Power Distribution System Characterization With Active Probing: Real-World Testing and Analysis

Power distribution systems are traditionally characterized using passive means such as parameter estimation and topology identification. This work investigates an active way to test and characterize dynamically changing distribution systems. The method actively perturbs local distribution networks with programmable pulses using a Grid Resonance Probe (GRP) and observes the response using a micro-phasor measurement unit ( $\mu $ PMU). After applying advanced data analytics, the perturbation and response measurements can reveal characteristics of distribution systems, such as feeder parameters and topologies. To validate the proposed approach, three case studies are executed on a real distribution system, including visualization, feeder connection identification, and feeder impedance estimation. Real data processing considerations and sensitivity analysis are also discussed. The proposed testing and analysis approach is expected to provide engineers a new solution to measure, parameterize, and characterize distribution systems.


I. INTRODUCTION
A N ELECTRIC power grid can be roughly categorized into transmission and distribution systems. In the past, the primary service of distribution systems was delivering energy to end-users. In conjunction with the deployment of information communication technologies (ICTs) and distributed energy resources (DERs), new applications and services (e.g., renewable generation, demand response, distribution automation systems, etc.) are available in today's distribution systems [1], [2], [3], [4]. As the complexity of distribution systems has significantly increased, there are new challenges to model, simulate, plan, and operate the distribution system [5].
Feeder impedance estimation can support methods for fault detection and grid unbalance analysis [6], [7], [8], among other applications, especially as the modern distribution grid changes to incorporate a high penetration of renewable energy [9]. Inaccurate feeder impedance parameters may impact operator understanding of power distribution, power quality, and system reliability. Therefore, grid impedance estimation is essential to validate and tune a power system model for further power system studies.
In recent years, several new power system technologies have been introduced which can support feeder impedance estimation by providing high-quality power grid data. For example, µPMUs are designed to measure time-stamped voltage phasors, current phasors, and frequency with high precision and high frequency, enabling improved diagnostics through affordable, high-resolution metering [10], [11], [12].
Currently, several impedance estimation and topology identification techniques have been developed. In general, these techniques can be classified as either passive or active [13] depending on whether perturbations are externally injected or not. Passive approaches [14], [15], [16], [17] utilize internal signals which already exist on a distribution line, such as non-characteristic voltage and current harmonics. The advantage is that the passive estimation schemes may avoid negative impacts on power quality by not injecting external signals into a distribution line. However, the low signal-tonoise ratio (SNR) may lead to a poor estimation result. For a more accurate impedance estimation method, various active impedance estimation techniques have been proposed. The intent is to actively perturb the distribution system locally with programmable pulses and observe the response to identify a system's characteristics. The work of [18] intentionally creates short circuit events at the measurement point by using a thyristor. The current and voltage signals during a short circuit event are utilized for measuring power system harmonic impedance. In [19], a wavelet-based impedance estimation method has been developed by injecting an inter-harmonic current signal into the grid. In [20], a high-frequency signal injection method has been proposed to measure grid impedance and detect the islanding of microgrids. In [21] a current controller is used to inject non-characteristic harmonic current signals to obtain the impedance parameters. However, the existing active impedance estimation methods are based on stationary devices to generate and inject signals into the power system. These estimation methods may experience lower accuracy as the distance between the signal source and line of interest increase, due to the stationary or limited set up options.
In this work, an active impedance estimation approach is proposed using the Grid Resonance Probe (GRP) to inject small voltage disturbance signals into distribution lines. The GRP is a mobile system, able to be loaded on a trailer, which interconnects at low voltage, either 208VAC or 480VAC, to inject voltage signals into distribution lines and meter voltage and current at its connection point. Therefore, a GRP system is adaptable enough to be connected at various strategic points to inject probing signals with less deployment effort, less preparation time, and minimal electrical signal decay because of its flexibility to be moved around compared to more permanent set ups. Several µPMUs are deployed to monitor and collect voltage readings for the estimation analysis. This method requires only low voltage, single phase (e.g. 120V wall outlet) voltage measurement devices deployed in the distribution system, which are much easier and cheaper to install than current measurement devices on the medium voltage line, as would be required for a traditional on-line determination of line impedance. The proposed approach is expected to provide engineers and researchers with a low-cost mechanism to measure, parameterize, and characterize dynamically changing distribution networks. The main contributions of this paper include: • A proposed utilization of the GRP for active probing applications in a distribution system.
• Exploration of three analyses enabled by the proposed approach, namely grid topology visualization, feeder connection identification, and impedance estimation.
• Execution on a real-world test power system and detailed impedance estimation results.
The rest of this paper is organized as follows: Section II describes the proposed approach, Section III demonstrates the proposed approach with case studies, and Section IV discusses the conclusions and future work.

II. GRP APPROACH AND APPLICATIONS A. APPROACH
In this work, novel applications for active testing and characterization of a distribution system using fast changing load steps are investigated. In this approach the distribution system is actively perturbed with programmable pulses using the GRP, a precision load bank and measurement tool intended for grid testing and characterization. The GRP can generate large, precisely-timed pulses of resistive power, subtly disrupting steady-state voltage and phase angles to reveal oscillation and stability characteristics. The system response is observed using built-in data recording via µPMUs.
Recently, PMUs have been introduced for monitoring transmission systems with synchronized voltage/current phasor and frequency measurements, and higher data rates compared to SCADA systems [22]. Wide deployment enables several new real-time power system applications and improves the reliability of the power grid. However, the complexity of the distribution system can be higher than the transmission network. Therefore µPMUs have been developed to improve situational awareness in distribution systems, having a higher data sampling rate and accuracy. Typically, a µPMU measures phase angle to within ±0.01 degree, while the precision is ±0.05%. The resolution of phase angle and magnitude are 0.001 and 0.0002%, respectively [23].
Through advanced data analytics the perturbation and response measurements can uncover unique characteristics of the distribution system, such as feeder parameters and topologies. Typical GRP output measurements, frequency and each of the three phases for current and voltage magnitude, during a test are shown in Fig. 1

B. APPLICATION
Feeder impedance is an important parameter for distribution system operations and planning and the proposed GRP application for feeder impedance estimation is explained as follows. By Thevenin's Theorem, a feeder circuit can be converted into a simple equivalent circuit as shown in Fig. 2, where the voltage at the source, the terminal, and the GRP, and time are represented by V S (t), V T (t), V GRP (t), and t, respectively. The impedance of the source and the feeder are denoted by Z S and Z , respectively. Lastly, the current through the source and the feeder is denoted by I (t). Therefore, if no pulses are injected into the feeder at t 1 , the relationship between voltage, current, and impedance is represented by (1): When the GRP perturbs the feeder with a pulse at time t 2 , the equation can be written as (2): (2) VOLUME 10, 2023  Furthermore, (2) can be rewritten as: where I GRP (t 2 ) is the additional current draw due to the GRP pulse. The feeder impedance is assumed to be constant during the pulse injection, which typically lasts only a few milliseconds depending on the pulse period. Subtracting (1) and (3) and rearranging yields: For each cycle, or period n, let V GRP (n), V T (n), and I GRP (n) represent the difference between the nominal (peak) and trough of the pulse, which includes the values at both t 1 and t 2 . Though t 2 − t 1 is very small, these precise and time-synchronized voltage and current values can be obtained via µPMU technology. Thus, for each pulse the feeder impedance Z can be estimated by (4).

III. CASE STUDIES
In this section, the proposed approach is demonstrated with the following three case studies: • Descriptive Analysis: visualizing the response of a distribution grid when injecting GRP signal.
• Diagnostic Analysis: analyzing the data to identify feeder connection status.
• Discovery Analysis: estimating feeder impedance to determine the characteristics of a distribution grid. The case study experiments are executed on a real system consisting of the five nodes shown in Fig. 3.

A. DESCRIPTIVE ANALYSIS
Descriptive analysis provides a foundational starting point to visualize and understand what happened in the past. In this case study, the GRP is used to generate periodic pulses (i.e., perturbations), with pulse amplitude, width, and period set to 200A, 10%, and 1 second, respectively. µPMUs are used to measure the voltage phasor and frequency at each node (i.e., response). The GRP system is designed to include current metering, whereas it is difficult and expensive to retroactively add current metering on the feeder. In this way, the voltage phasor and frequency at each node, and the voltage phasor, current phasor, and frequency at the GRP can be measured in a high-precision but low-cost and non-invasive manner. Select voltage magnitude measurements are shown in Fig. 4 and demonstrate the system response to the GRP perturbations.

B. DIAGNOSTIC ANALYSIS
To better understand what happened in a distribution system, diagnostic analysis seeks out why something happened in the past. As shown in Fig. 4, the GRP pulse causes voltage sag with decreasing magnitude as the distance between the node of interest and the GRP increases. It indicates that the GRP pulse signals do propagate through the distribution grid. According to this observation, the GRP pulses and the corresponding voltage sags can be used to validate the physical location of nodes and measurements.
Moreover, the GRP pulses and response measurements can help engineers quickly determine the connection status between the GRP and the node/measurement. With sufficient measurements the feeder topology can be identified, which is especially useful during system restoration. For example, when a series of pulses at Node 5 induces synchronized voltage sags at Node 4, it is inferred that the switch between Node 5 and Node 4 is closed. Otherwise, it is assumed to be open.

C. DISCOVERY ANALYSIS
Compared with descriptive and diagnostic analysis, discovery analysis dives deeper into data analytics to investigate the system characteristics. In this case study, a discovery analysis method to estimate the feeder impedance between Node 2 and Node 5 is developed based on the feeder impedance estimation application introduced in Section II.B. The main test parameters are summarized in Table 1, where multiple power levels from 60kW to 160kW are programmed with three different configurations of pulse signal period and duty percentage. Fig. 5 shows the impedance estimation results of Tests 1-6, including both a scatter plot of the estimated impedance during each pulse and the resulting probability density function (pdf) for each test, with resistance peaks occurring between 0.0628 and 0.0668 and reactance peaks occurring between 0.0698 and 0.0749. Additional metrics (mean and standard deviation, σ , of pulse-wise estimates) which summarize the results are provided in Table 2.
When the power level is 100kW or 160kW, the estimates strongly cluster around the same values, as seen in the pdfs and variance metrics. When the power level is higher, the VOLUME 10, 2023 period is longer, or the duty cycle is larger, there is less variance in the estimates, as seen in the sharper peak and shorter tail of the pdf plots. Thus, it is suggested that with the strategic selection of the pulse parameters, more precise estimates can be obtained. In practice though, the generation of larger pulses has higher hardware requirements, potentially yielding higher costs. Additionally, the injection of larger pulses may precipitate local distribution network safety and stability issues. Fortunately, the proposed method can still obtain sufficiently precise estimates as seen in the collection of 100kW level results, specifically comparing Test 1 and Test 3 in Fig. 5a and 5e. The proposed method provides a practical way to estimate feeder impedances, which may be uncertain or unknown in distribution systems, but are critical inputs to system operations and resilience-enhancing applications. Fig. 6 shows the measurements at the terminal in Tests 3 and 7, which are configured with the same period and duty cycle but with different power levels, 100kW and 60kW, respectively. It can be seen in Fig. 6(c) and 6(d) that at the smaller power level on this system the pulse cannot trigger sufficiently significant voltage sags at the terminal, compared to those when the power level is 100kW, see Fig. 6a and 6b. For example, the peaks and troughs are much less consistent in the voltage magnitude measurement in Fig. 6c, and there are no clear sags in the voltage angle measurements in Fig. 6d. The same observation applies to Tests 8-10, which were performed with a smaller duty and/or a shorter period than Test 7. Thus, the proposed method is not applicable when the pulse is too small to generate noticeable voltage sags, indistinguishable from baseload fluctuations or noise.

D. REAL DATA CONSIDERATIONS
In tandem with the data analysis discussed above, it is advantageous to discuss the discrepancies between expected (theoretical) and experimental results with real data. The perturbations applied can introduce transients and fluctuations which affect the experimental values and data processing techniques should be explored to improve the results of the proposed methods. Due to limited space, only the discrepancy effects and considerations relevant to the impedance estimation study is discussed in this section. As an illustration, notional (theoretical) and measured values for an impedance estimation test are presented in the left and right sides of Fig. 7, respectively. To determine the impedance per (4), the difference in voltage between the normal condition (without pulse) and the disturbance condition (with pulse) needs to be ascertained.
For voltage magnitude, the difference during a pulse ( V in Fig. 7) can be found by subtracting the peak and trough voltage magnitude values. When processing the experimental data, it is not so straightforward to accurately determine the peaks and troughs in the presence of real system noise and variations. This is because the pulse injection often induces impulsive transients, oscillatory transients, and voltage fluctuations, introducing noise that obfuscates the identification of peaks and troughs in the measurements. To mitigate those impacts, in each cycle (e.g., each period), the mean value of the voltage magnitude measurements in the peak and in the trough are used to determine the estimated impedance for that cycle. So as not to include intermediate values on the rising and falling edges of the pulse, a threshold of 3σ around both peaks in the distribution of the voltage magnitude measurements is defined. As a demonstration, the measurement distribution for all cycles in Test 6 is shown in Fig. 8, where the utilized values cover 99.7% of the provided data points. For voltage angle, the difference during a pulse ( θ in Fig. 7) cannot often be as easily determined. In an AC system, the voltage angle can drift with time, and the change specifically due to the active probing in a shorter window of time becomes more difficult to isolate during pulse injections. Because of the time synchronization and high-frequency data recording enabled by µPMUs, the following heuristics are applied to mitigate this challenge. First the time synchronization between the voltage magnitude and angle measurements is leveraged by applying the time index of the edges of the peak and trough of the voltage magnitude measurements to infer the edge of the peak and trough of the voltage angle measurements. Second, interpolation is applied to estimate the voltage angle values as if there were no pulses; the mean of the values in the trough can then be subtracted from the mean of the expected values of the peak to determine the difference. To not include intermediate values on the rising and falling edges of the pulse, a few data points around each pulse are removed, for each interpolation. This also helps to mitigate the impact of signal noise, since impulsive transients, oscillatory transients, and voltage fluctuations often result from the onset of the pulses. These adjustments coincide with the observation that longer periods and larger duty cycle produce more consistent estimates (see Fig. 5), as there is more time over which to average out noise and more valid data in the troughs over which to average, leading to estimated impedances less influenced by outliers.
It is also observed in Fig. 5 and Table 2 that the reactance estimates are generally less consistent (have higher variance) than the resistance estimates. To that end, sensitivity analysis is performed with respect to the resistance and reactance.
For simplicity, let V GRP (n)=V 1 θ 1 , V T (n) = V 2 θ 2 , and I GRP (n) = I θ 3 . Then (4) can be rewritten as (5), shown at the bottom of the page. The derivative of the resistance R and the reactance X with respect to θ 1 and θ 2 are: In the experiments shown, θ 1 and θ 2 varied within a very small range, such as [−2 o , 2 o ] in Test 6, implying sinθ 1 and sinθ 2 are close to 0, and thus yielding dX /dθ 1 > dR/dθ 1 and |dX /dθ 2 | > |dR/dθ 2 |. Hence, the reactance is more sensitive to the fluctuations of the angle deviation than the resistance is, especially the fluctuation of θ 1 . As a result, the distribution of the reactance estimates may present multiple peaks when the fluctuation is large.

IV. CONCLUSION
This paper presents an approach to probe and characterize dynamically changing distribution systems by injecting external signals into distribution lines. The GRP is deployed to inject programmable pulses to actively perturb the distribution network, while µPMUs are used to provide high-precision measurements for further data analysis. In this work, three analyses have been conducted on a real distribution system for determining the characteristics of the system under test, including (1) visualization of distribution system response, (2) feeder connectivity identification, and (3) feeder impedance estimation. The data processing challenges associated with real field data are also discussed. The proposed active probing-based method for testing and analysis provides a new low-cost alternative for measuring, understanding, and characterizing distribution systems. To further this work, additional testing and analysis of this method could be performed on more complex or larger distribution systems. Alternatively, it could be attempted to recreate these results with already installed loads, instead of utilizing the GRP which, if successful, would make this methodology easier to utilize in a wide variety of systems.