vary with time when islanding occurs. As a common approach, frequency measurement is widely used to detect islanding condition. In this paper, a novel frequency calculation algorithm based on extended Kalman filter was proposed to track dynamic frequency of the microgrid. Taylor series expansion was introduced to solve nonlinear state equations. In addition, a typical microgrid model was built using MATLAB/SIMULINK. Simulation results demonstrated that the proposed algorithm achieved great stability and strong robustness in of tracking dynamic frequency.

Distributed generation (DG) using renewable energy sources such as solar energy, wind energy, and hydroenergy has received considerable attention due to environmental pollution and exhaustion of fossil fuel. Many utilities around the world have a significant penetration of DGs in their systems. As a promising developing trend, the concept and techniques of microgrids (MGs) are proposed to improve DG’s utilization [

MG is a kind of regional electric power systems which include DGs and power loads. They have the ability to disconnect from or parallel with large electric power systems. MGs offer many potential benefits, such as improving the reliability of power supply by islanding operation during large electric power system outages, relieving overload problems by allowing a part of the power system to intentionally island, and so forth. However, there are also many issues to be solved before MGs become integral part of the utilities, such as how to achieve high power quality, efficiency, and safety. Especially, the most concerned problem is the islanding which refers to a condition that MG has an independent powering to a location even though the MG has been disconnected from the grid [

The mainly used islanding detection techniques may be broadly classified as remote and local techniques. Local techniques can be divided into passive and active detection methods [

For the passive detection method, one of the common passive approaches is based on the measurement of voltage vector and frequency of the common coupling point in real time. Variation in voltage and frequency from its normal value indicates the occurrence of islanding in most conditions. A large number of methods are available for the frequency estimation based on digitized samples of system voltage, methods such as discrete Fourier transforms, conventional Kalman filter, and phase lock loop [

In this paper, the necessity and basic methods of islanding detection of the MG are addressed. Considering the importance of frequency estimation, a novel algorithm based on extended Kalman filter is presented to enhance the precision and the speed of frequency tracking in islanding MGs. Simulation tests demonstrate that the proposed algorithm has excellent superiority on islanding detection.

The MG embedded in distribution systems has evolved overwhelmingly to help meet the load growth in existing networks. The typical topologies of MGs are suggested in IEEE 1547.4 [

Typical topologies of MGs.

The most important feature of MGs is that they have the ability to disconnect from or parallel with the area electric power system. The planned MG in Figure

As shown in Figure

In short, when islanding condition happens, not only the area electric power system operator needs to be aware of this operation, but also the control strategy of the MG needs to be adjusted. Therefore, islanding detection is one of the key issues for protection and control of MGs, as shown in Figure

Schematic diagram of protection and control of MGs.

There are basically two kinds of distributed generators in MGs. The first one, such as photovoltaic, fan, and storage battery, is based on inverter control. The other one, such as synchronous generator and microsteam turbine, is based on the principle of generator.

Assume that the active and reactive power outputs from DGs are

So

In (

It can be known from (

The distributed generators in MGs are mainly based on inverter control. Compared with conventional synchronous generators, the inverter-based distributed generators have small equivalent inertia constants and capacities. The frequency varies distinctly in islanding operation. Furthermore, inverter control may produce more harmonics and noises due to dead time of the inverter itself. In sum, the voltage and the frequency of MGs are comparatively stable in parallel operation, while in islanding operation, the variations of electric measurements are complex, so that the accurate frequency tracking must be achieved by reliable and advanced algorithms.

Frequency tracking could not be limited in islanding detection. It is needed in many other areas of power system, such as power quality monitoring, automation under frequency load shedding devices, and automatic accurate synchronizers. In theory, the frequency tracking methods can be investigated in all the situations that need frequency measurement.

A number of methods are available on the frequency estimation based on digitized samples of the system voltage. Discrete Fourier transform is one of the most commonly used algorithms due to its good filtering characteristics and strong resistance to disturbance. The main principle of discrete Fourier transforms is to calculate the phase angle difference between two adjacent data windows. Then the frequency can be estimated accordingly. However, discrete Fourier transforms may lead to inaccuracies due to leakage and picket-fence effects. Meanwhile, it is not ideal when the frequency is changing during a complete data window of Fourier transforms. For this reason, adaptive discrete Fourier transforms for frequency tracking are proposed to lock the fundamental frequency of incoming signal [

Kalman filter algorithm does well in addressing the general problem of trying to estimate the state

It is quite easy to make the Kalman filter self-tuned to the fundamental frequency without any hardware modification.

Harmonics are eliminated more effectively when the Kalman filter is adaptive with respect to the fundamental frequency.

The Kalman filter allows filtering preselected resonant nonharmonic frequencies, which is not possible with the adaptive discrete Fourier transforms.

Kalman filter is often adopted due to its low computation cost and robustness in estimating sinusoids signal embedded in an unknown measurement noise [

However, the calculation of conventional Kalman filter is based on the assumption that the measured system is linear in its mathematical model. Thus, it has to face several distortions for coping with the nonlinear signals. As for the frequency tracking of power system, the input signal is sampling voltage values generally. If the input signal is assumed to be an ideal sinusoid with constant amplitude, the mathematical model can be represented as

Conventional Kalman filter supposes that

The nonlinear stochastic difference equation can be written as

To calculate state variables

Generally, two-order Taylor series is adopted as an approximation solution in field calculation. This approximation is established based on three considerations:

By using two-order Taylor series (

For the extended Kalman filter,

The initial stage of extended Kalman filter design is to model the signal and derivation of state variables of it. This is because the signal model dynamics describe a mechanism for how the process may evolve. Considering the electric measurements (voltages, currents, and frequencies) in MGs may change irregularly, or nonlinearly in most cases, Taylor series is used to nonlinear calculation. The voltage at the point of common coupling in MGs can be described approximately as follows:

Using the cosine expansion, we can obtain the discrete expression of the following:

The amplitude and frequency of voltage at the point of common coupling are changing when islanding occurs. Therefore,

In (

In this paper, four state variables are defined as in-phase signal, quadrature signal, time-varying frequency, and time-varying amplitude, which are all changing in nonlinear way as proceeded.

Consider

Based on the relationship of

Predict the state with initials:

Compute the error covariance:

Compute the Kalman gain:

Update the state estimate:

Update the error covariance:

Compared with the other two common frequency tracking methods, adaptive discrete Fourier transforms (i.e., adaptive Fourier filter) and conventional Kalman filter, the performance of extended Kalman filter-based frequency calculation algorithm is experimentally evaluated. For the following simulation tests, the fundamental frequency and amplitude are assumed to be 50 Hz and 1p.u., respectively. The sampling frequency is set to be 1200 Hz, which is the conventional choice for protective relays.

Firstly, the observed signal is a voltage waveform with time-varying frequency; that is,

Voltage of observed signal with varying frequency.

Accordingly, frequency tracking performance of different algorithms is shown in Figure

Frequency tracking performance. (a) Frequency tracking comparison among different algorithms; (b) measured frequencies in stage 1; (c) measured frequencies in stage 2; (d) measured frequencies in stage 3.

To explain clearly, the test can be divided into three stages.

For the tracking time of ramp-changed frequency, extended Kalman filter and conventional Kalman filter are almost the same. However, extended Kalman filter is more stable and has less fluctuation than the conventional one. Besides, as the frequency changes sharply, the proposed method has clear superiority in tracking speed. In sum, it is confirmed that the proposed extended Kalman filter-based algorithm has excellent responding performance for signals with time-varying frequencies.

In addition, it is necessary to study the response of the extended Kalman filter and the other two algorithms in the presence of noise. Random noise is injected to the observed signal to test the stability of the algorithms. Generally, the signal-to-noise ratio, often written as SNR, is the measure of signal strength relative to background noise:

In (

Obviously, the observed signal is more unreadable with the larger noise. Even a little noise can cause a big error in frequency tracking. This is because such comprehensive signal is no longer ideal sine or cosine wave for noise added to pure wave. Based on the observed signal

Observed signal with noise and time-varying frequency. (a) Noise signal; (b) the observed signal with time-varying frequency and random noise.

For the signal

Frequency tracking performance for the signal with noise and time-varying frequency.

Since the linear characteristics of local signal were deteriorated by adding noise, conventional Kalman filter was influenced significantly. Apparently, the proposed algorithm based on extended Kalman filter and the algorithm based on adaptive Fourier filter achieved better performance in antinoise ability. For comparison, the measured frequency variances are 0.187 for adaptive Fourier filter-based algorithm and 0.151 for extended Kalman filter-based algorithm, respectively. Therefore, the proposed algorithm is more effective for frequency tracking under the conditions of islanding operation with time-varying frequency, noise, and so forth.

As shown in Figure

Generally speaking, the most commonly used method in islanding detection of MGs is both over/undervoltage relay and over/underfrequency relay (or ROCOF). Over/undervoltage relay mainly works when there is an active power imbalance, while over/underfrequency is more effective when there is a reactive power imbalance. Thus, frequency tracking ability of the proposed algorithm can be tested in a designed islanding simulation model.

By using MATLAB/SIMULINK, the model of distribution network with MGs is built to simulate various parallel and islanding operation conditions. As shown in Figure

Simulation model of distribution network with MGs.

Frequency shift when islanding occurs with imbalanced power.

As shown in Figure

The measurements of frequency changing rate

Change rate of the frequency when islanding occurs with imbalanced power.

Frequency variance when islanding occurs with imbalanced power.

As shown in Figure

Figure

Simulation results show that extended Kalman filter not only can detect frequency changes effectively but also has less fluctuation after islanding process.

In case 2, switch S-1 is disconnected; network load 1 is out of power consequently. The total numbers of generations are equal to the sum of loads for both active and reactive powers. The circuit breaker CB opens to form an MG at 0.3 s. In theory, the voltage and frequency of the MG will change a little. The measured voltage and frequency are shown in Figures

Measured voltage of islanding MG when islanding occurs with balanced power.

Frequency shift when islanding occurs with balanced power.

As shown in Figures

Figure

Change rate of the frequency when islanding occurs with balanced power.

Frequency variance when islanding occurs with imbalanced power.

Frequency shift when islanding occurs with active power imbalance only.

Change rate of the frequency when islanding occurs with active power imbalance only.

Frequency variance when islanding occurs with active power imbalance only.

This paper presents an extended Kalman filter for the frequency estimation to detect islanding in MGs. The mathematical model of nonlinear system is developed using analytical equations. In order to solve the nonlinear problem, Taylor series are used to linearize state equations, which is the main point of solving the nonlinear problem compared with other algorithms. To show the performance of extended Kalman filter, several tests have been applied. The simulation results show that extended Kalman filter not only has the fastest tracking speed compared with conventional Kalman filter and adaptive Fourier filter in test 1 but also has the best interference immunity in the presence of random noise in test 2. It can stand 40 dB or more noise without much distortion. By using extended Kalman filter, the islanding detection based on frequency is improved significantly in reliability and stability.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National High Technology Research and Development Program of China (2011AA05A106), Program for New Century Excellent Talents in Education Ministry of China (no. NCET-11-0367), and National Natural Science Foundation of Tianjin City (11JCYBJC07600).