# A New Approach to High Impedance Fault Detection Based on Correlation Functions

Najmeh Faridnia, Haidar Samet, Babak Doostani Dezfuli

► To cite this version:

Najmeh Faridnia, Haidar Samet, Babak Doostani Dezfuli. A New Approach to High Impedance Fault Detection Based on Correlation Functions. 8th International Conference on Artificial Intelligence Applications and Innovations (AIAI), Sep 2012, Halkidiki, Greece. pp.453-462, 10.1007/978-3-642-33409-2_47. hal-01521398

HAL Id: hal-01521398

https://inria.hal.science/hal-01521398

Submitted on 11 May 2017

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A New Approach to High Impedance Fault Detection Based on Correlation Functions

Najmeh Faridnia<fnref n="1" />, Haidar Samet<fnref n="2" />, Babak Doostani Dezfuli<fnref n="3" />

**Abstract.** Detection of High Impedance Fault (HIF) that is mainly occurred in MV power systems has been a challenge due to its low current magnitude. A new HIF detection approach based on correlation functions is applied on the voltage and current signals in this paper. Twelve indices based on correlation functions are implemented and tried on a lot of cases. Some of them which have clearly different values for no-fault and HIF conditions are chosen. Simulation results prove the efficiency of proposed method for HIF detection.

**Keywords:** high impedance fault detection (HIF), auto correlation function (ACF), partial auto correlation function (PACF), SACF, SPACF.

## 1 Introduction

The high impedance fault (HIF) is an abnormal electrical condition which may affect human lives wherever the feeders and the living areas have any overlaps. The HIF is usually occurred in the distribution feeders because of their low height in comparison with high voltage transmission lines. This fault is happened when an unexpected connection appears between a feeder and the ground by a high impedance object. Most of the time, it is generated by falling a broken conductor of an energized line on the ground or connection between tree branches to the line. In electrical point of view if a high impedance object produces a parallel loop with the load in a circuit while the line is loaded as much as nominal current, then the over-current which is imposed by fault would be low in contrast to load current. So, this phenomenon is called HIF. Since the basis of operation for conventional relays is current magnitude, HIF flow cannot be detected by mentioned relays.

A review of many approaches on HIF detection from classical to heuristically algorithms is done in [3] that is a useful guideline.

<footnote n="1">¹Research and designing department, Fars Regional Electric Company, Shiraz, Iran</footnote>

<footnote n="2">²School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran</footnote>

<footnote n="3">³Control and Instrumentation Engineering department, Iranian Offshore Oil company, Lavan, Iran</footnote>

<footnote n="1">¹faridnia@frec.co.ir, ²samet@shirazu.ac.ir, ³bdoostani@gmail.com</footnote>
Operating principle of HIF detection is reviewed and possible future technologies is discussed in [5]. Discrete wavelet transformer technique in [2], [6] and [7], artificial neural network in [4] is used to detection of HIF. Besides, some others such as [1] and [8] used low frequency harmonic analysis to detection.

In this paper, a new approach for HIF detection based on correlation functions is proposed. It is found that the values of correlation functions applied on voltage, current and also their derivations during the system healthy conditions are different from their values when high impedance fault occurs. To show the benefits of correlation functions in HIF detection, the paper will be continued with five sections. A brief summary of the correlation function theory and proposed indices for this purpose will be discussed in section 2. Then a case study system with using of two different models of high impedance fault is used for data collection in section 3. Simulation results of the case study system using PSCAD/EMTDC software are presented in section 4. The conclusion is given in section 5.

## 2 A brief theory of correlation functions

Auto correlation function (ACF) and partial auto correlation function (PACF) that are defined by equations 1 and 2 respectively are applied to detect any abnormal changes in a signal.

$$r_k = \frac{\sum_{t=1}^{n-k} (Z_t - \mu)(Z_{t+k} - \mu)}{\sum_{t=1}^{n} (Z_t - \mu)^2} \quad k = 1, 2, 3, \dots \quad (1)$$

$$r_{kk} = \begin{cases} \frac{r_1}{1 - \sum_{j=1}^{k-1} r_{k-1,j} r_j} & \text{if } k=1 \\ \frac{r_k - \sum_{j=1}^{k-1} r_{k-1,j} r_{k-j}}{1 - \sum_{j=1}^{k-1} r_{k-1,j} r_j} & \text{if } k=2, 3, \dots \end{cases} \quad (2)$$

where

$$r_{k,j} = r_{k-1,j} - r_{kk} r_{k-1,k-j} \quad j = 1, 2, \dots, k-1$$

$r_k$ and $r_{kk}$ symbolize ACF$_k$ and PACF$_k$ respectively. $n$ is time series window length and $\mu$ is the mean of time series. To get a good performance it's better to use summation of ACF and PACF components. So, in the present approach two more functions are defined to distinguish the normal case from HIF.

**SACF:** Summation of ACF components of a window including $k$ number of samples that is called SACF. Related equation is as follows:
$$SUM_{ACF} = \sum_{k=1}^{k_{max}} r_k \qquad (3)$$

**SPACF:** This function is defined similar to SACF but the difference is that the PACF components have been used to make it. Equation (4) belongs to SPACF.

$$SUM_{PACF} = \sum_{k=1}^{k_{max}} r_{kk} \qquad (4)$$

Here six signals are used instead of Z in equations (1) and (2) which are as follows:

$$di_n = i_{n-1}i_{n-1} \qquad (5)$$

$$dv_n = v_{n-1}v_{n-1} \qquad (6)$$

$$d^2i_n = di_{n-1}di_{n-1} \qquad (7)$$

$$d^2v_n = dv_{n-1}dv_{n-1} \qquad (8)$$

where i and v are the current and voltage at relay placement. d and d² denote the first and second differences. Both SACF and SPACF functions are applied to all six above signals to obtain 12 indices as follow:

$$sacfi = \sum_{k=1}^{k_{max}} r_k(i) \qquad (9) \qquad sacfv = \sum_{k=1}^{k_{max}} r_k(v) \qquad (10)$$

$$spacfi = \sum_{k=1}^{k_{max}} r_{kk}(i) \qquad (11) \qquad spacfv = \sum_{k=1}^{k_{max}} r_{kk}(v) \qquad (12)$$

$$sacfdi = \sum_{k=1}^{k_{max}} r_k(di) \qquad (13) \qquad sacfdv = \sum_{k=1}^{k_{max}} r_k(dv) \qquad (14)$$

$$spacfdi = \sum_{k=1}^{k_{max}} r_{kk}(di) \qquad (15) \qquad spacfdv = \sum_{k=1}^{k_{max}} r_{kk}(dv) \qquad (16)$$

$$sacfd^2i = \sum_{k=1}^{k_{max}} r_k(d^2i) \qquad (18) \qquad sacfd^2v = \sum_{k=1}^{k_{max}} r_k(d^2v) \qquad (19)$$

$$spacfd^2i = \sum_{k=1}^{k_{max}} r_{kk}(d^2i) \qquad (20) \qquad spacfd^2v = \sum_{k=1}^{k_{max}} r_{kk}(d^2v) \qquad (21)$$

where $r_k(v)$ denotes kth component of voltage's ACF. Other equations are similarly defined.

### 3 Case Study system

One case study system with two different HIF models is implemented in figures 1 and 2. Case study system belongs to a radial cable feeder of a medium voltage (25 kv) system. Single line diagram of the case study system with the HIF model 1 is given in
figure.1. $V_s$ and $I_{st}$ are the relay voltage and current which are used for sensing the HIF. The connected load to the feeder is assumed to be constant at the end of the line. HIF model 1 is explained through equation (22) and figure.1.

$$L_f = 3mH, R_f = R_{f0}(1 + \alpha(\frac{i_f}{i_{f0}})^\beta) \quad (22)$$

Where $R_{f0}= 20$, $i_{f0}= 70$, $\alpha= 0.6$, $\beta=2$, $V_{L-L}= 25 kV$, $f=60 Hz$

<figure><img src="image_2.png" /><figcaption>Fig. 1. The case study system with HIF model 1</figcaption></figure>

The model circuit with the description of second HIF model is given in figure.2. Figure.3 shows the case study system used in figure.1 which applied HIF model 2 in figure.2. Where $i(t)$, $u_p$, $R$ and $l_p$ represent arc current, constant voltage parameter per arc length, resistive component per arc length and arc length respectively. It is considered that $R$ ($R=9\Omega/cm$) and $l_p$ ($l_p=10 cm$) are constant. The fault is occurred in the middle of the feeder.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Circuit and description of HIF model 2 [2]</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3. The case study system with HIF model 2</figcaption></figure>

The voltage and current curves of the case study system with both of HIF models which are simulated in PSCAD/EMTDC software are shown in figures 4 and 5. In these simulations, the time duration is 500 ms, the fault occurs in 202 ms and the sampling time is 50 µs.

As can be seen in figure.5, no sign of any events for model 2 is visible in both
current and voltage of relay.

<figure><img src="image_5.png" /><figcaption>Fig. 4. (a) current and (b) voltage results of case study system with HIF model 1</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b)</figcaption></figure>

Fig. 5 (a) current and (b) voltage results of case study system with HIF model 2

## 4 Implementation of new approach

After utilizing correlation functions on voltage, current and also their derivations samples, it is specified that both SACF and SPACF can be acceptable factors for HIF detection. For better perception, stem diagrams of some indices for both HIF models are shown in figure.6. $k$ on the horizontal axis is plotted against ACF and PACF values. In this case, $k_{max}$ is equal to 20. As can be seen, the majority of pacfi (PACF$_i$) and pacfddv (PACF$_d^2$) values and all of acfdv (ACF$_{dv}$) values are positive in no fault condition while in HIF phenomenon there are both positive and negative. Briefly, feature pattern of three indices show differences for both conditions. If in each diagram the summation of all 20 data is calculated, the summation result will be a big positive number in no fault condition while it will be approximately zero in HIF event. So, it can be used for HIF detection. SACF and SPACF functions for all six of relay-side signals are introduced in section.2.

<figure><img src="image_8.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 6. comparing feature pattern of (a) pacf1 (b) acfd2v (c) acfdv for both no-fault and HIF conditions (n=100, k=1,...,20)</figcaption></figure>

On the first step, the time window (including *N* samples with sampling time equal to 50 µs) is assumed. Two different windows are considered.

The two windows are assumed to have the same length.

The indices values are experimented for *n*=40, 80, 100, 200 and *k*<sub>max</sub>=10, 20, 40 in both HIF and no fault states. The values of all 12 mentioned indices for *n*=40 and *k*<sub>max</sub>=10 are given in tables I to IV.

<table><caption>**Table 1.** Current's ACF results for static window in no fault condition (n=40 and kmax=10)</caption><thead><tr><th rowspan="2">Fault time (s)</th><th colspan="7">Current</th></tr><tr><th>sacfv</th><th>sacfdv</th><th>sacfd<sup>2</sup>v</th><th>spacfv</th><th>spacfdv</th><th>spacfd<sup>2</sup>v</th></tr></thead><tbody><tr><td>0.200</td><td>6.5900</td><td>6.5085</td><td>6.3878</td><td>4.0011</td><td>4.5190</td><td>4.6588</td></tr><tr><td>0.201</td><td>6.6192</td><td>6.4370</td><td>6.4153</td><td>4.0940</td><td>4.4195</td><td>4.6484</td></tr><tr><td>0.202</td><td>6.6264</td><td>5.3030</td><td>6.4222</td><td>4.5049</td><td>4.9448</td><td>5.1292</td></tr><tr><td>0.203</td><td>6.6248</td><td>6.2117</td><td>6.4206</td><td>4.2429</td><td>4.7193</td><td>5.0486</td></tr><tr><td>0.204</td><td>6.6116</td><td>6.4814</td><td>6.4083</td><td>4.4522</td><td>4.6284</td><td>4.7855</td></tr><tr><td>0.205</td><td>6.5568</td><td>6.5176</td><td>6.3564</td><td>4.4555</td><td>4.8640</td><td>5.0938</td></tr><tr><td>0.206</td><td>5.9560</td><td>6.5267</td><td>5.7754</td><td>4.3321</td><td>4.6874</td><td>4.8726</td></tr><tr><td>0.207</td><td>6.1057</td><td>6.5263</td><td>5.9225</td><td>4.1080</td><td>4.4797</td><td>4.7678</td></tr><tr><td>0.208</td><td>6.5651</td><td>6.5162</td><td>6.3643</td><td>4.5088</td><td>4.6646</td><td>4.8468</td></tr><tr><td>0.209</td><td>6.6134</td><td>6.4754</td><td>6.4099</td><td>3.8506</td><td>4.3387</td><td>4.6272</td></tr><tr><td>0.210</td><td>6.6252</td><td>6.1363</td><td>6.4210</td><td>3.5469</td><td>4.3965</td><td>4.6285</td></tr></tbody></table>

<table><caption>**Table 2.** Voltage's acf results for static window in no fault condition (n=40 and kmax=10)</caption><thead><tr><th rowspan="2">Fault time (s)</th><th colspan="7">Voltage</th></tr><tr><th>sacfv</th><th>sacfdv</th><th>sacfd2v</th><th>spacfv</th><th>spacfdv</th><th>spacfd2v</th></tr></thead><tbody><tr><td>0.200</td><td>6.6228</td><td>6.3595</td><td>6.4187</td><td>5.0753</td><td>5.9513</td><td>7.0459</td></tr></tbody></table>
<table><caption>Table 3. Current's acf results for static window in hif condition (n=40 and kmax=10)</caption><thead><tr><th rowspan="2">Fault time (s)</th><th colspan="7">Voltage</th></tr><tr><th>sacfv</th><th>sacfdv</th><th>sacfd2v</th><th>spacfv</th><th>spacfdv</th><th>spacfd2v</th></tr></thead><tbody><tr><td>0.201</td><td>6.6040</td><td>6.4967</td><td>6.4011</td><td>4.2844</td><td>4.8190</td><td>5.2745</td></tr><tr><td>0.202</td><td>6.5153</td><td>6.5213</td><td>6.3171</td><td>4.0917</td><td>4.5285</td><td>4.8304</td></tr><tr><td>0.203</td><td>4.8080</td><td>6.5273</td><td>4.5936</td><td>4.3407</td><td>4.6798</td><td>5.0479</td></tr><tr><td>0.204</td><td>6.3758</td><td>6.5249</td><td>6.1840</td><td>4.3514</td><td>4.7660</td><td>5.1581</td></tr><tr><td>0.205</td><td>6.5861</td><td>6.5103</td><td>6.3841</td><td>4.3868</td><td>4.9144</td><td>5.4635</td></tr><tr><td>0.206</td><td>6.6182</td><td>6.4469</td><td>6.4144</td><td>4.0035</td><td>4.2751</td><td>4.5497</td></tr><tr><td>0.207</td><td>6.6263</td><td>5.5800</td><td>6.4220</td><td>4.6931</td><td>5.3362</td><td>5.6569</td></tr><tr><td>0.208</td><td>6.6251</td><td>6.1491</td><td>6.4210</td><td>9.7443</td><td>9.7535</td><td>10.0218</td></tr><tr><td>0.209</td><td>6.6131</td><td>6.4764</td><td>6.4097</td><td>4.3266</td><td>4.7334</td><td>5.4211</td></tr><tr><td>0.210</td><td>6.5639</td><td>6.5164</td><td>6.3632</td><td>4.2424</td><td>4.8392</td><td>5.1792</td></tr></tbody></table>

<table><caption>Table 4. Voltage's acf results for static window in hif condition (n=40 and kmax=10)</caption><thead><tr><th rowspan="2">Fault time (s)</th><th colspan="7">Voltage</th></tr><tr><th>sacfv</th><th>sacfdv</th><th>sacfd2v</th><th>spacfv</th><th>spacfdv</th><th>spacfd2v</th></tr></thead><tbody><tr><td>0.200</td><td>6.3466</td><td>3.0206</td><td>1.6699</td><td>0.3590</td><td>0.2429</td><td>0.6375</td></tr><tr><td>0.201</td><td>2.6460</td><td>0.8672</td><td>-1.0995</td><td>-0.0993</td><td>1.0627</td><td>0.1453</td></tr><tr><td>0.202</td><td>0.1420</td><td>0.1680</td><td>-0.4644</td><td>-0.8723</td><td>2.4235</td><td>0.1064</td></tr><tr><td>0.203</td><td>-0.9982</td><td>0.0624</td><td>-0.1323</td><td>0.2219</td><td>1.8844</td><td>-0.3442</td></tr><tr><td>0.204</td><td>-1.4295</td><td>-0.0277</td><td>-0.1417</td><td>0.2232</td><td>1.8580</td><td>-0.2611</td></tr><tr><td>0.205</td><td>-1.5050</td><td>0.0226</td><td>-0.3410</td><td>-0.6238</td><td>1.7768</td><td>-0.1060</td></tr><tr><td>0.206</td><td>-0.1160</td><td>0.2922</td><td>-1.0224</td><td>-0.3133</td><td>1.2205</td><td>0.5994</td></tr><tr><td>0.207</td><td>4.8707</td><td>1.6456</td><td>-0.9479</td><td>-0.0176</td><td>0.6933</td><td>0.2696</td></tr><tr><td>0.208</td><td>7.2593</td><td>2.4569</td><td>2.1355</td><td>-0.1606</td><td>0.4349</td><td>0.0973</td></tr><tr><td>0.209</td><td>3.8737</td><td>1.6491</td><td>-1.0497</td><td>0.0396</td><td>0.8800</td><td>0.2729</td></tr><tr><td>0.210</td><td>0.8931</td><td>0.2576</td><td>-1.0511</td><td>0.1691</td><td>0.8014</td><td>0.5908</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Fault time (s)</th><th colspan="7">Voltage</th></tr><tr><th>sacfv</th><th>sacfdv</th><th>sacfd2v</th><th>spacfv</th><th>spacfdv</th><th>spacfd2v</th></tr></thead><tbody><tr><td>0.200</td><td>6.9339</td><td>1.6671</td><td>-0.4695</td><td>0.2669</td><td>0.1739</td><td>0.0934</td></tr><tr><td>0.201</td><td>5.4783</td><td>-0.9503</td><td>-0.2817</td><td>0.5827</td><td>0.0167</td><td>0.7039</td></tr><tr><td>0.202</td><td>3.4873</td><td>-0.4204</td><td>-0.2167</td><td>0.6335</td><td>0.0104</td><td>0.2035</td></tr><tr><td>0.203</td><td>0.9900</td><td>-0.0886</td><td>-0.0216</td><td>0.7565</td><td>-0.4900</td><td>-0.1591</td></tr><tr><td>0.204</td><td>0.5949</td><td>-0.0708</td><td>-0.0063</td><td>0.6957</td><td>-0.5060</td><td>-0.8871</td></tr><tr><td>0.205</td><td>3.2958</td><td>-0.1868</td><td>-0.0500</td><td>0.5217</td><td>-0.3864</td><td>-1.9170</td></tr><tr><td>0.206</td><td>5.4064</td><td>-0.8062</td><td>-0.5091</td><td>-0.1666</td><td>0.6426</td><td>-0.8450</td></tr><tr><td>0.207</td><td>6.5456</td><td>-1.2097</td><td>-0.8134</td><td>0.5620</td><td>0.1342</td><td>0.6332</td></tr><tr><td>0.208</td><td>7.0033</td><td>0.8362</td><td>-0.0565</td><td>0.4719</td><td>0.1510</td><td>0.6231</td></tr><tr><td>0.209</td><td>6.0259</td><td>-0.7936</td><td>0.2544</td><td>0.5499</td><td>0.0080</td><td>0.5214</td></tr><tr><td>0.210</td><td>4.2548</td><td>-0.8951</td><td>-0.3937</td><td>-0.0565</td><td>0.5887</td><td>0.1744</td></tr></tbody></table>

These tables clearly show that all indices values are positive and almost large for both current and voltage in no-fault case, while most of them are around zero in HIF phenomenon. In this stage, *sacfv*, *sacfd* and *sacfdi* indices are put aside because their values in HIF are far from zero and they are not suitable for fault detection.

Now, it's time to go one step ahead and analyze the results of moving time window for different values of *n* and *k*. Finally, feature patterns of two indices for HIF with clear changes are shown in figure.7. These features belong to *spacfdv* and *spacfdv* for HIF model 1.

Using a low-pass filter would be useful to make the curve flat to get a good and clear feature pattern for HIF detection. So, it is suggested that use a filter of degree 4 with equation number (23). Filtering of SPACF curve can be got similarly.
$$f_n(SACF) = \sum_{k=(n-3)}^{n} SACF_k \quad (23)$$

Some indices curves like sacfd²i, sacfd²v and spacfi for HIF model 2 before and after filtering are brought in figure.8.

Although voltage and current of relay don't show any problem in appearance, HIF can be detected easily by using of SACF and SPACF functions.

<figure><img src="image_11.png" /><figcaption>Fig. 7. Feature pattern of (a) spacfdv, (b) spacfd2v for HIF condition (time duration=3 s)</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Feature pattern of (a) sacfd2i, (b) sacfd2v and (c) spacfi for HIF (model 2) before and after using filter (time duration=3 s)</figcaption></figure>
**5 Conclusion**

A new approach for HIF detection in distribution systems based on correlation functions is proposed in this paper. After simulating a sample system, SACF and SPACF functions were experimented on *i*, *di*, $d^2i$, *v*, *dv* and $d^2v$ signals that resulted in twelve indices to HIF detection. After getting the results of both normal and HIF conditions for different values of variables, it was founded that SACF and SPACF operators can detect HIF phenomenon from voltage and current samples of relay.

**6 References**

1. A. M. Sharaf and Guosheng Wang, "High Impedance Fault Detection using Feature-Pattern Based Relaying", Transmission and distribution conference and exposition, 2003 IEEE PES, Pages 222 - 226 Vol.1

2. Marek Michalik, Waldemar Rebizant, Miroslaw Lukowicz, Seung-Jae Lee, Sang-Hee Kang, "Wavelet Transform Approach to High Impedance Fault Detection in MV Networks", Power Tech, 2005 IEEE Russia, Pages 1-7.

3. M. Sedighizadeh, A. Rezazadeh, Nagy I. Elkalashy, "Approaches in High Impedance Fault Detection A Chronological Review", Advances in Electrical and Computer Engineering, Volume 10, Number 3, 2010

4. Hassan Khorashadi Zadeh, "An ANN-Based High Impedance Fault Detection Scheme: Design and Implementation", International Journal of Emerging Electric Power Systems, Volume 4, Issue 2, 2005.

5. Mark Adamiak, Craig Wester, Manish Thakur, Charles Jensen, "High Impedance Fault Detection On Distribution Feeders", GE Industrial solutions.

6. N. I. Elkalashy, M. Lehtonen, H. A. Darwish, M. A. Izzularab, A. I. Taalab, "Modeling and Experimental Verification of a High Impedance Arcing Fault in MV Networks", Power system conference and exposition, IEEE 2006, Pages 1950-1956.

7. Doaa khalil Ibrahim, El Sayed Tag Eldin, "High-Impedance Fault Detection in EHV Transmission Lines", Power system conference, MEPCON 2008, International Middle-East, Pages 192-199.

8. A. M. Sharaf, L. A. Snider and K. Debnath, "Residual Third Harmonic Detection of High Impedance Fault in Distribution System Using perception Neural Networks", Proceeding of the ISEDEM 93, Singapore, October 1993.

9. A. M. Sharaf, L. A. Snider and K. Debnath, "Harmonic based Detection of High Impedance Faults in Distribution Networks Using Neural Networks", Proceeding of the IASTED conference 1993, Pittsburg, PA.

10. A. M. Sharaf, R. M. El-Sharkawy, H. Jalaat and M. A. Badr, "Fault Detection on Radial and Meshed Transmission Systems.