**4. Short circuit analysis**

This adaptive method is based on short circuit analysis for all types of occurred faults in different phases. Also the contribution of main feeder and each DG for various fault current in each bus must be determined. Short circuit analysis calculations have to be changed and updated after major changes in load, DG or system configuration. So after each change, short circuit analysis is performed online and required information will be send to adaptive relay in order to analysis and Prescription (Sukumar ,2001).

A New Adaptive Method for Distribution System Protection

zone Bus

IDG1 - Calculated

IDG2 - Calculated

ISource - Calculated

zone Bus

IDG1 - measured

IDG2 - measured

ISource - measured

EDG1 EDG2 ESource

i=1

i=1

Table 2. Synthesized table in adaptive relay

Table 1. A look-up table for fault location determination

Considering Distributed Generation Units Using Simulated Annealing Method 57

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

3 2 DG i DG-Calculated DG-measured i

3 2

command to faulted zone circuit breaker and prepares Table 2 for new conditions.

Source i Source-Calculated Source-measured i

When a fault is sensed in distribution system, adaptive relay forms the Table 2 immediately according to short circuit analysis and direct measurements for all system buses and calculates the error for each bus. The minimum value of error is obtained from the calculated error so the faulted bus is determined. The adaptive relay sends the trip

E= I - I (2)

E =I - I (3)

After the fault is occurred in distribution system, the adaptive relay synthesizes Table 2 with Table 1. In this table the measured currents for sources (DG's and main source) and measurement error for each source according to (2)-(3) are placed (Kotamarty et al., 2008).

In case of normal operation, total flow of all sources (main source and all DG's) is equal to load current. In case of short circuit conditions the current balance equation is written as following:

$$\mathbf{I}\_{\rm F} = \sum\_{i=1}^{N} \mathbf{I}\_{\rm F\_i} \tag{1}$$

Where: IF is total fault current, IFi is the contribution of each DG in fault current and N is the number of DG's.

In the proposed protective method, if a fault occurs in DG, total source currents are approximately equal to load current according to (1). With the difference that all source currents increased significantly. In this case the protection system of faulted DG sense the fault current and send the trip command to DG's circuit breakers and related zone circuit breaker. But if fault occurs in each part of system, total short circuit currents become significantly higher than load current. Thus the fault in DG is detected from fault in system. If the system fault is transient, first the trip command is sent to DG circuit breaker in faulted zone. This DG's never connected to system until the fault is removed from system. Also adaptive relay performs short circuit analysis and load flow immediately according to new network configuration (without DG's in faulted zone). After about 20 cycles, a reclosing command is sent to faulty zone circuit breaker. In this stage if the transient fault is removed, the adaptive relay send a command to DG circuit breaker after about 2s and after the synchronism operation DG connected to system. After this step, adaptive relay perform the short circuit analysis for going situation. If the transient fault is unresolved in first stage of reclosing, relay sent trip command to zone circuit breaker immediately and the reclosing operation is done until three stages.

#### **5. Fault location determination**

In the proposed Adaptive method, a fast detection method is needed for faulted zone diagnosis. So the adaptive relay can send the trip command to each zone and faulted zone circuit breakers. It is necessary to note that faulted zone identification is enough for operation of this method. However if the faulted zone is not specified as precise as possible, much effort will be imposed to maintenance personnel to fault location determination. In order to precise fault location determination, least square method is used. This method is one of the most famous and the most practical methods in system identification theory. There is always a difference between intended structure for modeled system and actual system. Because of nonlinear specification of actual system that be considered linear in modeled system. So there is a difference et between measured output and model output at any moment. The objective in the least square method is to minimize the sum of the squared errors (**∑**et 2).

In the presented adaptive scheme for distribution system, there is always a difference between measured current and obtained current from short circuit analysis. Since the contribution of measured currents from measurement devices and short circuit analysis of each source is available online, the adaptive method can use these currents for placement in least square method. For this purpose, a look-up table as shown in Table 1 according to short circuit analysis for each bus in each zone is formed (Dugan & McDermott, 2002).

In case of normal operation, total flow of all sources (main source and all DG's) is equal to load current. In case of short circuit conditions the current balance equation is written as

> N F F i=1

Where: IF is total fault current, IFi is the contribution of each DG in fault current and N is the

In the proposed protective method, if a fault occurs in DG, total source currents are approximately equal to load current according to (1). With the difference that all source currents increased significantly. In this case the protection system of faulted DG sense the fault current and send the trip command to DG's circuit breakers and related zone circuit breaker. But if fault occurs in each part of system, total short circuit currents become significantly higher than load current. Thus the fault in DG is detected from fault in system. If the system fault is transient, first the trip command is sent to DG circuit breaker in faulted zone. This DG's never connected to system until the fault is removed from system. Also adaptive relay performs short circuit analysis and load flow immediately according to new network configuration (without DG's in faulted zone). After about 20 cycles, a reclosing command is sent to faulty zone circuit breaker. In this stage if the transient fault is removed, the adaptive relay send a command to DG circuit breaker after about 2s and after the synchronism operation DG connected to system. After this step, adaptive relay perform the short circuit analysis for going situation. If the transient fault is unresolved in first stage of reclosing, relay sent trip command to zone circuit breaker immediately and the reclosing

In the proposed Adaptive method, a fast detection method is needed for faulted zone diagnosis. So the adaptive relay can send the trip command to each zone and faulted zone circuit breakers. It is necessary to note that faulted zone identification is enough for operation of this method. However if the faulted zone is not specified as precise as possible, much effort will be imposed to maintenance personnel to fault location determination. In order to precise fault location determination, least square method is used. This method is one of the most famous and the most practical methods in system identification theory. There is always a difference between intended structure for modeled system and actual system. Because of nonlinear specification of actual system that be considered linear in modeled system. So there is a difference et between measured output and model output at any moment. The objective in the least square method is to minimize the sum of the squared

In the presented adaptive scheme for distribution system, there is always a difference between measured current and obtained current from short circuit analysis. Since the contribution of measured currents from measurement devices and short circuit analysis of each source is available online, the adaptive method can use these currents for placement in least square method. For this purpose, a look-up table as shown in Table 1 according to short circuit analysis for each bus in each zone is formed (Dugan & McDermott, 2002).

I= I (1)

following:

number of DG's.

operation is done until three stages.

**5. Fault location determination** 

errors (**∑**et

2).

i


Table 1. A look-up table for fault location determination

After the fault is occurred in distribution system, the adaptive relay synthesizes Table 2 with Table 1. In this table the measured currents for sources (DG's and main source) and measurement error for each source according to (2)-(3) are placed (Kotamarty et al., 2008).


Table 2. Synthesized table in adaptive relay

$$\mathbf{E}\_{\rm DG} = \sum\_{\mathbf{i}=1}^{3} \left[ \left( \mathbf{I}\_{\rm i} \right)\_{\rm DG-Calculated} \text{--} \left( \mathbf{I}\_{\rm i} \right)\_{\rm DG-measured} \right]^{2} \tag{2}$$

$$\mathbf{E}\_{\text{Source}} = \sum\_{\mathbf{i}=1}^{3} \left[ \left( \mathbf{I}\_{\mathbf{i}} \right)\_{\text{Source-Calculated}} \cdot \left( \mathbf{I}\_{\mathbf{i}} \right)\_{\text{Source-measured}} \right]^2 \tag{3}$$

When a fault is sensed in distribution system, adaptive relay forms the Table 2 immediately according to short circuit analysis and direct measurements for all system buses and calculates the error for each bus. The minimum value of error is obtained from the calculated error so the faulted bus is determined. The adaptive relay sends the trip command to faulted zone circuit breaker and prepares Table 2 for new conditions.

A New Adaptive Method for Distribution System Protection

The estimate xˆ is the one which minimizes the scalar

Mathematically stated:

**7. State estimation and simulated annealing method** 

Considering Distributed Generation Units Using Simulated Annealing Method 59

The basic idea of the state estimation method proposed in this paper is quite simple (Mori & Saito, 2006). Besides real-time measurements, there exists other information which does not need to be measured. For sub-transmission networks, active power is always drawn from buses connected to the distribution side via transformers. On the other hand, active power taken from the transmission level is injected into a few buses of the sub-transmission portion. In general, it is possible to assert whether the specified real power for each node is less, greater than or equal to zero. This knowledge can be incorporated into the estimation process in the form of inequality constraints. The estimation problem thus becomes that of minimizing a non-linear function subject to non-linear inequality constraints.

For a given set of bus-voltage and line-current magnitude measurements, z, related to the

J(x) z f(x) R z f(x) v R v

In equation (4) the rows corresponding to a voltage measurement are trivial. For a current

ij i j i j ij ij <sup>2</sup> <sup>2</sup> ij ij sh 2 2 ij ij 2

I AV BV 2V V Ccosθ Dsinθ

ij ij ij sh

Matrix R in equation (5) is the inverse of the measurement covariance matrix. Inequalities

C (x) V V G cosθ B sinθ

Where, for load buses, the minus sign must be used. Although zero injection buses may be indistinctly regarded as loads or generators, it is advantageous, for accuracy improvement, to treat them as equality constraints. A clear advantage of current and voltage magnitude measurements is the simplicity for a pre filtering to be implemented. Voltage magnitudes

ij sh

j 1

C g b b b /2

 <sup>N</sup> i i j ij ij ij ij

(7)

C (x) 0 i 1,2,...,N

T T

z fx v (4)

(5)

(6)

vectors of state variables, x, and measurement error, v, by the following equation,

i

2 2

A g b b /2

Subject to

measurement between nodes i and j the following equation is used,

Bg b

D g b /2

are the real components of the well-known Power Flow equations,

Where gij, bij and bsh are the *π*-equivalent line parameters.

#### **6. Proposed adaptive protection scheme algorithm**

The proposed method for adaptive protection of distribution system is shown in figure 3. The adaptive relay receives source currents from measurement devices and compares the sum of source currents with load current. If the total current is approximately equal with load current and a fault occurs in a DG, adaptive relay waits until DG local protection system operates. If the total current be more than load current significantly, adaptive relay determines fault location and recalls the look-up table obtained from short circuit analysis. Then calculates the error of calculated current and measured current for each bus of system, considers the minimum error and determines the faulted zone. As it shown in figure 3, if there is a transient or permanent fault in system, sends the trip command to DG circuit breaker that equipped with synchronization system immediately. Then reclosing operation is done on DG circuit breaker in three stages for t1, t2 and t3 duration time.

Fig. 3. Proposed adaptive protection scheme for distribution system

#### **7. State estimation and simulated annealing method**

58 Modeling and Optimization of Renewable Energy Systems

The proposed method for adaptive protection of distribution system is shown in figure 3. The adaptive relay receives source currents from measurement devices and compares the sum of source currents with load current. If the total current is approximately equal with load current and a fault occurs in a DG, adaptive relay waits until DG local protection system operates. If the total current be more than load current significantly, adaptive relay determines fault location and recalls the look-up table obtained from short circuit analysis. Then calculates the error of calculated current and measured current for each bus of system, considers the minimum error and determines the faulted zone. As it shown in figure 3, if there is a transient or permanent fault in system, sends the trip command to DG circuit breaker that equipped with synchronization system immediately. Then reclosing operation is done on DG circuit breaker in three stages for

Start

Input: Source current measurements

State estimation in distribution system. Using current measurements & Simulated Annealing Method

> If sum of source currents = load current

> If sum of source currents >> load current

No

No

Yes A fault is in system

Load system information and topology <sup>A</sup>


End

Yes

If source currents increase significantly

Yes Fault is in DG. Local DG protection system must operate

No

**6. Proposed adaptive protection scheme algorithm** 

i=1 Input: Source currents from state estimation algorithm Caculate error for each source and each bus using equations (2) , (3) -Determine minimum error -Determine faulted zone If i=1 No

Yes

Send Trip command to zone C.B -Goto A -t=t+0.4

Reclose zone C.B after time delay of t

> If Fault is sensed yet? Yes If i=3

No

Send trip command to DG C.B

Fig. 3. Proposed adaptive protection scheme for distribution system

Send close command to DG C.B considering synchronization condition

No

Yes


Send Trip command to zone C.B and DG C.B

t1, t2 and t3 duration time.

i=i+1

B

The basic idea of the state estimation method proposed in this paper is quite simple (Mori & Saito, 2006). Besides real-time measurements, there exists other information which does not need to be measured. For sub-transmission networks, active power is always drawn from buses connected to the distribution side via transformers. On the other hand, active power taken from the transmission level is injected into a few buses of the sub-transmission portion. In general, it is possible to assert whether the specified real power for each node is less, greater than or equal to zero. This knowledge can be incorporated into the estimation process in the form of inequality constraints. The estimation problem thus becomes that of minimizing a non-linear function subject to non-linear inequality constraints. Mathematically stated:

For a given set of bus-voltage and line-current magnitude measurements, z, related to the vectors of state variables, x, and measurement error, v, by the following equation,

$$\mathbf{z} = \mathbf{f}\begin{pmatrix} \mathbf{x} \\ \end{pmatrix} + \mathbf{v} \tag{4}$$

The estimate xˆ is the one which minimizes the scalar

$$\begin{aligned} \mathbf{J}(\mathbf{x}) &= \left[\mathbf{z} - \mathbf{f}(\mathbf{x})\right]^\top \mathbf{R} \left[\mathbf{z} - \mathbf{f}(\mathbf{x})\right] = \mathbf{v}^\top \mathbf{R} \ \mathbf{v} \\ \text{Subject to} \\ \mathbf{C}\_{\mathbf{i}}(\mathbf{x}) &\ge 0 \qquad \mathbf{i} = 1, 2, \dots, \mathbf{N} \end{aligned} \tag{5}$$

In equation (4) the rows corresponding to a voltage measurement are trivial. For a current measurement between nodes i and j the following equation is used,

$$\begin{aligned} \mathbf{I}\_{\mathrm{ij}} &= \sqrt{\mathbf{A} \mathbf{V}\_{\mathrm{i}}^{2} + \mathbf{B} \mathbf{V}\_{\mathrm{j}}^{2} - 2 \mathbf{V}\_{\mathrm{i}} \mathbf{V}\_{\mathrm{j}} \left( \mathbf{C} \cos \theta\_{\mathrm{i}\overline{\mathrm{j}}} - \mathbf{D} \sin \theta\_{\mathrm{i}\overline{\mathrm{j}}} \right)} \\ \mathbf{A} &= \mathbf{g}\_{\mathrm{ij}}^{2} + \left( \mathbf{b}\_{\mathrm{ij}} + \mathbf{b}\_{\mathrm{sh}} / 2 \right)^{2} \\ \mathbf{B} &= \mathbf{g}\_{\mathrm{ij}}^{2} + \mathbf{b}\_{\mathrm{ij}}^{2} \\ \mathbf{C} &= \mathbf{g}\_{\mathrm{ij}}^{2} + \mathbf{b}\_{\mathrm{ij}} \left( \mathbf{b}\_{\mathrm{ij}} + \mathbf{b}\_{\mathrm{sh}} / 2 \right) \\ \mathbf{D} &= \mathbf{g}\_{\mathrm{ij}} \mathbf{b}\_{\mathrm{sh}} / 2 \end{aligned} \tag{6}$$

Where gij, bij and bsh are the *π*-equivalent line parameters.

Matrix R in equation (5) is the inverse of the measurement covariance matrix. Inequalities are the real components of the well-known Power Flow equations,

$$\mathbf{C}\_{i}(\mathbf{x}) = \pm \sum\_{j=1}^{N} \mathbf{V}\_{i} \mathbf{V}\_{j} \left( \mathbf{G}\_{i\bar{\mathbf{j}}} \cos \theta\_{i\bar{\mathbf{j}}} + \mathbf{B}\_{i\bar{\mathbf{j}}} \sin \theta\_{i\bar{\mathbf{j}}} \right) \tag{7}$$

Where, for load buses, the minus sign must be used. Although zero injection buses may be indistinctly regarded as loads or generators, it is advantageous, for accuracy improvement, to treat them as equality constraints. A clear advantage of current and voltage magnitude measurements is the simplicity for a pre filtering to be implemented. Voltage magnitudes

A New Adaptive Method for Distribution System Protection

2

7

<sup>8</sup> <sup>9</sup> 10 11 C.B Zone 2

12

65 kW- 80 kVAR

20 21

60 kW- 75 kVAR

26 27 28

150 kW

13 14

20 kW

120 kW

10 kVAR

10 kW

29

Zone 3

30 kVAR

<sup>22</sup> 23 24

85 kW- 85 kVAR

30

15 kW

C.B Zone 4

Zone 4

49 50

The adaptive algorithm is tested under different conditions and faults to ensure of proper performance. These conditions are fault in DG, permanent and transient fault in system

In case of fault occurred in DG, Adaptive relay waits until DG protection system operates and issues the trip command. As it seen in figure 5, while a fault occurs in DG1, current comparator in adaptive relay permits that DG over current relay operates. While a fault occurs in a DG, only the faulted DG must be disconnected from network and the other parts

In case of studying permanent faults in a system bus, it is assumed that a fault occurs in bus 41 in zone 4. This fault occurs at t=2 s and the fault duration is 3 s. Figures 6 shows that the adaptive relay sends a trip command to DG4, DG5 and zone 4 circuit breaker immediately. As the fault is permanent, adaptive relays doesn't allow DG's to connect on network, even after clearing the fault. After disconnecting DG4 and DG5, the adaptive relay does a reclosing operation on zone 4 circuit breaker. First reclosing is done on the circuit breaker at 0.4 s after fault occurrence. Second and third reclosing are done 1.2 s and 2.4 s after fault occurrence. This is shown in figure 6. Since the fault is permanent, in each reclosing stage, the adaptive relay senses the fault and sends trip command. After the third reclosing, trip

command is sent to zone 4 circuit breaker and zone 4 is disconnected from network.

75 kW- 30 kVAR

30 kW

buses. The performance of adaptive relay has been studied for some of these faults.

R1

3

60 kW

15 kW- 15 kVAR

Fig. 4. Proposed adaptive protection scheme for distribution system

must continue their normal operations as it seen in figure 5.

55 kW- 55 kVAR

4 5 6

150 kW- 50 kVAR

70 kW- 55 kVAR

Zone 2

60 kVAR

135 kW

15 kVAR

63kV/20kV C.B Zone 1 1

56

Zone 1

: Fuse : Circuit Breaker : Recloser

Considering Distributed Generation Units Using Simulated Annealing Method 61

15 16 17

75 kW

25

60 kVAR

31

36

48 47

45 kW- 45 kVAR

R2

60 kW- 75 kVAR

C.B DG2

C.B Zone 3 C.B DG3

90 kW

130 kW

34 35

60 kW- 45 kVAR

37 38

46

C.B DG5

C.B DG4

40 41 42 43

30 kVAR

30 kW- 45 kVAR

30 kVAR

DG1

55

DG2

54

75 kW- 30 kVAR

18

C.B DG1

75 kW- 30 kVAR

19

45 kW

32 33

45 kW- 45 kVAR

DG3

30 kW

39

DG4

52

53

44 45

45 kW 60 kW- 45 kVAR

15 kW

DG5

51

45 kW- 45 kVAR

differ more than a certain threshold from 1 p.u. should be discarded. Similarly, ampere measurements at both line ends should be almost equal for lines with negligible shunt susceptance.

In this paper the Simulated Annealing Method (SA) is used in optimization part. Simulated annealing is a method for solving unconstrained and bound-constrained optimization problems (Ingber, 1993). The method models the physical process of heating a material and then slowly lowering the temperature to decrease defects, thus minimizing the system energy. In iterations of simulated annealing algorithm, a new point is randomly generated. The distance of the new point from the current point, or the extent of the search, is based on a probability distribution with a scale proportional to the temperature. The algorithm accepts all new points that lower the objective, but also, with a certain probability, points that raise the objective. By accepting points that raise the objective, the algorithm avoids being trapped in local minima, and is able to explore globally for more possible solutions. An annealing schedule is selected to systematically decrease the temperature as the algorithm proceeds. As the temperature decreases, the algorithm reduces the extent of its search to converge to a minimum. Many standard optimization algorithms get stuck in local minima. Because the simulated annealing algorithm performs a wide random search, the chance of being trapped in local minima is decreased.
