Hybrid intelligent water drop bundled wavelet neural network to solve the islanding detection by inverter-based DG

Abstract

In this paper, a passive neuro-wavelet based islanding detection technique for grid-connected inverter-based distributed generation was developed. The weight parameters of the neural network were optimized by intelligent water drop (IWD) to improve the capability of the proposed technique in the proposed problem. The proposed method utilizes and combines wavelet analysis and artificial neural network (ANN) to detect islanding. Connecting distributed generator to the distribution network has many benefits such as increasing the capacity of the grid and enhancing the power quality. However, it gives rise to many problems. This is mainly due to the fact that distribution networks are designed without any generation units at that level. Hence, integrating distributed generators into the existing distribution network is not problem-free. Unintentional islanding is one of the encountered problems. Discrete wavelet transform (DWT) is capable of decomposing the signals into different frequency bands. It can be utilized in extracting discriminative features from the acquired voltage signals. In passive schemes with a large non-detection zone (NDZ), concern has been raised on active method due to its degrading power quality effect. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. The simulation results from Matlab/Simulink shows that the proposed method has a small non-detection zone, and is capable of detecting islanding accurately within the minimum standard time.

Graphical abstract

Keywords

islanding detection / neuro-wavelet / intelligent water drop (IWD) / non-detection zone (NDZ) / distributed generation (DG)

1 Introduction

Distributed generation (DG) may be defined as generating resources, other than central generating stations, which is placed close to the load being served, usually at customer site. In fact, many utilities around the world already have a significant penetration of DG in their system. But there are many issues to be taken into account with the DG and one of the main issues is islanding [1,2].

Classical view of power system is characterized by a unidirectional power flow from centralized generation to consumers. Power system restructuring gave impetus to a modern view by introducing DGs into distribution systems, causing a bi-directional power flow. Actually, the concept of embedding DG into the distribution system was proposed assuming that DGs will always be operating in a grid-connected mode [3]. However, a few years later, it has been perceived that several operational issues are associated with DG when operating in an island mode [4]. The island formation including a distributed generator is presented in Fig. 1.

It is expected that inverter-based DG technologies will be increasingly used in electrical power systems in the near future. The increased expanding of DG in utility systems has been mainly caused by the liberalization of the electricity markets. Recent improvement in energy conversion systems and the environmental drive has been used to promote green energy. These recent advances in energy conversion include the emergence of cheaper and more efficient power generation systems using renewable and hybrid power schemes. The attractions of “green energy” have been and will continue to be a powerful force in the expansion of DG. DG may be defined as generating resources, other than umbilical generating stations, which is located close to the load being served, usually at a customer site. In fact, many utilities around the world already have significant penetration of DGs in their system. When the DG systems are operated in parallel with utility power systems, particularly with reverse power flow, the power quality problems become significant. Power quality drawbacks include frequency deviation, voltage fluctuation, harmonics and reliability of the power system. Furthermore, one of the technical topics created by DG interconnection is inadvertent islanding [5,6]. Islanding condition causes abnormal operation in the power system and also causes negative impacts on protection, operation, and handling of distribution systems. So, it is of importance to immediately and effectively detect the islanding conditions and swiftly disconnect DG from the network.

Under this situation, a so-called island is formed, resulting in unexpected consequences that may include an increased complexity of orderly restoration (out of phase switching of re-closers leading to damage of the DG, neighboring loads, and utility equipment), a degraded stability of system voltage and worst of all, a raised risk to related maintenance personnel. In other words, under the scenario of islanding, line crew members may misjudge the load-side of the line as inactive where DGs are indeed feeding power to loads; hence jeopardizing the life of operators and meanwhile illuminating the importance of a reliable forewarning mechanism to such events. Therefore, during the interruptions of utility power, the connected DG must detect the loss of utility power and disconnect itself from the power grid as soon as possible [7].

There are many proposed techniques for detection of an island [8–17]. The non-detection zone (NDZ) can be defined as the range (in terms of the power difference between the DG inverter and the load or load parameters) in which an islanding detection scheme under test fails to detect this condition [10]. The second feature is associated with the type of loads (potential loads inside island), which can be modeled as a parallel RLC circuit. This circuit is primarily used because it raises more difficulties for islanding detection techniques than others. Generally, nonlinear loads that produce current harmonics, or constant power loads, do not represent significant problems for islanding detection [11]. Most islanding detection methods suffer from large NDZs [18,19] and/or have a run-on time between half a second to two seconds [20], and thus cannot be used for uninterruptible autonomous operation of an island. These techniques can be broadly classified into local and remote techniques. Local techniques can be further classified into active and passive ones. Remote techniques for detection of islands are based on communication between the utility and the DGs. Although these techniques may have better reliability than local techniques, they are expensive to perform and hence uneconomical. These schemes include power line signaling and transfer trip [21,22]. Local techniques rely on the information and data at the DG site. Passive techniques depend on measuring certain system parameters and do not interfere with the DG operation. Over/under voltage and frequency is one of the simplest passive methods used in islanding detection. However, if the load and the generation on the island are closely matched, the change in voltage and frequency may be very small and within the thresholds, thus leading to an undetected islanding situation. The other passive strategies have been proposed based on monitoring rate of change of frequency (ROCOF), phase angle displacement, rate of change of generator power output, impedance monitoring, the THD technique and the wavelet transform (WT) function [23]. These strategies offer superior sensitivity as their settings allow the detection to take place within statutory limits, but their settings must be carefully selected to avoid mal-operation during network faults. The trade-off between the two performance criteria is especially difficult for these methods. If the threshold for permissible disturbance in these quantities is set to a low value, the nuisance tripping will become an issue, and if the threshold is set so high, islanding may not be detected. In active methods, the main theme exists in the design of control circuits such that the required variations can be produced at the outputs of distributed generators. Then, once the loss of grid takes place, this designated bias will accordingly enlarge sufficiently to trip the connected relays, notifying the occurrence of the event. On the contrary, when the utility supply is normally operated, the amount of variations will be insufficient to trip the relays, ensuring that there is no event misidentified. The main advantage of active techniques over passive ones is their small NDZ. Some important active techniques are impedance mensuration, frequency shift and active frequency drift, current injection, sandia frequency shift and sandia voltage shift, and negative phase sequence current injection. Under several circumstances, these active methods have won the confirmation. However, the complicated control circuit for the generation of designated bias may offset their merits [24,25]. Generally, if there are large changes in loading for DG after loss of the main power supply, the islanding conditions are easily detected by monitoring several parameters such as voltage magnitude, phase displacement, and frequency change. However, in case of small changes in loading for DG, the conventional methods have some difficulty in detecting such a particular islanding condition.

In this paper a passive neuro-wavelet based islanding detection method which reduces the NDZ to as close as possible and to keep the output power quality unchanged has been developed. The proposed strategy uses and combines wavelet analysis and artificial neural network (ANN) to detect islanding. The proposed strategy is based on the transient voltage signals generated during the islanding event. Discrete WT (DWT) is puissant of decomposing the signals into different frequency bands. It can be utilized in finding discriminative features from the acquired voltage signals. The features are then fed to a trained ANN model which is if well trained puissant of differentiating among islanding event and any other transient events such as switching or temporary fault. The trained typesetter was then tested using novel voltage waveforms. The achieved results demonstrate that this approach can detect islanding events with high degree of accuracy.

The problem model is suited for application of intelligent water drop (IWD) to find the optimal weight parameters of neural network. Flowing water drops are observed mostly in rivers, lakes. The paths followed by the natural river have been created by a swarm of water drops. As water drops move, they change their environment in which they are flowing. The path followed by the rivers or lakes includes many twists and turns. Due to these obstacles the real path that the water drops follow will be different from the ideal path (which is the shortest and straight). One feature of a water drop flowing in a river is its velocity. It is assumed that each water drop of a river can also carry an amount of soil. This soil is usually transferred from fast parts of the path to the slow parts. As the fast parts get deeper by being removed from soil, they can hold more volume of water and may attract more water. The removed soils, which are carried in the water drops, are unloaded in slower beds of the river. A water drop will always try to choose an easy path rather than the harder one when there are many options in the paths to be chosen.

The following properties are assumed for a flowing water drop: A high speed water drop gathers more soil than a slower water drop; the velocity of a water drop increases more on a path with low soil than a path with high soil; and a water drop prefers a path with less soil than a path with more soil.

2 Problem statement

The islanding detection schemes proposed in literature can be grouped into two categories: remote and local, as shown in Fig. 2. Remote techniques are based on the communication between the electric utility and the DG units. Despite the fact that remote techniques are reliable and effective, they suffer high implementation cost. On the other hand, local islanding schemes can further be divided into active, passive and hybrid. Islanding detection schemes are commonly evaluated based on the NDZ. The NDZ corresponds to the range of active and reactive load-generation mismatches within the island in which the islanding detection approach fails to identify the islanding state.

This section provides a state-space mathematical model for the islanded system. It is assumed that the DG unit and the local load are balanced three-phase subsystems within the island. The state space equations of the potential island in the standard state space form are

$$\begin{gathered} \dot{\mathit{X}}\left(t\right)=\mathit{A}\mathit{X}\left(t\right)+\mathit{B}\mathit{u}\left(t\right), \\ \mathit{y}\left(t\right)=\mathit{C}\mathit{X}\left(t\right), \\ \mathit{u}\left(t\right)={\mathit{v}}_{\mathrm{t}d}, \end{gathered}$$

where

\mathit{A}=\left[\begin{array}{cccc}\hfill -{\displaystyle \frac{R_{\mathrm{t}}}{L_{\mathrm{t}}}}\hfill & \hfill {\omega }_0\hfill & \hfill 0\hfill & \hfill -{\displaystyle \frac{1}{L_{\mathrm{t}}}}\hfill \\ \hfill {\omega }_{\mathrm{0}}\hfill & \hfill -{\displaystyle \frac{R_{\mathrm{l}}}{L}}\hfill & \hfill -2{\omega }_0\hfill & \hfill \left({\displaystyle \frac{R_{\mathrm{l}}C{\omega }_{\mathrm{0}}}{L}}-{\displaystyle \frac{{\omega }_0}{R}}\right)\hfill \\ \hfill 0\hfill & \hfill {\omega }_0\hfill & \hfill -{\displaystyle \frac{R_{\mathrm{l}}}{L}}\hfill & \hfill \left({\displaystyle \frac{1}{L}}-{\omega }_{\mathrm{0}}^{\mathrm{2}}C\right)\hfill \\ \hfill {\displaystyle \frac{1}{C}}\hfill & \hfill \mathrm{0}\hfill & \hfill -{\displaystyle \frac{1}{C}}\hfill & \hfill -{\displaystyle \frac{1}{RC}}\hfill \end{array}\right],

{\mathit{B}}^{\mathrm{T}}=\left[\begin{array}{cccc}{\displaystyle \frac{\mathrm{1}}{L_{\mathrm{t}}}}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \end{array}\right],

\mathit{C}=\left[\begin{array}{llll}\mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \end{array}\right],

\mathit{D}=\left[\mathrm{0}\right],

{\mathit{X}}^{\mathrm{T}}=\left[\begin{array}{llll}{i}_{\mathrm{t}d}\hfill & i_{\mathrm{t}q}\hfill & i_{\mathrm{L}d}\hfill & v_d\hfill \end{array}\right].

Figure 3 demonstrates the step response of the system in the islanding mode. The response time constant of the island system is selected as the analyzing time of adaptive neuro fuzzy inference system (ANFIS) output.

The system under study consists of one 80 kW inverter based DG connected to an RLC load having a quality factor of 1.8 and a grid. The system, controller, and load parameters are given in Ref. [6]. The performance of the DG under normal and islanded operating conditions was studied and simulated on Matlab/Simulink. The inverter performs two main functions:

1) Controlling the active power output of the DG and, in some cases, injecting a suitable amount of reactive power to mitigate a power quality problem.

2) According to the IEEE Standard 1547, the DG should be equipped with an anti-islanding detection algorithm, which could be performed using the inverter interface control.

The DG interface control is designed to supply constant current output as shown in Ref. [6]. For this interface control, both the I_d and I_q components of the DG output current are controlled to be equal to a preset value (I_{d\mathrm{ref}} and I_{q\mathrm{ref}}). The DG was operated at unity power factor by setting I_{q\mathrm{ref}} to zero. In particular, parallel RLC loads with a high Q factor often present problems for island detection. The quality factor Q is defined by

Q=R\sqrt{{\displaystyle \frac{C}{L}}},

and is the ratio of the amount of energy stored in the reactive elements of the load to the amount of energy dissipated in the resistance of the load. (For example, for Q=\mathrm{2}, there is twice as much energy stored in the L and C of the load as is being dissipated in R). The loads that are near resonance at {\omega }_{\mathrm{0}} and have a high Q–factor are the ones that cause difficulty in islanding detection. Unfortunately, the level of real or reactive power mismatch is not uniquely determined by load parameters. Specifically, the reactive power consumption of the load is given by

Q_{\mathrm{Load}}=V_{\mathrm{rms}}^2\left[{\left(\omega L\right)}^{-\mathrm{1}}-\left(\omega C\right)\right]=\mathrm{\Delta }Q.

This equation clearly shows that there are infinitely many combinations of L and C that will yield the same \mathrm{\Delta }Q.

3 NDZ

An islanding detection method may have a NDZ. The NDZ is mainly associated with a range of active and reactive power (ΔP, ΔQ) in which the detection method fails to detect the occurrence of an island. A positive ΔP indicates an excess of the power consumed by the load within an island resulting in under voltage. On the other hand, a positive ΔQ indicates an excess of reactive power consumed by the load resulting in an over frequency. A small mismatch in the active and reactive power will not be sufficient to cause tripping of voltage and frequency relays which will be fully discussed in this section. An accepted way of comparing and evaluating two anti-islanding detection techniques is by comparing the area of the NDZ. A method resulting in a smaller NDZ will be able to detect the islanding more reliably. It can either be represented in terms of power mismatch or in terms of the R, L, and C of the load. In Refs. [6,30], an approximate representation of the NDZ for over/under voltage protection (OVP/UVP) was derived. An exact and accurate representation of the NDZ is presented in this part of paper. It examines the NDZ of an OVP/UVP and over frequency protection (OFP)/UVP islanding scheme when implemented for constant current controlled inverters. In order to determine the amount of mismatch for which the OVP/UVP and OFP/UFP will fail to detect islanding, the amount of active power mismatch in terms of load resistance can be expressed as

\mathrm{\Delta }P=\mathrm{3}V\times I-\mathrm{3}\left(V+\mathrm{\Delta }V\right)\times I=-\mathrm{3}V\times \mathrm{\Delta }V\times I,

where V and I indicate the rated current and voltage, respectively. In distributed networks, voltage values between 0.88 pu and 1.1 pu are in acceptable range for voltage relays. These voltage levels are equivalent to \mathrm{\Delta }V=-\mathrm{0.12} and \mathrm{\Delta }V=\mathrm{0.1}, respectively. The calculated imbalance amount for the test network mentioned in this paper (the inverter rated output power is 80 kW), are 9.6kW and −8 kW, respectively. The frequency and voltage of an RLC load has the active and reactive power as

P_{\mathrm{L}}={\displaystyle \frac{V_{\mathrm{L}}^{\mathrm{2}}}{R_{\mathrm{L}}}},

Q_{\mathrm{L}}=V_{\mathrm{L}}^{\mathrm{2}}\left({\displaystyle \frac{\mathrm{1}}{\omega L}}-\omega C\right),

where V, ω, P and Q are the load voltage, frequency, active power and reactive power, respectively. In normal operating conditions, a common coupling point voltage is determined by the power grid, and DG system has no control over voltage and until it is connected to the network the voltage is fixed at a nominal value of 1 pu. Once the island occurs, the distribution system cannot control the voltage and the amount of active power imbalance determines the voltage deviation from the nominal values. In view of the fact that the output power of the inverter is in unity power factor, the reactive power of load is supplied just by network before islanding. Besides, this amount of reactive power imbalance is equal to the consumed load after islanding, hence there is

\mathrm{\Delta }Q=\mathrm{3}{\displaystyle \frac{V^{\mathrm{2}}}{{\omega }_{\mathrm{n}}L}}\left(\mathrm{1}-{\omega }^{\mathrm{2}}LC\right)=\mathrm{3}{\displaystyle \frac{V^{\mathrm{2}}}{{\omega }_{\mathrm{n}}L}}\left(\mathrm{1}-{\displaystyle \frac{{\omega }_{\mathrm{n}}^2}{{\omega }_{\mathrm{r}}^2}}\right),

where {\omega }_{\mathrm{n}} and {\omega }_{\mathrm{r}} are the system frequency and resonance frequency of load, respectively. Reactive power imbalance leads to the resonance frequency, then the frequency changes after the islanding occurrence is equal to the difference between network frequency and load resonance frequency.

{\omega }_{\mathrm{r}}={\omega }_{\mathrm{n}}\pm \mathrm{\Delta }\omega ,{\omega }_{\mathrm{r}}={\displaystyle \frac{\mathrm{1}}{\sqrt{LC}}}.

Thus, the reactive power imbalance needed for certain changes in frequency can be obtained by

\mathrm{\Delta }Q=\mathrm{3}{\displaystyle \frac{V^{\mathrm{2}}}{{\omega }_{n}L}}\left(\mathrm{1}-{\displaystyle \frac{f_n^{\mathrm{2}}}{{\left(f_n\pm \mathrm{\Delta }f\right)}^{\mathrm{2}}}}\right).

In distributed networks of Iran, the acceptable frequency range is between 49.7 Hz and 50.3 Hz which are equal to Δf = 0.3 Hz and Δf = −0.3 Hz. In the test system in this paper, as presented in Fig. 4, the amounts of reactive power imbalances are 3.05 kvar and −5.16 kvar, respectively.

4 IWD

4.1 Overview of IWD algorithm

The IWD algorithm [26] is a swarm-based nature-inspired optimization algorithm, which has been inspired from natural rivers and how they find almost optimal path to their destination. A natural river often finds good paths among lots of possible paths in its ways from the source to the destination. These near optimal or optimal paths follow from actions and reactions occurring among the water drops and the water drops with their riverbeds. In the IWD algorithm, several artificial water drops cooperate to change their environment in such a way that the optimal path is revealed as the one with the lowest soil on its links. The solutions are incrementally constructed by the IWD algorithm. Consequently, the IWD algorithm is generally a constructive population-based optimization algorithm. The IWD for short, consists of two important properties: the amount of the soil it carries now, soil (IWD); and the velocity that it is moving now, velocity (IWD). This environment depends on the problem at hand. In an environment, there are usually lots of paths from a given source to a desired destination whose position may be known or unknown [27]. If the position of the destination is known, the goal is to find the best (often the shortest) path from the source to the destination. In some cases in which the destination is unknown, the goal is to find the optimum destination in terms of cost or any suitable measure for the problem. An IWD is considered to move in discrete finite-length steps. From its current location to its next location, the IWD velocity is increased by the amount nonlinearly proportional to the inverse of the soil between the two locations. Moreover, the soil of IWD is increased by removing some soils of the path joining the two locations. The amount of soil added to the IWD is inversely (and nonlinearly) proportional to the time needed for the IWD to pass from its current location to the next location. This duration of time is calculated by the simple laws of physics for linear motion. Thus, the time taken is proportional to the velocity of the IWD and inversely proportional to the distance between the two locations. Another mechanism that exists in the behavior of an IWD is that it prefers the paths with low soils on its beds to the paths with higher soils on its beds. To implement this behavior of path choosing, a uniform random distribution among the soils of the available paths is used such that the probability of the next path to choose is inversely proportional to the soils of the available paths. The lower the soil of the path, the more chance it has for being selected by IWD.

4.2 IWD algorithm

The IWD algorithm gets a representation of the problem in the form of a graph (N, E) with the node set N and edge set E. Then, each IWD begins constructing its solution gradually by traveling on the nodes of the graph along the edges of the graph until the IWD finally completes its solution. One iteration of the algorithm is complete when all IWDs have completed their solutions. After each iteration, the iteration best solution T^IB is found and it is used to update the total best solution T^TB. The amount of soil on the edges of the iteration-best solution T^IB is reduced based on the goodness (quality) of the solution. Then, the algorithm begins another iteration with new IWDs but with the same soils on the paths of the graph and the whole process is repeated. The algorithm stops when it reaches the maximum number of iterations itermax or the total-best solution T^TB reaches the expected quality. The IWD algorithm has two kinds of parameters. One kind is those that remain constant during the lifetime of the algorithm, which are called ‘static parameters’. The other kind is those parameters of the algorithm, which are dynamic and are reinitialized after each iteration of the algorithm [28,29].

The algorithm of IWD is specified in the following steps:

1) The graph (N, E) of the problem is given to the algorithm. The quality of the total-best solution T^TB is initially set to the worst value: q(T^TB) = ∞. The maximum number of iterations itermax is specified by the user. The iteration count itercount is set to zero. The number of water drops NIWD is set to a positive integer value, which is usually set to the number of nodes N_c of the graph. For velocity updating, the parameters are a_v =1, b_v =0.01 and c_v = 1. For soil updating, a_s =1, b_s =0.01 and c_s = 1. The local soil updating parameter ρ_n=0.9, which is a small positive number less than one. The global soil updating parameter ρ_IWD=0.9, which is chosen from [0,1]. Moreover, the initial soil on each path (edge) is denoted by the constant InitSoil such that the soil of the path between every two nodes i and j is set by soil(i, j) = InitSoil. The initial velocity of each IWD is set to InitV_el. Both parameters InitSoil and InitV_el are user selected and they should be tuned experimentally for the application.

2) Every IWD has a visited node list V_c(IWD), which is initially empty: V_c(IWD)=0. Each velocity of IWD is set to InitVel. All IWDs are set to have zero amount of soil.

3) Spread the IWDs randomly on the nodes of the graph as their first visited nodes.

4) Update the visited node list of each IWD to include the nodes just visited.

5) Repeat Steps 1 to 4 for those IWDs with partial solutions.

For the IWD residing in node i, choose the next node j, which does not violate any constraints of the problem and is not in the visited node list V_c (IWD) of the IWD, using the following probability

p_i^{\mathrm{IWD}}\left(j\right)={\displaystyle \frac{f\left(\mathrm{soil}\left(i,j\right)\right)}{{\displaystyle \sum _{k\notin V_{\mathrm{c}}\left(\mathrm{IWD}\right)}f\left(\mathrm{soil}\left(i,k\right)\right)}}},

such that

f\left(\mathrm{soil}\left(i,j\right)\right)={\displaystyle \frac{\mathrm{1}}{{\in }_s+g\left(\mathrm{soil}\left(i,j\right)\right)}}.

In this paper it is considered that the value of {\in }_s =0.2, and

g\left(\mathrm{soil}\left(i,j\right)\right)=\{\begin{array}{l}\mathrm{soil}\left(i,j\right)\mathrm{if}\underset{l\notin V_{\mathrm{c}}\left(\mathrm{IWD}\right)}{\min }\left(\mathrm{soil}\left(i,j\right)\right)\ge \mathrm{0},\hfill \\ \\ \mathrm{soil}\left(i,j\right)-\underset{l\notin V_{\mathrm{c}}\left(\mathrm{IWD}\right)}{\min }\left(\mathrm{soil}\left(i,j\right)\right)\ge \mathrm{0}\mathrm{else}.\hfill \end{array}

Then, add the newly visited node j to the V_c(IWD).

For each IWD moving from node i to node j, update its velocity vel^IWD (t) by

{\mathrm{vel}}^{\mathrm{IWD}}\left(t+\mathrm{1}\right)={\mathrm{vel}}^{\mathrm{IWD}}\left(t\right){\displaystyle \frac{a_{\mathrm{v}}}{b_{\mathrm{v}}+c_{\mathrm{v}}{\mathrm{soil}}^{\mathrm{2}}\left(i,j\right)}},

where vel^IWD (t+1) is the updated velocity of the IWD.

For the IWD moving on the path from node i to j, compute the Δsoil(i, j) that the IWD load from the path by

\mathrm{\Delta }\mathrm{soil}(i,j)={\displaystyle \frac{a_{\mathrm{s}}}{b_{\mathrm{s}}+c_{\mathrm{s}}{\mathrm{time}}^{\mathrm{2}}(i,j\mathrm{;}{\mathrm{vel}}^{\mathrm{IWD}}(t+\mathrm{1}\left)\right)}},

such that

\mathrm{time}(i,j\mathrm{;}{\mathrm{vel}}^{\mathrm{IWD}}(t+\mathrm{1}\left)\right)={\displaystyle \frac{\mathrm{HUD}\left(j\right)}{{\mathrm{vel}}^{\mathrm{IWD}}(t+\mathrm{1})}},

where the heuristic undesirability HUD(j) is defined appropriately for the given problem.

Update the soil(i,j) of the path from node i to node j traversed by that IWD and also update the soil that the IWD carries soil^IWD by

$$\begin{gathered} \mathrm{soil}\left(i,j\right)=\left(\mathrm{1}-{\rho }_{\mathrm{n}}\right)\mathrm{soil}\left(i,j\right)-{\rho }_{\mathrm{n}}\mathrm{\Delta }\mathrm{soil}\left(i,j\right), \\ {\mathrm{soil}}^{\mathrm{IWD}}={\mathrm{soil}}^{\mathrm{IWD}}+\mathrm{\Delta }\mathrm{soil}\left(i,j\right). \end{gathered}$$

6) Find the iteration-best solution T^IB from all the solutions T^IWD found by the IWDs using

T^{\mathrm{IB}}=\arg \underset{\forall T^{\mathrm{IWD}}}{\max }q\left(T^{\mathrm{IWD}}\right).

where function q(·) gives the quality of the solution.

7) Update the soils on the path that form the current iteration-best solution T^IB by

\mathrm{soil}\left(i,j\right)=\left(\mathrm{1}+{\rho }_{\mathrm{IWD}}\right)\mathrm{soil}{\left(i,j\right)}^{-{\rho }_{\mathrm{IWD}}.\frac{\mathrm{1}}{\left(N_{\mathrm{IB}}-\mathrm{1}\right)}{\mathrm{soil}}_{\mathrm{IB}}^{\mathrm{IWD}}}

\forall \left(i,j\right)\in T^{\mathrm{IB}},

where N_IB is the number of nodes in the solution T^IB.

8) Update the total best solution T^TB by the current iteration-best solution T^IB using

T^{\mathrm{TB}}=\{\begin{array}{l}{T}^{\mathrm{TB}}q\left(T^{\mathrm{TB}}\right)\ge q\left(T^{\mathrm{IB}}\right),\hfill \\ T^{\mathrm{IB}}\mathrm{otherwise}.\hfill \end{array}

9) Increment the iteration number by Itercount = Itercount + 1. Then, go to Step 2 if Itercount<Itermax.

10) The algorithm stops here with the total-best solution T^TB.

The flowchart of the proposed IWD algorithm which has been applied for reactive dispatch problem is given in Fig. 5.

5 Neuro-wavelet based islanding detection

This section introduces the WT as a time-frequency analyzing tool to address the problem of islanding detection in a distribution system embedded with DG. Recently, WT has been successfully implemented in solving many power system problems including fault detection, power quality event localization and load disaggregation. The capability of wavelet in handling non-stationary signals while preserving both time and frequency information makes it a suitable candidate for islanding detection problem.

ANNs have been used in many potential applications in power systems operation and control. ANNs are often used as classifiers since they have the capability of learning complex mapping, linear or nonlinear from the input space to the output space [30]. The architecture and the training algorithm of the feed forward ANN are described in the following sections.

5.1 ANN architecture

ANN consists of simple processing units, called neurons, operating in parallel to solve specific problems. Figure 6 depicts a simple neuron with input vector P of dimension R\times \mathrm{1}. The input P is multiplied by a weight W of dimension \mathrm{1}\times R. Then, a bias b is added to the product WP. f is a transfer function (called also the activation function) that takes the argument n and produces the net output a.

The idea of ANN is that these parameters (W and P) are adjusted so that the network exhibits some desired behavior. Thus the network can be trained to do a particular job by adjusting the weight or bias parameters [31].

A neuron with a hard-limit activation function is called a perceptron and it is used for classification purposes. Since the hard-limit activation function divides the input space into two regions, the perceptron produces 1.0 if the net output is greater or equal to 0, otherwise it produces a 0. On the other hand, a neuron with purelin activation function is used for linear approximation purposes. The linear (purelin) and sigmoid (tansig, logsig) activation functions are used in back propagation networks which will be explained later in this section since they are differentiable [30]. A number of neurons can be combined to form a layer of neurons. A one layer of R input elements and S neuron is illustrated in Fig. 7.

A network can have many layers of neurons to form multiple layers of neurons. In Fig. 7 three layers of R input elements and S neurons are presented by applying the IWD. The layer that produces the network output is called an output layer. All other layers are called hidden layers. The three layer network displayed in Fig. 8 has one output layer and two hidden layers.

5.2 Training the ANN

A training algorithm is defined as a procedure of updating the weights and biases of a network so that the network will be able to perform the particular design task. The training algorithm is divided into two main categorizes: supervised learning, and unsupervised learning. ANN is classified under supervised learning. In the training stage, the training data set and the corresponding targets are entered to the model. Once the network weights and biases are initialized, the network is ready for training. The weights and biases are then adjusted in order to minimize the mean square error (MSE). This can be achieved using the gradient of the MSE.

5.3 WT

Real time transients classification of power transients is very challenging since the high frequency content superimposed on the power frequency signals are usually aperiodic, short term and non-stationary waveforms. WT is proposed in order to extract discriminative features which will help in differentiating between transients associated with islanding event and those created from any other event such as switching of capacitor bank and temporary fault.

WT is an effective mathematical tool which has been widely used in many engineering applications such as speech and image processing. WT has found many numerous applications in the power system field, some of which are power system protection, power quality, and partial discharge.

WTs can be mainly divided into two categories: continuous wavelet transform (CWT) and DWT. The continuous WT W(a,b) of signal f(x) with respect to a wavelet \varphi(x) is given by [32,33]

W\left(a,b\right)={\displaystyle \frac{\mathrm{1}}{\sqrt{a}}}{\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}f\left(x\right)\varphi \left({\displaystyle \frac{x-b}{a}}\right)\mathrm{d}x},

where scale parameter a controls the spread of the wavelet and translation factor b determines its central position. \varphi(x) is also called mother wavelet. A W(a,b) coefficient, represents how well the original signal f(x) and the scaled/translated mother wavelet match. Thus, the set of all wavelet coefficients W(a,b), associated to a particular signal, is the wavelet representation of the signal with respect to the mother wavelet. Since the CWT is achieved by continuously scaling and translating the mother wavelet, substantial redundant information is generated. Therefore, instead of doing that, the mother wavelet can be scaled and translated using certain scales and positions usually based on the powers of the two [32,33]. This scheme is more efficient and just as accurate as the CWT [20]. It is known as the DWT:

W\left(m,n\right)={\mathrm{2}}^{-\left(m/\mathrm{2}\right)}{\displaystyle \sum _{t=\mathrm{0}}^{T-\mathrm{1}}f\left(t\right)\varphi \left({\displaystyle \frac{t-n\cdot {\mathrm{2}}^m}{{\mathrm{2}}^m}}\right)},

where T is the length of the signal f(t). The scaling and translation parameters are functions of the integer variables m and n (a=2m, and b=n·2^m); t is the discrete time index.

In wavelets applications, the choice of appropriate mother wavelet plays an important role in the analysis. Different basis functions have been proposed. These include Haar, Morlet, Mexican, Daubechies, etc. The choice of mother wavelet depends on the application. For example, in signal processing in real time, computation efficiency may be of importance to be considered. For classification of power quality disturbance signals, the choice revolves of discrimination between various transients [34].

Daubechies wavelet family is one of the most suitable wavelet families in analyzing power system transients as investigated in Ref. [34]. In the present work, the db1 wavelet shown in Fig. 9 (with two filter coefficients) has been used as the mother wavelet for analyzing the transients associated with islanding. db1 is a short wavelet and, therefore, it can efficiently detect transients.

WT will be carried out on the obtained voltage signals to extract the features. The purpose of feature extraction is to identify specific signature of the voltage waveforms that can detect islanding and differentiate between islanding and any other transient condition. A transient signal can be fully decomposed into smoothed signals and detailed signals for L wavelet levels. The frequency band information of the wavelet analysis is presented in Table1. The sampling frequency is 10 kHz.

The energy content in detail of each decomposition level for all voltage signals was calculated using the detailed coefficients in the corresponding level. The energy content in the other decomposition levels can be calculated as

\Vert {\mathrm{ED}}_{\mathrm{1}a}\Vert ={\left[{\displaystyle \sum _k{d}_k^{\mathrm{2}}}\right]}^{\mathrm{1}/\mathrm{2}},

where ED_1a is the energy content of D1 for the voltage signal of phase (a) and d_k is the kth coefficient in the first decomposition level. After collecting the features for the simulated different cases, the features will be fed to a trained ANN in order to identify whether the event took place is an islanding or non-islanding event. The flowchart of the proposed technique is presented in Fig. 10.

6 Simulation results

The test system shown in Fig. 11 has been simulated by Matlab/Simulink. The system, DG, and load parameters can be referred to in Ref. [35]. The Effective voltage waveform of the common coupling point for islanding mode is presented in Fig. 12.

Figures 13 to 15 illustrate an example of the wavelet details (D3, D4 and D6) of 2 cycles voltage waveform acquired from phase (a) at DG when four different events have taken place. These events have taken place at time= 1.5 s. In Figs. 13 to 15, the islanding when power match (a), islanding when power mismatch (b), switching of load (c), and three-phase-to-ground fault (d), are presented. It is noticed that during the fault, the details dropped to zero since the DG is equipped with under/over frequency (UOF)/ under/over voltage (UOV) protective relay which isolated the fault. The performance matrix of DG is presented in Table 2.

Voltage deviation in the distributed network, depending on the time period can be divided into three categories: ① Transient period: the time period for this voltage deviation is in milliseconds. ② Short-term period: the time period of this state is up to one minute. Voltage swell and voltage sag are of this deviation type. ③ Long term: for this the voltage deviation may be continued more than one minute. Islanding detection method should be kept safe from voltage changes. By adding an adaptive system with a delay system, the detection method can be kept safe from the voltage changes. Thus, the inverter output current is monitored continuously and once the difference between this current and the rated current is observed the comparator detects automatically these abnormal conditions. These abnormal conditions can be the sign of either an electrical island or a voltage deviation. Table 3 shows voltage relay responses when an abnormal condition is observed in the standard distribution network IEEEStd.1547. Simple voltage relays should detect the voltage changes at the appropriate time and then eliminates the DG from the grid.

The performance of the proposed method is analyzed in this mode for the various conditions which are listed in Table 4. The three phase voltage waveform of the common coupling point for each cases are shown in Fig. 16 and the rate of change of active power for all cases studied are demonstrated in Fig. 17. Immediately following these change at the time t = 1 s, the rates of change of active power for each condition are increased or decreased. Finally, in Fig. 18 the output of detection method for all cases studied are exhibited. It is obvious from Fig. 18 that in all cases studied, the value of the proposed algorithm has not changed and the output of proposed method remained 0. Therefore, the proposed method does not send a trip signal to DG and works in a reliable mode.

7 Conclusions

A new technique for islanding detection of DG is proposed based on hybrid wavelet neural network with IWD. Many schemes have been proposed to detect islanding such as passive, active and communication based techniques. IWD is a swarm based nature-inspired optimization algorithm, which has been inspired from natural rivers and how they find almost optimal path to their destination. A natural river often finds good paths among lots of possible paths in its ways from the source to destination. Passive techniques work well when there is power imbalance between the power generated from the DG and the power consumed form the load. On the other hand, active methods affect the power quality and do not perform well in the presence of multiple DGs. Though communication based islanding detection techniques have no NDZ techniques, they are costly and complex. WT is capable of decomposing the voltage signals into different frequency bands. It can be utilized in extracting discriminative features from the acquired voltage signals. The energy content of wavelet details are then calculated and fed to a trained ANN which is capable of differentiating between islanding and non-islanding events. Following the increased number and enlarged size of distributed generating units installed in a modern power system, the protection against islanding has become extremely challenging nowadays. Islanding detection is also important as islanding operation of distributed system is seen as a viable option in the future to improve the reliability and quality of the supply. The islanding situation needs to be prevented with DG due to safety reasons and to maintain quality of power supplied to the customers. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and this technique can also overcome the problem of setting the detection thresholds inherent in the existing techniques. Simulation results have verified that the islanding cases are successfully detected in case of adding untrained identical DGs since the voltage transients generated is identical.

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